cuSPARSE :: CUDA Toolkit Documentation

cuSPARSE

1. Introduction

The cuSPARSE library contains a set of basic linear algebra subroutines used for handling sparse matrices. It is implemented on top of the NVIDIA® CUDA™ runtime (which is part of the CUDA Toolkit) and is designed to be called from C and C++. The library routines can be classified into four categories:

Level 1: operations between a vector in sparse format and a vector in dense format
Level 2: operations between a matrix in sparse format and a vector in dense format
Level 3: operations between a matrix in sparse format and a set of vectors in dense format (which can also usually be viewed as a dense tall matrix)
Conversion: operations that allow conversion between different matrix formats, and compression of csr matrices.

The cuSPARSE library allows developers to access the computational resources of the NVIDIA graphics processing unit (GPU), although it does not auto-parallelize across multiple GPUs. The cuSPARSE API assumes that input and output data reside in GPU (device) memory, unless it is explicitly indicated otherwise by the string DevHostPtr in a function parameter's name (for example, the parameter *resultDevHostPtr in the function cusparse<t>doti()).

It is the responsibility of the developer to allocate memory and to copy data between GPU memory and CPU memory using standard CUDA runtime API routines, such as cudaMalloc(), cudaFree(), cudaMemcpy(), and cudaMemcpyAsync().

Note: The cuSPARSE library requires hardware with compute capability (CC) of at least 2.0 or higher. Please see the NVIDIA CUDA C Programming Guide, Appendix A for a list of the compute capabilities corresponding to all NVIDIA GPUs.

1.1. Naming Conventions

The cuSPARSE library functions are available for data types float, double, cuComplex, and cuDoubleComplex. The sparse Level 1, Level 2, and Level 3 functions follow this naming convention:

cusparse<t>[<matrix data format>]<operation>[<output matrix data format>]

where <t> can be S, D, C, Z, or X, corresponding to the data types float, double, cuComplex, cuDoubleComplex, and the generic type, respectively.

The <matrix data format> can be dense, coo, csr, csc, or hyb, corresponding to the dense, coordinate, compressed sparse row, compressed sparse column, and hybrid storage formats, respectively.

Finally, the <operation> can be axpyi, doti, dotci, gthr, gthrz, roti, or sctr, corresponding to the Level 1 functions; it also can be mv or sv, corresponding to the Level 2 functions, as well as mm or sm, corresponding to the Level 3 functions.

All of the functions have the return type cusparseStatus_t and are explained in more detail in the chapters that follow.

1.2. Asynchronous Execution

The cuSPARSE library functions are executed asynchronously with respect to the host and may return control to the application on the host before the result is ready. Developers can use the cudaDeviceSynchronize() function to ensure that the execution of a particular cuSPARSE library routine has completed.

A developer can also use the cudaMemcpy() routine to copy data from the device to the host and vice versa, using the cudaMemcpyDeviceToHost and cudaMemcpyHostToDevice parameters, respectively. In this case there is no need to add a call to cudaDeviceSynchronize() because the call to cudaMemcpy() with the above parameters is blocking and completes only when the results are ready on the host.

Static Library support

Starting with release 6.5, the cuSPARSE Library is also delivered in a static form as libcusparse_static.a on Linux and Mac OSes. The static cuSPARSE library and all others static maths libraries depend on a common thread abstraction layer library called libculibos.a on Linux and Mac and culibos.lib on Windows.

For example, on linux, to compile a small application using cuSPARSE against the dynamic library, the following command can be used:

    nvcc myCusparseApp.c  -lcusparse  -o myCusparseApp

Whereas to compile against the static cuSPARSE library, the following command has to be used:

     
    nvcc myCusparseApp.c  -lcusparse_static   -lculibos -o myCusparseApp

It is also possible to use the native Host C++ compiler. Depending on the Host Operating system, some additional libraries like pthread or dl might be needed on the linking line. The following command on Linux is suggested :

        
    g++ myCusparseApp.c  -lcusparse_static   -lculibos -lcudart_static -lpthread -ldl -I <cuda-toolkit-path>/include -L <cuda-toolkit-path>/lib64 -o myCusparseApp

Note that in the latter case, the library cuda is not needed. The CUDA Runtime will try to open explicitly the cuda library if needed. In the case of a system which does not have the CUDA driver installed, this allows the application to gracefully manage this issue and potentially run if a CPU-only path is available.

2. Using the cuSPARSE API

This chapter describes how to use the cuSPARSE library API. It is not a reference for the cuSPARSE API data types and functions; that is provided in subsequent chapters.

2.1. Thread Safety

The library is thread safe and its functions can be called from multiple host threads.

2.2. Scalar Parameters

In the cuSPARSE API, the scalar parameters $α$ and $β$ can be passed by reference on the host or the device.

The few functions that return a scalar result, such as doti() and nnz(), return the resulting value by reference on the host or the device. Even though these functions return immediately, similarly to those that return matrix and vector results, the scalar result is not ready until execution of the routine on the GPU completes. This requires proper synchronization be used when reading the result from the host.

This feature allows the cuSPARSE library functions to execute completely asynchronously using streams, even when $α$ and $β$ are generated by a previous kernel. This situation arises, for example, when the library is used to implement iterative methods for the solution of linear systems and eigenvalue problems [3].

2.3. Parallelism with Streams

If the application performs several small independent computations, or if it makes data transfers in parallel with the computation, CUDA streams can be used to overlap these tasks.

The application can conceptually associate a stream with each task. To achieve the overlap of computation between the tasks, the developer should create CUDA streams using the function cudaStreamCreate() and set the stream to be used by each individual cuSPARSE library routine by calling cusparseSetStream() just before calling the actual cuSPARSE routine. Then, computations performed in separate streams would be overlapped automatically on the GPU, when possible. This approach is especially useful when the computation performed by a single task is relatively small and is not enough to fill the GPU with work, or when there is a data transfer that can be performed in parallel with the computation.

When streams are used, we recommend using the new cuSPARSE API with scalar parameters and results passed by reference in the device memory to achieve maximum computational overlap.

Although a developer can create many streams, in practice it is not possible to have more than 16 concurrent kernels executing at the same time.

3. cuSPARSE Indexing and Data Formats

The cuSPARSE library supports dense and sparse vector, and dense and sparse matrix formats.

3.1. Index Base Format

The library supports zero- and one-based indexing. The index base is selected through the cusparseIndexBase_t type, which is passed as a standalone parameter or as a field in the matrix descriptor cusparseMatDescr_t type.

3.2. Vector Formats

This section describes dense and sparse vector formats.

3.2.1. Dense Format

Dense vectors are represented with a single data array that is stored linearly in memory, such as the following $7 \times 1$ dense vector.

$[\begin{matrix} 1.0 & 0.0 & 0.0 & 2.0 & 3.0 & 0.0 & 4.0 \end{matrix}]$

(This vector is referenced again in the next section.)

3.2.2. Sparse Format

Sparse vectors are represented with two arrays.

The data array has the nonzero values from the equivalent array in dense format.
The integer index array has the positions of the corresponding nonzero values in the equivalent array in dense format.

For example, the dense vector in section 3.2.1 can be stored as a sparse vector with one-based indexing.

$\begin{array}{rcl} [\begin{matrix} 1.0 & 2.0 & 3.0 & 4.0 \end{matrix}] \\ [\begin{matrix} 1 & 4 & 5 & 7 \end{matrix}] \end{array}$

It can also be stored as a sparse vector with zero-based indexing.

$\begin{array}{rcl} [\begin{matrix} 1.0 & 2.0 & 3.0 & 4.0 \end{matrix}] \\ [\begin{matrix} 0 & 3 & 4 & 6 \end{matrix}] \end{array}$

In each example, the top row is the data array and the bottom row is the index array, and it is assumed that the indices are provided in increasing order and that each index appears only once.

3.3. Matrix Formats

Dense and several sparse formats for matrices are discussed in this section.

3.3.1. Dense Format

The dense matrix X is assumed to be stored in column-major format in memory and is represented by the following parameters.

`m`	(integer)	The number of rows in the matrix.
`n`	(integer)	The number of columns in the matrix.
`ldX`	(integer)	The leading dimension of `X`, which must be greater than or equal to `m`. If `ldX` is greater than `m`, then `X` represents a sub-matrix of a larger matrix stored in memory
`X`	(pointer)	Points to the data array containing the matrix elements. It is assumed that enough storage is allocated for `X` to hold all of the matrix elements and that cuSPARSE library functions may access values outside of the sub-matrix, but will never overwrite them.

For example, m×n dense matrix X with leading dimension ldX can be stored with one-based indexing as shown.

$[\begin{matrix} X_{1, 1} & X_{1, 2} & \dots & X_{1, n} \\ X_{2, 1} & X_{2, 2} & \dots & X_{2, n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ X_{m, 1} & X_{m, 2} & \dots & X_{m, n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ X_{l d X, 1} & X_{l d X, 2} & \dots & X_{l d X, n} \end{matrix}]$

Its elements are arranged linearly in memory in the order below.

$[\begin{matrix} X_{1, 1} & X_{2, 1} & \dots & X_{m, 1} & \dots & X_{l d X, 1} & \dots & X_{1, n} & X_{2, n} & \dots & X_{m, n} & \dots & X_{l d X, n} \end{matrix}]$

Note: This format and notation are similar to those used in the NVIDIA CUDA cuBLAS library.

3.3.2. Coordinate Format (COO)

The m×n sparse matrix A is represented in COO format by the following parameters.

`nnz`	(integer)	The number of nonzero elements in the matrix.
`cooValA`	(pointer)	Points to the data array of length `nnz` that holds all nonzero values of `A` in row-major format.
`cooRowIndA`	(pointer)	Points to the integer array of length `nnz` that contains the row indices of the corresponding elements in array `cooValA`.
`cooColIndA`	(pointer)	Points to the integer array of length `nnz` that contains the column indices of the corresponding elements in array `cooValA`.

A sparse matrix in COO format is assumed to be stored in row-major format: the index arrays are first sorted by row indices and then within the same row by compressed column indices. It is assumed that each pair of row and column indices appears only once.

For example, consider the following $4 \times 5$ matrix A.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 \end{matrix}]$

It is stored in COO format with zero-based indexing this way.

$\begin{array}{rcl} cooValA & = & [\begin{matrix} 1.0 & 4.0 & 2.0 & 3.0 & 5.0 & 7.0 & 8.0 & 9.0 & 6.0 \end{matrix}] \\ cooRowIndA & = & [\begin{matrix} 0 & 0 & 1 & 1 & 2 & 2 & 2 & 3 & 3 \end{matrix}] \\ cooColIndA & = & [\begin{matrix} 0 & 1 & 1 & 2 & 0 & 3 & 4 & 2 & 4 \end{matrix}] \end{array}$

In the COO format with one-based indexing, it is stored as shown.

$\begin{array}{rcl} cooValA & = & [\begin{matrix} 1.0 & 4.0 & 2.0 & 3.0 & 5.0 & 7.0 & 8.0 & 9.0 & 6.0 \end{matrix}] \\ cooRowIndA & = & [\begin{matrix} 1 & 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4 \end{matrix}] \\ cooColIndA & = & [\begin{matrix} 1 & 2 & 2 & 3 & 1 & 4 & 5 & 3 & 5 \end{matrix}] \end{array}$

3.3.3. Compressed Sparse Row Format (CSR)

The only way the CSR differs from the COO format is that the array containing the row indices is compressed in CSR format. The m×n sparse matrix A is represented in CSR format by the following parameters.

`nnz`	(integer)	The number of nonzero elements in the matrix.
`csrValA`	(pointer)	Points to the data array of length `nnz` that holds all nonzero values of A in row-major format.
`csrRowPtrA`	(pointer)	Points to the integer array of length `m+1` that holds indices into the arrays `csrColIndA` and `csrValA`. The first `m` entries of this array contain the indices of the first nonzero element in the `i`th row for `i=i,...,m`, while the last entry contains `nnz+csrRowPtrA(0)`. In general, `csrRowPtrA(0)` is `0` or `1` for zero- and one-based indexing, respectively.
`csrColIndA`	(pointer)	Points to the integer array of length `nnz` that contains the column indices of the corresponding elements in array `csrValA`.

Sparse matrices in CSR format are assumed to be stored in row-major CSR format, in other words, the index arrays are first sorted by row indices and then within the same row by column indices. It is assumed that each pair of row and column indices appears only once.

Consider again the $4 \times 5$ matrixA.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 \end{matrix}]$

It is stored in CSR format with zero-based indexing as shown.

$\begin{array}{rcl} csrValA & = & [\begin{matrix} 1.0 & 4.0 & 2.0 & 3.0 & 5.0 & 7.0 & 8.0 & 9.0 & 6.0 \end{matrix}] \\ csrRowPtrA & = & [\begin{matrix} 0 & 2 & 4 & 7 & 9 \end{matrix}] \\ csrColIndA & = & [\begin{matrix} 0 & 1 & 1 & 2 & 0 & 3 & 4 & 2 & 4 \end{matrix}] \end{array}$

This is how it is stored in CSR format with one-based indexing.

$\begin{array}{rcl} csrValA & = & [\begin{matrix} 1.0 & 4.0 & 2.0 & 3.0 & 5.0 & 7.0 & 8.0 & 9.0 & 6.0 \end{matrix}] \\ csrRowPtrA & = & [\begin{matrix} 1 & 3 & 5 & 8 & 10 \end{matrix}] \\ csrColIndA & = & [\begin{matrix} 1 & 2 & 2 & 3 & 1 & 4 & 5 & 3 & 5 \end{matrix}] \end{array}$

3.3.4. Compressed Sparse Column Format (CSC)

The CSC format is different from the COO format in two ways: the matrix is stored in column-major format, and the array containing the column indices is compressed in CSC format. The m×n matrix A is represented in CSC format by the following parameters.

`nnz`	(integer)	The number of nonzero elements in the matrix.
`cscValA`	(pointer)	Points to the data array of length `nnz` that holds all nonzero values of `A` in column-major format.
`cscRowIndA`	(pointer)	Points to the integer array of length `nnz` that contains the row indices of the corresponding elements in array `cscValA`.
`cscColPtrA`	(pointer)	Points to the integer array of length `n+1` that holds indices into the arrays `cscRowIndA` and `cscValA`. The first `n` entries of this array contain the indices of the first nonzero element in the `i`th row for `i=i,...,n`, while the last entry contains `nnz+cscColPtrA(0)`. In general, `cscColPtrA(0)` is `0` or `1` for zero- and one-based indexing, respectively.

Note: The matrix A in CSR format has exactly the same memory layout as its transpose in CSC format (and vice versa).

For example, consider once again the $4 \times 5$ matrix A.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 \end{matrix}]$

It is stored in CSC format with zero-based indexing this way.

$\begin{array}{rcl} cscValA & = & [\begin{matrix} 1.0 & 5.0 & 4.0 & 2.0 & 3.0 & 9.0 & 7.0 & 8.0 & 6.0 \end{matrix}] \\ cscRowIndA & = & [\begin{matrix} 0 & 2 & 0 & 1 & 1 & 3 & 2 & 2 & 3 \end{matrix}] \\ cscColPtrA & = & [\begin{matrix} 0 & 2 & 4 & 6 & 7 & 9 \end{matrix}] \end{array}$

In CSC format with one-based indexing, this is how it is stored.

$\begin{array}{rcl} cscValA & = & [\begin{matrix} 1.0 & 5.0 & 4.0 & 2.0 & 3.0 & 9.0 & 7.0 & 8.0 & 6.0 \end{matrix}] \\ cscRowIndA & = & [\begin{matrix} 1 & 3 & 1 & 2 & 2 & 4 & 3 & 3 & 4 \end{matrix}] \\ cscColPtrA & = & [\begin{matrix} 1 & 3 & 5 & 7 & 8 & 10 \end{matrix}] \end{array}$

Each pair of row and column indices appears only once.

3.3.5. Ellpack-Itpack Format (ELL)

An m×n sparse matrix A with at most k nonzero elements per row is stored in the Ellpack-Itpack (ELL) format [2] using two dense arrays of dimension m×k. The first data array contains the values of the nonzero elements in the matrix, while the second integer array contains the corresponding column indices.

For example, consider the $4 \times 5$ matrix A.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 \end{matrix}]$

This is how it is stored in ELL format with zero-based indexing.

$\begin{array}{rcl} data & = & [\begin{matrix} 1.0 & 4.0 & 0.0 \\ 2.0 & 3.0 & 0.0 \\ 5.0 & 7.0 & 8.0 \\ 9.0 & 6.0 & 0.0 \end{matrix}] \\ indices & = & [\begin{matrix} 0 & 1 & - 1 \\ 1 & 2 & - 1 \\ 0 & 3 & 4 \\ 2 & 4 & - 1 \end{matrix}] \end{array}$

It is stored this way in ELL format with one-based indexing.

$\begin{array}{rcl} data & = & [\begin{matrix} 1.0 & 4.0 & 0.0 \\ 2.0 & 3.0 & 0.0 \\ 5.0 & 7.0 & 8.0 \\ 9.0 & 6.0 & 0.0 \end{matrix}] \\ indices & = & [\begin{matrix} 1 & 2 & - 1 \\ 2 & 3 & - 1 \\ 1 & 4 & 5 \\ 3 & 5 & - 1 \end{matrix}] \end{array}$

Sparse matrices in ELL format are assumed to be stored in column-major format in memory. Also, rows with less than k nonzero elements are padded in the data and indices arrays with zero and $- 1$ , respectively.

The ELL format is not supported directly, but it is used to store the regular part of the matrix in the HYB format that is described in the next section.

3.3.6. Hybrid Format (HYB)

The HYB sparse storage format is composed of a regular part, usually stored in ELL format, and an irregular part, usually stored in COO format [1]. The ELL and COO parts are always stored using zero-based indexing. HYB is implemented as an opaque data format that requires the use of a conversion operation to store a matrix in it. The conversion operation partitions the general matrix into the regular and irregular parts automatically or according to developer-specified criteria.

For more information, please refer to the description of cusparseHybPartition_t type, as well as the description of the conversion routines dense2hyb, csc2hyb and csr2hyb.

3.3.7. Block Compressed Sparse Row Format (BSR)

The only difference between the CSR and BSR formats is the format of the storage element. The former stores primitive data types (single, double, cuComplex, and cuDoubleComplex) whereas the latter stores a two-dimensional square block of primitive data types. The dimension of the square block is $b l o c k D i m$ . The m×n sparse matrix A is equivalent to a block sparse matrix $A_{b}$ with $m b = \frac{m + b l o c k D i m - 1}{b l o c k D i m}$ block rows and $n b = \frac{n + b l o c k D i m - 1}{b l o c k D i m}$ block columns. If $m$ or $n$ is not multiple of $b l o c k D i m$ , then zeros are filled into $A_{b}$ .

A is represented in BSR format by the following parameters.

`blockDim`	(integer)	Block dimension of matrix `A`.
`mb`	(integer)	The number of block rows of `A`.
`nb`	(integer)	The number of block columns of `A`.
`nnzb`	(integer)	The number of nonzero blocks in the matrix.
`bsrValA`	(pointer)	Points to the data array of length $n n z b * b l o c k D i m^{2}$ that holds all elements of nonzero blocks of `A`. The block elements are stored in either column-major order or row-major order.
`bsrRowPtrA`	(pointer)	Points to the integer array of length `mb+1` that holds indices into the arrays `bsrColIndA` and `bsrValA`. The first `mb` entries of this array contain the indices of the first nonzero block in the `i`th block row for `i=1,...,mb`, while the last entry contains `nnzb+bsrRowPtrA(0)`. In general, `bsrRowPtrA(0)` is `0` or `1` for zero- and one-based indexing, respectively.
`bsrColIndA`	(pointer)	Points to the integer array of length `nnzb` that contains the column indices of the corresponding blocks in array `bsrValA`.

As with CSR format, (row, column) indices of BSR are stored in row-major order. The index arrays are first sorted by row indices and then within the same row by column indices.

For example, consider again the 4×5 matrix A.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 \end{matrix}]$

If $b l o c k D i m$ is equal to 2, then $m b$ is 2, $n b$ is 3, and matrix A is split into 2×3 block matrix $A_{b}$ . The dimension of $A_{b}$ is 4×6, slightly bigger than matrix $A$ , so zeros are filled in the last column of $A_{b}$ . The element-wise view of $A_{b}$ is this.

$[\begin{matrix} 1.0 & 4.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 2.0 & 3.0 & 0.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 0.0 & 7.0 & 8.0 & 0.0 \\ 0.0 & 0.0 & 9.0 & 0.0 & 6.0 & 0.0 \end{matrix}]$

Based on zero-based indexing, the block-wise view of $A_{b}$ can be represented as follows.

A_{b} = [\begin{matrix} A_{00} & A_{01} & A_{02} \\ A_{10} & A_{11} & A_{12} \end{matrix}]

The basic element of BSR is a nonzero $A_{i j}$ block, one that contains at least one nonzero element of A. Five of six blocks are nonzero in $A_{b}$ .

A_{00} = [\begin{matrix} 1 & 4 \\ 0 & 2 \end{matrix}], A_{01} = [\begin{matrix} 0 & 0 \\ 3 & 0 \end{matrix}], A_{10} = [\begin{matrix} 5 & 0 \\ 0 & 0 \end{matrix}], A_{11} = [\begin{matrix} 0 & 7 \\ 9 & 0 \end{matrix}], A_{12} = [\begin{matrix} 8 & 0 \\ 6 & 0 \end{matrix}]

BSR format only stores the information of nonzero blocks, including block indices $(i, j)$ and values $A_{i j}$ . Also row indices are compressed in CSR format.

$\begin{array}{rcl} bsrValA & = & [\begin{matrix} A_{00} & A_{01} & A_{10} & A_{11} & A_{12} \end{matrix}] \\ bsrRowPtrA & = & [\begin{matrix} 0 & 2 & 5 \end{matrix}] \\ bsrColIndA & = & [\begin{matrix} 0 & 1 & 0 & 1 & 2 \end{matrix}] \end{array}$

There are two ways to arrange the data element of block $A_{i j}$ : row-major order and column-major order. Under column-major order, the physical storage of bsrValA is this.

\begin{array}{ccccc} b s r V a l A = [1 0 4 2 & 0 3 0 0 & 5 0 0 0 & 0 9 7 0 & 8 6 0 0] \end{array}

Under row-major order, the physical storage of bsrValA is this.

\begin{array}{ccccc} b s r V a l A = [1 4 0 2 & 0 0 3 0 & 5 0 0 0 & 0 7 9 0 & 8 0 6 0] \end{array}

Similarly, in BSR format with one-based indexing and column-major order, A can be represented by the following.

A_{b} = [\begin{matrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \end{matrix}]

\begin{array}{ccccc} b s r V a l A = [1 0 4 2 & 0 3 0 0 & 5 0 0 0 & 0 9 7 0 & 8 6 0 0] \end{array}

$\begin{array}{rcl} bsrRowPtrA & = & [\begin{matrix} 1 & 3 & 6 \end{matrix}] \\ bsrColIndA & = & [\begin{matrix} 1 & 2 & 1 & 2 & 3 \end{matrix}] \end{array}$

Note: The general BSR format has two parameters, rowBlockDim and colBlockDim. rowBlockDim is number of rows within a block and colBlockDim is number of columns within a block. If rowBlockDim=colBlockDim, general BSR format is the same as BSR format. If rowBlockDim=colBlockDim=1, general BSR format is the same as CSR format. The conversion routine gebsr2gebsr is used to do conversion among CSR, BSR and general BSR.

Note: In the cuSPARSE Library, the storage format of blocks in BSR format can be column-major or row-major, independently of the base index. However, if the developer uses BSR format from the Math Kernel Library (MKL) and wants to directly interface with the cuSPARSE Library, then cusparseDirection_tCUSPARSE_DIRECTION_COLUMN should be used if the base index is one; otherwise, cusparseDirection_tCUSPARSE_DIRECTION_ROW should be used.

3.3.8. Extended BSR Format (BSRX)

BSRX is the same as the BSR format, but the array bsrRowPtrA is separated into two parts. The first nonzero block of each row is still specified by the array bsrRowPtrA, which is the same as in BSR, but the position next to the last nonzero block of each row is specified by the array bsrEndPtrA. Briefly, BSRX format is simply like a 4-vector variant of BSR format.

Matrix A is represented in BSRX format by the following parameters.

`blockDim`	(integer)	Block dimension of matrix `A`.
`mb`	(integer)	The number of block rows of `A`.
`nb`	(integer)	The number of block columns of `A`.
`nnzb`	(integer)	number of nonzero blocks in the matrix `A`.
`bsrValA`	(pointer)	Points to the data array of length $n n z b * b l o c k D i m^{2}$ that holds all the elements of the nonzero blocks of `A`. The block elements are stored in either column-major order or row-major order.
`bsrRowPtrA`	(pointer)	Points to the integer array of length `mb` that holds indices into the arrays `bsrColIndA` and `bsrValA`; `bsrRowPtrA(i)` is the position of the first nonzero block of the `i`th block row in `bsrColIndA` and `bsrValA`.
`bsrEndPtrA`	(pointer)	Points to the integer array of length `mb` that holds indices into the arrays `bsrColIndA` and `bsrValA`; `bsrRowPtrA(i)` is the position next to the last nonzero block of the `i`th block row in `bsrColIndA` and `bsrValA`.
`bsrColIndA`	(pointer)	Points to the integer array of length `nnzb` that contains the column indices of the corresponding blocks in array `bsrValA`.

A simple conversion between BSR and BSRX can be done as follows. Suppose the developer has a 2×3 block sparse matrix $A_{b}$ represented as shown.

A_{b} = [\begin{matrix} A_{00} & A_{01} & A_{02} \\ A_{10} & A_{11} & A_{12} \end{matrix}]

Assume it has this BSR format.

$\begin{array}{rcl} bsrValA of BSR & = & [\begin{matrix} A_{00} & A_{01} & A_{10} & A_{11} & A_{12} \end{matrix}] \\ bsrRowPtrA of BSR & = & [\begin{matrix} 0 & 2 & 5 \end{matrix}] \\ bsrColIndA of BSR & = & [\begin{matrix} 0 & 1 & 0 & 1 & 2 \end{matrix}] \end{array}$

The bsrRowPtrA of the BSRX format is simply the first two elements of the bsrRowPtrA BSR format. The bsrEndPtrA of BSRX format is the last two elements of the bsrRowPtrA of BSR format.

$\begin{array}{rcl} bsrRowPtrA of BSRX & = & [\begin{matrix} 0 & 2 \end{matrix}] \\ bsrEndPtrA of BSRX & = & [\begin{matrix} 2 & 5 \end{matrix}] \end{array}$

The advantage of the BSRX format is that the developer can specify a submatrix in the original BSR format by modifying bsrRowPtrA and bsrEndPtrA while keeping bsrColIndA and bsrValA unchanged.

For example, to create another block matrix $\tilde{A} = [\begin{matrix} O & O & O \\ O & A_{11} & O \end{matrix}]$ that is slightly different from $A$ , the developer can keep bsrColIndA and bsrValA, but reconstruct $\tilde{A}$ by properly setting of bsrRowPtrA and bsrEndPtrA. The following 4-vector characterizes $\tilde{A}$ .

$\begin{array}{rcl} bsrValA of \tilde{A} & = & [\begin{matrix} A_{00} & A_{01} & A_{10} & A_{11} & A_{12} \end{matrix}] \\ bsrColIndA of \tilde{A} & = & [\begin{matrix} 0 & 1 & 0 & 1 & 2 \end{matrix}] \\ bsrRowPtrA of \tilde{A} & = & [\begin{matrix} 0 & 3 \end{matrix}] \\ bsrEndPtrA of \tilde{A} & = & [\begin{matrix} 0 & 4 \end{matrix}] \end{array}$

4. cuSPARSE Types Reference

4.1. Data types

The float, double, cuComplex, and cuDoubleComplex data types are supported. The first two are standard C data types, while the last two are exported from cuComplex.h.

4.2. cusparseAction_t

This type indicates whether the operation is performed only on indices or on data and indices.

Value	Meaning
`CUSPARSE_ACTION_SYMBOLIC`	the operation is performed only on indices.
`CUSPARSE_ACTION_NUMERIC`	the operation is performed on data and indices.

4.3. cusparseDirection_t

This type indicates whether the elements of a dense matrix should be parsed by rows or by columns (assuming column-major storage in memory of the dense matrix) in function cusparse[S|D|C|Z]nnz. Besides storage format of blocks in BSR format is also controlled by this type.

Value	Meaning
`CUSPARSE_DIRECTION_ROW`	the matrix should be parsed by rows.
`CUSPARSE_DIRECTION_COLUMN`	the matrix should be parsed by columns.

4.4. cusparseHandle_t

This is a pointer type to an opaque cuSPARSE context, which the user must initialize by calling prior to calling cusparseCreate() any other library function. The handle created and returned by cusparseCreate() must be passed to every cuSPARSE function.

4.5. cusparseHybMat_t

This is a pointer type to an opaque structure holding the matrix in HYB format, which is created by cusparseCreateHybMat and destroyed by cusparseDestroyHybMat.

4.5.1. cusparseHybPartition_t

This type indicates how to perform the partitioning of the matrix into regular (ELL) and irregular (COO) parts of the HYB format.

The partitioning is performed during the conversion of the matrix from a dense or sparse format into the HYB format and is governed by the following rules. When CUSPARSE_HYB_PARTITION_AUTO is selected, the cuSPARSE library automatically decides how much data to put into the regular and irregular parts of the HYB format. When CUSPARSE_HYB_PARTITION_USER is selected, the width of the regular part of the HYB format should be specified by the caller. When CUSPARSE_HYB_PARTITION_MAX is selected, the width of the regular part of the HYB format equals to the maximum number of non-zero elements per row, in other words, the entire matrix is stored in the regular part of the HYB format.

The default is to let the library automatically decide how to split the data.

Value	Meaning
`CUSPARSE_HYB_PARTITION_AUTO`	the automatic partitioning is selected (default).
`CUSPARSE_HYB_PARTITION_USER`	the user specified treshold is used.
`CUSPARSE_HYB_PARTITION_MAX`	the data is stored in ELL format.

4.6. cusparseMatDescr_t

This structure is used to describe the shape and properties of a matrix.

typedef struct {
    cusparseMatrixType_t MatrixType;
    cusparseFillMode_t FillMode;
    cusparseDiagType_t DiagType;
    cusparseIndexBase_t IndexBase;
} cusparseMatDescr_t;

4.6.1. cusparseDiagType_t

This type indicates if the matrix diagonal entries are unity. The diagonal elements are always assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.

Value	Meaning
`CUSPARSE_DIAG_TYPE_NON_UNIT`	the matrix diagonal has non-unit elements.
`CUSPARSE_DIAG_TYPE_UNIT`	the matrix diagonal has unit elements.

4.6.2. cusparseFillMode_t

This type indicates if the lower or upper part of a matrix is stored in sparse storage.

Value	Meaning
`CUSPARSE_FILL_MODE_LOWER`	the lower triangular part is stored.
`CUSPARSE_FILL_MODE_UPPER`	the upper triangular part is stored.

4.6.3. cusparseIndexBase_t

This type indicates if the base of the matrix indices is zero or one.

Value	Meaning
`CUSPARSE_INDEX_BASE_ZERO`	the base index is zero.
`CUSPARSE_INDEX_BASE_ONE`	the base index is one.

4.6.4. cusparseMatrixType_t

This type indicates the type of matrix stored in sparse storage. Notice that for symmetric, Hermitian and triangular matrices only their lower or upper part is assumed to be stored.

The whole idea of matrix type and fill mode is to keep minimum storage for symmetric/Hermitian matrix, and also to take advantage of symmetric property on SpMV (Sparse Matrix Vector multiplication). To compute y=A*x when A is symmetric and only lower triangular part is stored, two steps are needed. First step is to compute y=(L+D)*x and second step is to compute y=L^T*x + y. Given the fact that the transpose operation y=L^T*x is 10x slower than non-transpose version y=L*x, the symmetric property does not show up any performance gain. It is better for the user to extend the symmetric matrix to a general matrix and apply y=A*x with matrix type CUSPARSE_MATRIX_TYPE_GENERAL.

In general, SpMV, preconditioners (incomplete Cholesky or incomplete LU) and triangular solver are combined together in iterative solvers, for example PCG and GMRES. If the user always uses general matrix (instead of symmetric matrix), there is no need to support other than general matrix in preconditioners. Therefore the new routines, [bsr|csr]sv2 (triangular solver), [bsr|csr]ilu02 (incomplete LU) and [bsr|csr]ic02 (incomplete Cholesky), only support matrix type CUSPARSE_MATRIX_TYPE_GENERAL.

Value	Meaning
`CUSPARSE_MATRIX_TYPE_GENERAL`	the matrix is general.
`CUSPARSE_MATRIX_TYPE_SYMMETRIC`	the matrix is symmetric.
`CUSPARSE_MATRIX_TYPE_HERMITIAN`	the matrix is Hermitian.
`CUSPARSE_MATRIX_TYPE_TRIANGULAR`	the matrix is triangular.

4.7. cusparseOperation_t

This type indicates which operations need to be performed with the sparse matrix.

Value	Meaning
`CUSPARSE_OPERATION_NON_TRANSPOSE`	the non-transpose operation is selected.
`CUSPARSE_OPERATION_TRANSPOSE`	the transpose operation is selected.
`CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE`	the conjugate transpose operation is selected.

Value

Meaning

CUSPARSE_OPERATION_NON_TRANSPOSE

the non-transpose operation is selected.

CUSPARSE_OPERATION_TRANSPOSE

the transpose operation is selected.

CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE

the conjugate transpose operation is selected.

4.8. cusparsePointerMode_t

This type indicates whether the scalar values are passed by reference on the host or device. It is important to point out that if several scalar values are passed by reference in the function call, all of them will conform to the same single pointer mode. The pointer mode can be set and retrieved using cusparseSetPointerMode() and cusparseGetPointerMode() routines, respectively.

Value	Meaning
`CUSPARSE_POINTER_MODE_HOST`	the scalars are passed by reference on the host.
`CUSPARSE_POINTER_MODE_DEVICE`	the scalars are passed by reference on the device.

4.9. cusparseSolvePolicy_t

This type indicates whether level information is generated and used in csrsv2, csric02, csrilu02, bsrsv2, bsric02 and bsrilu02.

Value	Meaning
`CUSPARSE_SOLVE_POLICY_NO_LEVEL`	no level information is generated and used.
`CUSPARSE_SOLVE_POLICY_USE_LEVEL`	generate and use level information.

4.10. cusparseSolveAnalysisInfo_t

This is a pointer type to an opaque structure holding the information collected in the analysis phase of the solution of the sparse triangular linear system. It is expected to be passed unchanged to the solution phase of the sparse triangular linear system.

cusparseSolveAnalysisInfo_t

4.12. csrsv2Info_t

This is a pointer type to an opaque structure holding the information used in csrsv2_bufferSize(), csrsv2_analysis(), and csrsv2_solve().

4.13. csric02Info_t

This is a pointer type to an opaque structure holding the information used in csric02_bufferSize(), csric02_analysis(), and csric02().

4.14. csrilu02Info_t

This is a pointer type to an opaque structure holding the information used in csrilu02_bufferSize(), csrilu02_analysis(), and csrilu02().

4.15. bsrsv2Info_t

This is a pointer type to an opaque structure holding the information used in bsrsv2_bufferSize(), bsrsv2_analysis(), and bsrsv2_solve().

bsrsm2Info_t

This is a pointer type to an opaque structure holding the information used in bsrsm2_bufferSize(), bsrsm2_analysis(), and bsrsm2_solve().

4.17. bsric02Info_t

This is a pointer type to an opaque structure holding the information used in bsric02_bufferSize(), bsric02_analysis(), and bsric02().

4.18. bsrilu02Info_t

This is a pointer type to an opaque structure holding the information used in bsrilu02_bufferSize(), bsrilu02_analysis(), and bsrilu02().

4.19. csrgemm2Info_t

This is a pointer type to an opaque structure holding the information used in csrgemm2_bufferSizeExt(), and csrgemm2().

4.20. cusparseStatus_t

This is a status type returned by the library functions and it can have the following values.

`CUSPARSE_STATUS_SUCCESS`	The operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	The cuSPARSE library was not initialized. This is usually caused by the lack of a prior call, an error in the CUDA Runtime API called by the cuSPARSE routine, or an error in the hardware setup. To correct: call `cusparseCreate()` prior to the function call; and check that the hardware, an appropriate version of the driver, and the cuSPARSE library are correctly installed.
`CUSPARSE_STATUS_ALLOC_FAILED`	Resource allocation failed inside the cuSPARSE library. This is usually caused by a `cudaMalloc()` failure. To correct: prior to the function call, deallocate previously allocated memory as much as possible.
`CUSPARSE_STATUS_INVALID_VALUE`	An unsupported value or parameter was passed to the function (a negative vector size, for example). To correct: ensure that all the parameters being passed have valid values.
`CUSPARSE_STATUS_ARCH_MISMATCH`	The function requires a feature absent from the device architecture; usually caused by the lack of support for atomic operations or double precision. To correct: compile and run the application on a device with appropriate compute capability, which is 1.1 for 32-bit atomic operations and 1.3 for double precision.
`CUSPARSE_STATUS_MAPPING_ERROR`	An access to GPU memory space failed, which is usually caused by a failure to bind a texture. To correct: prior to the function call, unbind any previously bound textures.
`CUSPARSE_STATUS_EXECUTION_FAILED`	The GPU program failed to execute. This is often caused by a launch failure of the kernel on the GPU, which can be caused by multiple reasons. To correct: check that the hardware, an appropriate version of the driver, and the cuSPARSE library are correctly installed.
`CUSPARSE_STATUS_INTERNAL_ERROR`	An internal cuSPARSE operation failed. This error is usually caused by a `cudaMemcpyAsync()` failure. To correct: check that the hardware, an appropriate version of the driver, and the cuSPARSE library are correctly installed. Also, check that the memory passed as a parameter to the routine is not being deallocated prior to the routine’s completion.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	The matrix type is not supported by this function. This is usually caused by passing an invalid matrix descriptor to the function. To correct: check that the fields in `cusparseMatDescr_t descrA` were set correctly.

5. cuSPARSE Helper Function Reference

The cuSPARSE helper functions are described in this section.

5.1. cusparseCreate()

cusparseStatus_t
cusparseCreate(cusparseHandle_t *handle)

This function initializes the cuSPARSE library and creates a handle on the cuSPARSE context. It must be called before any other cuSPARSE API function is invoked. It allocates hardware resources necessary for accessing the GPU.

Output

handle

the pointer to the handle to the cuSPARSE context.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the initialization succeeded.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the CUDA Runtime initialization failed.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device compute capability (CC) is less than 1.1. The CC of at least 1.1 is required.

5.5. cusparseCreateSolveAnalysisInfo()

cusparseStatus_t
cusparseCreateSolveAnalysisInfo(cusparseSolveAnalysisInfo_t *info)

This function creates and initializes the solve and analysis structure to default values.

Input

info

the pointer to the solve and analysis structure.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.3. cusparseCreateHybMat()

cusparseStatus_t
cusparseCreateHybMat(cusparseHybMat_t *hybA)

This function creates and initializes the hybA opaque data structure.

Input

hybA

the pointer to the hybrid format storage structure.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.4. cusparseCreateMatDescr()

cusparseStatus_t
cusparseCreateMatDescr(cusparseMatDescr_t *descrA)

This function initializes the matrix descriptor. It sets the fields MatrixType and IndexBase to the default values CUSPARSE_MATRIX_TYPE_GENERAL and CUSPARSE_INDEX_BASE_ZERO , respectively, while leaving other fields uninitialized.

Input

descrA

the pointer to the matrix descriptor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the descriptor was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

cusparseCreateSolveAnalysisInfo()

cusparseStatus_t
cusparseCreateSolveAnalysisInfo(cusparseSolveAnalysisInfo_t *info)

This function creates and initializes the solve and analysis structure to default values.

Input

info

the pointer to the solve and analysis structure.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.6. cusparseDestroy()

cusparseStatus_t
cusparseDestroy(cusparseHandle_t handle)

This function releases CPU-side resources used by the cuSPARSE library. The release of GPU-side resources may be deferred until the application shuts down.

Input

handle

the handle to the cuSPARSE context.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the shutdown succeeded.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.

5.10. cusparseDestroySolveAnalysisInfo()

cusparseStatus_t
cusparseDestroySolveAnalysisInfo(cusparseSolveAnalysisInfo_t info)

This function destroys and releases any memory required by the structure.

Input

info

the solve and analysis structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.8. cusparseDestroyHybMat()

cusparseStatus_t
cusparseDestroyHybMat(cusparseHybMat_t hybA)

This function destroys and releases any memory required by the hybA structure.

Input

hybA

the hybrid format storage structure.

Status Returned

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.9. cusparseDestroyMatDescr()

cusparseStatus_t
cusparseDestroyMatDescr(cusparseMatDescr_t descrA)

This function releases the memory allocated for the matrix descriptor.

Input

descrA

the matrix descriptor.

Status Returned

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

cusparseDestroySolveAnalysisInfo()

cusparseStatus_t
cusparseDestroySolveAnalysisInfo(cusparseSolveAnalysisInfo_t info)

This function destroys and releases any memory required by the structure.

Input

info

the solve and analysis structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.11. cusparseGetLevelInfo()

cusparseStatus_t 
cusparseGetLevelInfo(cusparseHandle_t handle, 
                     cusparseSolveAnalysisInfo_t info, 
                     int *nlevels, 
                     int **levelPtr, 
                     int **levelInd)

This function returns the number of levels and the assignment of rows into the levels computed by either the csrsv_analysis, csrsm_analysis or hybsv_analysis routines.

Input

`handle`	handle to the cuSPARSE library context.
`info`	the pointer to the solve and analysis structure.

Output

`nlevels`	number of levels.
`levelPtr`	integer array of `nlevels+1` elements that contains the start of every level and the end of the last level plus one.
`levelInd`	integer array of `m` (number of rows in the matrix) elements that contains the row indices belonging to every level.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library or the solve analysis structure was not initialized.

5.12. cusparseGetMatDiagType()

cusparseDiagType_t
cusparseGetMatDiagType(const cusparseMatDescr_t descrA)

This function returns the DiagType field of the matrix descriptor descrA.

Input

descrA

the matrix descriptor.

Returned

One of the enumerated diagType types.

5.13. cusparseGetMatFillMode()

cusparseFillMode_t
cusparseGetMatFillMode(const cusparseMatDescr_t descrA)

This function returns the FillMode field of the matrix descriptor descrA.

Input

descrA

the matrix descriptor.

Returned

One of the enumerated fillMode types.

5.14. cusparseGetMatIndexBase()

cusparseIndexBase_t
cusparseGetMatIndexBase(const cusparseMatDescr_t descrA)

This function returns the IndexBase field of the matrix descriptor descrA.

Input

descrA

the matrix descriptor.

Returned

One of the enumerated indexBase types.

5.15. cusparseGetMatType()

cusparseMatrixType_t
cusparseGetMatType(const cusparseMatDescr_t descrA)

This function returns the MatrixType field of the matrix descriptor descrA.

Input

descrA

the matrix descriptor.

Returned

One of the enumerated matrix types.

5.16. cusparseGetPointerMode()

cusparseStatus_t
cusparseGetPointerMode(cusparseHandlet handle, 
                       cusparsePointerMode_t *mode)

This function obtains the pointer mode used by the cuSPARSE library. Please see the section on the cusparsePointerMode_t type for more details.

Input

handle

the handle to the cuSPARSE context.

Output

mode

One of the enumerated pointer mode types.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the pointer mode was returned successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.

5.17. cusparseGetVersion()

cusparseStatus_t
cusparseGetVersion(cusparseHandle_t handle, int *version)

This function returns the version number of the cuSPARSE library.

Input

handle

the handle to the cuSPARSE context.

Output

version

the version number of the library.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the version was returned successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.

5.18. cusparseSetMatDiagType()

cusparseStatus_t
cusparseSetMatDiagType(cusparseMatDescr_t descrA, 
                       cusparseDiagType_t diagType)

This function sets the DiagType field of the matrix descriptor descrA.

Input

diagType

One of the enumerated diagType types.

Output

descrA

the matrix descriptor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the field `DiagType` was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	An invalid `diagType` parameter was passed.

5.19. cusparseSetMatFillMode()

cusparseStatus_t
cusparseSetMatFillMode(cusparseMatDescr_t descrA, 
                       cusparseFillMode_t fillMode)

This function sets the FillMode field of the matrix descriptor descrA.

Input

fillMode

One of the enumerated fillMode types.

Output

descrA

the matrix descriptor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the `FillMode` field was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	An invalid `fillMode` parameter was passed.

5.20. cusparseSetMatIndexBase()

cusparseStatus_t
cusparseSetMatIndexBase(cusparseMatDescr_t descrA, 
                        cusparseIndexBase_t base)

This function sets the IndexBase field of the matrix descriptor descrA.

Input

base

One of the enumerated indexBase types.

Output

descrA

the matrix descriptor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the `IndexBase` field was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	An invalid `base` parameter was passed.

5.21. cusparseSetMatType()

cusparseStatus_t
cusparseSetMatType(cusparseMatDescr_t descrA, cusparseMatrixType_t type)

This function sets the MatrixType field of the matrix descriptor descrA.

Input

type

One of the enumerated matrix types.

Output

descrA

the matrix descriptor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the `MatrixType` field was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	An invalid `type` parameter was passed.

5.22. cusparseSetPointerMode()

cusparseStatus_t
cusparseSetPointerMode(cusparseHandle_t handle, 
                       cusparsePointerMode_t mode)

This function sets the pointer mode used by the cuSPARSE library. The default is for the values to be passed by reference on the host. Please see the section on the cublasPointerMode_t type for more details.

Input

`handle`	the handle to the cuSPARSE context.
`mode`	One of the enumerated pointer mode types.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the pointer mode was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	the library was not initialized.

5.23. cusparseSetStream()

cusparseStatus_t
cusparseSetStream(cusparseHandle_t handle, cudaStream_t streamId)

This function sets the stream to be used by the cuSPARSE library to execute its routines.

Input

`handle`	the handle to the cuSPARSE context.
`streamId`	the stream to be used by the library.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the stream was set successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	the library was not initialized.

5.24. cusparseGetStream()

cusparseStatus_t
cusparseGetStream(cusparseHandle_t handle, cudaStream_t *streamId)

This function gets the cuSPARSE library stream, which is being used to to execute all calls to the cuSPARSE library functions. If the cuSPARSE library stream is not set, all kernels use the default NULL stream.

Input

handle

the handle to the cuSPARSE context.

Output

streamId

the stream to be used by the library.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the stream was returned successfully.
`CUSPARSE_STATUS_INVALID_VALUE`	the library was not initialized.

5.25. cusparseCreateCsrsv2Info()

cusparseStatus_t 
cusparseCreateCsrsv2Info(csrsv2Info_t *info);

This function creates and initializes the solve and analysis structure of csrsv2 to default values.

Input

info

the pointer to the solve and analysis structure of csrsv2.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.26. cusparseDestroyCsrsv2Info()

cusparseStatus_t 
cusparseDestroyCsrsv2Info(csrsv2Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (csrsv2_solve) and analysis (csrsv2_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.27. cusparseCreateCsric02Info()

cusparseStatus_t 
cusparseCreateCsric02Info(csric02Info_t *info);

This function creates and initializes the solve and analysis structure of incomplete Cholesky to default values.

Input

info

the pointer to the solve and analysis structure of incomplete Cholesky.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.28. cusparseDestroyCsric02Info()

cusparseStatus_t 
cusparseDestroyCsric02Info(csric02Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (csric02_solve) and analysis (csric02_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.29. cusparseCreateCsrilu02Info()

cusparseStatus_t 
cusparseCreateCsrilu02Info(csrilu02Info_t *info);

This function creates and initializes the solve and analysis structure of incomplete LU to default values.

Input

info

the pointer to the solve and analysis structure of incomplete LU.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.30. cusparseDestroyCsrilu02Info()

cusparseStatus_t 
cusparseDestroyCsrilu02Info(csrilu02Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (csrilu02_solve) and analysis (csrilu02_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.31. cusparseCreateBsrsv2Info()

cusparseStatus_t
cusparseCreateBsrsv2Info(bsrsv2Info_t *info);

This function creates and initializes the solve and analysis structure of bsrsv2 to default values.

Input

info

the pointer to the solve and analysis structure of bsrsv2.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.32. cusparseDestroyBsrsv2Info()

cusparseStatus_t
cusparseDestroyBsrsv2Info(bsrsv2Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (bsrsv2_solve) and analysis (bsrsv2_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.33. cusparseCreateBsrsm2Info()

cusparseStatus_t
cusparseCreateBsrsm2Info(bsrsm2Info_t *info);

This function creates and initializes the solve and analysis structure of bsrsm2 to default values.

Input

info

the pointer to the solve and analysis structure of bsrsm2.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.34. cusparseDestroyBsrsm2Info()

cusparseStatus_t
cusparseDestroyBsrsm2Info(bsrsm2Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (bsrsm2_solve) and analysis (bsrsm2_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.35. cusparseCreateBsric02Info()

cusparseStatus_t 
cusparseCreateBsric02Info(bsric02Info_t *info);

This function creates and initializes the solve and analysis structure of block incomplete Cholesky to default values.

Input

info

the pointer to the solve and analysis structure of block incomplete Cholesky.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.36. cusparseDestroyBsric02Info()

cusparseStatus_t 
cusparseDestroyBsric02Info(bsric02Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (bsric02_solve) and analysis (bsric02_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.37. cusparseCreateBsrilu02Info()

cusparseStatus_t 
cusparseCreateBsrilu02Info(bsrilu02Info_t *info);

This function creates and initializes the solve and analysis structure of block incomplete LU to default values.

Input

info

the pointer to the solve and analysis structure of block incomplete LU.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.38. cusparseDestroyBsrilu02Info()

cusparseStatus_t 
cusparseDestroyBsrilu02Info(bsrilu02Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

the solve (bsrilu02_solve) and analysis (bsrilu02_analysis) structure.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.39. cusparseCreateCsrgemm2Info()

cusparseStatus_t 
cusparseCreateCsrgemm2Info(csrgemm2Info_t *info);

This function creates and initializes analysis structure of general sparse matrix-matrix multiplication.

Input

info

the pointer to the analysis structure of general sparse matrix-matrix multiplication.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.40. cusparseDestroyCsrgemm2Info()

cusparseStatus_t 
cusparseDestroyCsrgemm2Info(csrgemm2Info_t info);

This function destroys and releases any memory required by the structure.

Input

info

opaque structure of csrgemm2.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

5.41. cusparseCreatePruneInfo()

cusparseStatus_t 
cusparseCreatePruneInfo(pruneInfo_t *info);

This function creates and initializes structure of prune to default values.

Input

info

the pointer to the structure of prune.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the structure was initialized successfully.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.

5.42. cusparseDestroyPruneInfo()

cusparseStatus_t 
cusparseDestroyPruneInfo(pruneInfo_t info);

This function destroys and releases any memory required by the structure.

Input

info

the structure of prune.

Status Returened

CUSPARSE_STATUS_SUCCESS

the resources were released successfully.

6. cuSPARSE Level 1 Function Reference

This chapter describes sparse linear algebra functions that perform operations between dense and sparse vectors.

6.1. cusparse<t>axpyi()

cusparseStatus_t 
cusparseSaxpyi(cusparseHandle_t handle, int nnz, 
               const float           *alpha, 
               const float           *xVal, const int *xInd, 
               float           *y, cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDaxpyi(cusparseHandle_t handle, int nnz, 
               const double          *alpha, 
               const double          *xVal, const int *xInd, 
               double          *y, cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCaxpyi(cusparseHandle_t handle, int nnz, 
               const cuComplex       *alpha, 
               const cuComplex       *xVal, const int *xInd, 
               cuComplex       *y, cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZaxpyi(cusparseHandle_t handle, int nnz, 
               const cuDoubleComplex *alpha, 
               const cuDoubleComplex *xVal, const int *xInd, 
               cuDoubleComplex *y, cusparseIndexBase_t idxBase)

This function multiplies the vector x in sparse format by the constant $α$ and adds the result to the vector y in dense format. This operation can be written as

y = y + α * x

In other words,

for i=0 to nnz-1
    y[xInd[i]-idxBase] = y[xInd[i]-idxBase] + alpha*xVal[i]

This function requires no extra storage. It is executed asynchronously with respect to the host, and it may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`alpha`	<type> scalar used for multiplication.
`xVal`	<type> vector with `nnz` nonzero values of vector `x`.
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`y`	<type> vector in dense format.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

`y`	<type> updated vector in dense format (that is unchanged if `nnz == 0`).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

6.2. cusparse<t>doti()

cusparseStatus_t 
cusparseSdoti(cusparseHandle_t handle, int nnz, 
              const float           *xVal, 
              const int *xInd, const float           *y, 
              float           *resultDevHostPtr, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDdoti(cusparseHandle_t handle, int nnz, 
              const double          *xVal, 
              const int *xInd, const double          *y, 
              double          *resultDevHostPtr, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCdoti(cusparseHandle_t handle, int nnz, 
              const cuComplex       *xVal, 
              const int *xInd, const cuComplex       *y, 
              cuComplex       *resultDevHostPtr, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZdoti(cusparseHandle_t handle, int nnz, const 
              cuDoubleComplex *xVal, 
              const int *xInd, const cuDoubleComplex *y, 
              cuDoubleComplex *resultDevHostPtr, 
              cusparseIndexBase_t idxBase)

This function returns the dot product of a vector x in sparse format and vector y in dense format. This operation can be written as

r e s u l t = y^{T} x

In other words,

for i=0 to nnz-1
    resultDevHostPtr += xVal[i]*y[xInd[i-idxBase]]

This function requires some temporary extra storage that is allocated internally. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`xVal`	<type> vector with `nnz` nonzero values of vector `x`.
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`y`	<type> vector in dense format.
`resultDevHostPtr`	pointer to the location of the result in the device or host memory.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

resultDevHostPtr

scalar result in the device or host memory (that is zero if nnz == 0).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the reduction buffer could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

6.3. cusparse<t>dotci()

cusparseStatus_t 
cusparseCdotci(cusparseHandle_t handle, int nnz, 
               const cuComplex       *xVal, 
               const int *xInd, const cuComplex       *y, 
               cuComplex       *resultDevHostPtr, cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZdotci(cusparseHandle_t handle, int nnz, 
               const cuDoubleComplex *xVal, 
               const int *xInd, const cuDoubleComplex *y, 
               cuDoubleComplex *resultDevHostPtr, cusparseIndexBase_t idxBase)

This function returns the dot product of a complex conjugate of vector x in sparse format and vector y in dense format. This operation can be written as

r e s u l t = x^{H} y

In other words,

for i=0 to nnz-1
	resultDevHostPtr +=  $\bar{xVal[i]}$ *y[xInd[i-idxBase]]

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`xVal`	<type> vector with `nnz` nonzero values of vector `x`.
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`y`	<type> vector in dense format.
`resultDevHostPtr`	pointer to the location of the result in the device or host memory.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

resultDevHostPtr

scalar result in the device or host memory (that is zero if nnz == 0).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the reduction buffer could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

6.4. cusparse<t>gthr()

cusparseStatus_t 
cusparseSgthr(cusparseHandle_t handle, int nnz, 
              const float           *y, 
              float           *xVal, const int *xInd, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDgthr(cusparseHandle_t handle, int nnz, 
              const double          *y, 
              double          *xVal, const int *xInd, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCgthr(cusparseHandle_t handle, int nnz, 
              const cuComplex       *y, 
              cuComplex       *xVal, const int *xInd, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZgthr(cusparseHandle_t handle, int nnz, 
              const cuDoubleComplex *y, 
              cuDoubleComplex *xVal, const int *xInd, 
              cusparseIndexBase_t idxBase)

This function gathers the elements of the vector y listed in the index array xInd into the data array xVal.

This function requires no extra storage. It is executed asynchronously with respect to the host and it may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`y`	<type> vector in dense format (of `size≥max(xInd)-idxBase+1`).
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

xVal

<type> vector with nnz nonzero values that were gathered from vector y (that is unchanged if nnz == 0).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

6.5. cusparse<t>gthrz()

cusparseStatus_t 
cusparseSgthrz(cusparseHandle_t handle, int nnz, float           *y, 
               float           *xVal, const int *xInd, 
               cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDgthrz(cusparseHandle_t handle, int nnz, double          *y, 
               double          *xVal, const int *xInd, 
               cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCgthrz(cusparseHandle_t handle, int nnz, cuComplex       *y, 
               cuComplex       *xVal, const int *xInd, 
               cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZgthrz(cusparseHandle_t handle, int nnz, cuDoubleComplex *y, 
               cuDoubleComplex *xVal, const int *xInd, 
               cusparseIndexBase_t idxBase)

This function gathers the elements of the vector y listed in the index array xInd into the data array xVal. Also, it zeros out the gathered elements in the vector y.

This function requires no extra storage. It is executed asynchronously with respect to the host, and it may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`y`	<type> vector in dense format (of `size≥max(xInd)-idxBase+1`).
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

`xVal`	<type> vector with `nnz` nonzero values that were gathered from vector `y` (that is unchanged if `nnz == 0`).
`y`	<type> vector in dense format with elements indexed by `xInd` set to zero (it is unchanged if `nnz == 0`).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

6.6. cusparse<t>roti()

cusparseStatus_t 
cusparseSroti(cusparseHandle_t handle, int nnz, float  *xVal, 
              const int *xInd, 
              float  *y, const float  *c, const float  *s, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDroti(cusparseHandle_t handle, int nnz, double *xVal, 
              const int *xInd, 
              double *y, const double *c, const double *s, 
              cusparseIndexBase_t idxBase)

This function applies the Givens rotation matrix

$G = (\begin{array}{rr} c & s \\ - s & c \end{array})$

to sparse x and dense y vectors. In other words,

for i=0 to nnz-1
    y[xInd[i]-idxBase] = c * y[xInd[i]-idxBase] - s*xVal[i]
    x[i]               = c * xVal[i]            + s * y[xInd[i]-idxBase]

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`xVal`	<type> vector with `nnz` nonzero values of vector `x`.
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`y`	<type> vector in dense format.
`c`	cosine element of the rotation matrix.
`s`	sine element of the rotation matrix.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

`xVal`	<type> updated vector in sparse format (that is unchanged if `nnz == 0`).
`y`	<type> updated vector in dense format (that is unchanged if `nnz == 0`).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

6.7. cusparse<t>sctr()

cusparseStatus_t 
cusparseSsctr(cusparseHandle_t handle, int nnz, 
              const float           *xVal, 
              const int *xInd, float           *y, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDsctr(cusparseHandle_t handle, int nnz, 
              const double          *xVal, 
              const int *xInd, double          *y, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCsctr(cusparseHandle_t handle, int nnz, 
              const cuComplex       *xVal, 
              const int *xInd, cuComplex       *y, 
              cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZsctr(cusparseHandle_t handle, int nnz, 
              const cuDoubleComplex *xVal, 
              const int *xInd, cuDoubleComplex *y, 
              cusparseIndexBase_t idxBase)

This function scatters the elements of the vector x in sparse format into the vector y in dense format. It modifies only the elements of y whose indices are listed in the array xInd.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`nnz`	number of elements in vector `x`.
`xVal`	<type> vector with `nnz` nonzero values of vector `x`.
`xInd`	integer vector with `nnz` indices of the nonzero values of vector `x`.
`y`	<type> dense vector (of `size≥max(xInd)-idxBase+1`).
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

`y`	<type> vector with `nnz` nonzero values that were scattered from vector `x` (that is unchanged if `nnz == 0`).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the `idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE.`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

7. cuSPARSE Level 2 Function Reference

This chapter describes the sparse linear algebra functions that perform operations between sparse matrices and dense vectors.

In particular, the solution of sparse triangular linear systems is implemented in two phases. First, during the analysis phase, the sparse triangular matrix is analyzed to determine the dependencies between its elements by calling the appropriate csrsv_analysis() function. The analysis is specific to the sparsity pattern of the given matrix and to the selected cusparseOperation_t type. The information from the analysis phase is stored in the parameter of type cusparseSolveAnalysisInfo_t that has been initialized previously with a call to cusparseCreateSolveAnalysisInfo().

Second, during the solve phase, the given sparse triangular linear system is solved using the information stored in the cusparseSolveAnalysisInfo_t parameter by calling the appropriate csrsv_solve() function. The solve phase may be performed multiple times with different right-hand sides, while the analysis phase needs to be performed only once. This is especially useful when a sparse triangular linear system must be solved for a set of different right-hand sides one at a time, while its coefficient matrix remains the same.

Finally, once all the solves have completed, the opaque data structure pointed to by the cusparseSolveAnalysisInfo_t parameter can be released by calling cusparseDestroySolveAnalysisInfo(). For more information please refer to [3].

7.1. cusparse<t>bsrmv()

cusparseStatus_t
cusparseSbsrmv(cusparseHandle_t handle, cusparseDirection_t dir,
    cusparseOperation_t trans, int mb, int nb, int nnzb,
    const float *alpha, const cusparseMatDescr_t descr,
    const float *bsrVal, const int *bsrRowPtr, const int *bsrColInd,
    int  blockDim, const float *x, 
    const float *beta, float *y)
cusparseStatus_t
cusparseDbsrmv(cusparseHandle_t handle, cusparseDirection_t dir,
    cusparseOperation_t trans, int mb, int nb, int nnzb,
    const double *alpha, const cusparseMatDescr_t descr,
    const double *bsrVal, const int *bsrRowPtr, const int *bsrColInd,
    int  blockDim, const double *x, 
    const double *beta, double *y)
cusparseStatus_t
cusparseCbsrmv(cusparseHandle_t handle, cusparseDirection_t dir,
    cusparseOperation_t trans, int mb, int nb, int nnzb,
    const cuComplex *alpha, const cusparseMatDescr_t descr,
    const cuComplex *bsrVal, const int *bsrRowPtr, const int *bsrColInd,
    int  blockDim, const cuComplex *x, 
    const cuComplex *beta, cuComplex *y)
cusparseStatus_t
cusparseZbsrmv(cusparseHandle_t handle, cusparseDirection_t dir,
    cusparseOperation_t trans, int mb, int nb, int nnzb,
    const cuDoubleComplex *alpha, const cusparseMatDescr_t descr,
    const cuDoubleComplex *bsrVal, const int *bsrRowPtr, const int *bsrColInd,
    int  blockDim, const cuDoubleComplex *x, 
    const cuDoubleComplex *beta, cuDoubleComplex *y)

This function performs the matrix-vector operation

y = α * op (A) * x + β * y

where $A is an (m b * b l o c k D i m) \times (n b * b l o c k D i m)$ sparse matrix that is defined in BSR storage format by the three arrays bsrVal, bsrRowPtr, and bsrColInd); x and y are vectors; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Several comments on bsrmv():

Only CUSPARSE_OPERATION_NON_TRANSPOSE is supported, that is

y = α * A * x + β * y

Only CUSPARSE_MATRIX_TYPE_GENERAL is supported.
The size of vector x should be $(n b * b l o c k D i m)$ at least, and the size of vector y should be $(m b * b l o c k D i m)$ at least; otherwise, the kernel may return CUSPARSE_STATUS_EXECUTION_FAILED because of an out-of-bounds array.

For example, suppose the user has a CSR format and wants to try bsrmv(), the following code demonstrates how to use csr2bsr() conversion and bsrmv() multiplication in single precision.

// Suppose that A is m x n sparse matrix represented by CSR format, 
// hx is a host vector of size n, and hy is also a host vector of size m. 
// m and n are not multiple of blockDim.
// step 1: transform CSR to BSR with column-major order 
int base, nnz;
int nnzb;
cusparseDirection_t dirA = CUSPARSE_DIRECTION_COLUMN;
int mb = (m + blockDim-1)/blockDim;
int nb = (n + blockDim-1)/blockDim;
cudaMalloc((void**)&bsrRowPtrC, sizeof(int) *(mb+1));
cusparseXcsr2bsrNnz(handle, dirA, m, n, 
        descrA, csrRowPtrA, csrColIndA, blockDim, 
        descrC, bsrRowPtrC, &nnzb);
cudaMalloc((void**)&bsrColIndC, sizeof(int)*nnzb);
cudaMalloc((void**)&bsrValC, sizeof(float)*(blockDim*blockDim)*nnzb);
cusparseScsr2bsr(handle, dirA, m, n, 
        descrA, csrValA, csrRowPtrA, csrColIndA, blockDim,
        descrC, bsrValC, bsrRowPtrC, bsrColIndC);
// step 2: allocate vector x and vector y large enough for bsrmv 
cudaMalloc((void**)&x, sizeof(float)*(nb*blockDim));
cudaMalloc((void**)&y, sizeof(float)*(mb*blockDim));
cudaMemcpy(x, hx, sizeof(float)*n, cudaMemcpyHostToDevice);
cudaMemcpy(y, hy, sizeof(float)*m, cudaMemcpyHostToDevice);
// step 3: perform bsrmv
cusparseSbsrmv(handle, dirA, transA, mb, nb, nnzb, &alpha, 
   descrC, bsrValC, bsrRowPtrC, bsrColIndC, blockDim, x, &beta, y);

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`trans`	the operation $op (A)$ . Only `CUSPARSE_OPERATION_NON_TRANSPOSE` is supported.
`mb`	number of block rows of matrix $A$ .
`nb`	number of block columns of matrix $A$ .
`nnzb`	number of nonzero blocks of matrix $A$ .
`alpha`	<type> scalar used for multiplication.
`descr`	the descriptor of matrix $A$ . The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrVal`	<type> array of `nnz` $(=$ `csrRowPtrA(mb)` $-$ `csrRowPtrA(0)` $)$ nonzero blocks of matrix $A$ .
`bsrRowPtr`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColInd`	integer array of `nnz` $(=$ `csrRowPtrA(mb)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix $A$ .
`blockDim`	block dimension of sparse matrix $A$ , larger than zero.
`x`	<type> vector of $n b * b l o c k D i m$ elements.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> vector of $m b * b l o c k D i m$ elements.

Output

`y`	<type> updated vector.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`, `trans != CUSPARSE_OPERATION_NON_TRANSPOSE`, $b l o c k D i m < 1$ , `dir` is not row-major or column-major, or `IndexBase of descr` is not base-0 or base-1 ).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.2. cusparse<t>bsrxmv()

cusparseStatus_t 
cusparseSbsrxmv(cusparseHandle_t handle, 
                cusparseDirection_t dir,
                cusparseOperation_t trans, 
                int sizeOfMask,
                int mb, 
                int nb, 
                int nnzb,
                const float *alpha, 
                const cusparseMatDescr_t descr,
                const float *bsrVal, 
                const int *bsrMaskPtr, 
                const int *bsrRowPtr, 
                const int *bsrEndPtr, 
                const int *bsrColInd,
                int blockDim, 
                const float *x, 
                const float *beta, 
                float *y)
cusparseStatus_t 
cusparseDbsrxmv(cusparseHandle_t handle, 
                cusparseDirection_t dir,
                cusparseOperation_t trans, 
                int sizeOfMask,
                int mb, 
                int nb, 
                int nnzb,
                const double *alpha, 
                const cusparseMatDescr_t descr,
                const double *bsrVal, 
                const int *bsrMaskPtr,
                const int *bsrRowPtr, 
                const int *bsrEndPtr, 
                const int *bsrColInd,
                int blockDim, 
                const double *x, 
                const double *beta, 
                double *y)
cusparseStatus_t 
cusparseCbsrxmv(cusparseHandle_t handle, 
                cusparseDirection_t dir,
                cusparseOperation_t trans, 
                int sizeOfMask,
                int mb, 
                int nb, 
                int nnzb,
                const cuComplex *alpha, 
                const cusparseMatDescr_t descr,
                const cuComplex *bsrVal, 
                const int *bsrMaskPtr,
                const int *bsrRowPtr, 
                const int *bsrEndPtr, 
                const int *bsrColInd,
                int blockDim, 
                const cuComplex *x, 
                const cuComplex *beta, 
                cuComplex *y)
cusparseStatus_t 
cusparseZbsrxmv(cusparseHandle_t handle, 
                cusparseDirection_t dir,
                cusparseOperation_t trans, 
                int sizeOfMask,
                int mb, 
                int nb, 
                int nnzb,
                const cuDoubleComplex *alpha, 
                const cusparseMatDescr_t descr,
                const cuDoubleComplex *bsrVal, 
                const int *bsrMaskPtr,
                const int *bsrRowPtr, 
                const int *bsrEndPtr, 
                const int *bsrColInd,
                int blockDim, 
                const cuDoubleComplex *x, 
                const cuDoubleComplex *beta, 
                cuDoubleComplex *y)

This function performs a bsrmv and a mask operation

y(mask) = (α * op (A) * x + β * y) (mask)

where $A is an (m b * b l o c k D i m) \times (n b * b l o c k D i m)$ sparse matrix that is defined in BSRX storage format by the four arrays bsrVal, bsrRowPtr, bsrEndPtr, and bsrColInd); x and y are vectors; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

The mask operation is defined by array bsrMaskPtr which contains updated block row indices of $y$ . If row $i$ is not specified in bsrMaskPtr, then bsrxmv() does not touch row block $i$ of $A$ and $y$ .

For example, consider the $2 \times 3$ block matrix $A$ :

\begin{aligned} A = [\begin{matrix} A_{11} & A_{12} & O \\ A_{21} & A_{22} & A_{23} \end{matrix}] \end{aligned}

and its one-based BSR format (three vector form) is

\begin{array}{rcl} bsrVal & = & [\begin{matrix} A_{11} & A_{12} & A_{21} & A_{22} & A_{23} \end{matrix}] \\ bsrRowPtr & = & [\begin{matrix} 1 & 3 & 6 \end{matrix}] \\ bsrColInd & = & [\begin{matrix} 1 & 2 & 1 & 2 & 3 \end{matrix}] \end{array}

Suppose we want to do the following bsrmv operation on a matrix $\bar{A}$ which is slightly different from $A$ .

[\begin{matrix} y_{1} \\ y_{2} \end{matrix}] := a l p h a * (\tilde{A} = [\begin{matrix} O & O & O \\ O & A_{22} & O \end{matrix}]) * [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] + [\begin{matrix} y_{1} \\ b e t a * y_{2} \end{matrix}]

We don’t need to create another BSR format for the new matrix $\bar{A}$ , all that we should do is to keep bsrVal and bsrColInd unchanged, but modify bsrRowPtr and add an additional array bsrEndPtr which points to the last nonzero elements per row of $\bar{A}$ plus 1.

For example, the following bsrRowPtr and bsrEndPtr can represent matrix $\bar{A}$ :

\begin{array}{rcl} bsrRowPtr & = & [\begin{matrix} 1 & 4 \end{matrix}] \\ bsrEndPtr & = & [\begin{matrix} 1 & 5 \end{matrix}] \end{array}

Further we can use a mask operator (specified by array bsrMaskPtr) to update particular block row indices of $y$ only because $y_{1}$ is never changed. In this case, bsrMaskPtr $=$ [2] and sizeOfMask=1.

The mask operator is equivalent to the following operation:

[\begin{matrix} ? \\ y_{2} \end{matrix}] := a l p h a * [\begin{matrix} ? & ? & ? \\ O & A_{22} & O \end{matrix}] * [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] + b e t a * [\begin{matrix} ? \\ y_{2} \end{matrix}]

If a block row is not present in the bsrMaskPtr, then no calculation is performed on that row, and the corresponding value in y is unmodified. The question mark "?" is used to inidcate row blocks not in bsrMaskPtr.

In this case, first row block is not present in bsrMaskPtr, so bsrRowPtr[0] and bsrEndPtr[0] are not touched also.

\begin{array}{rcl} bsrRowPtr & = & [\begin{matrix} ? & 4 \end{matrix}] \\ bsrEndPtr & = & [\begin{matrix} ? & 5 \end{matrix}] \end{array}

A couple of comments on bsrxmv():

Only CUSPARSE_OPERATION_NON_TRANSPOSE and CUSPARSE_MATRIX_TYPE_GENERAL are supported.
Parameters bsrMaskPtr, bsrRowPtr, bsrEndPtr and bsrColInd are consistent with base index, either one-based or zero-based. The above example is one-based.

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`trans`	the operation $op (A)$ . Only `CUSPARSE_OPERATION_NON_TRANSPOSE` is supported.
`sizeOfMask`	number of updated block rows of $y$ .
`mb`	number of block rows of matrix $A$ .
`nb`	number of block columns of matrix $A$ .
`nnzb`	number of nonzero blocks of matrix $A$ .
`alpha`	<type> scalar used for multiplication.
`descr`	the descriptor of matrix $A$ . The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrVal`	<type> array of `nnz` nonzero blocks of matrix $A$ .
`bsrMaskPtr`	integer array of `sizeOfMask` elements that contains the indices corresponding to updated block rows.
`bsrRowPtr`	integer array of `mb` elements that contains the start of every block row.
`bsrEndPtr`	integer array of `mb` elements that contains the end of the every block row plus one.
`bsrColInd`	integer array of `nnzb` column indices of the nonzero blocks of matrix $A$ .
`blockDim`	block dimension of sparse matrix $A$ , larger than zero.
`x`	<type> vector of $n b * b l o c k D i m$ elements.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> vector of $m b * b l o c k D i m$ elements.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`, `trans != CUSPARSE_OPERATION_NON_TRANSPOSE`, $b l o c k D i m < 1$ , `dir` is not row-major or column-major, or `IndexBase of descr` is not base-0 or base-1 ).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.3. cusparse<t>csrmv()

cusparseStatus_t 
cusparseScsrmv(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, const float           *alpha, 
               const cusparseMatDescr_t descrA, 
               const float           *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const float           *x, const float           *beta, 
               float           *y)
cusparseStatus_t 
cusparseDcsrmv(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, const double          *alpha, 
               const cusparseMatDescr_t descrA, 
               const double          *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const double          *x, const double          *beta, 
               double          *y)
cusparseStatus_t 
cusparseCcsrmv(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, const cuComplex       *alpha, 
               const cusparseMatDescr_t descrA, 
               const cuComplex       *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const cuComplex       *x, const cuComplex       *beta, 
               cuComplex       *y)
cusparseStatus_t 
cusparseZcsrmv(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, const cuDoubleComplex *alpha, 
               const cusparseMatDescr_t descrA, 
               const cuDoubleComplex *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA, 
               const cuDoubleComplex *x, const cuDoubleComplex *beta, 
               cuDoubleComplex *y)

This function performs the matrix-vector operation

y = α * op (A) * x + β * y

A is an m×n sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); x and y are vectors; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

When using the (conjugate) transpose of a general matrix or a Hermitian/symmetric matrix, this routine may produce slightly different results during different runs with the same input parameters. For these matrix types it uses atomic operations to compute the final result, consequently many threads may be adding floating point numbers to the same memory location without any specific ordering, which may produce slightly different results for each run.

If exactly the same output is required for any input when multiplying by the transpose of a general matrix, the following procedure can be used:

1. Convert the matrix from CSR to CSC format using one of the csr2csc() functions. Notice that by interchanging the rows and columns of the result you are implicitly transposing the matrix.

2. Call the csrmv() function with the cusparseOperation_t parameter set to CUSPARSE_OPERATION_NON_TRANSPOSE and with the interchanged rows and columns of the matrix stored in CSC format. This (implicitly) multiplies the vector by the transpose of the matrix in the original CSR format.

This function requires no extra storage for the general matrices when operation CUSPARSE_OPERATION_NON_TRANSPOSE is selected. It requires some extra storage for Hermitian/symmetric matrices and for the general matrices when an operation different than CUSPARSE_OPERATION_NON_TRANSPOSE is selected. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, `CUSPARSE_MATRIX_TYPE_SYMMETRIC`, and `CUSPARSE_MATRIX_TYPE_HERMITIAN`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`x`	<type> vector of `n` elements if $op (A) = A$ , and `m` elements if $op (A) = A^{T}$ or $op (A) = A^{H}$
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> vector of `m` elements if $op (A) = A$ , and `n` elements if $op (A) = A^{T}$ or $op (A) = A^{H}$

Output

`y`	<type> updated vector.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision (compute capability (c.c.) >= 1.3 required), symmetric/Hermitian matrix (c.c. >= 1.2 required), or transpose operation (c.c. >= 1.1 required).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.4. cusparseCsrmvEx()

cusparseStatus_t 
cusparseCsrmvEx(cusparseHandle_t handle, 
                cusparseAlgMode_t alg,
                cusparseOperation_t transA, 
                int m, int n, int nnz,
                const void *alpha, cudaDataType alphatype,
                const cusparseMatDescr_t descrA,
                const void *csrValA, cudaDataType csrValAtype,
                const int *csrRowPtrA,
                const int *csrColIndA,
                const void *x, cudaDataType xtype,
                const void *beta, cudaDataType betatype,
                void *y, cudaDataType ytype,
                cudaDataType executiontype,
                void* buffer);

This function is an extended version of cusparse<t>csrmv() which performs the matrix-vector multiply operation. For detailed description of the functionality, see cusparse<t>csrmv().

For half-precision execution type, the minimum GPU architecture is SM_53. Also, for both half-precision IO and execution, only CUSPARSE_MATRIX_TYPE_GENERAL and CUSPARSE_OPERATION_NON_TRANSPOSE are supported.

All pointers should be aligned with 128 bytes.

Input specifically required by cusparseCsrmvEx

`alg`	Not currently used. Will be used for future algorithms such as MergePath or Multi-GPU.
`alphatype`	Data type of `alpha`.
`csrValAtype`	Data type of `csrValA`.
`xtype`	Data type of `x`.
`betatype`	Data type of `beta`.
`ytype`	Data type of `y`.
`executiontype`	Data type used for computation.
`buffer`	Pointer to workspace buffer. Not currently used, however must be allocated and be aligned with word boundaries. Recommended to always use `cusparseCsrmvEx_bufferSize` to obtain the right size for this buffer.

cusparseCsrmvEx_bufferSize()

cusparseCsrmvEx_bufferSize(cusparseHandle_t handle, 
                                                 cusparseAlgMode_t alg,
                                                 cusparseOperation_t transA, 
                                                 int m, int n, int nnz,
                                                 const void *alpha, cudaDataType alphatype,
                                                 const cusparseMatDescr_t descrA,
                                                 const void *csrValA, cudaDataType csrValAtype,
                                                 const int *csrRowPtrA,
                                                 const int *csrColIndA,
                                                 const void *x, cudaDataType xtype,
                                                 const void *beta, cudaDataType betatype,
                                                 void *y, cudaDataType ytype,
                                                 cudaDataType executiontype,
                                                 size_t *bufferSizeInBytes);

This function returns the size of the workspace needed by cusparseCsrmvEx. User needs to allocate a buffer of this size and give that buffer to cusparseCsrmvEx as an argument. All the arguments are similar to cusparseCsrmvEx except the following output argument.

Output specifically required by cusparseCsrmvEx_bufferSize

bufferSizeInBytes

Pointer to a size_t variable, which will be assigned with the size of workspace needed by cusparseCsrmv. Since workspace is not currently used by cusparseCsrmv, this function returns the number 16 as an arbitrary number.

7.6. cusparse<t>csrmv_mp()

cusparseStatus_t 
cusparseScsrmv_mp(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, 
               const float           *alpha, 
               const cusparseMatDescr_t descrA, 
               const float           *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const float           *x, const float           *beta, 
               float           *y)
cusparseStatus_t 
cusparseDcsrmv_mp(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, 
               const double          *alpha, 
               const cusparseMatDescr_t descrA, 
               const double          *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const double          *x, const double          *beta, 
               double          *y)
cusparseStatus_t 
cusparseCcsrmv_mp(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, 
               const cuComplex       *alpha, 
               const cusparseMatDescr_t descrA, 
               const cuComplex       *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA,
               const cuComplex       *x, const cuComplex       *beta, 
               cuComplex       *y)
cusparseStatus_t 
cusparseZcsrmv_mp(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, int nnz, 
               const cuDoubleComplex *alpha, 
               const cusparseMatDescr_t descrA, 
               const cuDoubleComplex *csrValA, 
               const int *csrRowPtrA, const int *csrColIndA, 
               const cuDoubleComplex *x, const cuDoubleComplex *beta, 
               cuDoubleComplex *y)

This function performs a load-balanced matrix-vector operation

y = α * op (A) * x + β * y

A is an m×n sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); x and y are vectors; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

This routine was introduced specifically to address some of the loss of performance in the regular csrmv() code due to irregular sparsity patterns and transpose operations. The core kernels are based on the "MergePath" approach created by Duanne Merril. By using this approach, we are able to provide performance independent of a sparsity pattern, transpose or non-transpose, across data types.

Appendix C provides a simple example of csrmv_mp.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, `CUSPARSE_MATRIX_TYPE_SYMMETRIC`, and `CUSPARSE_MATRIX_TYPE_HERMITIAN`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`x`	<type> vector of `n` elements if $op (A) = A$ , and `m` elements if $op (A) = A^{T}$ or $op (A) = A^{H}$
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> vector of `m` elements if $op (A) = A$ , and `n` elements if $op (A) = A^{T}$ or $op (A) = A^{H}$

Output

`y`	<type> updated vector.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision (compute capability (c.c.) >= 1.3 required), symmetric/Hermitian matrix (c.c. >= 1.2 required), or transpose operation (c.c. >= 1.1 required).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.7. cusparse<t>gemvi()

cusparseStatus_t 
cusparseSgemvi(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, const float           *alpha, 
               const float *A, 
               int lda, int nnz,
               const float           *x, 
               const int             *xInd,
               const float           *beta, 
               float                 *y,
               cusparseIndexBase_t    idxBase,
               void                  *pBuffer)
cusparseStatus_t 
cusparseDgemvi(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, const double           *alpha, 
               const double *A, 
               int lda, int nnz,
               const double          *x, 
               const int             *xInd,
               const double          *beta, 
               double                *y,
               cusparseIndexBase_t    idxBase,
               void                  *pBuffer)
cusparseStatus_t 
cusparseCgemvi(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, const cuComplex           *alpha, 
               const cuComplex *A, 
               int lda, int nnz,
               const cuComplex       *x, 
               const int             *xInd,
               const cuComplex       *beta, 
               cuComplex             *y,
               cusparseIndexBase_t    idxBase,
               void                  *pBuffer)
cusparseStatus_t 
cusparseZgemvi(cusparseHandle_t handle, cusparseOperation_t transA, 
               int m, int n, const cuDoubleComplex           *alpha, 
               const cuDoubleComplex *A, 
               int lda, int nnz,
               const cuDoubleComplex       *x, 
               const int             *xInd,
               const cuDoubleComplex       *beta, 
               cuDoubleComplex             *y,
               cusparseIndexBase_t    idxBase,
               void                  *pBuffer)

This function performs the matrix-vector operation

y = α * op (A) * x + β * y

A is an m×n dense matrix and a sparse vector x that is defined in a sparse storage format by the two arrays xVal, xInd of length nnz, and y is a dense vector; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

To simplify the implementation, we have not (yet) optimized the transpose multiple case. We recommend the following for users interested in this case.

1. Convert the matrix from CSR to CSC format using one of the csr2csc() functions. Notice that by interchanging the rows and columns of the result you are implicitly transposing the matrix.

2. Call the gemvi() function with the cusparseOperation_t parameter set to CUSPARSE_OPERATION_NON_TRANSPOSE and with the interchanged rows and columns of the matrix stored in CSC format. This (implicitly) multiplies the vector by the transpose of the matrix in the original CSR format.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`A`	the pointer to dense matrix `A`.
`lda`	size of the leading dimension of `A`.
`nnz`	number of nonzero elements of vector `x`.
`x`	<type> sparse vector of `nnz` elements of size `n` if $op (A) = A$ , and size `m` if $op (A) = A^{T}$ or $op (A) = A^{H}$
`xInd`	Indices of non-zero values in `x`
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> dense vector of `m` elements if $op (A) = A$ , and `n` elements if $op (A) = A^{T}$ or $op (A) = A^{H}$
`idxBase`	0 or 1, for 0 based or 1 based indexing, respectively
`pBuffer`	working space buffer, of size given by `Xgemvi_getBufferSize()`

Output

`y`	<type> updated dense vector.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision (compute capability (c.c.) >= 1.3 required), symmetric/Hermitian matrix (c.c. >= 1.2 required), or transpose operation (c.c. >= 1.1 required).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.8. cusparse<t>gemvi_bufferSize()

cusparseStatus_t 
cusparseSgemvi_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int n,
                           int nnz,
                           int *pBufferSize)

cusparseStatus_t 
cusparseDgemvi_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int n,
                           int nnz,
                           int *pBufferSize)

cusparseStatus_t 
cusparseCgemvi_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int n,
                           int nnz,
                           int *pBufferSize)

cusparseStatus_t 
cusparseZgemvi_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int n,
                           int nnz,
                           int *pBufferSize)

This function returns size of buffer used in gemvi()

A is an (m)x(n) dense matrix.

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation `op(A)`.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `Y`.
`nnz`	number of nonzero entries of vector `x` multiplying `A`.

Output

pBufferSize

number of elements needed the buffer used in gemvi().

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n, nnz<=0`)
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.9. cusparse<t>bsrsv2_bufferSize()

cusparseStatus_t 
cusparseSbsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           float *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDbsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           double *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCbsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZbsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuDoubleComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsv2Info_t info,
                           int *pBufferSizeInBytes);

This function returns size of the buffer used in bsrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

A is an (mb*blockDim)x(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA); x and y are the right-hand-side and the solution vectors; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Although there are six combinations in terms of parameter trans and the upper (lower) triangular part of A, bsrsv2_bufferSize() returns the maximum size buffer among these combinations. The buffer size depends on the dimensions mb, blockDim, and the number of nonzero blocks of the matrix nnzb. If the user changes the matrix, it is necessary to call bsrsv2_bufferSize() again to have the correct buffer size; otherwise a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation $op (A)$ .
`mb`	number of block rows of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A; must be larger than zero.

Output

`info`	record of internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in the `bsrsv2_analysis()` and `bsrsv2_solve()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.10. cusparse<t>bsrsv2_analysis()

cusparseStatus_t 
cusparseSbsrsv2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         int mb,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const float *bsrValA,
                         const int *bsrRowPtrA,
                         const int *bsrColIndA,
                         int blockDim,
                         bsrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseDbsrsv2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         int mb,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const double *bsrValA,
                         const int *bsrRowPtrA,
                         const int *bsrColIndA,
                         int blockDim,
                         bsrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseCbsrsv2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         int mb,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const cuComplex *bsrValA,
                         const int *bsrRowPtrA,
                         const int *bsrColIndA,
                         int blockDim,
                         bsrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseZbsrsv2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         int mb,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const cuDoubleComplex *bsrValA,
                         const int *bsrRowPtrA,
                         const int *bsrColIndA,
                         int blockDim,
                         bsrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

This function performs the analysis phase of bsrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

A is an (mb*blockDim)x(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA); x and y are the right-hand side and the solution vectors; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

The block of BSR format is of size blockDim*blockDim, stored as column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_COLUMN or CUSPARSE_DIRECTION_ROW. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored.

It is expected that this function will be executed only once for a given matrix and a particular operation type.

This function requires a buffer size returned by bsrsv2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsrsv2_analysis() reports a structural zero and computes level information, which stored in the opaque structure info. The level information can extract more parallelism for a triangular solver. However bsrsv2_solve() can be done without level information. To disable level information, the user needs to specify the policy of the triangular solver as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function bsrsv2_analysis() always reports the first structural zero, even when parameter policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. No structural zero is reported if CUSPARSE_DIAG_TYPE_UNIT is specified, even if block A(j,j) is missing for some j. The user needs to call cusparseXbsrsv2_zeroPivot() to know where the structural zero is.

It is the user's choice whether to call bsrsv2_solve() if bsrsv2_analysis() reports a structural zero. In this case, the user can still call bsrsv2_solve(), which will return a numerical zero at the same position as a structural zero. However the result x is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation $op (A)$ .
`mb`	number of block rows of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A, larger than zero.
`info`	structure initialized using `cusparseCreateBsrsv2Info()`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is return by `bsrsv2_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.11. cusparse<t>bsrsv2_solve()

cusparseStatus_t 
cusparseSbsrsv2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      int mb,
                      int nnzb,
                      const float *alpha,
                      const cusparseMatDescr_t descrA,
                      const float *bsrValA,
                      const int *bsrRowPtrA,
                      const int *bsrColIndA,
                      int blockDim,
                      bsrsv2Info_t info,
                      const float *x,
                      float *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseDbsrsv2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      int mb,
                      int nnzb,
                      const double *alpha,
                      const cusparseMatDescr_t descrA,
                      const double *bsrValA,
                      const int *bsrRowPtrA,
                      const int *bsrColIndA,
                      int blockDim,
                      bsrsv2Info_t info,
                      const double *x,
                      double *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseCbsrsv2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      int mb,
                      int nnzb,
                      const cuComplex *alpha,
                      const cusparseMatDescr_t descrA,
                      const cuComplex *bsrValA,
                      const int *bsrRowPtrA,
                      const int *bsrColIndA,
                      int blockDim,
                      bsrsv2Info_t info,
                      const cuComplex *x,
                      cuComplex *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseZbsrsv2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      int mb,
                      int nnzb,
                      const cuDoubleComplex *alpha,
                      const cusparseMatDescr_t descrA,
                      const cuDoubleComplex *bsrValA,
                      const int *bsrRowPtrA,
                      const int *bsrColIndA,
                      int blockDim,
                      bsrsv2Info_t info,
                      const cuDoubleComplex *x,
                      cuDoubleComplex *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

This function performs the solve phase of bsrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

The block in BSR format is of size blockDim*blockDim, stored as column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_COLUMN or CUSPARSE_DIRECTION_ROW. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored. Function bsrsv02_solve() can support an arbitrary blockDim.

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires a buffer size returned by bsrsv2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although bsrsv2_solve() can be done without level information, the user still needs to be aware of consistency. If bsrsv2_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, bsrsv2_solve() can be run with or without levels. On the other hand, if bsrsv2_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, bsrsv2_solve() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

The level information may not improve the performance, but may spend extra time doing analysis. For example, a tridiagonal matrix has no parallelism. In this case, CUSPARSE_SOLVE_POLICY_NO_LEVEL performs better than CUSPARSE_SOLVE_POLICY_USE_LEVEL. If the user has an iterative solver, the best approach is to do bsrsv2_analysis() with CUSPARSE_SOLVE_POLICY_USE_LEVEL once. Then do bsrsv2_solve() with CUSPARSE_SOLVE_POLICY_NO_LEVEL in the first run, and with CUSPARSE_SOLVE_POLICY_USE_LEVEL in the second run, and pick the fastest one to perform the remaining iterations.

Function bsrsv02_solve() has the same behavior as csrsv02_solve(). That is, bsr2csr(bsrsv02(A)) = csrsv02(bsr2csr(A)). The numerical zero of csrsv02_solve() means there exists some zero A(j,j). The numerical zero of bsrsv02_solve() means there exists some block A(j,j) that is not invertible.

Function bsrsv2_solve() reports the first numerical zero, including a structural zero. No numerical zero is reported if CUSPARSE_DIAG_TYPE_UNIT is specified, even if A(j,j) is not invertible for some j. The user needs to call cusparseXbsrsv2_zeroPivot() to know where the numerical zero is.

For example, suppose L is a lower triangular matrix with unit diagonal, then the following code solves L*y=x by level information.

// Suppose that L is m x m sparse matrix represented by BSR format, 
// The number of block rows/columns is mb, and 
// the number of nonzero blocks is nnzb.
// L is lower triangular with unit diagonal. 
// Assumption:
// - dimension of matrix L is m(=mb*blockDim),
// - matrix L has nnz(=nnzb*blockDim*blockDim) nonzero elements,
// - handle is already created by cusparseCreate(),
// - (d_bsrRowPtr, d_bsrColInd, d_bsrVal) is BSR of L on device memory,
// - d_x is right hand side vector on device memory.
// - d_y is solution vector on device memory.
// - d_x and d_y are of size m.
cusparseMatDescr_t descr = 0;
bsrsv2Info_t info = 0;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;

// step 1: create a descriptor which contains
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has unit diagonal, specified by parameter CUSPARSE_DIAG_TYPE_UNIT
//   (L may not have all diagonal elements.) 
cusparseCreateMatDescr(&descr);
cusparseSetMatIndexBase(descr, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatFillMode(descr, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr, CUSPARSE_DIAG_TYPE_UNIT);

// step 2: create a empty info structure
cusparseCreateBsrsv2Info(&info);

// step 3: query how much memory used in bsrsv2, and allocate the buffer
cusparseDbsrsv2_bufferSize(handle, dir, trans, mb, nnzb, descr,
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, &pBufferSize);

// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis 
cusparseDbsrsv2_analysis(handle, dir, trans, mb, nnzb, descr, 
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim,
    info, policy, pBuffer);
// L has unit diagonal, so no structural zero is reported.
status = cusparseXbsrsv2_zeroPivot(handle, info, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is missing\n", structural_zero, structural_zero);
}

// step 5: solve L*y = x
cusparseDbsrsv2_solve(handle, dir, trans, mb, nnzb, &alpha, descr,
   d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info,
   d_x, d_y, policy, pBuffer);
// L has unit diagonal, so no numerical zero is reported.
status = cusparseXbsrsv2_zeroPivot(handle, info, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is zero\n", numerical_zero, numerical_zero);
}

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyBsrsv2Info(info);
cusparseDestroyMatDescr(descr);
cusparseDestroy(handle);

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation $op (A)$ .
`mb`	number of block rows and block columns of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`, larger than zero.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`x`	<type> right-hand-side vector of size `m`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is returned by `bsrsv2_bufferSize()`.

Output

`y`	<type> solution vector of size `m`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXbsrsv2_zeroPivot()

cusparseStatus_t 
cusparseXbsrsv2_zeroPivot(cusparseHandle_t handle,
                          bsrsv2Info_t info,
                          int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) is either structural zero or numerical zero (singular block). Otherwise position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXbsrsv2_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains a structural zero or numerical zero if the user already called `bsrsv2_analysis()` or `bsrsv2_solve()`.

Output

position

if no structural or numerical zero, position is -1; otherwise if A(j,j) is missing or U(j,j) is zero, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

7.13. cusparse<t>csrsv_analysis()

cusparseStatus_t 
cusparseScsrsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, 
                        int nnz, 
                        const cusparseMatDescr_t descrA,
                        const float *csrValA, 
                        const int *csrRowPtrA, 
                        const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseDcsrsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, 
                        int nnz, 
                        const cusparseMatDescr_t descrA,
                        const double *csrValA, 
                        const int *csrRowPtrA, 
                        const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)    
cusparseStatus_t 
cusparseCcsrsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, 
                        int nnz, 
                        const cusparseMatDescr_t descrA,
                        const cuComplex *csrValA, 
                        const int *csrRowPtrA, 
                        const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)    
cusparseStatus_t 
cusparseZcsrsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, 
                        int nnz, 
                        const cusparseMatDescr_t descrA,
                        const cuDoubleComplex *csrValA, 
                        const int *csrRowPtrA, 
                        const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)

This function performs the analysis phase of the solution of a sparse triangular linear system

op (A) * y = α * x

where A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); x and y are the right-hand-side and the solution vectors; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

The routine csrsv_analysis supports analysis phase of csrsv_solve, csric0 and csrilu0. The user has to be careful of which routine is called after csrsv_analysis. The matrix descriptor must be the same for csrsv_analysis and its subsequent call to csrsv_solve, csric0 and csrilu0.

For csrsv_solve, the matrix type must be CUSPARSE_MATRIX_TYPE_TRIANGULAR or CUSPARSE_MATRIX_TYPE_GENERAL.

For csrilu0, the matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL.

For csric0, the matrix type must be CUSPARSE_MATRIX_TYPE_SYMMETRIC or CUSPARSE_MATRIX_TYPE_HERMITIAN.

It is expected that this function will be executed only once for a given matrix and a particular operation type.

This function requires a significant amount of extra storage that is proportional to the matrix size. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation $op (A)$
`m`	number of rows of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`descrA`	the descriptor of matrix $A$ . The supported matrix types are `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and `CUSPARSE_MATRIX_TYPE_GENERAL` for `csrsv_solve`, `CUSPARSE_MATRIX_TYPE_SYMMETRIC` and `CUSPARSE_MATRIX_TYPE_HERMITIAN` for `csric0`, `CUSPARSE_MATRIX_TYPE_GENERAL` for `csrilu0`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure initialized using `cusparseCreateSolveAnalysisInfo`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.14. cusparseCsrsv_analysisEx()

cusparseStatus_t cusparseCsrsv_analysisEx(cusparseHandle_t handle, 
                                          cusparseOperation_t transA, 
                                          int m, int nnz,
                                          const cusparseMatDescr_t descrA, 
                                          const void *csrSortedValA, cudaDataType csrSortedValAtype,
                                          const int *csrSortedRowPtrA, 
                                          const int *csrSortedColIndA, 
                                          cusparseSolveAnalysisInfo_t info,
                                          cudaDataType executiontype);

This function is an extended version of cusparse<t>csrsv_analysis(). For detailed description of the functionality, see cusparse<t>csrsv_analysis().

This function does not support half-precision execution type, but it supports half-precision IO with single precision execution.

Input specifically required by cusparseCsrsv_analysisEx

`csrSortedValAtype`	Data type of `csrSortedValA`.
`executiontype`	Data type used for computation.

7.15. cusparse<t>csrsv_solve()

cusparseStatus_t cusparseScsrsv_solve(cusparseHandle_t handle, 
                                      cusparseOperation_t transA, 
                                      int m, const float *alpha, 
                                      const cusparseMatDescr_t descrA, 
                                      const float *csrSortedValA, 
                                      const int *csrSortedRowPtrA, const int *csrSortedColIndA, 
                                      cusparseSolveAnalysisInfo_t info, 
                                      const float *f, float *x);

cusparseStatus_t cusparseDcsrsv_solve(cusparseHandle_t handle, 
                                      cusparseOperation_t transA, 
                                      int m, const double *alpha, 
                                      const cusparseMatDescr_t descrA, 
                                      const double *csrSortedValA, 
                                      const int *csrSortedRowPtrA, const int *csrSortedColIndA, 
                                      cusparseSolveAnalysisInfo_t info, 
                                      const double *f, double *x);

cusparseStatus_t cusparseCcsrsv_solve(cusparseHandle_t handle, 
                                      cusparseOperation_t transA, 
                                      int m, const cuComplex *alpha, 
                                      const cusparseMatDescr_t descrA, 
                                      const cuComplex *csrSortedValA, 
                                      const int *csrSortedRowPtrA, const int *csrSortedColIndA, 
                                      cusparseSolveAnalysisInfo_t info, 
                                      const cuComplex *f, cuComplex *x);

cusparseStatus_t cusparseZcsrsv_solve(cusparseHandle_t handle, 
                                      cusparseOperation_t transA, 
                                      int m, const cuDoubleComplex *alpha, 
                                      const cusparseMatDescr_t descrA, 
                                      const cuDoubleComplex *csrSortedValA, 
                                      const int *csrSortedRowPtrA, const int *csrSortedColIndA, 
                                      cusparseSolveAnalysisInfo_t info, 
                                      const cuDoubleComplex *f, cuDoubleComplex *x);

This function performs the solve phase of the solution of a sparse triangular linear system

op (A) * x = α * f

where A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrSortedValA, csrSortedRowPtrA, and csrSortedColIndA); f and x are the right-hand-side and the solution vectors; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation $op (A)$
`m`	number of rows and columns of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix types are `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrSortedValA`	<type> array of `nnz` $(=$ `csrSortedRowPtrA(m)` $-$ `csrSortedRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrSortedRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrSortedColIndA`	integer array of `nnz` $(=$ `csrSortedRowPtrA(m)` $-$ `csrSortedRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`f`	<type> right-hand-side vector of size `m`.

Output

`x`	<type> solution vector of size `m`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.16. cusparseCsrsv_solveEx()

cusparseStatus_t cusparseCsrsv_solveEx(cusparseHandle_t handle, 
                                       cusparseOperation_t transA, 
                                       int m,
                                       const void *alpha, cudaDataType alphatype,
                                       const cusparseMatDescr_t descrA, 
                                       const void *csrSortedValA, cudaDataType csrSortedValAtype,
                                       const int *csrSortedRowPtrA, 
                                       const int *csrSortedColIndA, 
                                       cusparseSolveAnalysisInfo_t info, 
                                       const void *f, cudaDataType ftype,
                                       void *x, cudaDataType xtype,
                                       cudaDataType executiontype);

This function is an extended version of cusparse<t>csrsv_solve(). For detailed description of the functionality, see cusparse<t>csrsv_solve().

This function does not support half-precision execution type, but it supports half-precision IO with single precision execution.

Input specifically required by cusparseCsrsv_solveEx

`alphatype`	Data type of `alpha`.
`csrSortedValAtype`	Data type of `csrSortedValA`.
`ftype`	Data type of `f`.
`xtype`	Data type of `x`.
`executiontype`	Data type used for computation.

7.17. cusparse<t>csrsv2_bufferSize()

cusparseStatus_t 
cusparseScsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           float *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDcsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           double *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCcsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           cuComplex *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrsv2Info_t info,
                           int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZcsrsv2_bufferSize(cusparseHandle_t handle,
                           cusparseOperation_t transA,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           cuDoubleComplex *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrsv2Info_t info,
                           int *pBufferSizeInBytes);

This function returns the size of the buffer used in csrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); x and y are the right-hand-side and the solution vectors; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Although there are six combinations in terms of the parameter trans and the upper (lower) triangular part of A, csrsv2_bufferSize() returns the maximum size buffer of these combinations. The buffer size depends on the dimension and the number of nonzero elements of the matrix. If the user changes the matrix, it is necessary to call csrsv2_bufferSize() again to have the correct buffer size; otherwise, a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.

Output

`info`	record of internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in the `csrsv2_analysis` and `csrsv2_solve`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.18. cusparse<t>csrsv2_analysis()

cusparseStatus_t 
cusparseScsrsv2_analysis(cusparseHandle_t handle,
                         cusparseOperation_t transA,
                         int m,
                         int nnz,
                         const cusparseMatDescr_t descrA,
                         const float *csrValA,
                         const int *csrRowPtrA,
                         const int *csrColIndA,
                         csrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseDcsrsv2_analysis(cusparseHandle_t handle,
                         cusparseOperation_t transA,
                         int m,
                         int nnz,
                         const cusparseMatDescr_t descrA,
                         const double *csrValA,
                         const int *csrRowPtrA,
                         const int *csrColIndA,
                         csrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseCcsrsv2_analysis(cusparseHandle_t handle,
                         cusparseOperation_t transA,
                         int m,
                         int nnz,
                         const cusparseMatDescr_t descrA,
                         const cuComplex *csrValA,
                         const int *csrRowPtrA,
                         const int *csrColIndA,
                         csrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

cusparseStatus_t 
cusparseZcsrsv2_analysis(cusparseHandle_t handle,
                         cusparseOperation_t transA,
                         int m,
                         int nnz,
                         const cusparseMatDescr_t descrA,
                         const cuDoubleComplex *csrValA,
                         const int *csrRowPtrA,
                         const int *csrColIndA,
                         csrsv2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer);

This function performs the analysis phase of csrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

It is expected that this function will be executed only once for a given matrix and a particular operation type.

This function requires a buffer size returned by csrsv2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function csrsv2_analysis() reports a structural zero and computes level information that is stored in opaque structure info. The level information can extract more parallelism for a triangular solver. However csrsv2_solve() can be done without level information. To disable level information, the user needs to specify the policy of the triangular solver as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function csrsv2_analysis() always reports the first structural zero, even if the policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. No structural zero is reported if CUSPARSE_DIAG_TYPE_UNIT is specified, even if A(j,j) is missing for some j. The user needs to call cusparseXcsrsv2_zeroPivot() to know where the structural zero is.

It is the user's choice whether to call csrsv2_solve() if csrsv2_analysis() reports a structural zero. In this case, the user can still call csrsv2_solve() which will return a numerical zero in the same position as the structural zero. However the result x is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure initialized using `cusparseCreateCsrsv2Info()`.
`policy`	The supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is returned by `csrsv2_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.19. cusparse<t>csrsv2_solve()

cusparseStatus_t 
cusparseScsrsv2_solve(cusparseHandle_t handle,
                      cusparseOperation_t transA,
                      int m,
                      int nnz,
                      const float *alpha,
                      const cusparseMatDescr_t descra,
                      const float *csrValA,
                      const int *csrRowPtrA,
                      const int *csrColIndA,
                      csrsv2Info_t info,
                      const float *x,
                      float *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseDcsrsv2_solve(cusparseHandle_t handle,
                      cusparseOperation_t transA,
                      int m,
                      int nnz,
                      const double *alpha,
                      const cusparseMatDescr_t descra,
                      const double *csrValA,
                      const int *csrRowPtrA,
                      const int *csrColIndA,
                      csrsv2Info_t info,
                      const double *x,
                      double *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseCcsrsv2_solve(cusparseHandle_t handle,
                      cusparseOperation_t transA,
                      int m,
                      int nnz,
                      const cuComplex *alpha,
                      const cusparseMatDescr_t descra,
                      const cuComplex *csrValA,
                      const int *csrRowPtrA,
                      const int *csrColIndA,
                      csrsv2Info_t info,
                      const cuComplex *x,
                      cuComplex *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

cusparseStatus_t 
cusparseZcsrsv2_solve(cusparseHandle_t handle,
                      cusparseOperation_t transA,
                      int m,
                      int nnz,
                      const cuDoubleComplex *alpha,
                      const cusparseMatDescr_t descra,
                      const cuDoubleComplex *csrValA,
                      const int *csrRowPtrA,
                      const int *csrColIndA,
                      csrsv2Info_t info,
                      const cuDoubleComplex *x,
                      cuDoubleComplex *y,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer);

This function performs the solve phase of csrsv2, a new sparse triangular linear system op(A)*y = $α$ x.

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires the buffer size returned by csrsv2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although csrsv2_solve() can be done without level information, the user still needs to be aware of consistency. If csrsv2_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, csrsv2_solve() can be run with or without levels. On the contrary, if csrsv2_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, csrsv2_solve() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

The level information may not improve the performance but spend extra time doing analysis. For example, a tridiagonal matrix has no parallelism. In this case, CUSPARSE_SOLVE_POLICY_NO_LEVEL performs better than CUSPARSE_SOLVE_POLICY_USE_LEVEL. If the user has an iterative solver, the best approach is to do csrsv2_analysis() with CUSPARSE_SOLVE_POLICY_USE_LEVEL once. Then do csrsv2_solve() with CUSPARSE_SOLVE_POLICY_NO_LEVEL in the first run and with CUSPARSE_SOLVE_POLICY_USE_LEVEL in the second run, picking faster one to perform the remaining iterations.

Function csrsv2_solve() reports the first numerical zero, including a structural zero. If status is 0, no numerical zero was found. Furthermore, no numerical zero is reported if CUSPARSE_DIAG_TYPE_UNIT is specified, even if A(j,j) is zero for some j. The user needs to call cusparseXcsrsv2_zeroPivot() to know where the numerical zero is.

For example, suppose L is a lower triangular matrix with unit diagonal, the following code solves L*y=x by level information.

// Suppose that L is m x m sparse matrix represented by CSR format, 
// L is lower triangular with unit diagonal. 
// Assumption:
// - dimension of matrix L is m,
// - matrix L has nnz number zero elements,
// - handle is already created by cusparseCreate(),
// - (d_csrRowPtr, d_csrColInd, d_csrVal) is CSR of L on device memory,
// - d_x is right hand side vector on device memory,
// - d_y is solution vector on device memory.

cusparseMatDescr_t descr = 0;
csrsv2Info_t info = 0;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans = CUSPARSE_OPERATION_NON_TRANSPOSE;

// step 1: create a descriptor which contains
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has unit diagonal, specified by parameter CUSPARSE_DIAG_TYPE_UNIT
//   (L may not have all diagonal elements.) 
cusparseCreateMatDescr(&descr);
cusparseSetMatIndexBase(descr, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatFillMode(descr, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr, CUSPARSE_DIAG_TYPE_UNIT);

// step 2: create a empty info structure
cusparseCreateCsrsv2Info(&info);

// step 3: query how much memory used in csrsv2, and allocate the buffer
cusparseDcsrsv2_bufferSize(handle, trans, m, nnz, descr,
    d_csrVal, d_csrRowPtr, d_csrColInd, &pBufferSize);
// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis 
cusparseDcsrsv2_analysis(handle, trans, m, nnz, descr, 
    d_csrVal, d_csrRowPtr, d_csrColInd,
    info, policy, pBuffer);
// L has unit diagonal, so no structural zero is reported.
status = cusparseXcsrsv2_zeroPivot(handle, info, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is missing\n", structural_zero, structural_zero);
}

// step 5: solve L*y = x
cusparseDcsrsv2_solve(handle, trans, m, nnz, &alpha, descr,
   d_csrVal, d_csrRowPtr, d_csrColInd, info,
   d_x, d_y, policy, pBuffer);
// L has unit diagonal, so no numerical zero is reported.
status = cusparseXcsrsv2_zeroPivot(handle, info, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is zero\n", numerical_zero, numerical_zero);
}

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyCsrsv2Info(info);
cusparseDestroyMatDescr(descr);
cusparseDestroy(handle);

Remark: csrsv2_solve() needs more nonzeros per row to achieve good performance. It would perform better if more than 16 nonzeros per row in average.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ .
`m`	number of rows and columns of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`x`	<type> right-hand-side vector of size `m`.
`policy`	The supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is return by `csrsv2_bufferSize`.

Output

`y`	<type> solution vector of size `m`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXcsrsv2_zeroPivot()

cusparseStatus_t 
cusparseXcsrsv2_zeroPivot(cusparseHandle_t handle,
                          csrsv2Info_t info,
                          int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) has either a structural zero or a numerical zero. Otherwise position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXcsrsv2_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains structural zero or numerical zero if the user already called `csrsv2_analysis()` or `csrsv2_solve()`.

Output

position

if no structural or numerical zero, position is -1; otherwise, if A(j,j) is missing or U(j,j) is zero, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

7.21. cusparse<t>hybmv()

cusparseStatus_t
cusparseShybmv(cusparseHandle_t handle, cusparseOperation_t transA,
               const float           *alpha, 
               const cusparseMatDescr_t descrA,
               const cusparseHybMat_t hybA, const float           *x,
               const float           *beta, float           *y)
cusparseStatus_t
cusparseDhybmv(cusparseHandle_t handle, cusparseOperation_t transA,
               const double          *alpha, 
               const cusparseMatDescr_t descrA,
               const cusparseHybMat_t hybA, const double          *x,
               const double          *beta, double          *y)
cusparseStatus_t
cusparseChybmv(cusparseHandle_t handle, cusparseOperation_t transA,
               const cuComplex       *alpha, 
               const cusparseMatDescr_t descrA,
               const cusparseHybMat_t hybA, const cuComplex       *x,
               const cuComplex       *beta, cuComplex       *y)
cusparseStatus_t
cusparseZhybmv(cusparseHandle_t handle, cusparseOperation_t transA,
               const cuDoubleComplex *alpha, 
               const cusparseMatDescr_t descrA,
               const cusparseHybMat_t hybA, const cuDoubleComplex *x,
               const cuDoubleComplex *beta, cuDoubleComplex *y)

This function performs the matrix-vector operation

y = α * op (A) * x + β * y

A is an m×n sparse matrix that is defined in the HYB storage format by an opaque data structure hybA, x and y are vectors, $α and β$ are scalars, and

op (A) = \{\begin{cases} A & if transA == CUSPARSE_OPERATION_NON_TRANSPOSE \end{cases}

Notice that currently only $op (A) = A$ is supported.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ (currently only $op (A) = A$ is supported).
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`.
`hybA`	the matrix `A` in HYB storage format.
`x`	<type> vector of `n` elements.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`y`	<type> vector of `m` elements.

Output

`y`	<type> updated vector.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	the internally stored HYB format parameters are invalid.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.22. cusparse<t>hybsv_analysis()

cusparseStatus_t
cusparseShybsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA,
                        const cusparseMatDescr_t descrA, 
                        cusparseHybMat_t hybA,
                        cusparseSolveAnalysisInfo_t info)    
cusparseStatus_t
cusparseDhybsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA,
                        const cusparseMatDescr_t descrA, 
                        cusparseHybMat_t hybA,
                        cusparseSolveAnalysisInfo_t info)    
cusparseStatus_t
cusparseChybsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA,
                        const cusparseMatDescr_t descrA, 
                        cusparseHybMat_t hybA,
                        cusparseSolveAnalysisInfo_t info)    
cusparseStatus_t
cusparseZhybsv_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA,
                        const cusparseMatDescr_t descrA, 
                        cusparseHybMat_t hybA,
                        cusparseSolveAnalysisInfo_t info)

This function performs the analysis phase of the solution of a sparse triangular linear system

op (A) * y = α * x

A is an m×m sparse matrix that is defined in HYB storage format by an opaque data structure hybA, x and y are the right-hand-side and the solution vectors, $α$ is a scalar, and

op (A) = \{\begin{cases} A & if transA == CUSPARSE_OPERATION_NON_TRANSPOSE \end{cases}

Notice that currently only $op (A) = A$ is supported.

It is expected that this function will be executed only once for a given matrix and a particular operation type.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ (currently only $op (A) = A$ is supported).
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and diagonal type `USPARSE_DIAG_TYPE_NON_UNIT`.
`hybA`	the matrix `A` in HYB storage format.
`info`	structure initialized using `cusparseCreateSolveAnalysisInfo()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	the internally stored HYB format parameters are invalid.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

7.23. cusparse<t>hybsv_solve()

cusparseStatus_t 
cusparseShybsv_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA,
                     const float           *alpha, 
                     const cusparseMatDescr_t descrA,
                     cusparseHybMat_t hybA, 
                     cusparseSolveAnalysisInfo_t info,
                     const float           *x, float           *y)
cusparseStatus_t 
cusparseDhybsv_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA,
                     const double          *alpha, 
                     const cusparseMatDescr_t descrA,
                     cusparseHybMat_t hybA, 
                     cusparseSolveAnalysisInfo_t info,
                     const double          *x, double          *y)
cusparseStatus_t 
cusparseChybsv_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA,
                     const cuComplex       *alpha, 
                     const cusparseMatDescr_t descrA,
                     cusparseHybMat_t hybA, 
                     cusparseSolveAnalysisInfo_t info,
                     const cuComplex       *x, cuComplex       *y)
cusparseStatus_t 
cusparseZhybsv_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA,
                     const cuDoubleComplex *alpha, 
                     const cusparseMatDescr_t descrA,
                     cusparseHybMat_t hybA, 
                     cusparseSolveAnalysisInfo_t info,
                     const cuDoubleComplex *x, cuDoubleComplex *y)

This function performs the solve phase of the solution of a sparse triangular linear system:

op (A) * y = α * x

A is an m×m sparse matrix that is defined in HYB storage format by an opaque data structure hybA, x and y are the right-hand-side and the solution vectors, $α$ is a scalar, and

op (A) = \{\begin{cases} A & if transA == CUSPARSE_OPERATION_NON_TRANSPOSE \end{cases}

Notice that currently only $op (A) = A$ is supported.

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ (currently only $op (A) = A$ is supported).
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and the diagonal type is `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`hybA`	the matrix `A` in HYB storage format.
`info`	structure with information collected during the analysis phase (that should be passed to the solve phase unchanged).
`x`	<type> right-hand-side vector of size `m`.

Output

`y`	<type> solution vector of size `m`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the internally stored hyb format parameters are invalid.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8. cuSPARSE Level 3 Function Reference

This chapter describes sparse linear algebra functions that perform operations between sparse and (usually tall) dense matrices.

In particular, the solution of sparse triangular linear systems with multiple right-hand sides is implemented in two phases. First, during the analysis phase, the sparse triangular matrix is analyzed to determine the dependencies between its elements by calling the appropriate csrsm_analysis() function. The analysis is specific to the sparsity pattern of the given matrix and to the selected cusparseOperation_t type. The information from the analysis phase is stored in the parameter of type cusparseSolveAnalysisInfo_t that has been initialized previously with a call to cusparseCreateSolveAnalysisInfo().

Second, during the solve phase, the given sparse triangular linear system is solved using the information stored in the cusparseSolveAnalysisInfo_t parameter by calling the appropriate csrsm_solve() function. The solve phase may be performed multiple times with different multiple right-hand sides, while the analysis phase needs to be performed only once. This is especially useful when a sparse triangular linear system must be solved for different sets of multiple right-hand sides one at a time, while its coefficient matrix remains the same.

8.1. cusparse<t>csrmm()

cusparseStatus_t 
cusparseScsrmm(cusparseHandle_t handle, 
    cusparseOperation_t transA, 
    int m, 
    int n, 
    int k, 
    int nnz, 
    const float *alpha, 
    const cusparseMatDescr_t descrA, 
    const float *csrValA, 
    const int *csrRowPtrA, 
    const int *csrColIndA,
    const float *B, 
    int ldb,
    const float *beta, 
    float *C, 
    int ldc)
cusparseStatus_t 
cusparseDcsrmm(cusparseHandle_t handle, 
    cusparseOperation_t transA, 
    int m, 
    int n, 
    int k, 
    int nnz, 
    const double *alpha, 
    const cusparseMatDescr_t descrA, 
    const double *csrValA, 
    const int *csrRowPtrA, 
    const int *csrColIndA,
    const double *B, 
    int ldb,
    const double *beta,
    double *C, 
    int ldc)
cusparseStatus_t 
cusparseCcsrmm(cusparseHandle_t handle, 
    cusparseOperation_t transA, 
    int m, 
    int n, 
    int k, 
    int nnz, 
    const cuComplex *alpha, 
    const cusparseMatDescr_t descrA, 
    const cuComplex *csrValA, 
    const int *csrRowPtrA, 
    const int *csrColIndA,
    const cuComplex *B, 
    int ldb,
    const cuComplex *beta, 
    cuComplex *C, 
    int ldc)
cusparseStatus_t 
cusparseZcsrmm(cusparseHandle_t handle, 
    cusparseOperation_t transA, 
    int m, 
    int n, 
    int k, 
    int nnz, 
    const cuDoubleComplex *alpha, 
    const cusparseMatDescr_t descrA, 
    const cuDoubleComplex *csrValA, 
    const int *csrRowPtrA, 
    const int *csrColIndA,
    const cuDoubleComplex *B, 
    int ldb,
    const cuDoubleComplex *beta,
    cuDoubleComplex *C, 
    int ldc)

This function performs one of the following matrix-matrix operations:

C = α * op (A) * B + β * C

A is an m×k sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); B and C are dense matrices; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

When using the (conjugate) transpose of a general matrix or a Hermitian/symmetric matrix, this routine may produce slightly different results with the same input parameters during different runs of this function. For these matrix types it uses atomic operations to compute the final result; consequently, many threads may be adding floating point numbers to the same memory location without any specific ordering, which may produce slightly different results for each run.

If exactly the same output is required for any input when multiplying by the transpose of a general matrix, the following procedure can be used:

1. Convert the matrix from CSR to CSC format using one of the csr2csc() functions. Notice that by interchanging the rows and columns of the result you are implicitly transposing the matrix.

2. Call the csrmm() function with the cusparseOperation_t parameter set to CUSPARSE_OPERATION_NON_TRANSPOSE and with the interchanged rows and columns of the matrix stored in CSC format. This (implicitly) multiplies the vector by the transpose of the matrix in the original CSR format.

This function requires no extra storage for the general matrices when operation CUSPARSE_OPERATION_NON_TRANSPOSE is selected. It requires some extra storage for Hermitian/symmetric matrices and for the general matrices when an operation different from CUSPARSE_OPERATION_NON_TRANSPOSE is selected. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$
`m`	number of rows of sparse matrix `A`.
`n`	number of columns of dense matrices `B` and `C`.
`k`	number of columns of sparse matrix `A`.
`nnz`	number of nonzero elements of sparse matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix types are `CUSPARSE_MATRIX_TYPE_GENERAL`, `CUSPARSE_MATRIX_TYPE_SYMMETRIC`, and `CUSPARSE_MATRIX_TYPE_HERMITIAN`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`B`	array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B`. It must be at least $max (1, k)$ if $op (A) = A$ and at least $max (1, m)$ otherwise.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `C` does not have to be a valid input.
`C`	array of dimensions `(ldc, n)`.
`ldc`	leading dimension of `C`. It must be at least $max (1, m)$ if $op (A) = A$ and at least $max (1, k)$ otherwise.

Output

`C`	<type> updated array of dimensions `(ldc, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n, k, nnz<0` or `ldb` and `ldc` are incorrect).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8.2. cusparse<t>csrmm2()

cusparseStatus_t 
cusparseScsrmm2(cusparseHandle_t         handle, 
                cusparseOperation_t      transA,    
                cusparseOperation_t      transB,    
                int                      m,         
                int                      n,         
                int                      k,         
                int                      nnz,       
                const float              *alpha,    
                const cusparseMatDescr_t descrA, 
                const float              *csrValA, 
                const int                *csrRowPtrA, 
                const int                *csrColIndA,
                const float              *B,
                int                      ldb,
                const float              *beta,
                float                    *C,
                int                      ldc)                
cusparseStatus_t 
cusparseDcsrmm2(cusparseHandle_t         handle, 
                cusparseOperation_t      transA, 
                cusparseOperation_t      transB,
                int                      m,
                int                      n,
                int                      k,
                int                      nnz, 
                const double             *alpha, 
                const cusparseMatDescr_t descrA, 
                const double             *csrValA, 
                const int                *csrRowPtrA,
                const int                *csrColIndA,
                const double             *B,
                int                      ldb,
                const double             *beta,
                double                   *C,
                int                      ldc)
cusparseStatus_t 
cusparseCcsrmm2(cusparseHandle_t         handle, 
                cusparseOperation_t      transA, 
                cusparseOperation_t      transB,
                int                      m,
                int                      n,
                int                      k,
                int                      nnz, 
                const cuComplex          *alpha, 
                const cusparseMatDescr_t descrA, 
                const cuComplex          *csrValA, 
                const int                *csrRowPtrA,
                const int                *csrColIndA,
                const cuComplex          *B,
                int                      ldb,
                const cuComplex          *beta,
                cuComplex                *C,
                int                      ldc)
cusparseStatus_t 
cusparseZcsrmm2(cusparseHandle_t         handle, 
                cusparseOperation_t      transA, 
                cusparseOperation_t      transB,
                int                      m,
                int                      n,
                int                      k,
                int                      nnz, 
                const cuDoubleComplex    *alpha, 
                const cusparseMatDescr_t descrA, 
                const cuDoubleComplex    *csrValA, 
                const int                *csrRowPtrA,
                const int                *csrColIndA,
                const cuDoubleComplex    *B,
                int                      ldb,
                const cuDoubleComplex    *beta,
                cuDoubleComplex          *C,
                int                      ldc)

This function performs one of the following matrix-matrix operations:

C = α * op (A) * op (B) + β * C

A is an m×k sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); B and C are dense matrices; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if transA == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if transA == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if transA == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

and

op (B) = \{\begin{cases} B & if transB == CUSPARSE_OPERATION_NON_TRANSPOSE \\ B^{T} & if transB == CUSPARSE_OPERATION_TRANSPOSE \\ B^{H} & not supported \end{cases}

If op(B)=B, cusparse<t>csrmm2() is the same as cusparse<t>csrmm(); otherwise, only op(A)=A is supported and the matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL.

The motivation of transpose(B) is to improve the memory access of matrix B. The computational pattern of A*transpose(B) with matrix B in column-major order is equivalent to A*B with matrix B in row-major order.

In practice, no operation in iterative solver or eigenvalue solver uses A*transpose(B). However we can perform A*transpose(transpose(B)) which is the same as A*B. For example, suppose A is m*k, B is k*n and C is m*n, the following code shows usage of cusparseDcsrmm().

// A is m*k, B is k*n and C is m*n 
    const int ldb_B = k; // leading dimension of B
    const int ldc   = m; // leading dimension of C
// perform C:=alpha*A*B + beta*C
    cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL );
    cusparseDcsrmm(cusparse_handle, 
               CUSPARSE_OPERATION_NON_TRANSPOSE,
               m, n, k, nnz, alpha,
               descrA, csrValA, csrRowPtrA, csrColIndA,
               B, ldb_B,
               beta, C, ldc);

Instead of using A*B, our proposal is to transpose B to Bt first by calling cublas<t>geam(), then to perform A*transpose(Bt).

// step 1: Bt := transpose(B)
    double *Bt; 
    const int ldb_Bt = n; // leading dimension of Bt
    cudaMalloc((void**)&Bt, sizeof(double)*ldb_Bt*k);
    double one  = 1.0;
    double zero = 0.0;
    cublasSetPointerMode(cublas_handle, CUBLAS_POINTER_MODE_HOST);
    cublasDgeam(cublas_handle, CUBLAS_OP_T, CUBLAS_OP_T,
        n, k, &one, B, int ldb_B, &zero, B, int ldb_B, Bt, ldb_Bt);

// step 2: perform C:=alpha*A*transpose(Bt) + beta*C
    cusparseDcsrmm2(cusparse_handle, 
               CUSPARSE_OPERATION_NON_TRANSPOSE,
               CUSPARSE_OPERATION_TRANSPOSE
               m, n, k, nnz, alpha,
               descrA, csrValA, csrRowPtrA, csrColIndA,
               Bt, ldb_Bt,
               beta, C, ldc);

Remark 1: cublas<t>geam() and cusparse<t>csrmm2() are memory bound. The complexity of cublas<t>geam() is 2*n*k, and the minimum complexity of cusparse<t>csrmm2() is about (nnz + nnz*n + 2*m*n). If nnz per column (=nnz/k) is large, it is worth paying the extra cost on transposition because A*transpose(B) may be 2× faster than A*B if the sparsity pattern of A is not good.

Remark 2: A*transpose(B) is only supported on compute capability 2.0 and above.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$
`transB`	the operation $op (B)$
`m`	number of rows of sparse matrix `A`.
`n`	number of columns of dense matrix $op(B)$ and `C`.
`k`	number of columns of sparse matrix `A`.
`nnz`	number of nonzero elements of sparse matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix types is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`B`	array of dimensions `(ldb, n)` if `op(B)=B` and `(ldb, k)` otherwise.
`ldb`	leading dimension of `B`. If `op(B)=B`, it must be at least $max (1, k)$ if $op (A) = A$ and at least $max (1, m)$ otherwise. If `op(B)!=B`, it must be at least `max(1, n`).
`beta`	<type> scalar used for multiplication. If `beta` is zero, `C` does not have to be a valid input.
`C`	array of dimensions `(ldc, n)`.
`ldc`	leading dimension of `C`. It must be at least $max (1, m)$ if $op (A) = A$ and at least $max (1, k)$ otherwise.

Output

`C`	<type> updated array of dimensions `(ldc, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n, k, nnz<0` or `ldb` and `ldc` are incorrect).
`CUSPARSE_STATUS_ARCH_MISMATCH`	if `op(B)=B`, the device does not support double precision or if `op(B)=transpose(B)` the device is below compute capability 2.0.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	only `CUSPARSE_MATRIX_TYPE_GENERAL` is supported otherwise.

8.3. cusparse<t>csrsm_analysis()

cusparseStatus_t 
cusparseScsrsm_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, int nnz, 
                        const cusparseMatDescr_t descrA, 
                        const float           *csrValA, 
                        const int *csrRowPtrA, const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseDcsrsm_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, int nnz, 
                        const cusparseMatDescr_t descrA, 
                        const double          *csrValA, 
                        const int *csrRowPtrA, const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseCcsrsm_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, int nnz, 
                        const cusparseMatDescr_t descrA, 
                        const cuComplex       *csrValA, 
                        const int *csrRowPtrA, const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseZcsrsm_analysis(cusparseHandle_t handle, 
                        cusparseOperation_t transA, 
                        int m, int nnz, 
                        const cusparseMatDescr_t descrA, 
                        const cuDoubleComplex *csrValA, 
                        const int *csrRowPtrA, const int *csrColIndA, 
                        cusparseSolveAnalysisInfo_t info)

This function performs the analysis phase of the solution of a sparse triangular linear system

op (A) * Y = α * X

with multiple right-hand sides, where A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA; X and Y are the right-hand-side and the solution dense matrices; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

It is expected that this function will be executed only once for a given matrix and a particular operation type.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$ .
`m`	number of rows of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix types are `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure initialized using `cusparseCreateSolveAnalysisInfo()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8.4. cusparse<t>csrsm_solve()

cusparseStatus_t 
cusparseScsrsm_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA, 
                     int m, int n, const float *alpha, 
                     const cusparseMatDescr_t descrA, 
                     const float           *csrValA, 
                     const int *csrRowPtrA, const int *csrColIndA, 
                     cusparseSolveAnalysisInfo_t info, 
                     const float           *X, int ldx,
                     float           *Y, int ldy)
cusparseStatus_t 
cusparseDcsrsm_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA, 
                     int m, int n, const double *alpha, 
                     const cusparseMatDescr_t descrA, 
                     const double          *csrValA, 
                     const int *csrRowPtrA, const int *csrColIndA, 
                     cusparseSolveAnalysisInfo_t info, 
                     const double          *X, int ldx,
                     double          *Y, int ldy)
cusparseStatus_t 
cusparseCcsrsm_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA, 
                     int m, int n, const cuComplex *alpha, 
                     const cusparseMatDescr_t descrA, 
                     const cuComplex       *csrValA, 
                     const int *csrRowPtrA, const int *csrColIndA, 
                     cusparseSolveAnalysisInfo_t info, 
                     const cuComplex       *X, int ldx,
                     cuComplex       *Y, int ldy)
cusparseStatus_t 
cusparseZcsrsm_solve(cusparseHandle_t handle, 
                     cusparseOperation_t transA, 
                     int m, int n, const cuDoubleComplex *alpha, 
                     const cusparseMatDescr_t descrA, 
                     const cuDoubleComplex *csrValA, 
                     const int *csrRowPtrA, const int *csrColIndA, 
                     cusparseSolveAnalysisInfo_t info, 
                     const cuDoubleComplex *X, int ldx,
                     cuDoubleComplex *Y, int ldy)

This function performs the solve phase of the solution of a sparse triangular linear system

op (A) * Y = α * X

with multiple right-hand sides, where A is an m×n sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA); X and Y are the right-hand-side and the solution dense matrices; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation `op(A)`.
`m`	number of rows and columns of matrix `A`.
`n`	number of columns of matrix `X` and `Y`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix types are `CUSPARSE_MATRIX_TYPE_TRIANGULAR` and `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should be passed to the solve phase unchanged).
`X`	<type> right-hand-side array of dimensions `(ldx, n)`.
`ldx`	leading dimension of `X` (that is ≥ $max (1, m)$ ).

Output

`Y`	<type> solution array of dimensions `(ldy, n)`.
`ldy`	leading dimension of `Y` (that is ≥ $max (1, m)$ ).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8.5. cusparse<t>bsrmm()

cusparseStatus_t 
cusparseSbsrmm(cusparseHandle_t handle,
               cusparseDirection_t dirA,
               cusparseOperation_t transA,
               cusparseOperation_t transB,
               int mb,
               int n,
               int kb,
               int nnzb,
               const float *alpha,
               const cusparseMatDescr_t descrA,
               const float *bsrValA,
               const int *bsrRowPtrA,
               const int *bsrColIndA,
               const int  blockDim,
               const float *B,
               const int ldb,
               const float *beta,
               float *C,
               int ldc)

cusparseStatus_t 
cusparseDbsrmm(cusparseHandle_t handle,
               cusparseDirection_t dirA,
               cusparseOperation_t transA,
               cusparseOperation_t transB,
               int mb,
               int n,
               int kb,
               int nnzb,
               const double *alpha,
               const cusparseMatDescr_t descrA,
               const double *bsrValA,
               const int *bsrRowPtrA,
               const int *bsrColIndA,
               const int  blockDim,
               const double *B,
               const int ldb,
               const double *beta,
               double *C,
               int ldc)

cusparseStatus_t 
cusparseCbsrmm(cusparseHandle_t handle,
               cusparseDirection_t dirA,
               cusparseOperation_t transA,
               cusparseOperation_t transB,
               int mb,
               int n,
               int kb,
               int nnzb,
               const cuComplex *alpha,
               const cusparseMatDescr_t descrA,
               const cuComplex *bsrValA,
               const int *bsrRowPtrA,
               const int *bsrColIndA,
               const int  blockDim,
               const cuComplex *B,
               const int ldb,
               const cuComplex *beta,
               cuComplex *C,
               int ldc)

cusparseStatus_t 
cusparseZbsrmm(cusparseHandle_t handle,
               cusparseDirection_t dirA,
               cusparseOperation_t transA,
               cusparseOperation_t transB,
               int mb,
               int n,
               int kb,
               int nnzb,
               const cuDoubleComplex *alpha,
               const cusparseMatDescr_t descrA,
               const cuDoubleComplex *bsrValA,
               const int *bsrRowPtrA,
               const int *bsrColIndA,
               const int  blockDim,
               const cuDoubleComplex *B,
               const int ldb,
               const cuDoubleComplex *beta,
               cuDoubleComplex *C,
               int ldc)

This function performs one of the following matrix-matrix operations:

C = α * op (A) * op (B) + β * C

A is an mb×kb sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA; B and C are dense matrices; $α and β$ are scalars; and

op (A) = \{\begin{cases} A & if transA == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if transA == CUSPARSE_OPERATION_TRANSPOSE (not supported) \\ A^{H} & if transA == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE (not supported) \end{cases}

and

op (B) = \{\begin{cases} B & if transB == CUSPARSE_OPERATION_NON_TRANSPOSE \\ B^{T} & if transB == CUSPARSE_OPERATION_TRANSPOSE \\ B^{H} & if transB == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE (not supported) \end{cases}

The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL.

The motivation of transpose(B) is to improve memory access of matrix B. The computational pattern of A*transpose(B) with matrix B in column-major order is equivalent to A*B with matrix B in row-major order.

In practice, no operation in an iterative solver or eigenvalue solver uses A*transpose(B). However, we can perform A*transpose(transpose(B)) which is the same as A*B. For example, suppose A is mb*kb, B is k*n and C is m*n, the following code shows usage of cusparseDbsrmm().

// A is mb*kb, B is k*n and C is m*n 
    const int m = mb*blockSize; 
    const int k = kb*blockSize;
    const int ldb_B = k; // leading dimension of B
    const int ldc   = m; // leading dimension of C
// perform C:=alpha*A*B + beta*C
    cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL );
    cusparseDbsrmm(cusparse_handle, 
               CUSPARSE_DIRECTION_COLUMN,
               CUSPARSE_OPERATION_NON_TRANSPOSE,
               CUSPARSE_OPERATION_NON_TRANSPOSE,
               mb, n, kb, nnzb, alpha,
               descrA, bsrValA, bsrRowPtrA, bsrColIndA, blockSize,
               B, ldb_B,
               beta, C, ldc);

Instead of using A*B, our proposal is to transpose B to Bt by first calling cublas<t>geam(), and then to perform A*transpose(Bt).

// step 1: Bt := transpose(B)
    const int m = mb*blockSize; 
    const int k = kb*blockSize;
    double *Bt; 
    const int ldb_Bt = n; // leading dimension of Bt
    cudaMalloc((void**)&Bt, sizeof(double)*ldb_Bt*k);
    double one  = 1.0;
    double zero = 0.0;
    cublasSetPointerMode(cublas_handle, CUBLAS_POINTER_MODE_HOST);
    cublasDgeam(cublas_handle, CUBLAS_OP_T, CUBLAS_OP_T,
        n, k, &one, B, int ldb_B, &zero, B, int ldb_B, Bt, ldb_Bt);

// step 2: perform C:=alpha*A*transpose(Bt) + beta*C
    cusparseDbsrmm(cusparse_handle, 
               CUSPARSE_DIRECTION_COLUMN,
               CUSPARSE_OPERATION_NON_TRANSPOSE,
               CUSPARSE_OPERATION_TRANSPOSE,
               mb, n, kb, nnzb, alpha,
               descrA, bsrValA, bsrRowPtrA, bsrColIndA, blockSize,
               Bt, ldb_Bt,
               beta, C, ldc);

Function bsrmm() is only supported on compute capability 2.0 and above.

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation `op(A)`.
`transB`	the operation `op(B)`.
`mb`	number of block rows of sparse matrix `A`.
`n`	number of columns of dense matrix `op(B)` and `A`.
`kb`	number of block columns of sparse matrix `A`.
`nnzb`	number of non-zero blocks of sparse matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`, larger than zero.
`B`	array of dimensions `(ldb, n)` if `op(B)=B` and `(ldb, k)` otherwise.
`ldb`	leading dimension of `B`. If `op(B)=B`, it must be at least $max (1, k)$ If `op(B) != B`, it must be at least `max(1, n)`.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `C` does not have to be a valid input.
`C`	array of dimensions `(ldc, n)`.
`ldc`	leading dimension of `C`. It must be at least $max (1, m)$ if `op(A)=A` and at least $max (1, k)$ otherwise.

Output

`C`	<type> updated array of dimensions `(ldc, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	Either invalid parameters were passed (`mb, n, kb, nnzb<0`; or `ldb` and `ldc` are incorrect). Either invalid or unsupported operations were passed (`op(A)` is different from CUSPARSE_OPERATION_NON_TRANSPOSE, or `op(B)` is different from CUSPARSE_OPERATION_NON_TRANSPOSE or CUSPARSE_OPERATION_TRANSPOSE).
`CUSPARSE_STATUS_ARCH_MISMATCH`	if device is below compute capability 2.0.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	only `CUSPARSE_MATRIX_TYPE_GENERAL` is supported otherwise.

8.6. cusparse<t>bsrsm2_bufferSize()

cusparseStatus_t 
cusparseSbsrsm2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           cusparseOperation_t transX,
                           int mb,
                           int n,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           float *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsm2Info_t info,
                           int *pBufferSizeInBytes)

cusparseStatus_t 
cusparseDbsrsm2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           cusparseOperation_t transX,
                           int mb,
                           int n,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           double *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsm2Info_t info,
                           int *pBufferSizeInBytes)

cusparseStatus_t 
cusparseCbsrsm2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           cusparseOperation_t transX,
                           int mb,
                           int n,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsm2Info_t info,
                           int *pBufferSizeInBytes)

cusparseStatus_t 
cusparseZbsrsm2_bufferSize(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           cusparseOperation_t transA,
                           cusparseOperation_t transX,
                           int mb,
                           int n,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuDoubleComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrsm2Info_t info,
                           int *pBufferSizeInBytes)

This function returns size of buffer used in bsrsm2(), a new sparse triangular linear system op(A)*Y = $α$ op(X).

A is an (mb*blockDim)x(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA); X and Y are the right-hand-side and the solution matrices; $α$ is a scalar; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Although there are six combinations in terms of parameter trans and the upper (and lower) triangular part of A, bsrsm2_bufferSize() returns the maximum size of the buffer among these combinations. The buffer size depends on dimension mb,blockDim and the number of nonzeros of the matrix, nnzb. If the user changes the matrix, it is necessary to call bsrsm2_bufferSize() again to get the correct buffer size, otherwise a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation `op(A)`.
`transX`	the operation `op(X)`.
`mb`	number of block rows of matrix `A`.
`n`	number of columns of matrix `Y` and `op(X)`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`; larger than zero.

Output

`info`	record internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in `bsrsm2_analysis()` and `bsrsm2_solve()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb, n, nnzb<=0`); base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8.7. cusparse<t>bsrsm2_analysis()

cusparseStatus_t 
cusparseSbsrsm2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         cusparseOperation_t transXY,
                         int mb,
                         int n,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const float *bsrVal,
                         const int *bsrRowPtr,
                         const int *bsrColInd,
                         int blockDim,
                         bsrsm2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer)

cusparseStatus_t 
cusparseDbsrsm2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         cusparseOperation_t transXY,
                         int mb,
                         int n,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const double *bsrVal,
                         const int *bsrRowPtr,
                         const int *bsrColInd,
                         int blockDim,
                         bsrsm2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer)

cusparseStatus_t 
cusparseCbsrsm2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         cusparseOperation_t transXY,
                         int mb,
                         int n,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const cuComplex *bsrVal,
                         const int *bsrRowPtr,
                         const int *bsrColInd,
                         int blockDim,
                         bsrsm2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer)

cusparseStatus_t 
cusparseZbsrsm2_analysis(cusparseHandle_t handle,
                         cusparseDirection_t dirA,
                         cusparseOperation_t transA,
                         cusparseOperation_t transXY,
                         int mb,
                         int n,
                         int nnzb,
                         const cusparseMatDescr_t descrA,
                         const cuDoubleComplex *bsrVal,
                         const int *bsrRowPtr,
                         const int *bsrColInd,
                         int blockDim,
                         bsrsm2Info_t info,
                         cusparseSolvePolicy_t policy,
                         void *pBuffer)

This function performs the analysis phase of bsrsm2(), a new sparse triangular linear system op(A)*op(Y) = $α$ op(X).

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

and

op (X) = \{\begin{cases} X & if transXY == CUSPARSE_OPERATION_NON_TRANSPOSE \\ X^{T} & if transX == CUSPARSE_OPERATION_TRANSPOSE \\ X^{H} & if transX == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE (not supported) \end{cases}

and op(X) and op(Y) are equal.

The block of BSR format is of size blockDim*blockDim, stored in column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_ROW or CUSPARSE_DIRECTION_COLUMN. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored.

It is expected that this function will be executed only once for a given matrix and a particular operation type.

This function requires the buffer size returned by bsrsm2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsrsm2_analysis() reports a structural zero and computes the level information stored in opaque structure info. The level information can extract more parallelism during a triangular solver. However bsrsm2_solve() can be done without level information. To disable level information, the user needs to specify the policy of the triangular solver as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function bsrsm2_analysis() always reports the first structural zero, even if the parameter policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. Besides, no structural zero is reported if CUSPARSE_DIAG_TYPE_UNIT is specified, even if block A(j,j) is missing for some j. The user must call cusparseXbsrsm2_query_zero_pivot() to know where the structural zero is.

Even when bsrsm2_analysis() reports a structural zero, the user can still call asynchronously bsrsm2_solve(). In this case, the solve will return a numerical zero in the same position as the structural zero but this result X is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation `op(A)`.
`transXY`	the operation `op(X)` and `op(Y)`.
`mb`	number of block rows of matrix `A`.
`n`	number of columns of matrix `Y` and `op(X)`.
`nnzb`	number of non-zero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`; larger than zero.
`info`	structure initialized using `cusparseCreateBsrsm2Info`.
`policy`	The supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is return by `bsrsm2_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	Either invalid parameters were passed (`mb, n, nnzb<=0`). Either invalid or unsupported operations were passed (`op(X) and op(Y)` are different from CUSPARSE_OPERATION_NON_TRANSPOSE or CUSPARSE_OPERATION_TRANSPOSE).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

8.8. cusparse<t>bsrsm2_solve()

cusparseStatus_t 
cusparseSbsrsm2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      cusparseOperation_t transXY,
                      int mb,
                      int n,
                      int nnzb,
                      const float *alpha,
                      const cusparseMatDescr_t descrA,
                      const float *bsrVal,
                      const int *bsrRowPtr,
                      const int *bsrColInd,
                      int blockDim,
                      bsrsm2Info_t info,
                      const float *X,
                      int ldx,
                      float *Y,
                      int ldy,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer)

cusparseStatus_t 
cusparseDbsrsm2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      cusparseOperation_t transXY,
                      int mb,
                      int n,
                      int nnzb,
                      const double *alpha,
                      const cusparseMatDescr_t descrA,
                      const double *bsrVal,
                      const int *bsrRowPtr,
                      const int *bsrColInd,
                      int blockDim,
                      bsrsm2Info_t info,
                      const double *X,
                      int ldx,
                      double *Y,
                      int ldy,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer)

cusparseStatus_t 
cusparseCbsrsm2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      cusparseOperation_t transXY,
                      int mb,
                      int n,
                      int nnzb,
                      const cuComplex *alpha,
                      const cusparseMatDescr_t descrA,
                      const cuComplex *bsrVal,
                      const int *bsrRowPtr,
                      const int *bsrColInd,
                      int blockDim,
                      bsrsm2Info_t info,
                      const cuComplex *X,
                      int ldx,
                      cuComplex *Y,
                      int ldy,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer)

cusparseStatus_t 
cusparseZbsrsm2_solve(cusparseHandle_t handle,
                      cusparseDirection_t dirA,
                      cusparseOperation_t transA,
                      cusparseOperation_t transXY,
                      int mb,
                      int n,
                      int nnzb,
                      const cuDoubleComplex *alpha,
                      const cusparseMatDescr_t descrA,
                      const cuDoubleComplex *bsrVal,
                      const int *bsrRowPtr,
                      const int *bsrColInd,
                      int blockDim,
                      bsrsm2Info_t info,
                      const cuDoubleComplex *X,
                      int ldx,
                      cuDoubleComplex *Y,
                      int ldy,
                      cusparseSolvePolicy_t policy,
                      void *pBuffer)

This function performs the solve phase of the solution of a sparse triangular linear system:

op (A) * op(Y) = α * op(X)

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

and

op (X) = \{\begin{cases} X & if transX == CUSPARSE_OPERATION_NON_TRANSPOSE \\ X^{T} & if transX == CUSPARSE_OPERATION_TRANSPOSE \\ X^{H} & not supported \end{cases}

Only op(A)=A is supported.

op(X) and op(Y) must be performed in the same way. In other words, if op(X)=X, op(Y)=Y.

The block of BSR format is of size blockDim*blockDim, stored as column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_ROW or CUSPARSE_DIRECTION_COLUMN. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored. Function bsrsm02_solve() can support an arbitrary blockDim.

This function may be executed multiple times for a given matrix and a particular operation type.

This function requires the buffer size returned by bsrsm2_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although bsrsm2_solve() can be done without level information, the user still needs to be aware of consistency. If bsrsm2_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, bsrsm2_solve() can be run with or without levels. On the other hand, if bsrsm2_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, bsrsm2_solve() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsrsm02_solve() has the same behavior as bsrsv02_solve(), reporting the first numerical zero, including a structural zero. The user must call cusparseXbsrsm2_query_zero_pivot() to know where the numerical zero is.

The motivation of transpose(X) is to improve the memory access of matrix X. The computational pattern of transpose(X) with matrix X in column-major order is equivalent to X with matrix X in row-major order.

In-place is supported and requires that X and Y point to the same memory block, and ldx=ldy.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`transA`	the operation `op(A)`.
`transXY`	the operation `op(X)` and `op(Y)`.
`mb`	number of block rows of matrix `A`.
`n`	number of columns of matrix `Y` and `op(X)`.
`nnzb`	number of non-zero blocks of matrix `A`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, while the supported diagonal types are `CUSPARSE_DIAG_TYPE_UNIT` and `CUSPARSE_DIAG_TYPE_NON_UNIT`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ non-zero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`; larger than zero.
`info`	structure initialized using `cusparseCreateBsrsm2Info()`.
`X`	<type> right-hand-side array.
`ldx`	leading dimension of `X`. If `op(X)=X`, `ldx>=k`; otherwise, `ldx>=n`.
`ldy`	leading dimension of `Y`. If `op(A)=A`, then `ldc>=m`. If `op(A)!=A`, then `ldx>=k`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `bsrsm2_bufferSize()`.

Output

`Y`	<type> solution array of dimensions `(ldy, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_MAPPING_ERROR`	the texture binding failed.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXbsrsm2_zeroPivot()

cusparseStatus_t 
cusparseXbsrsm2_zeroPivot(cusparseHandle_t handle,
                          bsrsm2Info_t info,
                          int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) is either a structural zero or a numerical zero (singular block). Otherwise position=-1.

The position can be 0-base or 1-base, the same as the matrix.

Function cusparseXbsrsm2_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains a structural zero or a numerical zero if the user already called `bsrsm2_analysis()` or `bsrsm2_solve()`.

Output

position

if no structural or numerical zero, position is -1; otherwise, if A(j,j) is missing or U(j,j) is zero, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

9. cuSPARSE Extra Function Reference

This chapter describes the extra routines used to manipulate sparse matrices.

9.1. cusparse<t>csrgeam()

cusparseStatus_t
cusparseXcsrgeamNnz(cusparseHandle_t handle, 
                    int m, 
                    int n,
                    const cusparseMatDescr_t descrA, 
                    int nnzA,
                    const int *csrRowPtrA, 
                    const int *csrColIndA,
                    const cusparseMatDescr_t descrB, 
                    int nnzB,
                    const int *csrRowPtrB, 
                    const int *csrColIndB,
                    const cusparseMatDescr_t descrC, 
                    int *csrRowPtrC,
                    int *nnzTotalDevHostPtr)
cusparseStatus_t
cusparseScsrgeam(cusparseHandle_t handle, 
                 int m, 
                 int n,
                 const float *alpha,
                 const cusparseMatDescr_t descrA, 
                 int nnzA,
                 const float *csrValA, 
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const float *beta,
                 const cusparseMatDescr_t descrB, 
                 int nnzB,
                 const float *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 float *csrValC, 
                 int *csrRowPtrC, 
                 int *csrColIndC)
cusparseStatus_t
cusparseDcsrgeam(cusparseHandle_t handle, 
                 int m, 
                 int n,
                 const double *alpha,
                 const cusparseMatDescr_t descrA, 
                 int nnzA,
                 const double *csrValA, 
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const double *beta,
                 const cusparseMatDescr_t descrB, 
                 int nnzB,
                 const double *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 double *csrValC, 
                 int *csrRowPtrC, 
                 int *csrColIndC)
cusparseStatus_t
cusparseCcsrgeam(cusparseHandle_t handle, 
                 int m, 
                 int n,
                 const cuComplex *alpha,
                 const cusparseMatDescr_t descrA, 
                 int nnzA,
                 const cuComplex *csrValA, 
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cuComplex *beta,
                 const cusparseMatDescr_t descrB, 
                 int nnzB,
                 const cuComplex *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 cuComplex *csrValC, 
                 int *csrRowPtrC, 
                 int *csrColIndC)
cusparseStatus_t
cusparseZcsrgeam(cusparseHandle_t handle, 
                 int m, 
                 int n,
                 const cuDoubleComplex *alpha,
                 const cusparseMatDescr_t descrA, 
                 int nnzA,
                 const cuDoubleComplex *csrValA, 
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cuDoubleComplex *beta,
                 const cusparseMatDescr_t descrB, 
                 int nnzB,
                 const cuDoubleComplex *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 cuDoubleComplex *csrValC, 
                 int *csrRowPtrC, 
                 int *csrColIndC)

This function performs following matrix-matrix operation

C = α * A + β * B

where A, B, and C are m×n sparse matrices (defined in CSR storage format by the three arrays csrValA|csrValB|csrValC, csrRowPtrA|csrRowPtrB|csrRowPtrC, and csrColIndA|csrColIndB|csrcolIndC respectively), and $α and β$ are scalars. Since A and B have different sparsity patterns, cuSPARSE adopts a two-step approach to complete sparse matrix C. In the first step, the user allocates csrRowPtrC of m+1elements and uses function cusparseXcsrgeamNnz() to determine csrRowPtrC and the total number of nonzero elements. In the second step, the user gathers nnzC (number of nonzero elements of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC(m)-csrRowPtrC(0)) and allocates csrValC, csrColIndC of nnzC elements respectively, then finally calls function cusparse[S|D|C|Z]csrgeam() to complete matrix C.

The general procedure is as follows:

int baseC, nnzC;
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzC;
cusparseSetPointerMode(handle, CUSPARSE_POINTER_MODE_HOST);
cudaMalloc((void**)&csrRowPtrC, sizeof(int)*(m+1));
cusparseXcsrgeamNnz(handle, m, n,
        descrA, nnzA, csrRowPtrA, csrColIndA,
        descrB, nnzB, csrRowPtrB, csrColIndB,
        descrC, csrRowPtrC, nnzTotalDevHostPtr);
if (NULL != nnzTotalDevHostPtr){
    nnzC = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzC, csrRowPtrC+m, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&baseC, csrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzC -= baseC;
}
cudaMalloc((void**)&csrColIndC, sizeof(int)*nnzC);
cudaMalloc((void**)&csrValC, sizeof(float)*nnzC);
cusparseScsrgeam(handle, m, n,
        alpha,
        descrA, nnzA,
        csrValA, csrRowPtrA, csrColIndA,
        beta,
        descrB, nnzB,
        csrValB, csrRowPtrB, csrColIndB,
        descrC,
        csrValC, csrRowPtrC, csrColIndC);

Several comments on csrgeam():

The other three combinations, NT, TN, and TT, are not supported by cuSPARSE. In order to do any one of the three, the user should use the routine csr2csc() to convert $A$ | $B$ to $A^{T}$ | $B^{T}$ .
Only CUSPARSE_MATRIX_TYPE_GENERAL is supported. If either A or B is symmetric or Hermitian, then the user must extend the matrix to a full one and reconfigure the MatrixType field of the descriptor to CUSPARSE_MATRIX_TYPE_GENERAL.
If the sparsity pattern of matrix C is known, the user can skip the call to function cusparseXcsrgeamNnz(). For example, suppose that the user has an iterative algorithm which would update A and B iteratively but keep the sparsity patterns. The user can call function cusparseXcsrgeamNnz() once to set up the sparsity pattern of C, then call function cusparse[S|D|C|Z]geam() only for each iteration.
The pointers alpha and beta must be valid.
When alpha or beta is zero, it is not considered a special case by cuSPARSE. The sparsity pattern of C is independent of the value of alpha and beta. If the user wants $C = 0 \times A + 1 \times B^{T}$ , then csr2csc() is better than csrgeam().

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of sparse matrix `A,B,C`.
`n`	number of columns of sparse matrix `A,B,C`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzA`	number of nonzero elements of sparse matrix `A`.
`csrValA`	<type> array of `nnzA` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnzA` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`beta`	<type> scalar used for multiplication. If `beta` is zero, `y` does not have to be a valid input.
`descrB`	the descriptor of matrix `B`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzB`	number of nonzero elements of sparse matrix `B`.
`csrValB`	<type> array of `nnzB` $(=$ `csrRowPtrB(m)` $-$ `csrRowPtrB(0)` $)$ nonzero elements of matrix `B`.
`csrRowPtrB`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndB`	integer array of `nnzB` $(=$ `csrRowPtrB(m)` $-$ `csrRowPtrB(0)` $)$ column indices of the nonzero elements of matrix `B`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.

Output

`csrValC`	<type> array of `nnzC` $(=$ `csrRowPtrC(m)` $-$ `csrRowPtrC(0)` $)$ nonzero elements of matrix `C`.
`csrRowPtrC`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	integer array of `nnzC` $(=$ `csrRowPtrC(m)` $-$ `csrRowPtrC(0)` $)$ column indices of the nonzero elements of matrix`C`.
`nnzTotalDevHostPtr`	total number of nonzero elements in device or host memory. It is equal to `(csrRowPtrC(m)-csrRowPtrC(0))`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`, `IndexBase` of `descrA,descrB,descrC` is not base-0 or base-1, or `alpha` or `beta` is nil )).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

9.2. cusparse<t>csrgemm()

cusparseStatus_t 
cusparseXcsrgemmNnz(cusparseHandle_t handle,
                    cusparseOperation_t transA, 
                    cusparseOperation_t transB,
                    int m, 
                    int n, 
                    int k,
                    const cusparseMatDescr_t descrA, 
                    const int nnzA,                                     
                    const int *csrRowPtrA, 
                    const int *csrColIndA,
                    const cusparseMatDescr_t descrB, 
                    const int nnzB,                                     
                    const int *csrRowPtrB, 
                    const int *csrColIndB,
                    const cusparseMatDescr_t descrC, 
                    int *csrRowPtrC,
                    int *nnzTotalDevHostPtr ) 
cusparseStatus_t
cusparseScsrgemm(cusparseHandle_t handle,
                 cusparseOperation_t transA, 
                 cusparseOperation_t transB,
                 int m, 
                 int n, 
                 int k,
                 const cusparseMatDescr_t descrA, 
                 const int nnzA,
                 const float *csrValA,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cusparseMatDescr_t descrB, 
                 const int nnzB,                                     
                 const float *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 float *csrValC,
                 const int *csrRowPtrC, 
                 int *csrColIndC )
cusparseStatus_t
cusparseDcsrgemm(cusparseHandle_t handle,
                 cusparseOperation_t transA, 
                 cusparseOperation_t transB,
                 int m, 
                 int n, 
                 int k,
                 const cusparseMatDescr_t descrA, 
                 const int nnzA,
                 const double *csrValA,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cusparseMatDescr_t descrB, 
                 const int nnzB,                            
                 const double *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 double *csrValC,
                 const int *csrRowPtrC, 
                 int *csrColIndC )
cusparseStatus_t
cusparseCcsrgemm(cusparseHandle_t handle,
                 cusparseOperation_t transA, 
                 cusparseOperation_t transB,
                 int m, 
                 int n, 
                 int k,
                 const cusparseMatDescr_t descrA, 
                 const int nnzA,
                 const cuComplex *csrValA,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cusparseMatDescr_t descrB, 
                 const int nnzB,                            
                 const cuComplex *csrValB, 
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 cuComplex *csrValC,
                 const int *csrRowPtrC, 
                 int *csrColIndC )
cusparseStatus_t
cusparseZcsrgemm(cusparseHandle_t handle,
                 cusparseOperation_t transA, 
                 cusparseOperation_t transB,
                 int m, 
                 int n, 
                 int k,
                 const cusparseMatDescr_t descrA, 
                 const int nnzA,
                 const cuDoubleComplex *csrValA,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,
                 const cusparseMatDescr_t descrB, 
                 const int nnzB,     
                 const cuDoubleComplex *csrValB,
                 const int *csrRowPtrB, 
                 const int *csrColIndB,
                 const cusparseMatDescr_t descrC,
                 cuDoubleComplex *csrValC,
                 const int *csrRowPtrC, int *csrColIndC )

This function performs following matrix-matrix operation:

C = op (A) * op (B)

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans != CUSPARSE_OPERATION_NON_TRANSPOSE \end{cases}

There are four versions, NN, NT, TN, and TT. NN stands for $C = A * B$ , NT stands for $C = A * B^{T}$ , TN stands for $C = A^{T} * B$ and TT stands for $C = A^{T} * B^{T}$ .

The cuSPARSE library adopts a two-step approach to complete sparse matrix. In the first step, the user allocates csrRowPtrC of m+1 elements and uses the function cusparseXcsrgemmNnz() to determine csrRowPtrC and the total number of nonzero elements. In the second step, the user gathers nnzC (the number of nonzero elements of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC(m)-csrRowPtrC(0)) and allocates csrValC and csrColIndC of nnzC elements respectively, then finally calls function cusparse[S|D|C|Z]csrgemm() to complete matrix C.

The general procedure is as follows:

int baseC, nnzC;
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzC;
cusparseSetPointerMode(handle, CUSPARSE_POINTER_MODE_HOST);
cudaMalloc((void**)&csrRowPtrC, sizeof(int)*(m+1));
cusparseXcsrgemmNnz(handle, transA, transB, m, n, k, 
        descrA, nnzA, csrRowPtrA, csrColIndA,
        descrB, nnzB, csrRowPtrB, csrColIndB,
        descrC, csrRowPtrC, nnzTotalDevHostPtr );
if (NULL != nnzTotalDevHostPtr){
    nnzC = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzC, csrRowPtrC+m, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&baseC, csrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzC -= baseC;
}
cudaMalloc((void**)&csrColIndC, sizeof(int)*nnzC);
cudaMalloc((void**)&csrValC, sizeof(float)*nnzC);
cusparseScsrgemm(handle, transA, transB, m, n, k,
        descrA, nnzA,
        csrValA, csrRowPtrA, csrColIndA,
        descrB, nnzB,
        csrValB, csrRowPtrB, csrColIndB,
        descrC,
        csrValC, csrRowPtrC, csrColIndC);

Several comments on csrgemm():

Although NN, NT, TN and TT are supported, only the NN version is implemented. For the NT, TN and TT versions, csr2csc() is used to transpose the relevant matrices, followed by a call to the NN version of csrgemm().
The NN version needs working space of size nnzA integers at least.
Only CUSPARSE_MATRIX_TYPE_GENERAL is supported. If either A or B is symmetric or Hermitian, the user must extend the matrix to a full one and reconfigure the MatrixType field descriptor to CUSPARSE_MATRIX_TYPE_GENERAL.
Only devices of compute capability 2.0 or above are supported.

Input

`handle`	handle to the cuSPARSE library context.
`transA`	the operation $op (A)$
`transB`	the operation $op (B)$
`m`	number of rows of sparse matrix $op (A)$ and `C`.
`n`	number of columns of sparse matrix $op (B)$ and `C`.
`k`	number of columns/rows of sparse matrix $op (A)$ / $op (B)$ .
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzA`	number of nonzero elements of sparse matrix `A`.
`csrValA`	<type> array of `nnzA` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of $\tilde{m} + 1$ elements that contains the start of every row and the end of the last row plus one. $\tilde{m} = m$ if `transA` == `CUSPARSE_OPERATION_NON_TRANSPOSE`, otherwise $\tilde{m} = k$ .
`csrColIndA`	integer array of `nnzA` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`descrB`	the descriptor of matrix `B`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzB`	number of nonzero elements of sparse matrix `B`.
`csrValB`	<type> array of `nnzB` nonzero elements of matrix `B`.
`csrRowPtrB`	integer array of $\tilde{k} + 1$ elements that contains the start of every row and the end of the last row plus one. $\tilde{k} = k$ if `transB == CUSPARSE_OPERATION_NON_TRANSPOSE`, otherwise $\tilde{k} = n$
`csrColIndB`	integer array of `nnzB` column indices of the nonzero elements of matrix `B`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.

Output

`csrValC`	<type> array of `nnzC` $(=$ `csrRowPtrC(m)` $-$ `csrRowPtrC(0)` $)$ nonzero elements of matrix `C`.
`csrRowPtrC`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	integer array of `nnzC` $(=$ `csrRowPtrC(m)` $-$ `csrRowPtrC(0)` $)$ column indices of the nonzero elements of matrix `C`.
`nnzTotalDevHostPtr`	total number of nonzero elements in device or host memory. It is equal to `(csrRowPtrC(m)-csrRowPtrC(0))`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,k<0`; `IndexBase` of `descrA,descrB,descrC` is not base-0 or base-1; or `alpha` or `beta` is nil )).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

9.3. cusparse<t>csrgemm2()

cusparseStatus_t 
cusparseScsrgemm2_bufferSizeExt(cusparseHandle_t handle,
                                int m,
                                int n,
                                int k,
                                const float *alpha,
                                const cusparseMatDescr_t descrA,
                                int nnzA,
                                const int *csrRowPtrA,
                                const int *csrColIndA,
                                const cusparseMatDescr_t descrB,
                                int nnzB,
                                const int *csrRowPtrB,
                                const int *csrColIndB,
                                const float *beta,
                                const cusparseMatDescr_t descrD,
                                int nnzD,
                                const int *csrRowPtrD,
                                const int *csrColIndD,
                                csrgemm2Info_t info,
                                size_t *pBufferSizeInBytes );

cusparseStatus_t 
cusparseDcsrgemm2_bufferSizeExt(cusparseHandle_t handle,
                                int m,
                                int n,
                                int k,
                                const double *alpha,
                                const cusparseMatDescr_t descrA,
                                int nnzA,
                                const int *csrRowPtrA,
                                const int *csrColIndA,
                                const cusparseMatDescr_t descrB,
                                int nnzB,
                                const int *csrRowPtrB,
                                const int *csrColIndB,
                                const double *beta,
                                const cusparseMatDescr_t descrD,
                                int nnzD,
                                const int *csrRowPtrD,
                                const int *csrColIndD,
                                csrgemm2Info_t info,
                                size_t *pBufferSizeInBytes );

cusparseStatus_t 
cusparseCcsrgemm2_bufferSizeExt(cusparseHandle_t handle,
                                int m,
                                int n,
                                int k,
                                const cuComplex *alpha,
                                const cusparseMatDescr_t descrA,
                                int nnzA,
                                const int *csrRowPtrA,
                                const int *csrColIndA,
                                const cusparseMatDescr_t descrB,
                                int nnzB,
                                const int *csrRowPtrB,
                                const int *csrColIndB,
                                const cuComplex *beta,
                                const cusparseMatDescr_t descrD,
                                int nnzD,
                                const int *csrRowPtrD,
                                const int *csrColIndD,
                                csrgemm2Info_t info,
                                size_t *pBufferSizeInBytes );

cusparseStatus_t 
cusparseZcsrgemm2_bufferSizeExt(cusparseHandle_t handle,
                                int m,
                                int n,
                                int k,
                                const cuDoubleComplex *alpha,
                                const cusparseMatDescr_t descrA,
                                int nnzA,
                                const int *csrRowPtrA,
                                const int *csrColIndA,
                                const cusparseMatDescr_t descrB,
                                int nnzB,
                                const int *csrRowPtrB,
                                const int *csrColIndB,
                                const cuDoubleComplex *beta,
                                const cusparseMatDescr_t descrD,
                                int nnzD,
                                const int *csrRowPtrD,
                                const int *csrColIndD,
                                csrgemm2Info_t info,
                                size_t *pBufferSizeInBytes );

cusparseStatus_t 
cusparseXcsrgemm2Nnz(cusparseHandle_t handle,
                     int m,
                     int n,
                     int k,
                     const cusparseMatDescr_t descrA,
                     int nnzA,
                     const int *csrRowPtrA,
                     const int *csrColIndA,
                     const cusparseMatDescr_t descrB,
                     int nnzB,
                     const int *csrRowPtrB,
                     const int *csrColIndB,
                     const cusparseMatDescr_t descrD,
                     int nnzD,
                     const int *csrRowPtrD,
                     const int *csrColIndD,
                     const cusparseMatDescr_t descrC,
                     int *csrRowPtrC,
                     int *nnzTotalDevHostPtr,
                     const csrgemm2Info_t info,
                     void *pBuffer );

cusparseStatus_t 
cusparseScsrgemm2(cusparseHandle_t handle,
                  int m,
                  int n,
                  int k,
                  const float *alpha,
                  const cusparseMatDescr_t descrA,
                  int nnzA,
                  const float *csrValA,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  const cusparseMatDescr_t descrB,
                  int nnzB,
                  const float *csrValB,
                  const int *csrRowPtrB,
                  const int *csrColIndB,
                  const float *beta,
                  const cusparseMatDescr_t descrD,
                  int nnzD,
                  const float *csrValD,
                  const int *csrRowPtrD,
                  const int *csrColIndD,
                  const cusparseMatDescr_t descrC,
                  float *csrValC,
                  const int *csrRowPtrC,
                  int *csrColIndC,
                  const csrgemm2Info_t info,
                  void *pBuffer );

cusparseStatus_t 
cusparseDcsrgemm2(cusparseHandle_t handle,
                  int m,
                  int n,
                  int k,
                  const double *alpha,
                  const cusparseMatDescr_t descrA,
                  int nnzA,
                  const double *csrValA,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  const cusparseMatDescr_t descrB,
                  int nnzB,
                  const double *csrValB,
                  const int *csrRowPtrB,
                  const int *csrColIndB,
                  const double *beta,
                  const cusparseMatDescr_t descrD,
                  int nnzD,
                  const double *csrValD,
                  const int *csrRowPtrD,
                  const int *csrColIndD,
                  const cusparseMatDescr_t descrC,
                  double *csrValC,
                  const int *csrRowPtrC,
                  int *csrColIndC,
                  const csrgemm2Info_t info,
                  void *pBuffer );

cusparseStatus_t 
cusparseCcsrgemm2(cusparseHandle_t handle,
                  int m,
                  int n,
                  int k,
                  const cuComplex *alpha,
                  const cusparseMatDescr_t descrA,
                  int nnzA,
                  const cuComplex *csrValA,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  const cusparseMatDescr_t descrB,
                  int nnzB,
                  const cuComplex *csrValB,
                  const int *csrRowPtrB,
                  const int *csrColIndB,
                  const cuComplex *beta,
                  const cusparseMatDescr_t descrD,
                  int nnzD,
                  const cuComplex *csrValD,
                  const int *csrRowPtrD,
                  const int *csrColIndD,
                  const cusparseMatDescr_t descrC,
                  cuComplex *csrValC,
                  const int *csrRowPtrC,
                  int *csrColIndC,
                  const csrgemm2Info_t info,
                  void *pBuffer );

cusparseStatus_t 
cusparseZcsrgemm2(cusparseHandle_t handle,
                  int m,
                  int n,
                  int k,
                  const cuDoubleComplex *alpha,
                  const cusparseMatDescr_t descrA,
                  int nnzA,
                  const cuDoubleComplex *csrValA,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  const cusparseMatDescr_t descrB,
                  int nnzB,
                  const cuDoubleComplex *csrValB,
                  const int *csrRowPtrB,
                  const int *csrColIndB,
                  const cuDoubleComplex *beta,
                  const cusparseMatDescr_t descrD,
                  int nnzD,
                  const cuDoubleComplex *csrValD,
                  const int *csrRowPtrD,
                  const int *csrColIndD,
                  const cusparseMatDescr_t descrC,
                  cuDoubleComplex *csrValC,
                  const int *csrRowPtrC,
                  int *csrColIndC,
                  const csrgemm2Info_t info,
                  void *pBuffer );

This function performs following matrix-matrix operation:

C = alpha * A * B + beta * D

We provide csrgemm2 as a generalization of csrgemm. It provides more operations in terms of alpha and beta. For example, C = -A*B+D can be done by csrgemm2.

The csrgemm2 uses alpha and beta to support the following operations:

`alpha`	`beta`	`operation`
`NULL`	`NULL`	invalid
`NULL`	`!NULL`	`C = beta*D`, `A` and `B` are not used
`!NULL`	`NULL`	`C = alphaAB`, `D` is not used
`!NULL`	`!NULL`	`C = alphaAB + beta*D`

The numerical value of alpha and beta only affects the numerical values of C, not its sparsity pattern. For example, if alpha and beta are not zero, the sparsity pattern of C is union of A*B and D, independent of numerical value of alpha and beta.

The following table shows different operations according to the value of m, n and k

`m,n,k`	`operation`
m<0 or n <0 or k<0	invalid
m is 0 or n is 0	`do nothing`
m >0 and n >0 and k is 0	invalid if `beta` is zero; `C = beta*D` if `beta` is not zero.
m >0 and n >0 and k >0	`C = betaD` if `alpha` is zero. `C = alphaAB` if `beta` is zero. `C = alphaAB + betaD` if `alpha` and `beta` are not zero.

This function requires the buffer size returned by csrgemm2_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

The cuSPARSE library adopts a two-step approach to complete sparse matrix. In the first step, the user allocates csrRowPtrC of m+1 elements and uses the function cusparseXcsrgemm2Nnz() to determine csrRowPtrC and the total number of nonzero elements. In the second step, the user gathers nnzC (the number of nonzero elements of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC(m)-csrRowPtrC(0)) and allocates csrValC and csrColIndC of nnzC elements respectively, then finally calls function cusparse[S|D|C|Z]csrgemm2() to evaluate matrix C.

The general procedure of C=-A*B+D is as follows:

// assume matrices A, B and D are ready.
int baseC, nnzC;
csrgemm2Info_t info = NULL;
size_t bufferSize;
void *buffer = NULL;
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzC;
double alpha = -1.0;
double beta  =  1.0;
cusparseSetPointerMode(handle, CUSPARSE_POINTER_MODE_HOST);

// step 1: create an opaque structure
cusparseCreateCsrgemm2Info(&info);

// step 2: allocate buffer for csrgemm2Nnz and csrgemm2
cusparseDcsrgemm2_bufferSizeExt(handle, m, n, k, &alpha,
    descrA, nnzA, csrRowPtrA, csrColIndA,
    descrB, nnzB, csrRowPtrB, csrColIndB,
    descrD, nnzD, csrRowPtrD, csrColIndD,
    &beta,
    info,
    &bufferSize);
cudaMalloc(&buffer, bufferSize);

// step 3: compute csrRowPtrC
cudaMalloc((void**)&csrRowPtrC, sizeof(int)*(m+1));
cusparseXcsrgemm2Nnz(handle, m, n, k, 
        descrA, nnzA, csrRowPtrA, csrColIndA,
        descrB, nnzB, csrRowPtrB, csrColIndB,
        &beta
        descrD, nnzD, csrRowPtrD, csrColIndD,
        descrC, csrRowPtrC, nnzTotalDevHostPtr,
        info, buffer );
if (NULL != nnzTotalDevHostPtr){
    nnzC = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzC, csrRowPtrC+m, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&baseC, csrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzC -= baseC;
}

// step 4: finish sparsity pattern and value of C
cudaMalloc((void**)&csrColIndC, sizeof(int)*nnzC);
cudaMalloc((void**)&csrValC, sizeof(double)*nnzC);
// Remark: set csrValC to null if only sparsity pattern is required.
cusparseDcsrgemm2(handle, m, n, k, &alpha,
        descrA, nnzA, csrValA, csrRowPtrA, csrColIndA,
        descrB, nnzB, csrValB, csrRowPtrB, csrColIndB,
        &beta,
        descrD, nnzD, csrValD, csrRowPtrD, csrColIndD,
        descrC, csrValC, csrRowPtrC, csrColIndC,
        info, buffer);

// step 5: destroy the opaque structure
cusparseDestroyCsrgemm2Info(info);

Several comments on csrgemm2():

Only the NN version is supported. For other modes, the user has to transpose A or B explicitly.
Only CUSPARSE_MATRIX_TYPE_GENERAL is supported. If either A or B is symmetric or Hermitian, the user must extend the matrix to a full one and reconfigure the MatrixType field descriptor to CUSPARSE_MATRIX_TYPE_GENERAL.
if csrValC is zero, only sparisty pattern of C is calculated.
Only devices of compute capability 2.0 or above are supported.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of sparse matrix `A`, `D` and `C`.
`n`	number of columns of sparse matrix `B`, `D` and `C`.
`k`	number of columns/rows of sparse matrix `A` / `B`.
`alpha`	<type> scalar used for multiplication.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzA`	number of nonzero elements of sparse matrix `A`.
`csrValA`	<type> array of `nnzA` nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnzA` column indices of the nonzero elements of matrix `A`.
`descrB`	the descriptor of matrix `B`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzB`	number of nonzero elements of sparse matrix `B`.
`csrValB`	<type> array of `nnzB` nonzero elements of matrix `B`.
`csrRowPtrB`	integer array of `k+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndB`	integer array of `nnzB` column indices of the nonzero elements of matrix `B`.
`descrD`	the descriptor of matrix `D`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`nnzD`	number of nonzero elements of sparse matrix `D`.
`csrValD`	<type> array of `nnzD` nonzero elements of matrix `D`.
`csrRowPtrD`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndD`	integer array of `nnzD` column indices of the nonzero elements of matrix `D`.
`beta`	<type> scalar used for multiplication.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL` only.
`info`	structure with information used in `csrgemm2Nnz` and `csrgemm2`.
`pBuffer`	buffer allocated by the user; the size is returned by `csrgemm2_bufferSizeExt`.

Output

`csrValC`	<type> array of `nnzC` nonzero elements of matrix `C`.
`csrRowPtrC`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	integer array of `nnzC` column indices of the nonzero elements of matrix `C`.
`pBufferSizeInBytes`	number of bytes of the buffer used in `csrgemm2Nnnz` and `csrgemm2`.
`nnzTotalDevHostPtr`	total number of nonzero elements in device or host memory. It is equal to `(csrRowPtrC(m)-csrRowPtrC(0))`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,k<0`; `IndexBase` of `descrA,descrB,descrD,descrC` is not base-0 or base-1 ).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10. cuSPARSE Preconditioners Reference

This chapter describes the routines that implement different preconditioners.

In particular, the incomplete factorizations are implemented in two phases. First, during the analysis phase, the sparse triangular matrix is analyzed to determine the dependencies between its elements by calling the appropriate csrsv_analysis() function. The analysis is specific to the sparsity pattern of the given matrix and the selected cusparseOperation_t type. The information from the analysis phase is stored in the parameter of type cusparseSolveAnalysisInfo_t that has been initialized previously with a call to cusparseCreateSolveAnalysisInfo().

Second, during the numerical factorization phase, the given coefficient matrix is factorized using the information stored in the cusparseSolveAnalysisInfo_t parameter by calling the appropriate csrilu0() or csric0() function.

The analysis phase is shared across the sparse triangular solve, and the incomplete factorization and must be performed only once. The resulting information can be passed to the numerical factorization and the sparse triangular solve multiple times.

Finally, once the incomplete factorization and all the sparse triangular solves have completed, the opaque data structure pointed to by the cusparseSolveAnalysisInfo_t parameter can be released by calling cusparseDestroySolveAnalysisInfo().

10.1. cusparse<t>csric0()

cusparseStatus_t 
cusparseScsric0(cusparseHandle_t handle, 
                cusparseOperation_t trans, 
                int m, 
                const cusparseMatDescr_t descrA, 
                float *csrValM,
                const int *csrRowPtrA, 
                const int *csrColIndA, 
                cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseDcsric0(cusparseHandle_t handle, 
                cusparseOperation_t trans, 
                int m, 
                const cusparseMatDescr_t descrA, 
                double *csrValM,
                const int *csrRowPtrA, 
                const int *csrColIndA,  
                cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseCcsric0(cusparseHandle_t handle, 
                cusparseOperation_t trans, 
                int m, 
                const cusparseMatDescr_t descrA, 
                cuComplex *csrValM,
                const int *csrRowPtrA, 
                const int *csrColIndA,  
                cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseZcsric0(cusparseHandle_t handle, 
                cusparseOperation_t trans, 
                int m, 
                const cusparseMatDescr_t descrA, 
                cuDoubleComplex *csrValM,
                const int *csrRowPtrA, 
                const int *csrColIndA,  
                cusparseSolveAnalysisInfo_t info)

This function computes the incomplete-Cholesky factorization with $0$ fill-in and no pivoting:

o p (A) \approx R^{T} R

A is an m $\times$ m Hermitian/symmetric positive definite sparse matrix that is defined in CSR storage format by the three arrays csrValM, csrRowPtrA, and csrColIndA; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Notice that only a lower or upper Hermitian/symmetric part of the matrix A is actually stored. It is overwritten by the lower or upper triangular factors $R^{T}$ and $R$ , respectively.

A call to this routine must be preceded by a call to the csrsv_analysis() routine.

The matrix descriptor for csrsv_analysis() and csric0() must be the same. Otherwise, runtime error would occur.

This function requires some extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation `op` $(A)$ .
`m`	number of rows and columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix types are `CUSPARSE_MATRIX_TYPE_SYMMETRIC` and `CUSPARSE_MATRIX_TYPE_HERMITIAN`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValM`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).

Output

csrValM

<type> matrix containing the incomplete-Cholesky lower or upper triangular factor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.2. cusparse<t>csric02_bufferSize()

cusparseStatus_t 
cusparseScsric02_bufferSize(cusparseHandle_t handle,
                            int m,
                            int nnz,
                            const cusparseMatDescr_t descrA,
                            float *csrValA,
                            const int *csrRowPtrA,
                            const int *csrColIndA,
                            csric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDcsric02_bufferSize(cusparseHandle_t handle,
                            int m,
                            int nnz,
                            const cusparseMatDescr_t descrA,
                            double *csrValA,
                            const int *csrRowPtrA,
                            const int *csrColIndA,
                            csric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCcsric02_bufferSize(cusparseHandle_t handle,
                            int m,
                            int nnz,
                            const cusparseMatDescr_t descrA,
                            cuComplex *csrValA,
                            const int *csrRowPtrA,
                            const int *csrColIndA,
                            csric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZcsric02_bufferSize(cusparseHandle_t handle,
                            int m,
                            int nnz,
                            const cusparseMatDescr_t descrA,
                            cuDoubleComplex *csrValA,
                            const int *csrRowPtrA,
                            const int *csrColIndA,
                            csric02Info_t info,
                            int *pBufferSizeInBytes);

This function returns size of buffer used in computing the incomplete-Cholesky factorization with $0$ fill-in and no pivoting:

A \approx L L^{H}

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA.

The buffer size depends on dimension m and nnz, the number of nonzeros of the matrix. If the user changes the matrix, it is necessary to call csric02_bufferSize() again to have the correct buffer size; otherwise, a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.

Output

`info`	record internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in `csric02_analysis()` and `csric02()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.3. cusparse<t>csric02_analysis()

cusparseStatus_t 
cusparseScsric02_analysis(cusparseHandle_t handle,
                          int m,
                          int nnz,
                          const cusparseMatDescr_t descrA,
                          const float *csrValA,
                          const int *csrRowPtrA,
                          const int *csrColIndA,
                          csric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseDcsric02_analysis(cusparseHandle_t handle,
                          int m,
                          int nnz,
                          const cusparseMatDescr_t descrA,
                          const double *csrValA,
                          const int *csrRowPtrA,
                          const int *csrColIndA,
                          csric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseCcsric02_analysis(cusparseHandle_t handle,
                          int m,
                          int nnz,
                          const cusparseMatDescr_t descrA,
                          const cuComplex *csrValA,
                          const int *csrRowPtrA,
                          const int *csrColIndA,
                          csric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseZcsric02_analysis(cusparseHandle_t handle,
                          int m,
                          int nnz,
                          const cusparseMatDescr_t descrA,
                          const cuDoubleComplex *csrValA,
                          const int *csrRowPtrA,
                          const int *csrColIndA,
                          csric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

This function performs the analysis phase of the incomplete-Cholesky factorization with $0$ fill-in and no pivoting:

A \approx L L^{H}

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA.

This function requires a buffer size returned by csric02_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function csric02_analysis() reports a structural zero and computes level information stored in the opaque structure info. The level information can extract more parallelism during incomplete Cholesky factorization. However csric02() can be done without level information. To disable level information, the user must specify the policy of csric02_analysis() and csric02() as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function csric02_analysis() always reports the first structural zero, even if the policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. The user needs to call cusparseXcsric02_zeroPivot() to know where the structural zero is.

It is the user's choice whether to call csric02() if csric02_analysis() reports a structural zero. In this case, the user can still call csric02(), which will return a numerical zero at the same position as the structural zero. However the result is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure initialized using `cusparseCreateCsric02Info()`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `csric02_bufferSize()`.

Output

info

number of bytes of the buffer used in csric02_analysis() and csric02().

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparse<t>csric02()

cusparseStatus_t 
cusparseScsric02(cusparseHandle_t handle,
                 int m,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 float *csrValA_valM,
                 const int *csrRowPtrA,
                 const int *csrColIndA,
                 csric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseDcsric02(cusparseHandle_t handle,
                 int m,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 double *csrValA_valM,
                 const int *csrRowPtrA,
                 const int *csrColIndA,
                 csric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseCcsric02(cusparseHandle_t handle,
                 int m,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 cuComplex *csrValA_valM,
                 const int *csrRowPtrA,
                 const int *csrColIndA,
                 csric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseZcsric02(cusparseHandle_t handle,
                 int m,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 cuDoubleComplex *csrValA_valM,
                 const int *csrRowPtrA,
                 const int *csrColIndA,
                 csric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

This function performs the solve phase of the computing the incomplete-Cholesky factorization with $0$ fill-in and no pivoting:

A \approx L L^{H}

This function requires a buffer size returned by csric02_bufferSize(). The address of pBuffer must be a multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although csric02() can be done without level information, the user still needs to be aware of consistency. If csric02_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, csric02() can be run with or without levels. On the other hand, if csric02_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, csric02() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function csric02() reports the first numerical zero, including a structural zero. The user must call cusparseXcsric02_zeroPivot() to know where the numerical zero is.

Function csric02() only takes the lower triangular part of matrix A to perform factorization. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, the fill mode and diagonal type are ignored, and the strictly upper triangular part is ignored and never touched. It does not matter if A is Hermitian or not. In other words, from the point of view of csric02()A is Hermitian and only the lower triangular part is provided.

Note: In practice, a positive definite matrix may not have incomplete cholesky factorization. To the best of our knowledge, only matrix M can guarantee the existence of incomplete cholesky factorization. If csric02() failed cholesky factorization and reported a numerical zero, it is possible that incomplete cholesky factorization does not exist.

For example, suppose A is a real m × m matrix, the following code solves the precondition system M*y = x where M is the product of Cholesky factorization L and its transpose.

M = L L^{H}

// Suppose that A is m x m sparse matrix represented by CSR format, 
// Assumption:
// - handle is already created by cusparseCreate(),
// - (d_csrRowPtr, d_csrColInd, d_csrVal) is CSR of A on device memory,
// - d_x is right hand side vector on device memory,
// - d_y is solution vector on device memory.
// - d_z is intermediate result on device memory.

cusparseMatDescr_t descr_M = 0;
cusparseMatDescr_t descr_L = 0;
csric02Info_t info_M  = 0;
csrsv2Info_t  info_L  = 0;
csrsv2Info_t  info_Lt = 0;
int pBufferSize_M;
int pBufferSize_L;
int pBufferSize_Lt;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy_M  = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_L  = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_Lt = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans_L  = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseOperation_t trans_Lt = CUSPARSE_OPERATION_TRANSPOSE;

// step 1: create a descriptor which contains
// - matrix M is base-1
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has non-unit diagonal 
cusparseCreateMatDescr(&descr_M);
cusparseSetMatIndexBase(descr_M, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_M, CUSPARSE_MATRIX_TYPE_GENERAL);

cusparseCreateMatDescr(&descr_L);
cusparseSetMatIndexBase(descr_L, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_L, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_L, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr_L, CUSPARSE_DIAG_TYPE_NON_UNIT);

// step 2: create a empty info structure
// we need one info for csric02 and two info's for csrsv2
cusparseCreateCsric02Info(&info_M);
cusparseCreateCsrsv2Info(&info_L);
cusparseCreateCsrsv2Info(&info_Lt);

// step 3: query how much memory used in csric02 and csrsv2, and allocate the buffer
cusparseDcsric02_bufferSize(handle, m, nnz,
    descr_M, d_csrVal, d_csrRowPtr, d_csrColInd, info_M, &bufferSize_M);
cusparseDcsrsv2_bufferSize(handle, trans_L, m, nnz, 
    descr_L, d_csrVal, d_csrRowPtr, d_csrColInd, info_L, &pBufferSize_L);
cusparseDcsrsv2_bufferSize(handle, trans_Lt, m, nnz, 
    descr_L, d_csrVal, d_csrRowPtr, d_csrColInd, info_Lt,&pBufferSize_Lt);

pBufferSize = max(bufferSize_M, max(pBufferSize_L, pBufferSize_Lt));

// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis of incomplete Cholesky on M
//         perform analysis of triangular solve on L
//         perform analysis of triangular solve on L' 
// The lower triangular part of M has the same sparsity pattern as L, so  
// we can do analysis of csric02 and csrsv2 simultaneously.

cusparseDcsric02_analysis(handle, m, nnz, descr_M,
    d_csrVal, d_csrRowPtr, d_csrColInd, info_M, 
    policy_M, pBuffer);
status = cusparseXcsric02_zeroPivot(handle, info_M, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("A(%d,%d) is missing\n", structural_zero, structural_zero);
}

cusparseDcsrsv2_analysis(handle, trans_L, m, nnz, descr_L, 
    d_csrVal, d_csrRowPtr, d_csrColInd,
    info_L, policy_L, pBuffer);

cusparseDcsrsv2_analysis(handle, trans_Lt, m, nnz, descr_L, 
    d_csrVal, d_csrRowPtr, d_csrColInd,
    info_Lt, policy_Lt, pBuffer);

// step 5: M = L * L'
cusparseDcsric02(handle, m, nnz, descr_M,
    d_csrVal, d_csrRowPtr, d_csrColInd, info_M, policy_M, pBuffer);
status = cusparseXcsric02_zeroPivot(handle, info_M, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is zero\n", numerical_zero, numerical_zero);
}

// step 6: solve L*z = x
cusparseDcsrsv2_solve(handle, trans_L, m, nnz, &alpha, descr_L,
   d_csrVal, d_csrRowPtr, d_csrColInd, info_L,
   d_x, d_z, policy_L, pBuffer);

// step 7: solve L'*y = z
cusparseDcsrsv2_solve(handle, trans_Lt, m, nnz, &alpha, descr_L,
   d_csrVal, d_csrRowPtr, d_csrColInd, info_Lt,
   d_z, d_y, policy_Lt, pBuffer);

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyMatDescr(descr_M);
cusparseDestroyMatDescr(descr_L);
cusparseDestroyCsric02Info(info_M);
cusparseDestroyCsrsv2Info(info_L);
cusparseDestroyCsrsv2Info(info_Lt);
cusparseDestroy(handle);

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA_valM`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `csric02_bufferSize()`.

Output

csrValA_valM

<type> matrix containing the incomplete-Cholesky lower triangular factor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXcsric02_zeroPivot()

cusparseStatus_t 
cusparseXcsric02_zeroPivot(cusparseHandle_t handle,
                           csric02Info_t info,
                           int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) has either a structural zero or a numerical zero; otherwise, position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXcsric02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains structural zero or numerical zero if the user already called `csric02_analysis()` or `csric02()`.

Output

position

if no structural or numerical zero, position is -1; otherwise, if A(j,j) is missing or L(j,j) is zero, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.6. cusparse<t>csrilu0()

cusparseStatus_t 
cusparseScsrilu0(cusparseHandle_t handle, 
                 cusparseOperation_t trans, 
                 int m, 
                 const cusparseMatDescr_t descrA, 
                 float *csrValM,
                 const int *csrRowPtrA, 
                 const int *csrColIndA, 
                 cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseDcsrilu0(cusparseHandle_t handle, 
                 cusparseOperation_t trans, 
                 int m, 
                 const cusparseMatDescr_t descrA, 
                 double *csrValM,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,  
                 cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseCcsrilu0(cusparseHandle_t handle, 
                 cusparseOperation_t trans, 
                 int m, 
                 const cusparseMatDescr_t descrA, 
                 cuComplex *csrValM,
                 const int *csrRowPtrA, 
                 const int *csrColIndA,  
                 cusparseSolveAnalysisInfo_t info)
cusparseStatus_t 
cusparseZcsrilu0(cusparseHandle_t handle, 
                 cusparseOperation_t trans, 
                 int m, 
                 const cusparseMatDescr_t descrA, 
                 cuDoubleComplex *csrValM,
                 const int *csrRowPtrA, 
                 const int *csrColIndA, 
                 cusparseSolveAnalysisInfo_t info)

This function computes the incomplete-LU factorization with $0$ fill-in and no pivoting:

o p (A) \approx L U

A is an m $\times$ m sparse matrix that is defined in CSR storage format by the three arrays csrValM, csrRowPtrA, and csrColIndA; and

op (A) = \{\begin{cases} A & if trans == CUSPARSE_OPERATION_NON_TRANSPOSE \\ A^{T} & if trans == CUSPARSE_OPERATION_TRANSPOSE \\ A^{H} & if trans == CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE \end{cases}

Notice that the diagonal of lower triangular factor $L$ is unitary and need not be stored. Therefore, the input matrix is overwritten with the resulting lower and upper triangular factors $L$ and $U$ , respectively.

A call to this routine must be preceded by a call to the csrsv_analysis() routine.

The matrix descriptor for csrsv_analysis() and csrilu0() must be the same. Otherwise, runtime error would occur.

This function requires some extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`trans`	the operation `op` $(A)$ .
`m`	number of rows and columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValM`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).

Output

csrValM

<type> matrix containing the incomplete-LU lower and upper triangular factors.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.7. cusparseCsrilu0Ex()

cusparseStatus_t CUSPARSEAPI cusparseCsrilu0Ex(cusparseHandle_t handle, 
                                              cusparseOperation_t trans, 
                                              int m, 
                                              const cusparseMatDescr_t descrA, 
                                              void *csrSortedValA_ValM, cudaDataType csrSortedValA_ValMtype,
                                              const int *csrSortedRowPtrA, 
                                              const int *csrSortedColIndA,
                                              cusparseSolveAnalysisInfo_t info,
                                              cudaDataType executiontype);

This function is an extended version of cusparse<t>csrilu0(). For detailed description of the functionality, see cusparse<t>csrilu0().

This function does not support half-precision execution type, but it supports half-precision IO with single precision execution.

Input specifically required by cusparseCsrilu0Ex

`csrSortedValA_ValMtype`	Data type of `csrSortedValA_ValM`.
`executiontype`	Data type used for computation.

cusparse<t>csrilu02_numericBoost()

cusparseStatus_t 
cusparseScsrilu02_numericBoost(cusparseHandle_t handle,
                               csrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               float *boost_val);

cusparseStatus_t 
cusparseDcsrilu02_numericBoost(cusparseHandle_t handle,
                               csrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               double *boost_val);

cusparseStatus_t 
cusparseCcsrilu02_numericBoost(cusparseHandle_t handle,
                               csrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               cuComplex *boost_val);

cusparseStatus_t 
cusparseZcsrilu02_numericBoost(cusparseHandle_t handle,
                               csrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               cuDoubleComplex *boost_val);

The user can use a boost value to replace a numerical value in incomplete LU factorization. The tol is used to determine a numerical zero, and the boost_val is used to replace a numerical zero. The behavior is

if tol >= fabs(A(j,j)), then A(j,j)=boost_val.

To enable a boost value, the user has to set parameter enable_boost to 1 before calling csrilu02(). To disable a boost value, the user can call csrilu02_numericBoost() again with parameter enable_boost=0.

If enable_boost=0, tol and boost_val are ignored.

Both tol and boost_val can be in the host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	structure initialized using `cusparseCreateCsrilu02Info()`.
`enable_boost`	disable boost by `enable_boost=0`; otherwise, boost is enabled.
`tol`	tolerance to determine a numerical zero.
`boost_val`	boost value to replace a numerical zero.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` or pointer mode is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.9. cusparse<t>csrilu02_bufferSize()

cusparseStatus_t 
cusparseScsrilu02_bufferSize(cusparseHandle_t handle,
                             int m,
                             int nnz,
                             const cusparseMatDescr_t descrA,
                             float *csrValA,
                             const int *csrRowPtrA,
                             const int *csrColIndA,
                             csrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDcsrilu02_bufferSize(cusparseHandle_t handle,
                             int m,
                             int nnz,
                             const cusparseMatDescr_t descrA,
                             double *csrValA,
                             const int *csrRowPtrA,
                             const int *csrColIndA,
                             csrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCcsrilu02_bufferSize(cusparseHandle_t handle,
                             int m,
                             int nnz,
                             const cusparseMatDescr_t descrA,
                             cuComplex *csrValA,
                             const int *csrRowPtrA,
                             const int *csrColIndA,
                             csrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZcsrilu02_bufferSize(cusparseHandle_t handle,
                             int m,
                             int nnz,
                             const cusparseMatDescr_t descrA,
                             cuDoubleComplex *csrValA,
                             const int *csrRowPtrA,
                             const int *csrColIndA,
                             csrilu02Info_t info,
                             int *pBufferSizeInBytes);

This function returns size of the buffer used in computing the incomplete-LU factorization with $0$ fill-in and no pivoting:

A \approx L U

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA.

The buffer size depends on the dimension m and nnz, the number of nonzeros of the matrix. If the user changes the matrix, it is necessary to call csrilu02_bufferSize() again to have the correct buffer size; otherwise, a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.

Output

`info`	record internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in `csrilu02_analysis()` and `csrilu02()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.10. cusparse<t>csrilu02_analysis()

cusparseStatus_t 
cusparseScsrilu02_analysis(cusparseHandle_t handle,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           const float *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseDcsrilu02_analysis(cusparseHandle_t handle,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           const double *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseCcsrilu02_analysis(cusparseHandle_t handle,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           const cuComplex *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseZcsrilu02_analysis(cusparseHandle_t handle,
                           int m,
                           int nnz,
                           const cusparseMatDescr_t descrA,
                           const cuDoubleComplex *csrValA,
                           const int *csrRowPtrA,
                           const int *csrColIndA,
                           csrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

This function performs the analysis phase of the incomplete-LU factorization with $0$ fill-in and no pivoting:

A \approx L U

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA, csrRowPtrA, and csrColIndA.

This function requires the buffer size returned by csrilu02_bufferSize(). The address of pBuffer must be a multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function csrilu02_analysis() reports a structural zero and computes level information stored in the opaque structure info. The level information can extract more parallelism during incomplete LU factorization; however csrilu02() can be done without level information. To disable level information, the user must specify the policy of csrilu02() as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

It is the user's choice whether to call csrilu02() if csrilu02_analysis() reports a structural zero. In this case, the user can still call csrilu02(), which will return a numerical zero at the same position as the structural zero. However the result is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure initialized using `cusparseCreateCsrilu02Info()`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is returned by `csrilu02_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.11. cusparse<t>csrilu02()

cusparseStatus_t 
cusparseScsrilu02(cusparseHandle_t handle,
                  int m,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  float *csrValA_valM,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  csrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseDcsrilu02(cusparseHandle_t handle,
                  int m,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  double *csrValA_valM,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  csrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseCcsrilu02(cusparseHandle_t handle,
                  int m,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuComplex *csrValA_valM,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  csrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseZcsrilu02(cusparseHandle_t handle,
                  int m,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuDoubleComplex *csrValA_valM,
                  const int *csrRowPtrA,
                  const int *csrColIndA,
                  csrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

This function performs the solve phase of the incomplete-LU factorization with $0$ fill-in and no pivoting:

A \approx L U

A is an m×m sparse matrix that is defined in CSR storage format by the three arrays csrValA_valM, csrRowPtrA, and csrColIndA.

This function requires a buffer size returned by csrilu02_bufferSize(). The address of pBuffer must be a multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL. The fill mode and diagonal type are ignored.

Although csrilu02() can be done without level information, the user still needs to be aware of consistency. If csrilu02_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, csrilu02() can be run with or without levels. On the other hand, if csrilu02_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, csrilu02() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function csrilu02() reports the first numerical zero, including a structural zero. The user must call cusparseXcsrilu02_zeroPivot() to know where the numerical zero is.

For example, suppose A is a real m × m matrix, the following code solves precondition system M*y = x where M is the product of LU factors L and U.

// Suppose that A is m x m sparse matrix represented by CSR format, 
// Assumption:
// - handle is already created by cusparseCreate(),
// - (d_csrRowPtr, d_csrColInd, d_csrVal) is CSR of A on device memory,
// - d_x is right hand side vector on device memory,
// - d_y is solution vector on device memory.
// - d_z is intermediate result on device memory.

cusparseMatDescr_t descr_M = 0;
cusparseMatDescr_t descr_L = 0;
cusparseMatDescr_t descr_U = 0;
csrilu02Info_t info_M  = 0;
csrsv2Info_t  info_L  = 0;
csrsv2Info_t  info_U  = 0;
int pBufferSize_M;
int pBufferSize_L;
int pBufferSize_U;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy_M = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_L = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_U = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans_L  = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseOperation_t trans_U  = CUSPARSE_OPERATION_NON_TRANSPOSE;

// step 1: create a descriptor which contains
// - matrix M is base-1
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has unit diagonal 
// - matrix U is base-1
// - matrix U is upper triangular
// - matrix U has non-unit diagonal
cusparseCreateMatDescr(&descr_M);
cusparseSetMatIndexBase(descr_M, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_M, CUSPARSE_MATRIX_TYPE_GENERAL);

cusparseCreateMatDescr(&descr_L);
cusparseSetMatIndexBase(descr_L, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_L, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_L, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr_L, CUSPARSE_DIAG_TYPE_UNIT);

cusparseCreateMatDescr(&descr_U);
cusparseSetMatIndexBase(descr_U, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_U, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_U, CUSPARSE_FILL_MODE_UPPER);
cusparseSetMatDiagType(descr_U, CUSPARSE_DIAG_TYPE_NON_UNIT);

// step 2: create a empty info structure
// we need one info for csrilu02 and two info's for csrsv2
cusparseCreateCsrilu02Info(&info_M);
cusparseCreateCsrsv2Info(&info_L);
cusparseCreateCsrsv2Info(&info_U);

// step 3: query how much memory used in csrilu02 and csrsv2, and allocate the buffer
cusparseDcsrilu02_bufferSize(handle, m, nnz,
    descr_M, d_csrVal, d_csrRowPtr, d_csrColInd, info_M, &pBufferSize_M);
cusparseDcsrsv2_bufferSize(handle, trans_L, m, nnz, 
    descr_L, d_csrVal, d_csrRowPtr, d_csrColInd, info_L, &pBufferSize_L);
cusparseDcsrsv2_bufferSize(handle, trans_U, m, nnz, 
    descr_U, d_csrVal, d_csrRowPtr, d_csrColInd, info_U, &pBufferSize_U);

pBufferSize = max(pBufferSize_M, max(pBufferSize_L, pBufferSize_U));

// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis of incomplete Cholesky on M
//         perform analysis of triangular solve on L
//         perform analysis of triangular solve on U 
// The lower(upper) triangular part of M has the same sparsity pattern as L(U), 
// we can do analysis of csrilu0 and csrsv2 simultaneously.

cusparseDcsrilu02_analysis(handle, m, nnz, descr_M,
    d_csrVal, d_csrRowPtr, d_csrColInd, info_M, 
    policy_M, pBuffer);
status = cusparseXcsrilu02_zeroPivot(handle, info_M, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("A(%d,%d) is missing\n", structural_zero, structural_zero);
}

cusparseDcsrsv2_analysis(handle, trans_L, m, nnz, descr_L, 
    d_csrVal, d_csrRowPtr, d_csrColInd,
    info_L, policy_L, pBuffer);

cusparseDcsrsv2_analysis(handle, trans_U, m, nnz, descr_U, 
    d_csrVal, d_csrRowPtr, d_csrColInd,
    info_U, policy_U, pBuffer);

// step 5: M = L * U
cusparseDcsrilu02(handle, m, nnz, descr_M,
    d_csrVal, d_csrRowPtr, d_csrColInd, info_M, policy_M, pBuffer);
status = cusparseXcsrilu02_zeroPivot(handle, info_M, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("U(%d,%d) is zero\n", numerical_zero, numerical_zero);
}
 
// step 6: solve L*z = x
cusparseDcsrsv2_solve(handle, trans_L, m, nnz, &alpha, descr_L,
   d_csrVal, d_csrRowPtr, d_csrColInd, info_L,
   d_x, d_z, policy_L, pBuffer);

// step 7: solve U*y = z
cusparseDcsrsv2_solve(handle, trans_U, m, nnz, &alpha, descr_U,
   d_csrVal, d_csrRowPtr, d_csrColInd, info_U,
   d_z, d_y, policy_U, pBuffer);

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyMatDescr(descr_M);
cusparseDestroyMatDescr(descr_L);
cusparseDestroyMatDescr(descr_U);
cusparseDestroyCsrilu02Info(info_M);
cusparseDestroyCsrsv2Info(info_L);
cusparseDestroyCsrsv2Info(info_U);
cusparseDestroy(handle);

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows and columns of matrix `A`.
`nnz`	number of nonzeros of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA_valM`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m` $+ 1$ elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `csrilu02_bufferSize()`.

Output

csrValA_valM

<type> matrix containing the incomplete-LU lower and upper triangular factors.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXcsrilu02_zeroPivot()

cusparseStatus_t 
cusparseXcsrilu02_zeroPivot(cusparseHandle_t handle,
                            csrilu02Info_t info,
                            int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) has either a structural zero or a numerical zero; otherwise, position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXcsrilu02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains structural zero or numerical zero if the user already called `csrilu02_analysis()` or `csrilu02()`.

Output

position

if no structural or numerical zero, position is -1; otherwise if A(j,j) is missing or U(j,j) is zero, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.13. cusparse<t>bsric02_bufferSize()

cusparseStatus_t 
cusparseSbsric02_bufferSize(cusparseHandle_t handle,
                            cusparseDirection_t dirA,
                            int mb,
                            int nnzb,
                            const cusparseMatDescr_t descrA,
                            float *bsrValA,
                            const int *bsrRowPtrA,
                            const int *bsrColIndA,
                            int blockDim,
                            bsric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDbsric02_bufferSize(cusparseHandle_t handle,
                            cusparseDirection_t dirA,
                            int mb,
                            int nnzb,
                            const cusparseMatDescr_t descrA,
                            double *bsrValA,
                            const int *bsrRowPtrA,
                            const int *bsrColIndA,
                            int blockDim,
                            bsric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCbsric02_bufferSize(cusparseHandle_t handle,
                            cusparseDirection_t dirA,
                            int mb,
                            int nnzb,
                            const cusparseMatDescr_t descrA,
                            cuComplex *bsrValA,
                            const int *bsrRowPtrA,
                            const int *bsrColIndA,
                            int blockDim,
                            bsric02Info_t info,
                            int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZbsric02_bufferSize(cusparseHandle_t handle,
                            cusparseDirection_t dirA,
                            int mb,
                            int nnzb,
                            const cusparseMatDescr_t descrA,
                            cuDoubleComplex *bsrValA,
                            const int *bsrRowPtrA,
                            const int *bsrColIndA,
                            int blockDim,
                            bsric02Info_t info,
                            int *pBufferSizeInBytes);

This function returns the size of a buffer used in computing the incomplete-Cholesky factorization with 0 fill-in and no pivoting

A \approx L L^{H}

A is an (mb*blockDim)*(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA.

The buffer size depends on the dimensions of mb, blockDim, and the number of nonzero blocks of the matrix nnzb. If the user changes the matrix, it is necessary to call bsric02_bufferSize() again to have the correct buffer size; otherwise, a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and block columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A, larger than zero.

Output

`info`	record internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in `bsric02_analysis()` and `bsric02()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`); the base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.14. cusparse<t>bsric02_analysis()

cusparseStatus_t 
cusparseSbsric02_analysis(cusparseHandle_t handle,
                          cusparseDirection_t dirA,
                          int mb,
                          int nnzb,
                          const cusparseMatDescr_t descrA,
                          const float *bsrValA,
                          const int *bsrRowPtrA,
                          const int *bsrColIndA,
                          int blockDim,
                          bsric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseDbsric02_analysis(cusparseHandle_t handle,
                          cusparseDirection_t dirA,
                          int mb,
                          int nnzb,
                          const cusparseMatDescr_t descrA,
                          const double *bsrValA,
                          const int *bsrRowPtrA,
                          const int *bsrColIndA,
                          int blockDim,
                          bsric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseCbsric02_analysis(cusparseHandle_t handle,
                          cusparseDirection_t dirA,
                          int mb,
                          int nnzb,
                          const cusparseMatDescr_t descrA,
                          const cuComplex *bsrValA,
                          const int *bsrRowPtrA,
                          const int *bsrColIndA,
                          int blockDim,
                          bsric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

cusparseStatus_t 
cusparseZbsric02_analysis(cusparseHandle_t handle,
                          cusparseDirection_t dirA,
                          int mb,
                          int nnzb,
                          const cusparseMatDescr_t descrA,
                          const cuDoubleComplex *bsrValA,
                          const int *bsrRowPtrA,
                          const int *bsrColIndA,
                          int blockDim,
                          bsric02Info_t info,
                          cusparseSolvePolicy_t policy,
                          void *pBuffer);

This function performs the analysis phase of the incomplete-Cholesky factorization with 0 fill-in and no pivoting

A \approx L L^{H}

A is an (mb*blockDim)x(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA. The block in BSR format is of size blockDim*blockDim, stored as column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_COLUMN or CUSPARSE_DIRECTION_ROW. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored.

This function requires a buffer size returned by bsric02_bufferSize90. The address of pBuffer must be a multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Functionbsric02_analysis() reports structural zero and computes level information stored in the opaque structure info. The level information can extract more parallelism during incomplete Cholesky factorization. However bsric02() can be done without level information. To disable level information, the user needs to specify the parameter policy of bsric02[_analysis| ] as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function bsric02_analysis always reports the first structural zero, even when parameter policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. The user must call cusparseXbsric02_zeroPivot() to know where the structural zero is.

It is the user's choice whether to call bsric02() if bsric02_analysis() reports a structural zero. In this case, the user can still call bsric02(), which returns a numerical zero in the same position as the structural zero. However the result is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and block columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A; must be larger than zero.
`info`	structure initialized using `cusparseCreateBsric02Info()`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `bsric02_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`); the base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparse<t>bsric02()

cusparseStatus_t 
cusparseSbsric02(cusparseHandle_t handle,
                 cusparseDirection_t dirA,
                 int mb,
                 int nnzb,
                 const cusparseMatDescr_t descrA,
                 float *bsrValA,
                 const int *bsrRowPtrA,
                 const int *bsrColIndA,
                 int blockDim,
                 bsric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseDbsric02(cusparseHandle_t handle,
                 cusparseDirection_t dirA,
                 int mb,
                 int nnzb,
                 const cusparseMatDescr_t descrA,
                 double *bsrValA,
                 const int *bsrRowPtrA,
                 const int *bsrColIndA,
                 int blockDim,
                 bsric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseCbsric02(cusparseHandle_t handle,
                 cusparseDirection_t dirA,
                 int mb,
                 int nnzb,
                 const cusparseMatDescr_t descrA,
                 cuComplex *bsrValA,
                 const int *bsrRowPtrA,
                 const int *bsrColIndA,
                 int blockDim,
                 bsric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

cusparseStatus_t 
cusparseZbsric02(cusparseHandle_t handle,
                 cusparseDirection_t dirA,
                 int mb,
                 int nnzb,
                 const cusparseMatDescr_t descrA,
                 cuDoubleComplex *bsrValA,
                 const int *bsrRowPtrA,
                 const int *bsrColIndA,
                 int blockDim,
                 bsric02Info_t info,
                 cusparseSolvePolicy_t policy,
                 void *pBuffer);

This function performs the solve phase of the incomplete-Cholesky factorization with 0 fill-in and no pivoting

A \approx L L^{H}

A is an (mb*blockDim)×(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA. The block in BSR format is of size blockDim*blockDim, stored as column-major or row-major as determined by parameter dirA, which is either CUSPARSE_DIRECTION_COLUMN or CUSPARSE_DIRECTION_ROW. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored.

This function requires a buffer size returned by bsric02_bufferSize(). The address of pBuffer must be a multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although bsric02() can be done without level information, the user must be aware of consistency. If bsric02_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, bsric02() can be run with or without levels. On the other hand, if bsric02_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, bsric02() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsric02() has the same behavior as csric02(). That is, bsr2csr(bsric02(A)) = csric02(bsr2csr(A)). The numerical zero of csric02() means there exists some zero L(j,j). The numerical zero of bsric02() means there exists some block Lj,j) that is not invertible.

Function bsric02 reports the first numerical zero, including a structural zero. The user must call cusparseXbsric02_zeroPivot() to know where the numerical zero is.

The bsric02() function only takes the lower triangular part of matrix A to perform factorization. The strictly upper triangular part is ignored and never touched. It does not matter if A is Hermitian or not. In other words, from the point of view of bsric02(), A is Hermitian and only the lower triangular part is provided. Moreover, the imaginary part of diagonal elements of diagonal blocks is ignored.

For example, suppose A is a real m-by-m matrix, where m=mb*blockDim. The following code solves precondition system M*y = x, where M is the product of Cholesky factorization L and its transpose.

M = L L^{H}

// Suppose that A is m x m sparse matrix represented by BSR format, 
// The number of block rows/columns is mb, and 
// the number of nonzero blocks is nnzb.
// Assumption:
// - handle is already created by cusparseCreate(),
// - (d_bsrRowPtr, d_bsrColInd, d_bsrVal) is BSR of A on device memory,
// - d_x is right hand side vector on device memory,
// - d_y is solution vector on device memory.
// - d_z is intermediate result on device memory.
// - d_x, d_y and d_z are of size m.
cusparseMatDescr_t descr_M = 0;
cusparseMatDescr_t descr_L = 0;
bsric02Info_t info_M  = 0;
bsrsv2Info_t  info_L  = 0;
bsrsv2Info_t  info_Lt = 0;
int pBufferSize_M;
int pBufferSize_L;
int pBufferSize_Lt;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy_M  = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_L  = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_Lt = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans_L  = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseOperation_t trans_Lt = CUSPARSE_OPERATION_TRANSPOSE;
const cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;

// step 1: create a descriptor which contains
// - matrix M is base-1
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has non-unit diagonal 
cusparseCreateMatDescr(&descr_M);
cusparseSetMatIndexBase(descr_M, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_M, CUSPARSE_MATRIX_TYPE_GENERAL);

cusparseCreateMatDescr(&descr_L);
cusparseSetMatIndexBase(descr_L, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_L, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_L, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr_L, CUSPARSE_DIAG_TYPE_NON_UNIT);

// step 2: create a empty info structure
// we need one info for bsric02 and two info's for bsrsv2
cusparseCreateBsric02Info(&info_M);
cusparseCreateBsrsv2Info(&info_L);
cusparseCreateBsrsv2Info(&info_Lt);

// step 3: query how much memory used in bsric02 and bsrsv2, and allocate the buffer
cusparseDbsric02_bufferSize(handle, dir, mb, nnzb,
    descr_M, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, &bufferSize_M);
cusparseDbsrsv2_bufferSize(handle, dir, trans_L, mb, nnzb, 
    descr_L, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_L, &pBufferSize_L);
cusparseDbsrsv2_bufferSize(handle, dir, trans_Lt, mb, nnzb, 
    descr_L, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_Lt, &pBufferSize_Lt);

pBufferSize = max(bufferSize_M, max(pBufferSize_L, pBufferSize_Lt));

// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis of incomplete Cholesky on M
//         perform analysis of triangular solve on L
//         perform analysis of triangular solve on L' 
// The lower triangular part of M has the same sparsity pattern as L, so  
// we can do analysis of bsric02 and bsrsv2 simultaneously.

cusparseDbsric02_analysis(handle, dir, mb, nnzb, descr_M,
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, 
    policy_M, pBuffer);
status = cusparseXbsric02_zeroPivot(handle, info_M, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("A(%d,%d) is missing\n", structural_zero, structural_zero);
}

cusparseDbsrsv2_analysis(handle, dir, trans_L, mb, nnzb, descr_L, 
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim,
    info_L, policy_L, pBuffer);

cusparseDbsrsv2_analysis(handle, dir, trans_Lt, mb, nnzb, descr_L, 
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim,
    info_Lt, policy_Lt, pBuffer);

// step 5: M = L * L'
cusparseDbsric02_solve(handle, dir, mb, nnzb, descr_M,
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, policy_M, pBuffer);
status = cusparseXbsric02_zeroPivot(handle, info_M, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == status){
   printf("L(%d,%d) is not positive definite\n", numerical_zero, numerical_zero);
}

// step 6: solve L*z = x
cusparseDbsrsv2_solve(handle, dir, trans_L, mb, nnzb, &alpha, descr_L,
   d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_L,
   d_x, d_z, policy_L, pBuffer);

// step 7: solve L'*y = z
cusparseDbsrsv2_solve(handle, dir, trans_Lt, mb, nnzb, &alpha, descr_L,
   d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_Lt,
   d_z, d_y, policy_Lt, pBuffer);

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyMatDescr(descr_M);
cusparseDestroyMatDescr(descr_L);
cusparseDestroyBsric02Info(info_M);
cusparseDestroyBsrsv2Info(info_L);
cusparseDestroyBsrsv2Info(info_Lt);
cusparseDestroy(handle);

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and block columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A, larger than zero.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is returned by `bsric02_bufferSize()`.

Output

bsrValA

<type> matrix containing the incomplete-Cholesky lower triangular factor.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`); the base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXbsric02_zeroPivot()

cusparseStatus_t 
cusparseXbsric02_zeroPivot(cusparseHandle_t handle,
                           bsric02Info_t info,
                           int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) has either a structural zero or a numerical zero (the block is not positive definite). Otherwise position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXbsric02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains a structural zero or a numerical zero if the user already called `bsric02_analysis()` or `bsric02()`.

Output

position

if no structural or numerical zero, position is -1, otherwise if A(j,j) is missing or L(j,j) is not positive definite, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

cusparse<t>bsrilu02_numericBoost()

cusparseStatus_t 
cusparseSbsrilu02_numericBoost(cusparseHandle_t handle,
                               bsrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               float *boost_val);

cusparseStatus_t 
cusparseDbsrilu02_numericBoost(cusparseHandle_t handle,
                               bsrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               double *boost_val);

cusparseStatus_t 
cusparseCbsrilu02_numericBoost(cusparseHandle_t handle,
                               bsrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               cuComplex *boost_val);

cusparseStatus_t 
cusparseZbsrilu02_numericBoost(cusparseHandle_t handle,
                               bsrilu02Info_t info,
                               int enable_boost,
                               double *tol,
                               cuDoubleComplex *boost_val);

The user can use a boost value to replace a numerical value in incomplete LU factorization. Parameter tol is used to determine a numerical zero, and boost_val is used to replace a numerical zero. The behavior is as follows:

if tol >= fabs(A(j,j)), then reset each diagonal element of block A(j,j) by boost_val.

To enable a boost value, the user sets parameter enable_boost to 1 before calling bsrilu02(). To disable the boost value, the user can call bsrilu02_numericBoost() with parameter enable_boost=0.

If enable_boost=0, tol and boost_val are ignored.

Both tol and boost_val can be in host memory or device memory. The user can set the proper mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	structure initialized using `cusparseCreateBsrilu02Info()`.
`enable_boost`	disable boost by setting `enable_boost=0`. Otherwise, boost is enabled.
`tol`	tolerance to determine a numerical zero.
`boost_val`	boost value to replace a numerical zero.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` or pointer mode is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.18. cusparse<t>bsrilu02_bufferSize()

cusparseStatus_t 
cusparseSbsrilu02_bufferSize(cusparseHandle_t handle,
                             cusparseDirection_t dirA,
                             int mb,
                             int nnzb,
                             const cusparseMatDescr_t descrA,
                             float *bsrValA,
                             const int *bsrRowPtrA,
                             const int *bsrColIndA,
                             int blockDim,
                             bsrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDbsrilu02_bufferSize(cusparseHandle_t handle,
                             cusparseDirection_t dirA,
                             int mb,
                             int nnzb,
                             const cusparseMatDescr_t descrA,
                             double *bsrValA,
                             const int *bsrRowPtrA,
                             const int *bsrColIndA,
                             int blockDim,
                             bsrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCbsrilu02_bufferSize(cusparseHandle_t handle,
                             cusparseDirection_t dirA,
                             int mb,
                             int nnzb,
                             const cusparseMatDescr_t descrA,
                             cuComplex *bsrValA,
                             const int *bsrRowPtrA,
                             const int *bsrColIndA,
                             int blockDim,
                             bsrilu02Info_t info,
                             int *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZbsrilu02_bufferSize(cusparseHandle_t handle,
                             cusparseDirection_t dirA,
                             int mb,
                             int nnzb,
                             const cusparseMatDescr_t descrA,
                             cuDoubleComplex *bsrValA,
                             const int *bsrRowPtrA,
                             const int *bsrColIndA,
                             int blockDim,
                             bsrilu02Info_t info,
                             int *pBufferSizeInBytes);

This function returns the size of the buffer used in computing the incomplete-LU factorization with 0 fill-in and no pivoting

A \approx L U

A is an (mb*blockDim)*(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA.

The buffer size depends on the dimensions of mb, blockDim, and the number of nonzero blocks of the matrix nnzb. If the user changes the matrix, it is necessary to call bsrilu02_bufferSize() again to have the correct buffer size; otherwise, a segmentation fault may occur.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A, larger than zero.

Output

`info`	record internal states based on different algorithms.
`pBufferSizeInBytes`	number of bytes of the buffer used in `bsrilu02_analysis()` and `bsrilu02()`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`), base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.19. cusparse<t>bsrilu02_analysis()

cusparseStatus_t 
cusparseSbsrilu02_analysis(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           float *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseDbsrilu02_analysis(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           double *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseCbsrilu02_analysis(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

cusparseStatus_t 
cusparseZbsrilu02_analysis(cusparseHandle_t handle,
                           cusparseDirection_t dirA,
                           int mb,
                           int nnzb,
                           const cusparseMatDescr_t descrA,
                           cuDoubleComplex *bsrValA,
                           const int *bsrRowPtrA,
                           const int *bsrColIndA,
                           int blockDim,
                           bsrilu02Info_t info,
                           cusparseSolvePolicy_t policy,
                           void *pBuffer);

This function performs the analysis phase of the incomplete-LU factorization with 0 fill-in and no pivoting

A \approx L U

This function requires a buffer size returned by bsrilu02_bufferSize(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsrilu02_analysis() reports a structural zero and computes level information stored in the opaque structure info. The level information can extract more parallelism during incomplete LU factorization. However bsrilu02() can be done without level information. To disable level information, the user needs to specify the parameter policy of bsrilu02[_analysis| ] as CUSPARSE_SOLVE_POLICY_NO_LEVEL.

Function bsrilu02_analysis() always reports the first structural zero, even with parameter policy is CUSPARSE_SOLVE_POLICY_NO_LEVEL. The user must call cusparseXbsrilu02_zeroPivot() to know where the structural zero is.

It is the user's choice whether to call bsrilu02() if bsrilu02_analysis() reports a structural zero. In this case, the user can still call bsrilu02(), which will return a numerical zero at the same position as the structural zero. However the result is meaningless.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and block columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A, larger than zero.
`info`	structure initialized using `cusparseCreateBsrilu02Info()`.
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user, the size is returned by `bsrilu02_bufferSize()`.

Output

info

structure filled with information collected during the analysis phase (that should be passed to the solve phase unchanged).

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`); the base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparse<t>bsrilu02()

cusparseStatus_t 
cusparseSbsrilu02(cusparseHandle_t handle,
                  cusparseDirection_t dirA,
                  int mb,
                  int nnzb,
                  const cusparseMatDescr_t descry,
                  float *bsrValA,
                  const int *bsrRowPtrA,
                  const int *bsrColIndA,
                  int blockDim,
                  bsrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseDbsrilu02(cusparseHandle_t handle,
                  cusparseDirection_t dirA,
                  int mb,
                  int nnzb,
                  const cusparseMatDescr_t descry,
                  double *bsrValA,
                  const int *bsrRowPtrA,
                  const int *bsrColIndA,
                  int blockDim,
                  bsrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseCbsrilu02(cusparseHandle_t handle,
                  cusparseDirection_t dirA,
                  int mb,
                  int nnzb,
                  const cusparseMatDescr_t descry,
                  cuComplex *bsrValA,
                  const int *bsrRowPtrA,
                  const int *bsrColIndA,
                  int blockDim,
                  bsrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

cusparseStatus_t 
cusparseZbsrilu02(cusparseHandle_t handle,
                  cusparseDirection_t dirA,
                  int mb,
                  int nnzb,
                  const cusparseMatDescr_t descry,
                  cuDoubleComplex *bsrValA,
                  const int *bsrRowPtrA,
                  const int *bsrColIndA,
                  int blockDim,
                  bsrilu02Info_t info,
                  cusparseSolvePolicy_t policy,
                  void *pBuffer);

This function performs the solve phase of the incomplete-LU factorization with 0 fill-in and no pivoting

A \approx L U

A is an (mb*blockDim)×(mb*blockDim) sparse matrix that is defined in BSR storage format by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA. The block in BSR format is of size blockDim*blockDim, stored as column-major or row-major determined by parameter dirA, which is either CUSPARSE_DIRECTION_COLUMN or CUSPARSE_DIRECTION_ROW. The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, and the fill mode and diagonal type are ignored. Function bsrilu02() supports an arbitrary blockDim.

This function requires a buffer size returned by bsrilu02_bufferSize(). The address of pBuffer must be a multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Although bsrilu02() can be used without level information, the user must be aware of consistency. If bsrilu02_analysis() is called with policy CUSPARSE_SOLVE_POLICY_USE_LEVEL, bsrilu02() can be run with or without levels. On the other hand, if bsrilu02_analysis() is called with CUSPARSE_SOLVE_POLICY_NO_LEVEL, bsrilu02() can only accept CUSPARSE_SOLVE_POLICY_NO_LEVEL; otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Function bsrilu02() has the same behavior as csrilu02(). That is, bsr2csr(bsrilu02(A)) = csrilu02(bsr2csr(A)). The numerical zero of csrilu02() means there exists some zero U(j,j). The numerical zero of bsrilu02() means there exists some block U(j,j) that is not invertible.

Function bsrilu02 reports the first numerical zero, including a structural zero. The user must call cusparseXbsrilu02_zeroPivot() to know where the numerical zero is.

For example, suppose A is a real m-by-m matrix where m=mb*blockDim. The following code solves precondition system M*y = x, where M is the product of LU factors L and U.

// Suppose that A is m x m sparse matrix represented by BSR format, 
// The number of block rows/columns is mb, and 
// the number of nonzero blocks is nnzb.
// Assumption:
// - handle is already created by cusparseCreate(),
// - (d_bsrRowPtr, d_bsrColInd, d_bsrVal) is BSR of A on device memory,
// - d_x is right hand side vector on device memory.
// - d_y is solution vector on device memory.
// - d_z is intermediate result on device memory.
// - d_x, d_y and d_z are of size m.
cusparseMatDescr_t descr_M = 0;
cusparseMatDescr_t descr_L = 0;
cusparseMatDescr_t descr_U = 0;
bsrilu02Info_t info_M = 0;
bsrsv2Info_t   info_L = 0;
bsrsv2Info_t   info_U = 0;
int pBufferSize_M;
int pBufferSize_L;
int pBufferSize_U;
int pBufferSize;
void *pBuffer = 0;
int structural_zero;
int numerical_zero;
const double alpha = 1.;
const cusparseSolvePolicy_t policy_M = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_L = CUSPARSE_SOLVE_POLICY_NO_LEVEL;
const cusparseSolvePolicy_t policy_U = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
const cusparseOperation_t trans_L  = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseOperation_t trans_U  = CUSPARSE_OPERATION_NON_TRANSPOSE;
const cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;

// step 1: create a descriptor which contains
// - matrix M is base-1
// - matrix L is base-1
// - matrix L is lower triangular
// - matrix L has unit diagonal 
// - matrix U is base-1
// - matrix U is upper triangular
// - matrix U has non-unit diagonal
cusparseCreateMatDescr(&descr_M);
cusparseSetMatIndexBase(descr_M, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_M, CUSPARSE_MATRIX_TYPE_GENERAL);

cusparseCreateMatDescr(&descr_L);
cusparseSetMatIndexBase(descr_L, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_L, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_L, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descr_L, CUSPARSE_DIAG_TYPE_UNIT);

cusparseCreateMatDescr(&descr_U);
cusparseSetMatIndexBase(descr_U, CUSPARSE_INDEX_BASE_ONE);
cusparseSetMatType(descr_U, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatFillMode(descr_U, CUSPARSE_FILL_MODE_UPPER);
cusparseSetMatDiagType(descr_U, CUSPARSE_DIAG_TYPE_NON_UNIT);

// step 2: create a empty info structure
// we need one info for bsrilu02 and two info's for bsrsv2
cusparseCreateBsrilu02Info(&info_M);
cusparseCreateBsrsv2Info(&info_L);
cusparseCreateBsrsv2Info(&info_U);

// step 3: query how much memory used in bsrilu02 and bsrsv2, and allocate the buffer
cusparseDbsrilu02_bufferSize(handle, dir, mb, nnzb,
    descr_M, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, &pBufferSize_M);
cusparseDbsrsv2_bufferSize(handle, dir, trans_L, mb, nnzb, 
    descr_L, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_L, &pBufferSize_L);
cusparseDbsrsv2_bufferSize(handle, dir, trans_U, mb, nnzb, 
    descr_U, d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_U, &pBufferSize_U);

pBufferSize = max(pBufferSize_M, max(pBufferSize_L, pBufferSize_U));

// pBuffer returned by cudaMalloc is automatically aligned to 128 bytes.
cudaMalloc((void**)&pBuffer, pBufferSize);

// step 4: perform analysis of incomplete LU factorization on M
//         perform analysis of triangular solve on L
//         perform analysis of triangular solve on U 
// The lower(upper) triangular part of M has the same sparsity pattern as L(U), 
// we can do analysis of bsrilu0 and bsrsv2 simultaneously.

cusparseDbsrilu02_analysis(handle, dir, mb, nnzb, descr_M,
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, 
    policy_M, pBuffer);
status = cusparseXbsrilu02_zeroPivot(handle, info_M, &structural_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == statuss){
   printf("A(%d,%d) is missing\n", structural_zero, structural_zero);
}

cusparseDbsrsv2_analysis(handle, dir, trans_L, mb, nnzb, descr_L, 
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim,
    info_L, policy_L, pBuffer);

cusparseDbsrsv2_analysis(handle, dir, trans_U, mb, nnzb, descr_U, 
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim,
    info_U, policy_U, pBuffer);

// step 5: M = L * U
cusparseDbsrilu02(handle, dir, mb, nnzb, descr_M,
    d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_M, policy_M, pBuffer);
status = cusparseXbsrilu02_zeroPivot(handle, info_M, &numerical_zero);
if (CUSPARSE_STATUS_ZERO_PIVOT == statuss){
   printf("block U(%d,%d) is not invertible\n", numerical_zero, numerical_zero);
}
 
// step 6: solve L*z = x
cusparseDbsrsv2_solve(handle, dir, trans_L, mb, nnzb, &alpha, descr_L,
   d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_L,
   d_x, d_z, policy_L, pBuffer);

// step 7: solve U*y = z
cusparseDbsrsv2_solve(handle, dir, trans_U, mb, nnzb, &alpha, descr_U,
   d_bsrVal, d_bsrRowPtr, d_bsrColInd, blockDim, info_U,
   d_z, d_y, policy_U, pBuffer);

// step 6: free resources
cudaFree(pBuffer);
cusparseDestroyMatDescr(descr_M);
cusparseDestroyMatDescr(descr_L);
cusparseDestroyMatDescr(descr_U);
cusparseDestroyBsrilu02Info(info_M);
cusparseDestroyBsrsv2Info(info_L);
cusparseDestroyBsrsv2Info(info_U);
cusparseDestroy(handle);

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	storage format of blocks: either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows and block columns of matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ nonzero blocks of matrix `A`.
`bsrRowPtrA`	integer array of `mb` $+ 1$ elements that contains the start of every block row and the end of the last block row plus one.
`bsrColIndA`	integer array of `nnzb` $(=$ `bsrRowPtrA(mb)` $-$ `bsrRowPtrA(0)` $)$ column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix A; must be larger than zero.
`info`	structure with information collected during the analysis phase (that should have been passed to the solve phase unchanged).
`policy`	the supported policies are `CUSPARSE_SOLVE_POLICY_NO_LEVEL` and `CUSPARSE_SOLVE_POLICY_USE_LEVEL`.
`pBuffer`	buffer allocated by the user; the size is returned by `bsrilu02_bufferSize()`.

Output

bsrValA

<type> matrix containing the incomplete-LU lower and upper triangular factors.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nnzb<=0`); the base index is not 0 or 1.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device only supports compute capability 2.0 and above.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

cusparseXbsrilu02_zeroPivot()

cusparseStatus_t 
cusparseXbsrilu02_zeroPivot(cusparseHandle_t handle,
                            bsrilu02Info_t info,
                            int *position);

If the returned error code is CUSPARSE_STATUS_ZERO_PIVOT, position=j means A(j,j) has either a structural zero or a numerical zero (the block is not invertible). Otherwise position=-1.

The position can be 0-based or 1-based, the same as the matrix.

Function cusparseXbsrilu02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done.

The position can be in the host memory or device memory. The user can set proper the mode with cusparseSetPointerMode().

Input

`handle`	handle to the cuSPARSE library context.
`info`	`info` contains structural zero or numerical zero if the user already called `bsrilu02_analysis()` or `bsrilu02()`.

Output

position

if no structural or numerical zero, position is -1; otherwise if A(j,j) is missing or U(j,j) is not invertible, position=j.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`info` is not valid.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.22. cusparse<t>gtsv()

cusparseStatus_t 
cusparseSgtsv(cusparseHandle_t handle, 
              int m, 
              int n,        
              const float *dl, 
              const float  *d,   
              const float *du, 
              float *B, 
              int ldb)                                
cusparseStatus_t
cusparseDgtsv(cusparseHandle_t handle, 
              int m, 
              int n,       
              const double *dl, 
              const double  *d,   
              const double *du, 
              double *B, 
              int ldb)
cusparseStatus_t 
cusparseCgtsv(cusparseHandle_t handle, 
              int m, 
              int n,       
              const cuComplex *dl, 
              const cuComplex  *d,  
              const cuComplex *du, 
              cuComplex *B, 
              int ldb)
cusparseStatus_t 
cusparseZgtsv(cusparseHandle_t handle, 
              int m, 
              int n,       
              const cuDoubleComplex *dl, 
              const cuDoubleComplex  *d,  
              const cuDoubleComplex *du, 
              cuDoubleComplex *B, 
              int ldb)

This function computes the solution of a tridiagonal linear system with multiple right-hand sides:

A * Y = α * X

The coefficient matrix A of each of these tri-diagonal linear system is defined with three vectors corresponding to its lower (dl), main (d), and upper (du) matrix diagonals; the right-hand sides are stored in the dense matrix X. Notice that solution Y overwrites right-hand-side matrix X on exit.

Assuming A is of size m and base-1, dl, d and du are defined by the following formula:

dl(i) := A(i, i-1) for i=1,2,...,m

The first element of dl is out-of-bound (dl(1) := A(1,0)), so dl(1) = 0.

d(i) = A(i,i) for i=1,2,...,m

du(i) = A(i,i+1) for i=1,2,...,m

The last element of du is out-of-bound (du(m) := A(m,m+1)), so du(m) = 0.

The routine does perform pivoting, which usually results in more accurate and more stable results than cusparse<t>gtsv_nopivot() at the expense of some execution time

This routine requires significant amount of temporary extra storage (min(m,8) ×(3+n)×sizeof(<type>)). The temporary storage is managed by cudaMalloc and cudaFree which stop concurrency. The user can call cusparse<t>gtsv2() which has no explicit cudaMalloc and cudaFree.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B` (that is ≥ $max (1, m))$ .

Output

`B`	<type> dense solution array of dimensions `(ldb, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.23. cusparse<t>gtsv_nopivot()

cusparseStatus_t 
cusparseSgtsv_nopivot(cusparseHandle_t handle, int m, int n,        
              const float           *dl, const float            *d,   
              const float           *du, float *B, int ldb)                                
cusparseStatus_t
cusparseDgtsv_nopivot(cusparseHandle_t handle, int m, int n,       
              const double          *dl, const double           *d,   
              const double          *du, double *B, int ldb)
cusparseStatus_t 
cusparseCgtsv_nopivot(cusparseHandle_t handle, int m, int n,       
              const cuComplex       *dl, const cuComplex        *d,  
              const cuComplex       *du, cuComplex       *B, int ldb)
cusparseStatus_t 
cusparseZgtsv_nopivot(cusparseHandle_t handle, int m, int n,       
              const cuDoubleComplex *dl, const cuDoubleComplex  *d,  
              const cuDoubleComplex *du, cuDoubleComplex *B, int ldb)

This function computes the solution of a tridiagonal linear system with multiple right-hand sides:

A * Y = α * X

The routine does not perform any pivoting and uses a combination of the Cyclic Reduction (CR) and the Parallel Cyclic Reduction (PCR) algorithms to find the solution. It achieves better performance when m is a power of 2.

This routine requires a significant amount of temporary extra storage (m×(3+n)×sizeof(<type>)). The temporary storage is managed by cudaMalloc and cudaFree which stop concurrency. The user can call cusparse<t>gtsv2_nopivot() which has no explicit cudaMalloc and cudaFree.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B`. (that is ≥ $max (1, m))$ .

Output

`B`	<type> dense solution array of dimensions `(ldb, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.24. cusparse<t>gtsvStridedBatch()

cusparseStatus_t 
cusparseSgtsvStridedBatch(cusparseHandle_t handle, int m,              
                          const float           *dl, 
                          const float            *d,   
                          const float           *du, float           *x,    
                          int batchCount, int batchStride)
cusparseStatus_t
cusparseDgtsvStridedBatch(cusparseHandle_t handle, int m,             
                          const double          *dl, 
                          const double           *d,   
                          const double          *du, double          *x,    
                          int batchCount, int batchStride)                                                                 
cusparseStatus_t 
cusparseCgtsvStridedBatch(cusparseHandle_t handle, int m,           
                          const cuComplex       *dl, 
                          const cuComplex        *d,  
                          const cuComplex       *du, cuComplex       *x,     
                          int batchCount, int batchStride)
cusparseStatus_t 
cusparseZgtsvStridedBatch(cusparseHandle_t handle, int m,         
                          const cuDoubleComplex *dl, 
                          const cuDoubleComplex  *d,  
                          const cuDoubleComplex *du, cuDoubleComplex *x,     
                          int batchCount, int batchStride)

This function computes the solution of multiple tridiagonal linear systems for i=0,…,batchCount:

A^{(i)} * y^{(i)} = α * x^{(i)}

This routine requires a significant amount of temporary extra storage ((batchCount×(4×m+2048)×sizeof(<type>))). The temporary storage is managed by cudaMalloc and cudaFree which stop concurrency. The user can call cusparse<t>gtsv2StridedBatch() which has no explicit cudaMalloc and cudaFree.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The lower diagonal $d l^{(i)}$ that corresponds to the i^th linear system starts at location `dl+batchStride×i` in memory. Also, the first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system. The main diagonal $d^{(i)}$ that corresponds to the i^th linear system starts at location `d+batchStride×i` in memory.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The upper diagonal $d u^{(i)}$ that corresponds to the i^th linear system starts at location `du+batchStride×i` in memory. Also, the last element of each upper diagonal must be zero.
`x`	<type> dense array that contains the right-hand-side of the tri-diagonal linear system. The right-hand-side $x^{(i)}$ that corresponds to the i^th linear system starts at location `x+batchStride×i`in memory.
`batchCount`	number of systems to solve.
`batchStride`	stride (number of elements) that separates the vectors of every system (must be at least `m`).

Output

`x`	<type> dense array that contains the solution of the tri-diagonal linear system. The solution $x^{(i)}$ that corresponds to the i^th linear system starts at location `x+batchStride×i`in memory.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, batchCount≤0, batchStride<m`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.25. cusparse<t>gtsv2_buffSizeExt()


cusparseStatus_t cusparseSgtsv2_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const float *dl,  
    const float  *d,    
    const float *du, 
    const float *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseDgtsv2_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const double *dl,  
    const double  *d,    
    const double *du, 
    const double *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseCgtsv2_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuComplex *dl,  
    const cuComplex  *d,    
    const cuComplex *du, 
    const cuComplex *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseZgtsv2_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuDoubleComplex *dl,  
    const cuDoubleComplex  *d,    
    const cuDoubleComplex *du, 
    const cuDoubleComplex *B,     
    int ldb,
    size_t *bufferSizeInBytes)

This function returns the size of the buffer used in gtsv2 which computes the solution of a tridiagonal linear system with multiple right-hand sides.

A * X = α * B

The coefficient matrix A of each of these tri-diagonal linear system is defined with three vectors corresponding to its lower (dl), main (d), and upper (du) matrix diagonals; the right-hand sides are stored in the dense matrix B. Notice that solution X overwrites right-hand-side matrix B on exit.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B` (that is ≥ $max (1, m))$ .

Output

pBufferSizeInBytes

number of bytes of the buffer used in the gtsv2.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.26. cusparse<t>gtsv2()


cusparseStatus_t cusparseSgtsv2(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const float *dl,  
    const float  *d,    
    const float *du, 
    float *B,     
    int ldb,
    void *pBuffer)

cusparseStatus_t cusparseDgtsv2(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const double *dl,  
    const double  *d,    
    const double *du, 
    double *B,     
    int ldb,
    void *pBuffer)

cusparseStatus_t cusparseCgtsv2(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuComplex *dl,  
    const cuComplex  *d,    
    const cuComplex *du, 
    cuComplex *B,     
    int ldb,
    void *pBuffer)

cusparseStatus_t cusparseZgtsv2(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuDoubleComplex *dl,  
    const cuDoubleComplex  *d,    
    const cuDoubleComplex *du, 
    cuDoubleComplex *B,     
    int ldb,
    void *pBuffer)

This function computes the solution of a tridiagonal linear system with multiple right-hand sides:

A * X = α * B

The coefficient matrix A of each of these tri-diagonal linear system is defined with three vectors corresponding to its lower (dl), main (d), and upper (du) matrix diagonals; the right-hand sides are stored in the dense matrix B. Notice that solution X overwrites right-hand-side matrix B on exit.

Assuming A is of size m and base-1, dl, d and du are defined by the following formula:

dl(i) := A(i, i-1) for i=1,2,...,m

The first element of dl is out-of-bound (dl(1) := A(1,0)), so dl(1) = 0.

d(i) = A(i,i) for i=1,2,...,m

du(i) = A(i,i+1) for i=1,2,...,m

The last element of du is out-of-bound (du(m) := A(m,m+1)), so du(m) = 0.

The routine does perform pivoting, which usually results in more accurate and more stable results than cusparse<t>gtsv_nopivot() or cusparse<t>gtsv2_nopivot() at the expense of some execution time.

This function requires a buffer size returned by gtsv2_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B` (that is ≥ $max (1, m))$ .
`pBuffer`	buffer allocated by the user, the size is return by `gtsv2_bufferSizeExt`.

Output

`B`	<type> dense solution array of dimensions `(ldb, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.27. cusparse<t>gtsv2_nopivot_bufferSizeExt()


cusparseStatus_t cusparseSgtsv2_nopivot_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const float *dl,  
    const float  *d,    
    const float *du, 
    const float *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseDgtsv2_nopivot_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const double *dl,  
    const double  *d,    
    const double *du, 
    const double *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseCgtsv2_nopivot_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuComplex *dl,  
    const cuComplex  *d,    
    const cuComplex *du, 
    const cuComplex *B,     
    int ldb,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseZgtsv2_nopivot_bufferSizeExt(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuDoubleComplex *dl,  
    const cuDoubleComplex  *d,    
    const cuDoubleComplex *du, 
    const cuDoubleComplex *B,     
    int ldb,
    size_t *bufferSizeInBytes)

This function returns the size of the buffer used in gtsv2_nopivot which computes the solution of a tridiagonal linear system with multiple right-hand sides.

A * X = α * B

The coefficient matrix A of each of these tri-diagonal linear system is defined with three vectors corresponding to its lower (dl), main (d), and upper (du) matrix diagonals; the right-hand sides are stored in the dense matrix B. Notice that solution X overwrites right-hand-side matrix B on exit.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B`. (that is ≥ $max (1, m))$ .

Output

pBufferSizeInBytes

number of bytes of the buffer used in the gtsv2_nopivot.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.28. cusparse<t>gtsv2_nopivot()


cusparseStatus_t cusparseSgtsv2_nopivot(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const float *dl,  
    const float  *d,   
    const float *du, 
    float *B,     
    int ldb,
    void* pBuffer)

cusparseStatus_t cusparseDgtsv2_nopivot(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const double *dl,  
    const double  *d,    
    const double *du, 
    double *B,     
    int ldb,
    void* pBuffer)

cusparseStatus_t cusparseCgtsv2_nopivot(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuComplex *dl,  
    const cuComplex  *d,    
    const cuComplex *du, 
    cuComplex *B,     
    int ldb,
    void* pBuffer)

cusparseStatus_t cusparseZgtsv2_nopivot(
    cusparseHandle_t handle,
    int m,        
    int n,        
    const cuDoubleComplex *dl,  
    const cuDoubleComplex  *d,    
    const cuDoubleComplex *du, 
    cuDoubleComplex *B,     
    int ldb,
    void* pBuffer)

This function computes the solution of a tridiagonal linear system with multiple right-hand sides:

A * X = α * B

The coefficient matrix A of each of these tri-diagonal linear system is defined with three vectors corresponding to its lower (dl), main (d), and upper (du) matrix diagonals; the right-hand sides are stored in the dense matrix B. Notice that solution X overwrites right-hand-side matrix B on exit.

This function requires a buffer size returned by gtsv2_nopivot_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Input

`handle`	handle to the cuSPARSE library context.
`m`	the size of the linear system (must be ≥ 3).
`n`	number of right-hand sides, columns of matrix `B`.
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The last element of each upper diagonal must be zero.
`B`	<type> dense right-hand-side array of dimensions `(ldb, n)`.
`ldb`	leading dimension of `B`. (that is ≥ $max (1, m))$ .
`pBuffer`	buffer allocated by the user, the size is return by `gtsv2_nopivot_bufferSizeExt`.

Output

`B`	<type> dense solution array of dimensions `(ldb, n)`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

10.29. cusparse<t>gtsv2StridedBatch_bufferSizeExt()


cusparseStatus_t cusparseSgtsv2StridedBatch_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    const float *dl,
    const float  *d,
    const float *du,
    const float *x,
    int batchCount,
    int batchStride,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseDgtsv2StridedBatch_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    const double *dl,
    const double  *d,
    const double *du,
    const double *x,
    int batchCount,
    int batchStride,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseCgtsv2StridedBatch_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    const cuComplex *dl,
    const cuComplex  *d,
    const cuComplex *du,
    const cuComplex *x,
    int batchCount,
    int batchStride,
    size_t *bufferSizeInBytes)

cusparseStatus_t cusparseZgtsv2StridedBatch_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    const cuDoubleComplex *dl,
    const cuDoubleComplex  *d,
    const cuDoubleComplex *du,
    const cuDoubleComplex *x,
    int batchCount,
    int batchStride,
    size_t *bufferSizeInBytes)

This function returns the size of the buffer used in gtsv2StridedBatch which computes the solution of multiple tridiagonal linear systems for i=0,…,batchCount:

A^{(i)} * y^{(i)} = α * x^{(i)}

Input

`handle`	handle to the cuSPARSE library context.
`n`	the size of the linear system (must be ≥ 3).
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The lower diagonal $d l^{(i)}$ that corresponds to the i^th linear system starts at location `dl+batchStride×i` in memory. Also, the first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system. The main diagonal $d^{(i)}$ that corresponds to the i^th linear system starts at location `d+batchStride×i` in memory.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The upper diagonal $d u^{(i)}$ that corresponds to the i^th linear system starts at location `du+batchStride×i` in memory. Also, the last element of each upper diagonal must be zero.
`x`	<type> dense array that contains the right-hand-side of the tri-diagonal linear system. The right-hand-side $x^{(i)}$ that corresponds to the i^th linear system starts at location `x+batchStride×i`in memory.
`batchCount`	number of systems to solve.
`batchStride`	stride (number of elements) that separates the vectors of every system (must be at least `m`).

Output

pBufferSizeInBytes

number of bytes of the buffer used in the gtsv2StridedBatch.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, batchCount≤0, batchStride<m`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

10.30. cusparse<t>gtsv2StridedBatch()


cusparseStatus_t cusparseSgtsv2StridedBatch(
    cusparseHandle_t handle,
    int m,
    const float *dl,
    const float  *d,
    const float *du,
    float *x,
    int batchCount,
    int batchStride,
    void *pBuffer)

cusparseStatus_t cusparseDgtsv2StridedBatch(
    cusparseHandle_t handle,
    int m,
    const double *dl,
    const double  *d,
    const double *du,
    double *x,
    int batchCount,
    int batchStride,
    void *pBuffer)

cusparseStatus_t cusparseCgtsv2StridedBatch(
    cusparseHandle_t handle,
    int m,
    const cuComplex *dl,
    const cuComplex  *d,
    const cuComplex *du,
    cuComplex *x,
    int batchCount,
    int batchStride,
    void *pBuffer)

cusparseStatus_t cusparseZgtsv2StridedBatch(
    cusparseHandle_t handle,
    int m,
    const cuDoubleComplex *dl,
    const cuDoubleComplex  *d,
    const cuDoubleComplex *du,
    cuDoubleComplex *x,
    int batchCount,
    int batchStride,
    void *pBuffer)

This function computes the solution of multiple tridiagonal linear systems for i=0,…,batchCount:

A^{(i)} * y^{(i)} = α * x^{(i)}

This function requires a buffer size returned by gtsv2StridedBatch_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If it is not, CUSPARSE_STATUS_INVALID_VALUE is returned.

Input

`handle`	handle to the cuSPARSE library context.
`n`	the size of the linear system (must be ≥ 3).
`dl`	<type> dense array containing the lower diagonal of the tri-diagonal linear system. The lower diagonal $d l^{(i)}$ that corresponds to the i^th linear system starts at location `dl+batchStride×i` in memory. Also, the first element of each lower diagonal must be zero.
`d`	<type> dense array containing the main diagonal of the tri-diagonal linear system. The main diagonal $d^{(i)}$ that corresponds to the i^th linear system starts at location `d+batchStride×i` in memory.
`du`	<type> dense array containing the upper diagonal of the tri-diagonal linear system. The upper diagonal $d u^{(i)}$ that corresponds to the i^th linear system starts at location `du+batchStride×i` in memory. Also, the last element of each upper diagonal must be zero.
`x`	<type> dense array that contains the right-hand-side of the tri-diagonal linear system. The right-hand-side $x^{(i)}$ that corresponds to the i^th linear system starts at location `x+batchStride×i`in memory.
`batchCount`	number of systems to solve.
`batchStride`	stride (number of elements) that separates the vectors of every system (must be at least `n`).
`pBuffer`	buffer allocated by the user, the size is return by `gtsv2StridedBatch_bufferSizeExt`.

Output

`x`	<type> dense array that contains the solution of the tri-diagonal linear system. The solution $x^{(i)}$ that corresponds to the i^th linear system starts at location `x+batchStride×i`in memory.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m<3, batchCount≤0, batchStride<m`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

11. cuSPARSE Reorderings Reference

This chapter describes the reordering routines used to manipulate sparse matrices.

cusparse<t>csrcolor()

cusparseStatus_t 
cusparseScsrcolor(cusparseHandle_t handle, int m, int nnz, 
             const cusparseMatDescr_t descrA, const float *csrValA, 
             const int *csrRowPtrA, const int *csrColIndA,
             const float *fractionToColor, int *ncolors, int *coloring, 
             int *reordering,cusparseColorInfo_t info);

cusparseStatus_t 
cusparseDcsrcolor(cusparseHandle_t handle, int m, int nnz, 
             const cusparseMatDescr_t descrA, const double *csrValA, 
             const int *csrRowPtrA, const int *csrColIndA,
             const double *fractionToColor,int *ncolors, int *coloring, 
             int *reordering, cusparseColorInfo_t info);

cusparseStatus_t 
cusparseCcsrcolor(cusparseHandle_t handle, int m, int nnz, 
             const cusparseMatDescr_t descrA, const cuComplex *csrValA, 
             const int *csrRowPtrA, const int *csrColIndA,
             const float *fractionToColor, int *ncolors, int *coloring, 
             int *reordering, cusparseColorInfo_t info);

cusparseStatus_t 
cusparseZcsrcolor(cusparseHandle_t handle, int m, int nnz, 
       const cusparseMatDescr_t descrA, const cuDoubleComplex *csrValA, 
             const int *csrRowPtrA, const int *csrColIndA,
             const double *fractionToColor,int *ncolors, int *coloring, 
             int *reordering, cusparseColorInfo_t info);

This function performs the coloring of the adjacency graph associated with the matrix A stored in CSR format. The coloring is an assignment of colors (integer numbers) to nodes, such that neighboring nodes have distinct colors. An approximate coloring algorithm is used in this routine, and is stopped when a certain percentage of nodes has been colored. The rest of the nodes are assigned distinct colors (an increasing sequence of integers numbers, starting from the last integer used previously). The last two auxiliary routines can be used to extract the resulting number of colors, their assignment and the associated reordering. The reordering is such that nodes that have been assigned the same color are reordered to be next to each other.

The matrix A passed to this routine, must be stored as a general matrix and have a symmetric sparsity pattern. If the matrix is nonsymmetric the user should pass A+A^T as a parameter to this routine.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`nnz`	number of nonzero elements of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`fractionToColor`	fraction of nodes to be colored, which should be in the interval [0.0,1.0], for example 0.8 implies that 80 percent of nodes will be colored.
`info`	structure with information to be passed to the coloring.

Output

`ncolors`	The number of distinct colors used (at most the size of the matrix, but likely much smaller).
`coloring`	The resulting coloring permutation
`reordering`	The resulting reordering permutation (untouched if NULL)

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision (compute capability (c.c.) >= 1.3 required).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12. cuSPARSE Format Conversion Reference

This chapter describes the conversion routines between different sparse and dense storage formats.

coosort, csrsort, cscsort, csru2csr and csr2csc_indexOnly are sorting routines without malloc inside, the following table estimates the buffer size

`routine`	`buffer size`	`maximum problem size if buffer is limited by 2GB`
`coosort`	`> 16*n bytes`	125M
`csrsort or cscsort`	`> 20*n bytes`	100M
`csru2csr`	`'d' > 28n bytes ; 'z' > 36n bytes`	71M for 'd' and 55M for 'z'
`csr2csc_indexOnly`	`> 16*n bytes`	125M

12.1. cusparse<t>bsr2csr()

cusparseStatus_t
cusparseSbsr2csr(cusparseHandle_t handle, 
    cusparseDirection_t dir,
    int mb, 
    int nb,
    const cusparseMatDescr_t descrA, 
    const float *bsrValA, 
    const int *bsrRowPtrA, 
    const int *bsrColIndA,
    int blockDim,
    const cusparseMatDescr_t descrC,
    float *csrValC, 
    int *csrRowPtrC, 
    int *csrColIndC)
cusparseStatus_t
cusparseDbsr2csr(cusparseHandle_t handle, 
    cusparseDirection_t dir,
    int mb, 
    int nb,
    const cusparseMatDescr_t descrA, 
    const double *bsrValA, 
    const int *bsrRowPtrA, 
    const int *bsrColIndA,
    int blockDim,
    const cusparseMatDescr_t descrC,
    double *csrValC, 
    int *csrRowPtrC, 
    int *csrColIndC)
cusparseStatus_t
cusparseCbsr2csr(cusparseHandle_t handle, 
    cusparseDirection_t dir,
    int mb, 
    int nb,
    const cusparseMatDescr_t descrA, 
    const cuComplex *bsrValA, 
    const int *bsrRowPtrA, 
    const int *bsrColIndA,
    int blockDim,
    const cusparseMatDescr_t descrC,
    cuComplex *csrValC, 
    int *csrRowPtrC, 
    int *csrColIndC)
cusparseStatus_t
cusparseZbsr2csr(cusparseHandle_t handle, 
    cusparseDirection_t dir,
    int mb, 
    int nb,
    const cusparseMatDescr_t descrA, 
    const cuDoubleComplex *bsrValA, 
    const int *bsrRowPtrA, 
    const int *bsrColIndA,
    int blockDim,
    const cusparseMatDescr_t descrC,
    cuDoubleComplex *csrValC, 
    int *csrRowPtrC, 
    int *csrColIndC)

This function converts a sparse matrix in BSR format that is defined by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA) into a sparse matrix in CSR format that is defined by arrays csrValC, csrRowPtrC, and csrColIndC.

Let m(=mb*blockDim) be the number of rows of A and n(=nb*blockDim) be number of columns of A, then A and C are m*n sparse matrices. The BSR format of A contains nnzb(=bsrRowPtrA[mb] - bsrRowPtrA[0]) nonzero blocks, whereas the sparse matrix A contains nnz(=nnzb*blockDim*blockDim) elements. The user must allocate enough space for arrays csrRowPtrC, csrColIndC, and csrValC. The requirements are as follows:

csrRowPtrC of m+1 elements

csrValC of nnz elements

csrColIndC of nnz elements

The general procedure is as follows:

// Given BSR format (bsrRowPtrA, bsrcolIndA, bsrValA) and 
// blocks of BSR format are stored in column-major order.
cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
int m = mb*blockDim;
int nnzb = bsrRowPtrA[mb] - bsrRowPtrA[0]; // number of blocks
int nnz  = nnzb * blockDim * blockDim; // number of elements
cudaMalloc((void**)&csrRowPtrC, sizeof(int)*(m+1));
cudaMalloc((void**)&csrColIndC, sizeof(int)*nnz);
cudaMalloc((void**)&csrValC, sizeof(float)*nnz);
cusparseSbsr2csr(handle, dir, mb, nb,
        descrA, 
        bsrValA, bsrRowPtrA, bsrColIndA,
        blockDim,
        descrC,
        csrValC, csrRowPtrC, csrColIndC);

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`descrA`	the descriptor of matrix `A`.
`bsrValA`	<type> array of `nnzbblockDimblockDim` nonzero elements of matrix `A`.
`bsrRowPtrA`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `A`.
`bsrColIndA`	integer array of `nnzb` column indices of the nonzero blocks of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`.
`descrC`	the descriptor of matrix `C`.

Output

`csrValC`	<type> array of `nnz(=csrRowPtrC[m]-csrRowPtrC[0])` nonzero elements of matrix `C`.
`csrRowPtrC`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one of matrix `C`.
`csrColIndC`	integer array of `nnz` column indices of the nonzero elements of matrix `C`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nb<0`, `IndexBase` of `descrA, descrC` is not base-0 or base-1, `dir` is not row-major or column-major, or `blockDim`<1).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.2. cusparse<t>gebsr2gebsc_bufferSize()

cusparseStatus_t 
cusparseSgebsr2gebsc_bufferSize(cusparseHandle_t handle,
    int mb,
    int nb,
    int nnzb,
    const float *bsrVal,
    const int *bsrRowPtr,
    const int *bsrColInd,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseDgebsr2gebsc_bufferSize(cusparseHandle_t handle,
    int mb,
    int nb,
    int nnzb,
    const double *bsrVal,
    const int *bsrRowPtr,
    const int *bsrColInd,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseCgebsr2gebsc_bufferSize(cusparseHandle_t handle,
    int mb,
    int nb,
    int nnzb,
    const cuComplex *bsrVal,
    const int *bsrRowPtr,
    const int *bsrColInd,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseZgebsr2gebsc_bufferSize(cusparseHandle_t handle,
    int mb,
    int nb,
    int nnzb,
    const cuDoubleComplex *bsrVal,
    const int *bsrRowPtr,
    const int *bsrColInd,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

This function returns size of buffer used in computing gebsr2gebsc().

Input

`handle`	handle to the cuSPARSE library context.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`bsrVal`	<type> array of `nnzbrowBlockDimcolBlockDim` non-zero elements of matrix `A`.
`bsrRowPtr`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one.
`bsrColInd`	integer array of `nnzb` column indices of the non-zero blocks of matrix `A`.
`rowBlockDim`	number of rows within a block of `A`.
`colBlockDim`	number of columns within a block of `A`.

Output

pBufferSize

host pointer containing number of bytes of the buffer used in gebsr2gebsc().

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb, nb, nnzb<0`, or `rowBlockDim`, `colBlockDim`<1).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.3. cusparse<t>gebsr2gebsc()

cusparseStatus_t
cusparseSgebsr2gebsc(cusparseHandle_t handle,
    int mb, 
    int nb, 
    int nnzb,
    const float *bsrVal, 
    const int *bsrRowPtr, 
    const int *bsrColInd,
    int rowBlockDim, 
    int colBlockDim,
    float *bscVal, 
    int *bscRowInd, 
    int *bscColPtr,
    cusparseAction_t copyValues, 
    cusparseIndexBase_t baseIdx,
    void *pBuffer)

cusparseStatus_t
cusparseDgebsr2gebsc(cusparseHandle_t handle,
    int mb, 
    int nb, 
    int nnzb,
    const double *bsrVal, 
    const int *bsrRowPtr, 
    const int *bsrColInd,
    int rowBlockDim, 
    int colBlockDim,
    double *bscVal, 
    int *bscRowInd, 
    int *bscColPtr,
    cusparseAction_t copyValues, 
    cusparseIndexBase_t baseIdx,
    void *pBuffer)

cusparseStatus_t
cusparseCgebsr2gebsc(cusparseHandle_t handle,
    int mb, 
    int nb, 
    int nnzb,
    const cuComplex *bsrVal, 
    const int *bsrRowPtr, 
    const int *bsrColInd,
    int rowBlockDim, 
    int colBlockDim,
    cuComplex *bscVal, 
    int *bscRowInd, 
    int *bscColPtr,
    cusparseAction_t copyValues,
    cusparseIndexBase_t baseIdx,
    void *pBuffer)

cusparseStatus_t
cusparseZgebsr2gebsc(cusparseHandle_t handle,
    int mb, 
    int nb, 
    int nnzb,
    const cuDoubleComplex *bsrVal, 
    const int *bsrRowPtr, 
    const int *bsrColInd,
    int rowBlockDim, 
    int colBlockDim,
    cuDoubleComplex *bscVal, 
    int *bscRowInd, 
    int *bscColPtr,
    cusparseAction_t copyValues, 
    cusparseIndexBase_t baseIdx,
    void *pBuffer)

This function can be seen as the same as csr2csc() when each block of size rowBlockDim*colBlockDim is regarded as a scalar.

This sparsity pattern of the result matrix can also be seen as the transpose of the original sparse matrix, but the memory layout of a block does not change.

The user must call gebsr2gebsc_bufferSize() to determine the size of the buffer required by gebsr2gebsc(), allocate the buffer, and pass the buffer pointer to gebsr2gebsc().

Input

`handle`	handle to the cuSPARSE library context.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`bsrVal`	<type> array of `nnzbrowBlockDimcolBlockDim` nonzero elements of matrix `A`.
`bsrRowPtr`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one.
`bsrColInd`	integer array of `nnzb` column indices of the non-zero blocks of matrix `A`.
`rowBlockDim`	number of rows within a block of `A`.
`colBlockDim`	number of columns within a block of `A`.
`copyValues`	`CUSPARSE_ACTION_SYMBOLIC` or `CUSPARSE_ACTION_NUMERIC`.
`baseIdx`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.
`pBuffer`	buffer allocated by the user; the size is return by `gebsr2gebsc_bufferSize()`.

Output

`bscVal`	<type> array of `nnzbrowBlockDimcolBlockDim` non-zero elements of matrix `A`. It is only filled-in if `copyValues` is set to `CUSPARSE_ACTION_NUMERIC`.
`bscRowInd`	integer array of `nnzb` row indices of the non-zero blocks of matrix `A`.
`bscColPtr`	integer array of `nb+1` elements that contains the start of every block column and the end of the last block column plus one.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb,nb,nnzb<0`, `baseIdx` is not base-0 or base-1, or `rowBlockDim`, `colBlockDim`<1).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.4. cusparse<t>gebsr2gebsr_bufferSize()

cusparseStatus_t 
cusparseSgebsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const float *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    int rowBlockDimC,
    int colBlockDimC,
    int *pBufferSize )

cusparseStatus_t 
cusparseDgebsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const double *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    int rowBlockDimC,
    int colBlockDimC,
    int *pBufferSize )

cusparseStatus_t 
cusparseCgebsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const cuComplex *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    int rowBlockDimC,
    int colBlockDimC,
    int *pBufferSize )

cusparseStatus_t 
cusparseZgebsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const cuDoubleComplex *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    int rowBlockDimC,
    int colBlockDimC,
    int *pBufferSize )

This function returns size of the buffer used in computing gebsr2gebsrNnz() and gebsr2gebsr().

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzbrowBlockDimAcolBlockDimA` non-zero elements of matrix `A`.
`bsrRowPtrA`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `A`.
`bsrColIndA`	integer array of `nnzb` column indices of the nonzero blocks of matrix `A`.
`rowBlockDimA`	number of rows within a block of `A`.
`colBlockDimA`	number of columns within a block of `A`.
`rowBlockDimC`	number of rows within a block of `C`.
`colBlockDimC`	number of columns within a block of `C`

Output

pBufferSize

host pointer containing number of bytes of the buffer used in gebsr2gebsr().

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb, nb, nnzb<0`; or `rowBlockDimA`, `colBlockDimA`, `rowBlockDimC`, `colBlockDimC`<1).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.5. cusparse<t>gebsr2gebsr()

cusparseStatus_t
cusparseXgebsr2gebsrNnz(cusparseHandle_t handle, 
    cusparseDirection_t dir,
    int mb, 
    int nb, 
    int nnzb,
    const cusparseMatDescr_t descrA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    const cusparseMatDescr_t descrC,
    int *bsrRowPtrC,
    int rowBlockDimC,
    int colBlockDimC,
    int *nnzTotalDevHostPtr,
    void *pBuffer)

cusparseStatus_t
cusparseSgebsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const float *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    const cusparseMatDescr_t descrC,
    float *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDimC,
    int colBlockDimC,
    void *pBuffer)

cusparseStatus_t
cusparseDgebsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const double *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    const cusparseMatDescr_t descrC,
    double *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDimC,
    int colBlockDimC,
    void *pBuffer)

cusparseStatus_t
cusparseCgebsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const cuComplex *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    const cusparseMatDescr_t descrC,
    cuComplex *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDimC,
    int colBlockDimC,
    void *pBuffer)

cusparseStatus_t
cusparseZgebsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    int nnzb,
    const cusparseMatDescr_t descrA,
    const cuDoubleComplex *bsrValA,
    const int *bsrRowPtrA,
    const int *bsrColIndA,
    int rowBlockDimA,
    int colBlockDimA,
    const cusparseMatDescr_t descrC,
    cuDoubleComplex *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDimC,
    int colBlockDimC,
    void *pBuffer)

This function converts a sparse matrix in general BSR format that is defined by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA into a sparse matrix in another general BSR format that is defined by arrays bsrValC, bsrRowPtrC, and bsrColIndC.

If rowBlockDimA=1 and colBlockDimA=1, cusparse[S|D|C|Z]gebsr2gebsr() is the same as cusparse[S|D|C|Z]csr2gebsr().

If rowBlockDimC=1 and colBlockDimC=1, cusparse[S|D|C|Z]gebsr2gebsr() is the same as cusparse[S|D|C|Z]gebsr2csr().

A is an m*n sparse matrix where m(=mb*rowBlockDim) is the number of rows of A, and n(=nb*colBlockDim) is the number of columns of A. The general BSR format of A contains nnzb(=bsrRowPtrA[mb] - bsrRowPtrA[0]) nonzero blocks. The matrix C is also general BSR format with a different block size, rowBlockDimC*colBlockDimC. If m is not a multiple of rowBlockDimC, or n is not a multiple of colBlockDimC, zeros are filled in. The number of block rows of C is mc(=(m+rowBlockDimC-1)/rowBlockDimC). The number of block rows of C is nc(=(n+colBlockDimC-1)/colBlockDimC). The number of nonzero blocks of C is nnzc.

The implementation adopts a two-step approach to do the conversion. First, the user allocates bsrRowPtrC of mc+1 elements and uses function cusparseXgebsr2gebsrNnz() to determine the number of nonzero block columns per block row of matrix C. Second, the user gathers nnzc (number of non-zero block columns of matrix C) from either (nnzc=*nnzTotalDevHostPtr) or (nnzc=bsrRowPtrC[mc]-bsrRowPtrC[0]) and allocates bsrValC of nnzc*rowBlockDimC*colBlockDimC elements and bsrColIndC of nnzc integers. Finally the function cusparse[S|D|C|Z]gebsr2gebsr() is called to complete the conversion.

The user must call gebsr2gebsr_bufferSize() to know the size of the buffer required by gebsr2gebsr(), allocate the buffer, and pass the buffer pointer to gebsr2gebsr().

The general procedure is as follows:

// Given general BSR format (bsrRowPtrA, bsrColIndA, bsrValA) and 
// blocks of BSR format are stored in column-major order.
cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
int base, nnzc;
int m = mb*rowBlockDimA;
int n = nb*colBlockDimA;
int mc = (m+rowBlockDimC-1)/rowBlockDimC;
int nc = (n+colBlockDimC-1)/colBlockDimC;
int bufferSize;
void *pBuffer;
cusparseSgebsr2gebsr_bufferSize(handle, dir, mb, nb, nnzb,
    descrA, bsrValA, bsrRowPtrA, bsrColIndA,
    rowBlockDimA, colBlockDimA,
    rowBlockDimC, colBlockDimC,
    &bufferSize);
cudaMalloc((void**)&pBuffer, bufferSize);
cudaMalloc((void**)&bsrRowPtrC, sizeof(int)*(mc+1));
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzc;
cusparseXgebsr2gebsrNnz(handle, dir, mb, nb, nnzb,
    descrA, bsrRowPtrA, bsrColIndA,
    rowBlockDimA, colBlockDimA,
    descrC, bsrRowPtrC,
    rowBlockDimC, colBlockDimC,
    nnzTotalDevHostPtr, 
    pBuffer);
if (NULL != nnzTotalDevHostPtr){
    nnzc = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzc, bsrRowPtrC+mc, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&base, bsrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzc -= base;
}
cudaMalloc((void**)&bsrColIndC, sizeof(int)*nnzc);
cudaMalloc((void**)&bsrValC, sizeof(float)*(rowBlockDimC*colBlockDimC)*nnzc);
cusparseSgebsr2gebsr(handle, dir, mb, nb, nnzb,
    descrA, bsrValA, bsrRowPtrA, bsrColIndA,
    rowBlockDimA, colBlockDimA,
    descrC, bsrValC, bsrRowPtrC, bsrColIndC,
    rowBlockDimC, colBlockDimC,
    pBuffer);

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`nnzb`	number of nonzero blocks of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzbrowBlockDimAcolBlockDimA` non-zero elements of matrix `A`.
`bsrRowPtrA`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `A`.
`bsrColIndA`	integer array of `nnzb` column indices of the non-zero blocks of matrix `A`.
`rowBlockDimA`	number of rows within a block of `A`.
`colBlockDimA`	number of columns within a block of `A`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`rowBlockDimC`	number of rows within a block of `C`.
`colBlockDimC`	number of columns within a block of `C`.
`pBuffer`	buffer allocated by the user; the size is return by `gebsr2gebsr_bufferSize()`.

Output

`bsrValC`	<type> array of `nnzcrowBlockDimCcolBlockDimC` non-zero elements of matrix `C`.
`bsrRowPtrC`	integer array of `mc+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `C`.
`bsrColIndC`	integer array of `nnzc` block column indices of the nonzero blocks of matrix `C`.
`nnzTotalDevHostPtr`	total number of nonzero blocks of `C`. `*nnzTotalDevHostPtr` is the same as `bsrRowPtrC[mc]-bsrRowPtrC[0]`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb, nb, nnzb<0`, `baseIdx` is not base-0 or base-1; or `rowBlockDimA`, `colBlockDimA`, `rowBlockDimC`, `colBlockDimC`<1).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.6. cusparse<t>gebsr2csr()

cusparseStatus_t
cusparseSgebsr2csr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    const cusparseMatDescr_t descrA,
    const float *bsrValA,
    const int    *bsrRowPtrA,
    const int    *bsrColIndA,
    int   rowBlockDim,
    int   colBlockDim,
    const cusparseMatDescr_t descrC,
    float  *csrValC,
    int    *csrRowPtrC,
    int    *csrColIndC )
cusparseStatus_t
cusparseDgebsr2csr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    const cusparseMatDescr_t descrA,
    const double *bsrValA,
    const int    *bsrRowPtrA,
    const int    *bsrColIndA,
    int   rowBlockDim,
    int   colBlockDim,
    const cusparseMatDescr_t descrC,
    double  *csrValC,
    int    *csrRowPtrC,
    int    *csrColIndC )
cusparseStatus_t
cusparseCgebsr2csr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    const cusparseMatDescr_t descrA,
    const cuComplex *bsrValA,
    const int    *bsrRowPtrA,
    const int    *bsrColIndA,
    int   rowBlockDim,
    int   colBlockDim,
    const cusparseMatDescr_t descrC,
    cuComplex  *csrValC,
    int    *csrRowPtrC,
    int    *csrColIndC )
cusparseStatus_t
cusparseZgebsr2csr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int mb,
    int nb,
    const cusparseMatDescr_t descrA,
    const cuDoubleComplex *bsrValA,
    const int    *bsrRowPtrA,
    const int    *bsrColIndA,
    int   rowBlockDim,
    int   colBlockDim,
    const cusparseMatDescr_t descrC,
    cuDoubleComplex  *csrValC,
    int    *csrRowPtrC,
    int    *csrColIndC )

This function converts a sparse matrix in general BSR format that is defined by the three arrays bsrValA, bsrRowPtrA, and bsrColIndA into a sparse matrix in CSR format that is defined by arrays csrValC, csrRowPtrC, and csrColIndC.

Let m(=mb*rowBlockDim) be number of rows of A and n(=nb*colBlockDim) be number of columns of A, then A and C are m*n sparse matrices. The general BSR format of A contains nnzb(=bsrRowPtrA[mb] - bsrRowPtrA[0]) non-zero blocks, whereas sparse matrix A contains nnz(=nnzb*rowBlockDim*colBlockDim) elements. The user must allocate enough space for arrays csrRowPtrC, csrColIndC, and csrValC. The requirements are as follows:

csrRowPtrC of m+1 elements

csrValC of nnz elements

csrColIndC of nnz elements

The general procedure is as follows:

// Given general BSR format (bsrRowPtrA, bsrColIndA, bsrValA) and 
// blocks of BSR format are stored in column-major order.
cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
int m = mb*rowBlockDim;
int n = nb*colBlockDim;
int nnzb = bsrRowPtrA[mb] - bsrRowPtrA[0]; // number of blocks
int nnz  = nnzb * rowBlockDim * colBlockDim; // number of elements
cudaMalloc((void**)&csrRowPtrC, sizeof(int)*(m+1));
cudaMalloc((void**)&csrColIndC, sizeof(int)*nnz);
cudaMalloc((void**)&csrValC, sizeof(float)*nnz);
cusparseSgebsr2csr(handle, dir, mb, nb,
        descrA, 
        bsrValA, bsrRowPtrA, bsrColIndA,
        rowBlockDim, colBlockDim,
        descrC,
        csrValC, csrRowPtrC, csrColIndC);

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`mb`	number of block rows of sparse matrix `A`.
`nb`	number of block columns of sparse matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`bsrValA`	<type> array of `nnzbrowBlockDimcolBlockDim` non-zero elements of matrix `A`.
`bsrRowPtrA`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `A`.
`bsrColIndA`	integer array of `nnzb` column indices of the non-zero blocks of matrix `A`.
`rowBlockDim`	number of rows within a block of `A`.
`colBlockDim`	number of columns within a block of `A`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.

Output

`csrValC`	<type> array of `nnz` non-zero elements of matrix `C`.
`csrRowPtrC`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one of matrix `C`.
`csrColIndC`	integer array of `nnz` column indices of the non-zero elements of matrix `C`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`mb, nb<0` is not base-0 or base-1, or `rowBlockDim`, `colBlockDim`<1).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.7. cusparse<t>csr2gebsr_bufferSize()

cusparseStatus_t 
cusparseScsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseDcsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseCcsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const cuComplex *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

cusparseStatus_t 
cusparseZcsr2gebsr_bufferSize(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const cuDoubleComplex *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    int rowBlockDim,
    int colBlockDim,
    int *pBufferSize)

This function returns the size of the buffer used in computing csr2gebsrNnz and csr2gebsr.

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`m`	number of rows of sparse matrix `A`.
`n`	number of columns of sparse matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one of matrix `A`.
`csrColIndA`	integer array of `nnz` column indices of the nonzero elements of matrix `A`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`rowBlockDim`	number of rows within a block of `C`.
`colBlockDim`	number of columns within a block of `C`.

Output

pBufferSize

host pointer containing number of bytes of the buffer used in csr2gebsrNnz() and csr2gebsr().

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n<0`, or `rowBlockDim`, `colBlockDim<1`).
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.8. cusparse<t>csr2gebsr()

cusparseStatus_t
cusparseXcsr2gebsrNnz(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const cusparseMatDescr_t descrC,
    int *bsrRowPtrC,
    int rowBlockDim,
    int colBlockDim,
    int *nnzTotalDevHostPtr,
    void *pBuffer )

cusparseStatus_t
cusparseScsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const cusparseMatDescr_t descrC,
    float *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDim,
    int colBlockDim,
    void *pBuffer)

cusparseStatus_t
cusparseDcsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const cusparseMatDescr_t descrC,
    double *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDim,
    int colBlockDim,
    void *pBuffer)

cusparseStatus_t
cusparseCcsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const cuComplex *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const cusparseMatDescr_t descrC,
    cuComplex *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDim,
    int colBlockDim,
    void *pBuffer)

cusparseStatus_t
cusparseZcsr2gebsr(cusparseHandle_t handle,
    cusparseDirection_t dir,
    int m,
    int n,
    const cusparseMatDescr_t descrA,
    const cuDoubleComplex *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const cusparseMatDescr_t descrC,
    cuDoubleComplex *bsrValC,
    int *bsrRowPtrC,
    int *bsrColIndC,
    int rowBlockDim,
    int colBlockDim,
    void *pBuffer)

This function converts a sparse matrix A in CSR format (that is defined by arrays csrValA, csrRowPtrA, and csrColIndA) into a sparse matrix C in general BSR format (that is defined by the three arrays bsrValC, bsrRowPtrC, and bsrColIndC).

The matrix A is a m*n sparse matrix and matrix C is a (mb*rowBlockDim)*(nb*colBlockDim) sparse matrix, where mb(=(m+rowBlockDim-1)/rowBlockDim) is the number of block rows of C, and nb(=(n+colBlockDim-1)/colBlockDim) is the number of block columns of C.

The block of C is of size rowBlockDim*colBlockDim. If m is not multiple of rowBlockDim or n is not multiple of colBlockDim, zeros are filled in.

The implementation adopts a two-step approach to do the conversion. First, the user allocates bsrRowPtrC of mb+1 elements and uses function cusparseXcsr2gebsrNnz() to determine the number of nonzero block columns per block row. Second, the user gathers nnzb (number of nonzero block columns of matrix C) from either (nnzb=*nnzTotalDevHostPtr) or (nnzb=bsrRowPtrC[mb]-bsrRowPtrC[0]) and allocates bsrValC of nnzb*rowBlockDim*colBlockDim elements and bsrColIndC of nnzb integers. Finally function cusparse[S|D|C|Z]csr2gebsr() is called to complete the conversion.

The user must obtain the size of the buffer required by csr2gebsr() by calling csr2gebsr_bufferSize(), allocate the buffer, and pass the buffer pointer to csr2gebsr().

The general procedure is as follows:

// Given CSR format (csrRowPtrA, csrColIndA, csrValA) and 
// blocks of BSR format are stored in column-major order.
cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
int base, nnzb;
int mb = (m + rowBlockDim-1)/rowBlockDim;
int nb = (n + colBlockDim-1)/colBlockDim;
int bufferSize;
void *pBuffer;
cusparseScsr2gebsr_bufferSize(handle, dir, m, n,
    descrA, csrValA, csrRowPtrA, csrColIndA,
    rowBlockDim, colBlockDim,
    &bufferSize);
cudaMalloc((void**)&pBuffer, bufferSize);
cudaMalloc((void**)&bsrRowPtrC, sizeof(int) *(mb+1));
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzb;
cusparseXcsr2gebsrNnz(handle, dir, m, n,
    descrA, csrRowPtrA, csrColIndA,
    descrC, bsrRowPtrC, rowBlockDim, colBlockDim,
    nnzTotalDevHostPtr,
    pBuffer);
if (NULL != nnzTotalDevHostPtr){
    nnzb = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzb, bsrRowPtrC+mb, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&base, bsrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzb -= base;
}
cudaMalloc((void**)&bsrColIndC, sizeof(int)*nnzb);
cudaMalloc((void**)&bsrValC, sizeof(float)*(rowBlockDim*colBlockDim)*nnzb);
cusparseScsr2gebsr(handle, dir, m, n,
        descrA,
        csrValA, csrRowPtrA, csrColIndA,
        descrC,
        bsrValC, bsrRowPtrC, bsrColIndC,
        rowBlockDim, colBlockDim,
        pBuffer);

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`m`	number of rows of sparse matrix `A`.
`n`	number of columns of sparse matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one of matrix `A`.
`csrColIndA`	integer array of `nnz` column indices of the nonzero elements of matrix `A`.
`descrC`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`rowBlockDim`	number of rows within a block of `C`.
`colBlockDim`	number of columns within a block of `C`.
`pBuffer`	buffer allocated by the user, the size is return by `csr2gebsr_bufferSize()`.

Output

`bsrValC`	<type> array of `nnzbrowBlockDimcolBlockDim` nonzero elements of matrix `C`.
`bsrRowPtrC`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `C`.
`bsrColIndC`	integer array of `nnzb` column indices of the nonzero blocks of matrix `C`.
`nnzTotalDevHostPtr`	total number of nonzero blocks of matrix `C`. Pointer `nnzTotalDevHostPtr` can point to a device memory or host memory.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n<0`, `baseIdx` is not base-0 or base-1, or `rowBlockDim`, `colBlockDim<1`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.9. cusparse<t>coo2csr()

cusparseStatus_t 
cusparseXcoo2csr(cusparseHandle_t handle, const int *cooRowInd,
                 int nnz, int m, int *csrRowPtr, cusparseIndexBase_t idxBase)

This function converts the array containing the uncompressed row indices (corresponding to COO format) into an array of compressed row pointers (corresponding to CSR format).

It can also be used to convert the array containing the uncompressed column indices (corresponding to COO format) into an array of column pointers (corresponding to CSC format).

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`cooRowInd`	integer array of `nnz` uncompressed row indices.
`nnz`	number of non-zeros of the sparse matrix (that is also the length of array `cooRowInd`).
`m`	number of rows of matrix `A`.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

csrRowPtr

integer array of m+1 elements that contains the start of every row and the end of the last row plus one.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

12.10. cusparse<t>csc2dense()

cusparseStatus_t 
cusparseScsc2dense(cusparseHandle_t handle, int m, int n, 
                   const cusparseMatDescr_t descrA, 
                   const float           *cscValA, 
                   const int *cscRowIndA, const int *cscColPtrA,
                   float           *A, int lda)
cusparseStatus_t 
cusparseDcsc2dense(cusparseHandle_t handle, int m, int n, 
                   const cusparseMatDescr_t descrA, 
                   const double          *cscValA, 
                   const int *cscRowIndA, const int *cscColPtrA,
                  double          *A, int lda)
cusparseStatus_t 
cusparseCcsc2dense(cusparseHandle_t handle, int m, int n, 
                   const cusparseMatDescr_t descrA, 
                   const cuComplex       *cscValA, 
                   const int *cscRowIndA, const int *cscColPtrA,
                   cuComplex       *A, int lda)
cusparseStatus_t 
cusparseZcsc2dense(cusparseHandle_t handle, int m, int n, 
                   const cusparseMatDescr_t descrA, 
                   const cuDoubleComplex *cscValA, 
                   const int *cscRowIndA, const int *cscColPtrA,
                   cuDoubleComplex *A, int lda)

This function converts the sparse matrix in CSC format that is defined by the three arrays cscValA, cscColPtrA, and cscRowIndA into the matrix A in dense format. The dense matrix A is filled in with the values of the sparse matrix and with zeros elsewhere.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`cscValA`	<type> array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ nonzero elements of matrix `A`.
`cscRowIndA`	integer array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ row indices of the nonzero elements of matrix `A`.
`cscColPtrA`	integer array of `n+1` elements that contains the start of every row and the end of the last column plus one.
`lda`	leading dimension of dense array `A`.

Output

`A`	array of dimensions `(lda, n)` that is filled in with the values of the sparse matrix.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.11. cusparse<t>csc2hyb()

cusparseStatus_t 
cusparseScsc2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const float           *cscValA,
            const int *cscRowIndA, const int *cscColPtrA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseDcsc2hyb(cusparseHandle_t handle, int m, int n,
            const cusparseMatDescr_t descrA, 
            const double          *cscValA,
            const int *cscRowIndA, const int *cscColPtrA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseCcsc2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const cuComplex       *cscValA, 
            const int *cscRowIndA, const int *cscColPtrA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseZcsc2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const cuDoubleComplex *cscValA, 
            const int *cscRowIndA, const int *cscColPtrA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)

This function converts a sparse matrix in CSC format into a sparse matrix in HYB format. It assumes that the hybA parameter has been initialized with the cusparseCreateHybMat() routine before calling this function.

This function requires some amount of temporary storage and a significant amount of storage for the matrix in HYB format. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`cscValA`	<type> array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ nonzero elements of matrix `A`.
`cscRowIndA`	integer array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`cscColPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`userEllWidth`	width of the regular (ELL) part of the matrix in HYB format, which should be less than the maximum number of nonzeros per row and is only required if `partitionType` == `CUSPARSE_HYB_PARTITION_USER`.
`partitionType`	partitioning method to be used in the conversion (please refer to `cusparseHybPartition_t` for details).

Output

hybA

the matrix A in HYB storage format.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.12. cusparse<t>csr2bsr()

cusparseStatus_t
cusparseXcsr2bsrNnz(cusparseHandle_t handle, 
      cusparseDirection_t dir,
      int m, 
      int n,
      const cusparseMatDescr_t descrA,
      const int *csrRowPtrA, 
      const int *csrColIndA,
      int blockDim,
      const cusparseMatDescr_t descrC,
      int *bsrRowPtrC,
      int *nnzTotalDevHostPtr)
cusparseStatus_t
cusparseScsr2bsr(cusparseHandle_t handle, 
      cusparseDirection_t dir,
      int m, 
      int n,
      const cusparseMatDescr_t descrA, 
      const float *csrValA, 
      const int *csrRowPtrA, 
      const int *csrColIndA,
      int blockDim,
      const cusparseMatDescr_t descrC,
      float *bsrValC, 
      int *bsrRowPtrC, 
      int *bsrColIndC)
cusparseStatus_t
cusparseDcsr2bsr(cusparseHandle_t handle, 
      cusparseDirection_t dir,
      int m, 
      int n,
      const cusparseMatDescr_t descrA, 
      const double *csrValA, 
      const int *csrRowPtrA, 
      const int *csrColIndA,
      int blockDim,
      const cusparseMatDescr_t descrC,
      double *bsrValC, 
      int *bsrRowPtrC, 
      int *bsrColIndC)
cusparseStatus_t
cusparseCcsr2bsr(cusparseHandle_t handle, 
      cusparseDirection_t dir,
      int m, 
      int n,
      const cusparseMatDescr_t descrA, 
      const cuComplex *csrValA, 
      const int *csrRowPtrA, 
      const int *csrColIndA,
      int blockDim,
      const cusparseMatDescr_t descrC,
      cuComplex *bsrValC, 
      int *bsrRowPtrC, 
      int *bsrColIndC)
cusparseStatus_t
cusparseZcsr2bsr(cusparseHandle_t handle, 
      cusparseDirection_t dir,
      int m, 
      int n,
      const cusparseMatDescr_t descrA, 
      const cuDoubleComplex *csrValA, 
      const int *csrRowPtrA, 
      const int *csrColIndA,
      int blockDim,
      const cusparseMatDescr_t descrC,
      cuDoubleComplex *bsrValC, 
      int *bsrRowPtrC, 
      int *bsrColIndC)

This function converts a sparse matrix in CSR format that is defined by the three arrays csrValA, csrRowPtrA, and csrColIndA into a sparse matrix in BSR format that is defined by arrays bsrValC, bsrRowPtrC, and bsrColIndC.

A is an m*n sparse matrix. The BSR format of A has mb block rows, nb block columns, and nnzb nonzero blocks, where mb=((m+blockDim-1)/blockDim) and nb=(n+blockDim-1)/blockDim.

If m or n is not multiple of blockDim, zeros are filled in.

The conversion in cuSPARSE entails a two-step approach. First, the user allocates bsrRowPtrC of mb+1 elements and uses function cusparseXcsr2bsrNnz() to determine the number of nonzero block columns per block row. Second, the user gathers nnzb (number of non-zero block columns of matrix C) from either (nnzb=*nnzTotalDevHostPtr) or (nnzb=bsrRowPtrC[mb]-bsrRowPtrC[0]) and allocates bsrValC of nnzb*blockDim*blockDim elements and bsrColIndC of nnzb elements. Finally function cusparse[S|D|C|Z]csr2bsr90 is called to complete the conversion.

The general procedure is as follows:

// Given CSR format (csrRowPtrA, csrcolIndA, csrValA) and 
// blocks of BSR format are stored in column-major order.
cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
int base, nnzb;
int mb = (m + blockDim-1)/blockDim;
cudaMalloc((void**)&bsrRowPtrC, sizeof(int) *(mb+1));
// nnzTotalDevHostPtr points to host memory
int *nnzTotalDevHostPtr = &nnzb;
cusparseXcsr2bsrNnz(handle, dir, m, n,
        descrA, csrRowPtrA, csrColIndA,
        blockDim,
        descrC, bsrRowPtrC,
        nnzTotalDevHostPtr);
if (NULL != nnzTotalDevHostPtr){
    nnzb = *nnzTotalDevHostPtr;
}else{
    cudaMemcpy(&nnzb, bsrRowPtrC+mb, sizeof(int), cudaMemcpyDeviceToHost);
    cudaMemcpy(&base, bsrRowPtrC, sizeof(int), cudaMemcpyDeviceToHost);
    nnzb -= base;
}
cudaMalloc((void**)&bsrColIndC, sizeof(int)*nnzb);
cudaMalloc((void**)&bsrValC, sizeof(float)*(blockDim*blockDim)*nnzb);
cusparseScsr2bsr(handle, dir, m, n,
        descrA, 
        csrValA, csrRowPtrA, csrColIndA,
        blockDim,
        descrC,
        bsrValC, bsrRowPtrC, bsrColIndC);

If blockDim is large (typically, a block cannot fit into shared memory), cusparse[S|D|C|Z]csr2bsr() allocates a temporary integer array of size mb*blockDim integers. If device memory is not available, CUSPARSE_STATUS_ALLOC_FAILED is returned.

Input

`handle`	handle to the cuSPARSE library context.
`dir`	storage format of blocks, either `CUSPARSE_DIRECTION_ROW` or `CUSPARSE_DIRECTION_COLUMN`.
`m`	number of rows of sparse matrix `A`.
`n`	number of columns of sparse matrix `A`.
`descrA`	the descriptor of matrix `A`.
`csrValA`	<type> array of `nnz(=csrRowPtrA[m]-csrRowPtr[0])` non-zero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` column indices of the non-zero elements of matrix `A`.
`blockDim`	block dimension of sparse matrix `A`. The range of `blockDim` is between 1 and `min(m,n)`.
`descrC`	the descriptor of matrix `C`.

Output

`bsrValC`	<type> array of `nnzbblockDimblockDim` nonzero elements of matrix `C`.
`bsrRowPtrC`	integer array of `mb+1` elements that contains the start of every block row and the end of the last block row plus one of matrix `C`.
`bsrColIndC`	integer array of `nnzb` column indices of the non-zero blocks of matrix `C`.
`nnzTotalDevHostPtr`	total number of nonzero elements in device or host memory. It is equal to `(bsrRowPtrC[mb]-bsrRowPtrC[0])`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`). `IndexBase` field of `descrA, descrC` is not base-0 or base-1, `dir` is not row-major or column-major, or `blockDim` is not between 1 and `min(m,n)`.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.13. cusparse<t>csr2coo()

cusparseStatus_t 
cusparseXcsr2coo(cusparseHandle_t handle, const int *csrRowPtr,
                 int nnz, int m, int *cooRowInd, 
                 cusparseIndexBase_t idxBase)

This function converts the array containing the compressed row pointers (corresponding to CSR format) into an array of uncompressed row indices (corresponding to COO format).

It can also be used to convert the array containing the compressed column indices (corresponding to CSC format) into an array of uncompressed column indices (corresponding to COO format).

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`csrRowPtr`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`nnz`	number of nonzeros of the sparse matrix (that is also the length of array `cooRowInd`).
`m`	number of rows of matrix `A`.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

cooRowInd

integer array of nnz uncompressed row indices.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	`idxBase` is neither `CUSPARSE_INDEX_BASE_ZERO` nor `CUSPARSE_INDEX_BASE_ONE`.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.

12.14. cusparse<t>csr2csc()

cusparseStatus_t 
cusparseScsr2csc(cusparseHandle_t handle, int m, int n, int nnz,
                 const float *csrVal, const int *csrRowPtr, 
                 const int *csrColInd, float           *cscVal,
                 int *cscRowInd, int *cscColPtr, 
                 cusparseAction_t copyValues, 
                 cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseDcsr2csc(cusparseHandle_t handle, int m, int n, int nnz,
                 const double *csrVal, const int *csrRowPtr, 
                 const int *csrColInd, double          *cscVal,
                 int *cscRowInd, int *cscColPtr, 
                 cusparseAction_t copyValues, 
                 cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseCcsr2csc(cusparseHandle_t handle, int m, int n, int nnz,
                 const cuComplex *csrVal, const int *csrRowPtr, 
                 const int *csrColInd, cuComplex       *cscVal,
                 int *cscRowInd, int *cscColPtr, 
                 cusparseAction_t copyValues, 
                 cusparseIndexBase_t idxBase)
cusparseStatus_t 
cusparseZcsr2csc(cusparseHandle_t handle, int m, int n, int nnz,
                 const cuDoubleComplex *csrVal, const int *csrRowPtr, 
                 const int *csrColInd, cuDoubleComplex *cscVal, 
                 int *cscRowInd, int *cscColPtr, 
                 cusparseAction_t copyValues, 
                 cusparseIndexBase_t idxBase)

This function converts a sparse matrix in CSR format (that is defined by the three arrays csrVal, csrRowPtr, and csrColInd) into a sparse matrix in CSC format (that is defined by arrays cscVal, cscRowInd, and cscColPtr). The resulting matrix can also be seen as the transpose of the original sparse matrix. Notice that this routine can also be used to convert a matrix in CSC format into a matrix in CSR format.

This function requires a significant amount of extra storage that is proportional to the matrix size. It is executed asynchronously with respect to the host, and it may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix $A$ .
`n`	number of columns of matrix $A$ .
`nnz`	number of nonzero elements of matrix $A$ .
`csrVal`	<type> array of `nnz` $(=$ `csrRowPtr(m)` $-$ `csrRowPtr(0)` $)$ nonzero elements of matrix $A$ .
`csrRowPtr`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColInd`	integer array of `nnz` $(=$ `csrRowPtr(m)` $-$ `csrRowPtr(0)` $)$ column indices of the nonzero elements of matrix $A$ .
`copyValues`	`CUSPARSE_ACTION_SYMBOLIC` or `CUSPARSE_ACTION_NUMERIC`.
`idxBase`	`CUSPARSE_INDEX_BASE_ZERO` or `CUSPARSE_INDEX_BASE_ONE`.

Output

`cscVal`	<type> array of `nnz` $(=$ `cscColPtr(n)` $-$ `cscColPtr(0)` $)$ nonzero elements of matrix $A$ . It is only filled in if `copyValues` is set to `CUSPARSE_ACTION_NUMERIC`.
`cscRowInd`	integer array of `nnz` $(=$ `cscColPtr(n)` $-$ `cscColPtr(0)` $)$ column indices of the nonzero elements of matrix $A$ .
`cscColPtr`	integer array of `n+1` elements that contains the start of every column and the end of the last column plus one.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.15. cusparseCsr2cscEx()

cusparseStatus_t cusparseCsr2cscEx(cusparseHandle_t handle,
                                   int m, int n, int nnz,
                                   const void  *csrSortedVal, cudaDataType csrSortedValtype,
                                   const int *csrSortedRowPtr, 
                                   const int *csrSortedColInd, 
                                   void *cscSortedVal, cudaDataType cscSortedValtype,
                                   int *cscSortedRowInd, 
                                   int *cscSortedColPtr, 
                                   cusparseAction_t copyValues, 
                                   cusparseIndexBase_t idxBase,
                                   cudaDataType executiontype);

This function is an extended version of cusparse<t>csr2csc(). For detailed description of the functionality, see cusparse<t>csr2csc().

This function does not support half-precision execution type, but it supports half-precision IO with single precision execution.

Input specifically required by cusparseCsr2cscEx

`csrSortedValAtype`	Data type of `csrSortedValA`.
`cscSortedValAtype`	Data type of `cscSortedValA`.
`executiontype`	Data type used for computation.

12.16. cusparse<t>csr2dense()

 
cusparseStatus_t cusparseScsr2dense(cusparseHandle_t handle,
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA,  
                                    const float *csrValA, 
                                    const int *csrRowPtrA, 
                                    const int *csrColIndA,
                                    float *A, 
                                    int lda)
    
cusparseStatus_t cusparseDcsr2dense(cusparseHandle_t handle, 
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const double *csrValA, 
                                    const int *csrRowPtrA, 
                                    const int *csrColIndA,
                                    double *A, 
                                    int lda)
    
cusparseStatus_t cusparseCcsr2dense(cusparseHandle_t handle, 
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const cuComplex *csrValA, 
                                    const int *csrRowPtrA, 
                                    const int *csrColIndA,
                                    cuComplex *A, 
                                    int lda)
    
cusparseStatus_t cusparseZcsr2dense(cusparseHandle_t handle,
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const cuDoubleComplex *csrValA, 
                                    const int *csrRowPtrA, 
                                    const int *csrColIndA,
                                    cuDoubleComplex *A, 
                                    int lda)

This function converts the sparse matrix in CSR format (that is defined by the three arrays csrValA, csrRowPtrA, and csrColIndA) into the matrix A in dense format. The dense matrix A is filled in with the values of the sparse matrix and with zeros elsewhere.

This function requires no extra storage. It is executed asynchronously with respect to the host, and it may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix $A$ .
`n`	number of columns of matrix $A$ .
`descrA`	the descriptor of matrix $A$ . The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix $A$ .
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix $A$ .
`lda`	leading dimension of array matrix`A`.

Output

`A`	array of dimensions `(lda,n)` that is filled in with the values of the sparse matrix.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.17. cusparse<t>csr2csr_compress()

 
cusparseStatus_t cusparseScsr2csr_compress(cusparseHandle_t handle,
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA,  
                                    const float *csrValA, 
                                    const int *csrColIndA,
                                    const int *csrRowPtrA, 
                                    int nnzA,
                                    const int *nnzPerRow,
                                    float *csrValC,
                                    int *csrColIndC,
                                    int *csrRowPtrC,
                                    float tol);
    
cusparseStatus_t cusparseDcsr2csr_compress(cusparseHandle_t handle, 
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const double *csrValA, 
                                    const int *csrColIndA,
                                    const int *csrRowPtrA, 
                                    int nnzA,
                                    const int *nnzPerRow, 
                                    double *csrValC,
                                    int *csrColIndC,
                                    int *csrRowPtrC,
                                    double tol);
    
cusparseStatus_t cusparseCcsr2csr_compress(cusparseHandle_t handle, 
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const cuComplex *csrValA, 
                                    const int *csrColIndA,
                                    const int *csrRowPtrA, 
                                    int nnzA,
                                    const int *nnzPerRow, 
                                    cuComplex *csrValC,
                                    int *csrColIndC,
                                    int *csrRowPtrC,
                                    cuComplex tol);
    
cusparseStatus_t cusparseZcsr2csr_compress(cusparseHandle_t handle,
                                    int m, 
                                    int n, 
                                    const cusparseMatDescr_t descrA, 
                                    const cuDoubleComplex *csrValA, 
                                    const int *csrColIndA,
                                    const int *csrRowPtrA, 
                                    int nnzA,
                                    const int *nnzPerRow, 
                                    cuDoubleComplex *csrValC,
                                    int *csrColIndC,
                                    int *csrRowPtrC,
                                    cuDoubleComplex tol);

This function compresses the sparse matrix in CSR format into compressed CSR format. Given a sparse matrix A and a non-negative value threshold(in the case of complex values, only the magnitude of the real part is used in the check), the function returns a sparse matrix C, defined by

\begin{array}{ll} C(i,j) = A(i,j) & if |A(i,j)| > threshold \end{array}

The implementation adopts a two-step approach to do the conversion. First, the user allocates csrRowPtrC of m+1 elements and uses function cusparse<t>nnz_compress() to determine nnzPerRow(the number of nonzeros columns per row) and nnzC(the total number of nonzeros). Second, the user allocates csrValC of nnzC elements and csrColIndC of nnzC integers. Finally function cusparse<t>csr2csr_compress() is called to complete the conversion.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix $A$ .
`n`	number of columns of matrix $A$ .
`descrA`	the descriptor of matrix $A$ . The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ elements of matrix $A$ .
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the elements of matrix $A$ .
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`nnzA`	number of nonzero elements in matrix $A$ .
`nnzPerRow`	this array contains the number of elements kept in the compressed matrix, by row.
tol	on input, this contains the non-negative tolerance value used for compression. Any values in matrix A less than or equal to this value will be dropped during compression.

Output

`csrValC`	on output, this array contains the typed values of elements kept in the compressed matrix. Size = nnzC.
`csrColIndC`	on output, this integer array contains the column indices of elements kept in the compressed matrix. Size = nnzC.
`csrRowPtrC`	on output, this integer array contains the row pointers for elements kept in the compressed matrix. Size = m+1

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

The following is a sample code to show how to use this API.

#include <stdio.h>
#include <sys/time.h>
#include <cusparse.h>

#define ERR_NE(X,Y) do { if ((X) != (Y)) { \
                             fprintf(stderr,"Error in %s at %s:%d\n",__func__,__FILE__,__LINE__); \
                             exit(-1);}} while(0)
#define CUDA_CALL(X) ERR_NE((X),cudaSuccess)
#define CUSPARSE_CALL(X) ERR_NE((X),CUSPARSE_STATUS_SUCCESS)
int main(){
    int m = 6, n = 5;
    cusparseHandle_t  handle;
    CUSPARSE_CALL( cusparseCreate(&handle) );
    cusparseMatDescr_t descrX;
    CUSPARSE_CALL(cusparseCreateMatDescr(&descrX));
    // Initialize sparse matrix
    float *X;
    CUDA_CALL(cudaMallocManaged( &X, sizeof(float) * m * n ));
    memset( X, 0, sizeof(float) * m * n );
    X[0 + 0*m] = 1.0;  X[0 + 1*m] = 3.0;
    X[1 + 1*m] = -4.0; X[1 + 2*m] = 5.0;
    X[2 + 0*m] = 2.0;  X[2 + 3*m] = 7.0;  X[2 + 4*m] = 8.0;
    X[3 + 2*m] = 6.0;  X[3 + 4*m] = 9.0;
    X[4 + 3*m] = 3.5;  X[4 + 4*m] = 5.5;
    X[5 + 0*m] = 6.5;  X[5 + 2*m] = -9.9;
    // Initialize total_nnz, and  nnzPerRowX for cusparseSdense2csr()
    int total_nnz = 13;
    int *nnzPerRowX;
    CUDA_CALL( cudaMallocManaged( &nnzPerRowX, sizeof(int) * m ));
    nnzPerRowX[0] = 2;  nnzPerRowX[1] = 2;  nnzPerRowX[2] = 3;
    nnzPerRowX[3] = 2;  nnzPerRowX[4] = 2;  nnzPerRowX[5] = 2;

    float *csrValX;
    int *csrRowPtrX;
    int *csrColIndX;
    CUDA_CALL( cudaMallocManaged( &csrValX, sizeof(float) * total_nnz) );
    CUDA_CALL( cudaMallocManaged( &csrRowPtrX, sizeof(int) * (m+1))) ;
    CUDA_CALL( cudaMallocManaged( &csrColIndX, sizeof(int) * total_nnz)) ;

Before calling this API, call two APIs to prepare the input.

/** Call cusparseSdense2csr to generate CSR format as the inputs for
    cusparseScsr2csr_compress  **/
    CUSPARSE_CALL( cusparseSdense2csr( handle, m, n, descrX, X,
                                       m, nnzPerRowX, csrValX,
                                       csrRowPtrX, csrColIndX )) ;
    float tol = 3.5;
    int *nnzPerRowY;
    int *testNNZTotal;
    CUDA_CALL (cudaMallocManaged( &nnzPerRowY, sizeof(int) * m ));
    CUDA_CALL (cudaMallocManaged( &testNNZTotal, sizeof(int)));
    memset( nnzPerRowY, 0, sizeof(int) * m );
    // cusparseSnnz_compress generates nnzPerRowY and testNNZTotal
    CUSPARSE_CALL( cusparseSnnz_compress(handle, m, descrX, csrValX,
                                         csrRowPtrX, nnzPerRowY,
                                         testNNZTotal, tol));

    float *csrValY;
    int *csrRowPtrY;
    int *csrColIndY;
    CUDA_CALL( cudaMallocManaged( &csrValY, sizeof(float) * (*testNNZTotal)));
    CUDA_CALL( cudaMallocManaged( &csrRowPtrY, sizeof(int) * (m+1)));
    CUDA_CALL( cudaMallocManaged( &csrColIndY, sizeof(int) * (*testNNZTotal)));

    CUSPARSE_CALL( cusparseScsr2csr_compress( handle, m, n, descrX, csrValX,
                                              csrColIndX, csrRowPtrX,
                                              total_nnz,  nnzPerRowY,
                                              csrValY, csrColIndY,
                                              csrRowPtrY, tol));
    /* Expect results
    nnzPerRowY:  0 2 2 2 1 2
    csrValY:     -4 5 7 8 6 9 5.5 6.5 -9.9
    csrColIndY:  1 2 3 4 2 4 4 0 2
    csrRowPtrY:  0 0 2 4 6 7 9
    */
    cudaFree(X);
    cusparseDestroy(handle);
    cudaFree(nnzPerRowX);
    cudaFree(csrValX);
    cudaFree(csrRowPtrX);
    cudaFree(csrColIndX);
    cudaFree(csrValY);
    cudaFree(nnzPerRowY);
    cudaFree(testNNZTotal);
    cudaFree(csrRowPtrY);
    cudaFree(csrColIndY);
    return 0;
}

12.18. cusparse<t>csr2hyb()

cusparseStatus_t 
cusparseScsr2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const float           *csrValA,
            const int *csrRowPtrA, const int *csrColIndA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseDcsr2hyb(cusparseHandle_t handle, int m, int n,
            const cusparseMatDescr_t descrA, 
            const double          *csrValA,
            const int *csrRowPtrA, const int *csrColIndA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseCcsr2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const cuComplex       *csrValA, 
            const int *csrRowPtrA, const int *csrColIndA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)
cusparseStatus_t 
cusparseZcsr2hyb(cusparseHandle_t handle, int m, int n, 
            const cusparseMatDescr_t descrA, 
            const cuDoubleComplex *csrValA, 
            const int *csrRowPtrA, const int *csrColIndA, 
            cusparseHybMat_t hybA, int userEllWidth, 
            cusparseHybPartition_t partitionType)

This function converts a sparse matrix in CSR format into a sparse matrix in HYB format. It assumes that the hybA parameter has been initialized with cusparseCreateHybMat() routine before calling this function.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.
`userEllWidth`	width of the regular (ELL) part of the matrix in HYB format, which should be less than maximum number of nonzeros per row and is only required if `partitionType` == `CUSPARSE_HYB_PARTITION_USER`.
`partitionType`	partitioning method to be used in the conversion (please refer to `cusparseHybPartition_t` for details).

Output

hybA

the matrix A in HYB storage format.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.19. cusparse<t>dense2csc()

cusparseStatus_t 
cusparseSdense2csc(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const float           *A, 
                int lda, const int *nnzPerCol, 
                float           *cscValA, 
                int *cscRowIndA, int *cscColPtrA)
cusparseStatus_t 
cusparseDdense2csc(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const double          *A, 
                int lda, const int *nnzPerCol, 
                double          *cscValA, 
                int *cscRowIndA, int *cscColPtrA)
cusparseStatus_t 
cusparseCdense2csc(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const cuComplex       *A, 
                int lda, const int *nnzPerCol, 
                cuComplex       *cscValA, 
                int *cscRowIndA, int *cscColPtrA)
cusparseStatus_t 
cusparseZdense2csc(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const cuDoubleComplex *A, 
                int lda, const int *nnzPerCol, 
                cuDoubleComplex *cscValA, 
                int *cscRowIndA, int *cscColPtrA)

This function converts the matrix A in dense format into a sparse matrix in CSC format. All the parameters are assumed to have been pre-allocated by the user, and the arrays are filled in based on nnzPerCol, which can be precomputed with cusparse<t>nnz().

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`A`	array of dimensions `(lda, n)`.
`lda`	leading dimension of dense array `A`.
`nnzPerCol`	array of size `n` containing the number of nonzero elements per column.

Output

`cscValA`	<type> array of `nnz` $(=$ `cscRowPtrA(m)` $-$ `cscRowPtrA(0)` $)$ nonzero elements of matrix `A`. It is only filled in if `copyValues` is set to `CUSPARSE_ACTION_NUMERIC`.
`cscRowIndA`	integer array of `nnz` $(=$ `cscRowPtrA(m)` $-$ `cscRowPtrA(0)` $)$ row indices of the nonzero elements of matrix `A`.
`cscColPtrA`	integer array of `n+1` elements that contains the start of every column and the end of the last column plus one.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.20. cusparse<t>dense2csr()

cusparseStatus_t 
cusparseSdense2csr(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const float           *A, 
                int lda, const int *nnzPerRow, 
                float           *csrValA, 
                int *csrRowPtrA, int *csrColIndA) 
cusparseStatus_t 
cusparseDdense2csr(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const double          *A, 
                int lda, const int *nnzPerRow, 
                double          *csrValA, 
                int *csrRowPtrA, int *csrColIndA) 
cusparseStatus_t 
cusparseCdense2csr(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const cuComplex       *A, 
                int lda, const int *nnzPerRow, 
                cuComplex       *csrValA, 
                int *csrRowPtrA, int *csrColIndA) 
cusparseStatus_t 
cusparseZdense2csr(cusparseHandle_t handle, int m, int n, 
                const cusparseMatDescr_t descrA, 
                const cuDoubleComplex *A, 
                int lda, const int *nnzPerRow, 
                cuDoubleComplex *csrValA, 
                int *csrRowPtrA, int *csrColIndA)

This function converts the matrix A in dense format into a sparse matrix in CSR format. All the parameters are assumed to have been pre-allocated by the user and the arrays are filled in based on nnzPerRow, which can be pre-computed with cusparse<t>nnz().

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`A`	array of dimensions `(lda, n)`.
`lda`	leading dimension of dense array `A`.
`nnzPerRow`	array of size `n` containing the number of non-zero elements per row.

Output

`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every column and the end of the last column plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the non-zero elements of matrix `A`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.21. cusparse<t>dense2hyb()

cusparseStatus_t
cusparseSdense2hyb(cusparseHandle_t handle, int m, int n,
                   const cusparseMatDescr_t descrA, 
                   const float           *A,
                   int lda, const int *nnzPerRow, cusparseHybMat_t hybA,
                   int userEllWidth, 
                   cusparseHybPartition_t partitionType)
cusparseStatus_t
cusparseDdense2hyb(cusparseHandle_t handle, int m, int n,
                   const cusparseMatDescr_t descrA, 
                   const double          *A,
                   int lda, const int *nnzPerRow, cusparseHybMat_t hybA, 
                   int userEllWidth, 
                   cusparseHybPartition_t partitionType)
cusparseStatus_t
cusparseCdense2hyb(cusparseHandle_t handle, int m, int n,
                   const cusparseMatDescr_t descrA, 
                   const cuComplex       *A,
                   int lda, const int *nnzPerRow, cusparseHybMat_t hybA,
                   int userEllWidth, 
                   cusparseHybPartition_t partitionType)
cusparseStatus_t
cusparseZdense2hyb(cusparseHandle_t handle, int m, int n,
                   const cusparseMatDescr_t descrA, 
                   const cuDoubleComplex *A,
                   int lda, const int *nnzPerRow, cusparseHybMat_t hybA,
                   int userEllWidth, 
                   cusparseHybPartition_t partitionType)

This function converts matrix A in dense format into a sparse matrix in HYB format. It assumes that the routine cusparseCreateHybMat() was used to initialize the opaque structure hybA and that the array nnzPerRow was pre-computed with cusparse<t>nnz().

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix $A$ .
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`.
`A`	array of dimensions `(lda, n)`.
`lda`	leading dimension of dense array `A`.
`nnzPerRow`	array of size `m` containing the number of nonzero elements per row.
`userEllWidth`	width of the regular (ELL) part of the matrix in HYB format, which should be less than maximum number of nonzeros per row and is only required if `partitionType` == `CUSPARSE_HYB_PARTITION_USER`.
`partitionType`	partitioning method to be used in the conversion (please refer to `cusparseHybPartition_t` for details).

Output

hybA

the matrix A in HYB storage format.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.22. cusparse<t>hyb2csc()

cusparseStatus_t 
cusparseShyb2csc(cusparseHandle_t handle, 
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 float       *cscValA, int *cscRowIndA, int *cscColPtrA)
cusparseStatus_t 
cusparseDhyb2csc(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 double      *cscValA, int *cscRowIndA, int *cscColPtrA)              
cusparseStatus_t 
cusparseChyb2csc(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 cuComplex   *cscValA, int *cscRowIndA, int *cscColPtrA)
cusparseStatus_t 
cusparseZhyb2csc(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 cuDoubleComplex *cscValA, int *cscRowIndA, int *cscColPtrA)

This function converts a sparse matrix in HYB format into a sparse matrix in CSC format.

This function requires some amount of temporary storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`descrA`	the descriptor of matrix `A` in Hyb format. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`.
`hybA`	the matrix `A` in HYB storage format.

Output

`cscValA`	<type> array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ nonzero elements of matrix `A`.
`cscRowIndA`	integer array of `nnz` $(=$ `cscColPtrA(m)` $-$ `cscColPtrA(0)` $)$ column indices of the non-zero elements of matrix `A`.
`cscColPtrA`	integer array of `m+1` elements that contains the start of every column and the end of the last row plus one.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.23. cusparse<t>hyb2csr()

cusparseStatus_t 
cusparseShyb2csr(cusparseHandle_t handle, 
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 float       *csrValA, int *csrRowPtrA, int *csrColIndA)
cusparseStatus_t 
cusparseDhyb2csr(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 double      *csrValA, int *csrRowPtrA, int *csrColIndA)              
cusparseStatus_t 
cusparseChyb2csr(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 cuComplex   *csrValA, int *csrRowPtrA, int *csrColIndA)
cusparseStatus_t 
cusparseZhyb2csr(cusparseHandle_t handle,
                 const cusparseMatDescr_t descrA, 
                 const cusparseHybMat_t hybA,
                 cuDoubleComplex *csrValA, int *csrRowPtrA, int *csrColIndA)

This function converts a sparse matrix in HYB format into a sparse matrix in CSR format.

This function requires some amount of temporary storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`descrA`	the descriptor of matrix `A` in Hyb format. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`.
`hybA`	the matrix `A` in HYB storage format.

Output

`csrValA`	<type> array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ nonzero elements of matrix `A`.
`csrRowPtrA`	integer array of `m+1` elements that contains the start of every column and the end of the last row plus one.
`csrColIndA`	integer array of `nnz` $(=$ `csrRowPtrA(m)` $-$ `csrRowPtrA(0)` $)$ column indices of the nonzero elements of matrix `A`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.24. cusparse<t>hyb2dense()

cusparseStatus_t 
cusparseShyb2dense(cusparseHandle_t handle,
                   const cusparseMatDescr_t descrA,
                   const cusparseHybMat_t hybA,
                   float *A,
                   int lda)
cusparseStatus_t 
cusparseDhyb2dense(cusparseHandle_t handle,
                   const cusparseMatDescr_t descrA,
                   const cusparseHybMat_t hybA,
                   double *A,
                   int lda)
cusparseStatus_t 
cusparseChyb2dense(cusparseHandle_t handle,
                   const cusparseMatDescr_t descrA,
                   const cusparseHybMat_t hybA,
                   cuComplex *A,
                   int lda)
cusparseStatus_t 
cusparseZhyb2dense(cusparseHandle_t handle,
                   const cusparseMatDescr_t descrA,
                   const cusparseHybMat_t hybA,
                   cuDoubleComplex *A,
                   int lda)

This function converts a sparse matrix in HYB format (contained in the opaque structure ) into matrix A in dense format. The dense matrix A is filled in with the values of the sparse matrix and with zeros elsewhere.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`descrA`	the descriptor of matrix `A` in Hyb format. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`.
`hybA`	the matrix `A` in HYB storage format.
`lda`	leading dimension of dense array `A`.

Output

`A`	array of dimensions `(lda, n)` that is filled in with the values of the sparse matrix.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	the internally stored hyb format parameters are invalid.
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.25. cusparse<t>nnz()

cusparseStatus_t 
cusparseSnnz(cusparseHandle_t handle, cusparseDirection_t dirA, int m, 
             int n, const cusparseMatDescr_t descrA, 
             const float           *A, 
             int lda, int *nnzPerRowColumn, int *nnzTotalDevHostPtr)
cusparseStatus_t 
cusparseDnnz(cusparseHandle_t handle, cusparseDirection_t dirA, int m, 
             int n, const cusparseMatDescr_t descrA, 
             const double          *A, 
             int lda, int *nnzPerRowColumn, int *nnzTotalDevHostPtr)
cusparseStatus_t 
cusparseCnnz(cusparseHandle_t handle, cusparseDirection_t dirA, int m, 
             int n, const cusparseMatDescr_t descrA, 
             const cuComplex       *A, 
             int lda, int *nnzPerRowColumn, int *nnzTotalDevHostPtr)
cusparseStatus_t 
cusparseZnnz(cusparseHandle_t handle, cusparseDirection_t dirA, int m, 
             int n, const cusparseMatDescr_t descrA, 
             const cuDoubleComplex *A, 
             int lda, int *nnzPerRowColumn, int *nnzTotalDevHostPtr)

This function computes the number of nonzero elements per row or column and the total number of nonzero elements in a dense matrix.

This function requires no extra storage. It is executed asynchronously with respect to the host and may return control to the application on the host before the result is ready.

Input

`handle`	handle to the cuSPARSE library context.
`dirA`	direction that specifies whether to count nonzero elements by `CUSPARSE_DIRECTION_ROW` or by `CUSPARSE_DIRECTION_COLUMN`.
`m`	number of rows of matrix `A`.
`n`	number of columns of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`A`	array of dimensions `(lda, n)`.
`lda`	leading dimension of dense array `A`.

Output

`nnzPerRowColumn`	array of size `m` or `n` containing the number of nonzero elements per row or column, respectively.
`nnzTotalDevHostPtr`	total number of nonzero elements in device or host memory.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.26. cusparseCreateIdentityPermutation()

cusparseStatus_t 
cusparseCreateIdentityPermutation(cusparseHandle_t handle,
                                  int n,
                                  int *p);

This function creates an identity map. The output parameter p represents such map by p = 0:1:(n-1).

This function is typically used with coosort, csrsort, cscsort, csr2csc_indexOnly.

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`n`	`host`	size of the map.

Output

`parameter`	`device or host`	`description`
`p`	`device`	integer array of dimensions `n`.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.27. cusparseXcoosort()

cusparseStatus_t 
cusparseXcoosort_bufferSizeExt(
                      cusparseHandle_t handle,
                      int m,
                      int n,
                      int nnz,
                      const int *cooRows,
                      const int *cooCols,
                      size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseXcoosortByRow(cusparseHandle_t handle,
                      int m,
                      int n,
                      int nnz,
                      int *cooRows,
                      int *cooCols,
                      int *P,
                      void *pBuffer);

cusparseStatus_t 
cusparseXcoosortByColumn(cusparseHandle_t handle,
                         int m,
                         int n,
                         int nnz,
                         int *cooRows,
                         int *cooCols,
                         int *P,
                         void *pBuffer);

This function sorts COO format. The sorting is in-place. Also the user can sort by row or sort by column.

A is an m×n sparse matrix that is defined in COO storage format by the three arrays cooVals, cooRows, and cooCols.

There is no assumption for the base index of the matrix. coosort uses stable sort on signed integer, so the value of cooRows or cooCols can be negative.

This function coosort() requires buffer size returned by coosort_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

The parameter P is both input and output. If the user wants to compute sorted cooVal, P must be set as 0:1:(nnz-1) before coosort(), and after coosort(), new sorted value array satisfies cooVal_sorted = cooVal(P).

Remark: the dimension m and n are not used. If the user does not know the value of m or n, just passes a value positive. This usually happens if the user only reads a COO array first and needs to decide the dimension m or n later.

Appendix D provides a simple example of coosort().

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnz`	`host`	number of nonzero elements of matrix `A`.
`cooRows`	`device`	integer array of `nnz` unsorted row indices of `A`.
`cooCols`	`device`	integer array of `nnz` unsorted column indices of `A`.
`P`	`device`	integer array of `nnz` unsorted map indices. To construct `cooVal`, the user has to set `P=0:1:(nnz-1)`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `coosort_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`cooRows`	`device`	integer array of `nnz` sorted row indices of `A`.
`cooCols`	`device`	integer array of `nnz` sorted column indices of `A`.
`P`	`device`	integer array of `nnz` sorted map indices.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.

12.28. cusparseXcsrsort()

cusparseStatus_t 
cusparseXcsrsort_bufferSizeExt(
                 cusparseHandle_t handle,
                 int m,
                 int n,
                 int nnz,
                 const int *csrRowPtr,
                 const int *csrColInd,
                 size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseXcsrsort(cusparseHandle_t handle,
                 int m,
                 int n,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 const int *csrRowPtr,
                 int *csrColInd,
                 int *P,
                 void *pBuffer);

This function sorts CSR format. The stable sorting is in-place.

The matrix type is regarded as CUSPARSE_MATRIX_TYPE_GENERAL implicitly. In other words, any symmetric property is ignored.

This function csrsort() requires buffer size returned by csrsort_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

The parameter P is both input and output. If the user wants to compute sorted csrVal, P must be set as 0:1:(nnz-1) before csrsort(), and after csrsort(), new sorted value array satisfies csrVal_sorted = csrVal(P).

The general procedure is as follows:

// A is a 3x3 sparse matrix, base-0
//     | 1 2 3 |
// A = | 4 5 6 |
//     | 7 8 9 |
const int m = 3;
const int n = 3;
const int nnz = 9;
csrRowPtr[m+1] = { 0, 3, 6, 9}; // on device
csrColInd[nnz] = { 2, 1, 0, 0, 2,1, 1, 2, 0}; // on device
csrVal[nnz] = { 3, 2, 1, 4, 6, 5, 8, 9, 7}; // on device
size_t pBufferSizeInBytes = 0;
void *pBuffer = NULL;
int *P = NULL;

// step 1: allocate buffer
cusparseXcsrsort_bufferSizeExt(handle, m, n, nnz, csrRowPtr, csrColInd, &pBufferSizeInBytes);
cudaMalloc( &pBuffer, sizeof(char)* pBufferSizeInBytes);

// step 2: setup permutation vector P to identity
cudaMalloc( (void**)&P, sizeof(int)*nnz);
cusparseCreateIdentityPermutation(handle, nnz, P);

// step 3: sort CSR format
cusparseXcsrsort(handle, m, n, nnz, descrA, csrRowPtr, csrColInd, P, pBuffer);

// step 4: gather sorted csrVal
cusparseDgthr(handle, nnz, csrVal, csrVal_sorted, P, CUSPARSE_INDEX_BASE_ZERO);

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnz`	`host`	number of nonzero elements of matrix `A`.
`csrRowsPtr`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColInd`	`device`	integer array of `nnz` unsorted column indices of `A`.
`P`	`device`	integer array of `nnz` unsorted map indices. To construct `csrVal`, the user has to set `P=0:1:(nnz-1)`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `csrsort_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`csrColInd`	`device`	integer array of `nnz` sorted column indices of `A`.
`P`	`device`	integer array of `nnz` sorted map indices.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.29. cusparseXcscsort()

cusparseStatus_t 
cusparseXcscsort_bufferSizeExt(
                 cusparseHandle_t handle,
                 int m,
                 int n,
                 int nnz,
                 const int *cscColPtr,
                 const int *cscRowInd,
                 size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseXcscsort(cusparseHandle_t handle,
                 int m,
                 int n,
                 int nnz,
                 const cusparseMatDescr_t descrA,
                 const int *cscColPtr,
                 int *cscRowInd,
                 int *P,
                 void *pBuffer);

This function sorts CSC format. The stable sorting is in-place.

The matrix type is regarded as CUSPARSE_MATRIX_TYPE_GENERAL implicitly. In other words, any symmetric property is ignored.

This function cscsort() requires buffer size returned by cscsort_bufferSizeExt(). The address of pBuffer must be multiple of 128 bytes. If not, CUSPARSE_STATUS_INVALID_VALUE is returned.

The parameter P is both input and output. If the user wants to compute sorted cscVal, P must be set as 0:1:(nnz-1) before cscsort(), and after cscsort(), new sorted value array satisfies cscVal_sorted = cscVal(P).

The general procedure is as follows:

// A is a 3x3 sparse matrix, base-0
//     | 1 2  |
// A = | 4 0  |
//     | 0 8  |
const int m = 3;
const int n = 2;
const int nnz = 4;
cscColPtr[n+1] = { 0, 2, 4}; // on device
cscRowInd[nnz] = { 1, 0, 2, 0}; // on device
cscVal[nnz]    = { 4.0, 1.0, 8.0, 2.0 }; // on device
size_t pBufferSizeInBytes = 0;
void *pBuffer = NULL;
int *P = NULL;

// step 1: allocate buffer
cusparseXcscsort_bufferSizeExt(handle, m, n, nnz, cscColPtr, cscRowInd, &pBufferSizeInBytes);
cudaMalloc( &pBuffer, sizeof(char)* pBufferSizeInBytes);

// step 2: setup permutation vector P to identity
cudaMalloc( (void**)&P, sizeof(int)*nnz);
cusparseCreateIdentityPermutation(handle, nnz, P);

// step 3: sort CSC format
cusparseXcscsort(handle, m, n, nnz, descrA, cscColPtr, cscRowInd, P, pBuffer);

// step 4: gather sorted cscVal
cusparseDgthr(handle, nnz, cscVal, cscVal_sorted, P, CUSPARSE_INDEX_BASE_ZERO);

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnz`	`host`	number of nonzero elements of matrix `A`.
`cscColPtr`	`device`	integer array of `n+1` elements that contains the start of every column and the end of the last column plus one.
`cscRowInd`	`device`	integer array of `nnz` unsorted row indices of `A`.
`P`	`device`	integer array of `nnz` unsorted map indices. To construct `cscVal`, the user has to set `P=0:1:(nnz-1)`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `cscsort_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`cscRowInd`	`device`	integer array of `nnz` sorted row indices of `A`.
`P`	`device`	integer array of `nnz` sorted map indices.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.30. cusparseXcsru2csr()


cusparseStatus_t cusparseCreateCsru2csrInfo(csru2csrInfo_t *info);

cusparseStatus_t cusparseDestroyCsru2csrInfo(csru2csrInfo_t info);

cusparseStatus_t 
cusparseScsru2csr_bufferSizeExt(
                          cusparseHandle_t handle,
                          int m,
                          int n,
                          int nnz,
                          float *csrVal,
                          const int *csrRowPtr,
                          int *csrColInd,
                          csru2csrInfo_t  info,
                          size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDcsru2csr_bufferSizeExt(
                          cusparseHandle_t handle,
                          int m,
                          int n,
                          int nnz,
                          double *csrVal,
                          const int *csrRowPtr,
                          int *csrColInd,
                          csru2csrInfo_t  info,
                          size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseCcsru2csr_bufferSizeExt(
                          cusparseHandle_t handle,
                          int m,
                          int n,
                          int nnz,
                          cuComplex *csrVal,
                          const int *csrRowPtr,
                          int *csrColInd,
                          csru2csrInfo_t  info,
                          size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseZcsru2csr_bufferSizeExt(
                          cusparseHandle_t handle,
                          int m,
                          int n,
                          int nnz,
                          cuDoubleComplex *csrVal,
                          const int *csrRowPtr,
                          int *csrColInd,
                          csru2csrInfo_t  info,
                          size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseScsru2csr(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  float *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseDcsru2csr(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  double *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t
cusparseCcsru2csr(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuComplex *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseZcsru2csr(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuDoubleComplex *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseScsr2csru(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  float *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseDcsr2csru(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  double *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseCcsr2csru(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuComplex *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

cusparseStatus_t 
cusparseZcsr2csru(cusparseHandle_t handle,
                  int m,
                  int n,
                  int nnz,
                  const cusparseMatDescr_t descrA,
                  cuDoubleComplex *csrVal,
                  const int *csrRowPtr,
                  int *csrColInd,
                  csru2csrInfo_t  info,
                  void *pBuffer);

This function transfers unsorted CSR format to CSR format, and vice versa. The operation is in-place.

This function is a wrapper of csrsort and gthr. The usecase is the following scenario.

If the user has a matrix A of CSR format which is unsorted, and implements his own code (which can be CPU or GPU kernel) based on this special order (for example, diagonal first, then lower triangle, then upper triangle), and wants to convert it to CSR format when calling CUSPARSE library, and then convert it back when doing something else on his/her kernel. For example, suppose the user wants to solve a linear system Ax=b by the following iterative scheme

x^{(k+1)} = x^{(k)} + L^{(-1)} * (b - A x^{(k)})

The code heavily uses SpMv and triangular solve. Assume that the user has an in-house design of SpMV (Sparse Matrix-Vector multiplication) based on special order of A. However the user wants to use CUSAPRSE library for triangular solver. Then the following code can work.

$\begin{matrix} do \\ step 1: compute residual vector & r & = & b & - & A & x^{(k)} & by in-house SpMV \\ step 2: B := sort(A), and L is lower triangular part of B \\ (only sort A once and keep the permutation vector) \\ step 3: solve & z & = & L^{(-1)} & * & ( & b & - & A & x^{(k)} & ) & by cusparseXcsrsv \\ step 4: add correction & x^{(k+1)} & = & x^{(k)} & + & z \\ step 5: A := unsort(B) \\ (use permutation vector to get back the unsorted CSR) \\ until convergence \end{matrix}$

The requirements of step 2 and step 5 are

1. In-place operation.

2. The permutation vector P is hidden in an opaque structure.

3. No cudaMalloc inside the conversion routine. Instead, the user has to provide the buffer explicitly.

4. The conversion between unsorted CSR and sorted CSR may needs several times, but the function only generates the permutation vector P once.

5. The function is based on csrsort, gather and scatter operations.

The operation is called csru2csr, which means unsorted CSR to sorted CSR. Also we provide the inverse operation, called csr2csru.

In order to keep the permutation vector invisible, we need an opaque structure called csru2csrInfo. Then two functions (cusparseCreateCsru2csrInfo, cusparseDestroyCsru2csrInfo) are used to initialize and to destroy the opaque structure.

cusparse[S|D|C|Z]csru2csr_bufferSizeExt returns the size of the buffer. The permutation vector P is also allcated inside csru2csrInfo. The lifetime of the permutation vector is the same as the lifetime of csru2csrInfo.

cusparse[S|D|C|Z]csru2csr performs forward transformation from unsorted CSR to sorted CSR. First call uses csrsort to generate the permutation vector P, and subsequent call uses P to do transformation.

cusparse[S|D|C|Z]csr2csru performs backward transformation from sorted CSR to unsorted CSR. P is used to get unsorted form back.

The following tables describe parameters of csr2csru_bufferSizeExt and csr2csru.

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnz`	`host`	number of nonzero elements of matrix `A`.
`descrA`	`host`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrVal`	`device`	<type> array of nnz unsorted nonzero elements of matrix `A`.
`csrRowsPtr`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColInd`	`device`	integer array of `nnz` unsorted column indices of `A`.
`info`	`host`	opaque structure initialized using `cusparseCreateCsru2csrInfo()`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `csru2csr_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`csrVal`	`device`	<type> array of nnz sorted nonzero elements of matrix `A`.
`csrColInd`	`device`	integer array of `nnz` sorted column indices of `A`.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n,nnz<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.31. cusparseXpruneDense2csr()


cusparseStatus_t 
cusparseHpruneDense2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    const __half *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseSpruneDense2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    const float *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDpruneDense2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    const double *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseHpruneDense2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneDense2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr,
    void *pBuffer);

cusparseStatus_t
cusparseDpruneDense2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr,
    void *pBuffer);

cusparseStatus_t 
cusparseHpruneDense2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    __half *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneDense2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    float *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneDense2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    double *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

This function prunes a dense matrix to a sparse matrix with CSR format.

Given a dense matrix A and a non-negative value threshold, the function returns a sparse matrix C, defined by

\begin{array}{ll} C(i,j) = A(i,j) & if |A(i,j)| > threshold \end{array}

The implementation adopts a two-step approach to do the conversion. First, the user allocates csrRowPtrC of m+1 elements and uses function pruneDense2csrNnz() to determine the number of nonzeros columns per row. Second, the user gathers nnzC (number of nonzeros of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC[m]-csrRowPtrC[0]) and allocates csrValC of nnzC elements and csrColIndC of nnzC integers. Finally function pruneDense2csr() is called to complete the conversion.

The user must obtain the size of the buffer required by pruneDense2csr() by calling pruneDense2csr_bufferSizeExt(), allocate the buffer, and pass the buffer pointer to pruneDense2csr().

Appendix E.1 provides a simple example of pruneDense2csr().

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`A`	`device`	array of dimension (lda, n).
`lda`	`device`	leading dimension of `A`. It must be at least max(1, m).
`threshold`	`host or device`	a value to drop the entries of A. `threshold` can point to a device memory or host memory.
`descrC`	`host`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `pruneDense2csr_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`nnzTotalDevHostPtr`	`device or host`	total number of nonzero of matrix `C`. `nnzTotalDevHostPtr` can point to a device memory or host memory.
`csrValC`	`device`	<type> array of `nnzC` nonzero elements of matrix `C`.
`csrRowsPtrC`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	`device`	integer array of `nnzC` column indices of `C`.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n <0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.32. cusparseXpruneCsr2csr()


cusparseStatus_t 
cusparseHpruneCsr2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    const __half *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseSpruneCsr2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    const float *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDpruneCsr2csr_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    const double *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    size_t *pBufferSizeInBytes);

cusparseStatus_t
cusparseHpruneCsr2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneCsr2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    void *pBuffer);

cusparseStatus_t
cusparseDpruneCsr2csrNnz(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    void *pBuffer);

cusparseStatus_t 
cusparseHpruneCsr2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const __half *threshold,
    const cusparseMatDescr_t descrC,
    __half *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneCsr2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const float *threshold,
    const cusparseMatDescr_t descrC,
    float *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneCsr2csr(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const double *threshold,
    const cusparseMatDescr_t descrC,
    double *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    void *pBuffer);

This function prunes a sparse matrix to a sparse matrix with CSR format.

Given a sparse matrix A and a non-negative value threshold, the function returns a sparse matrix C, defined by

\begin{array}{ll} C(i,j) = A(i,j) & if |A(i,j)| > threshold \end{array}

The implementation adopts a two-step approach to do the conversion. First, the user allocates csrRowPtrC of m+1 elements and uses function pruneCsr2csrNnz() to determine the number of nonzeros columns per row. Second, the user gathers nnzC (number of nonzeros of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC[m]-csrRowPtrC[0]) and allocates csrValC of nnzC elements and csrColIndC of nnzC integers. Finally function pruneCsr2csr() is called to complete the conversion.

The user must obtain the size of the buffer required by pruneCsr2csr() by calling pruneCsr2csr_bufferSizeExt(), allocate the buffer, and pass the buffer pointer to pruneCsr2csr().

Appendix E.2 provides a simple example of pruneCsr2csr().

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnzA`	`host`	number of nonzeros of matrix `A`.
`descrA`	`host`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	`device`	<type> array of `nnzA` nonzero elements of matrix `A`.
`csrRowsPtrA`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	`device`	integer array of `nnzA` column indices of `A`.
`threshold`	`host or device`	a value to drop the entries of A. `threshold` can point to a device memory or host memory.
`descrC`	`host`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `pruneCsr2csr_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`nnzTotalDevHostPtr`	`device or host`	total number of nonzero of matrix `C`. `nnzTotalDevHostPtr` can point to a device memory or host memory.
`csrValC`	`device`	<type> array of `nnzC` nonzero elements of matrix `C`.
`csrRowsPtrC`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	`device`	integer array of `nnzC` column indices of `C`.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n <0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.33. cusparseXpruneDense2csrPercentage()


cusparseStatus_t 
cusparseHpruneDense2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const __half *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t
cusparseSpruneDense2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const float *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseDpruneDense2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const double *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseHpruneDense2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneDense2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneDense2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseHpruneDense2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const __half *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    __half *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneDense2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const float *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    float *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneDense2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    const double *A,
    int lda,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    double *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

This function prunes a dense matrix to a sparse matrix by percentage.

Given a dense matrix A and a non-negative value percentage, the function computes sparse matrix C by the following three steps:

Step 1: sort absolute value of A in ascending order.

\begin{array}{ll} key := sort( |A| ) \end{array}

Step 2: choose threshold by the parameter percentage

\begin{array}{ll} pos = ceil(m*n*(percentage/100)) - 1 \\ pos = min(pos, m*n-1) \\ pos = max(pos, 0) \\ threshold = key[pos] \end{array}

Step 3: call pruneDense2csr() by with the parameter threshold.

The implementation adopts a two-step approach to do the conversion. First, the user allocates csrRowPtrC of m+1 elements and uses function pruneDense2csrNnzByPercentage() to determine the number of nonzeros columns per row. Second, the user gathers nnzC (number of nonzeros of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC[m]-csrRowPtrC[0]) and allocates csrValC of nnzC elements and csrColIndC of nnzC integers. Finally function pruneDense2csrByPercentage() is called to complete the conversion.

The user must obtain the size of the buffer required by pruneDense2csrByPercentage() by calling pruneDense2csrByPercentage_bufferSizeExt(), allocate the buffer, and pass the buffer pointer to pruneDense2csrByPercentage().

Remark 1: the value of percentage must be not greater than 100. Otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Remark 2: the zeros of A are not ignored. All entries are sorted, including zeros. This is different from pruneCsr2csrByPercentage()

Appendix E.3 provides a simple example of pruneDense2csrByPercentage().

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`A`	`device`	array of dimension (lda, n).
`lda`	`device`	leading dimension of `A`. It must be at least max(1, m).
`percentage`	`host`	percentage <=100 and percentage >= 0
`descrC`	`host`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `pruneDense2csrByPercentage_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`nnzTotalDevHostPtr`	`device or host`	total number of nonzero of matrix `C`. `nnzTotalDevHostPtr` can point to a device memory or host memory.
`csrValC`	`device`	<type> array of `nnzC` nonzero elements of matrix `C`.
`csrRowsPtrC`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	`device`	integer array of `nnzC` column indices of `C`.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n <0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.34. cusparseXpruneCsr2csrByPercentage()


cusparseStatus_t 
cusparseHpruneCsr2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const __half *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseSpruneCsr2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const float *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t
cusparseDpruneCsr2csrByPercentage_bufferSizeExt(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    const double *csrValC,
    const int *csrRowPtrC,
    const int *csrColIndC,
    pruneInfo_t info,
    size_t *pBufferSizeInBytes);

cusparseStatus_t 
cusparseHpruneCsr2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneCsr2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneCsr2csrNnzByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    int *csrRowPtrC,
    int *nnzTotalDevHostPtr, /* can be on host or device */
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseHpruneCsr2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const __half *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    __half *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseSpruneCsr2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    float *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

cusparseStatus_t 
cusparseDpruneCsr2csrByPercentage(
    cusparseHandle_t handle,
    int m,
    int n,
    int nnzA,
    const cusparseMatDescr_t descrA,
    const double *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    float percentage, /* between 0 to 100 */
    const cusparseMatDescr_t descrC,
    double *csrValC,
    const int *csrRowPtrC,
    int *csrColIndC,
    pruneInfo_t info,
    void *pBuffer);

This function prunes a sparse matrix to a sparse matrix by percentage.

Given a sparse matrix A and a non-negative value percentage, the function computes sparse matrix C by the following three steps:

Step 1: sort absolute value of A in ascending order.

\begin{array}{ll} key := sort( |csrValA| ) \end{array}

Step 2: choose threshold by the parameter percentage

\begin{array}{ll} pos = ceil(nnzA*(percentage/100)) - 1 \\ pos = min(pos, nnzA-1) \\ pos = max(pos, 0) \\ threshold = key[pos] \end{array}

Step 3: call pruneCsr2csr() by with the parameter threshold.

The implementation adopts a two-step approach to do the conversion. First, the user allocates csrRowPtrC of m+1 elements and uses function pruneCsr2csrNnzByPercentage() to determine the number of nonzeros columns per row. Second, the user gathers nnzC (number of nonzeros of matrix C) from either (nnzC=*nnzTotalDevHostPtr) or (nnzC=csrRowPtrC[m]-csrRowPtrC[0]) and allocates csrValC of nnzC elements and csrColIndC of nnzC integers. Finally function pruneCsr2csrByPercentage() is called to complete the conversion.

The user must obtain the size of the buffer required by pruneCsr2csrByPercentage() by calling pruneCsr2csrByPercentage_bufferSizeExt(), allocate the buffer, and pass the buffer pointer to pruneCsr2csrByPercentage().

Remark 1: the value of percentage must be not greater than 100. Otherwise, CUSPARSE_STATUS_INVALID_VALUE is returned.

Appendix E.4 provides a simple example of pruneCsr2csrByPercentage().

Input

`parameter`	`device or host`	`description`
`handle`	`host`	handle to the cuSPARSE library context.
`m`	`host`	number of rows of matrix `A`.
`n`	`host`	number of columns of matrix `A`.
`nnzA`	`host`	number of nonzeros of matrix `A`.
`descrA`	`host`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	`device`	<type> array of `nnzA` nonzero elements of matrix `A`.
`csrRowsPtrA`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndA`	`device`	integer array of `nnzA` column indices of `A`.
`percentage`	`host`	percentage <=100 and percentage >= 0
`descrC`	`host`	the descriptor of matrix `C`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`, Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`pBuffer`	`device`	buffer allocated by the user; the size is returned by `pruneCsr2csrByPercentage_bufferSizeExt()`.

Output

`parameter`	`device or host`	`description`
`nnzTotalDevHostPtr`	`device or host`	total number of nonzero of matrix `C`. `nnzTotalDevHostPtr` can point to a device memory or host memory.
`csrValC`	`device`	<type> array of `nnzC` nonzero elements of matrix `C`.
`csrRowsPtrC`	`device`	integer array of `m+1` elements that contains the start of every row and the end of the last row plus one.
`csrColIndC`	`device`	integer array of `nnzC` column indices of `C`.
`pBufferSizeInBytes`	`host`	number of bytes of the buffer.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m,n <0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

12.35. cusparse<t>nnz_compress()

cusparseStatus_t 
cusparseSnnz_compress(cusparseHandle_t handle,
                      int m,
                      const cusparseMatDescr_t descr,
                      const float *csrValA,
                      const int * csrRowPtrA,
                      int *nnzPerRow,
                      int *nnzC,
                      float tol)
cusparseStatus_t 
cusparseDnnz_compress(cusparseHandle_t handle,
                      int m,
                      const cusparseMatDescr_t descr,
                      const double *csrValA,
                      const int * csrRowPtrA,
                      int *nnzPerRow,
                      int *nnzC,
                      double tol)
cusparseStatus_t 
cusparseCnnz_compress(cusparseHandle_t handle,
                      int m,
                      const cusparseMatDescr_t descr,
                      const cuComplex *csrValA,
                      const int * csrRowPtrA,
                      int *nnzPerRow,
                      int *nnzC,
                      cuComplex tol)
cusparseStatus_t 
cusparseZnnz_compress(cusparseHandle_t handle,
                      int m,
                      const cusparseMatDescr_t descr,
                      const cuDoubleComplex *csrValA,
                      const int * csrRowPtrA,
                      int *nnzPerRow,
                      int *nnzC,
                      cuDoubleComplex tol)

This function is the step one to convert from csr format to compressed csr format.

Given a sparse matrix A and a non-negative value threshold, the function returns nnzPerRow(the number of nonzeros columns per row) and nnzC(the total number of nonzeros) of a sparse matrix C, defined by

\begin{array}{ll} C(i,j) = A(i,j) & if |A(i,j)| > threshold \end{array}

A key assumption for the cuComplex and cuDoubleComplex case is that this tolerance is given as the real part. For example tol = 1e-8 + 0*i and we extract cureal, that is the x component of this struct.

Input

`handle`	handle to the cuSPARSE library context.
`m`	number of rows of matrix `A`.
`descrA`	the descriptor of matrix `A`. The supported matrix type is `CUSPARSE_MATRIX_TYPE_GENERAL`. Also, the supported index bases are `CUSPARSE_INDEX_BASE_ZERO` and `CUSPARSE_INDEX_BASE_ONE`.
`csrValA`	csr noncompressed values array
`csrRowPtrA`	the corresponding input noncompressed row pointer.
`tol`	non-negative tolerance to determine if a number less than or equal to it.

Output

`nnzPerRow`	this array contains the number of elements whose absolute values are greater than tol per row.
`nnzC`	host/device pointer of the total number of elements whose absolute values are greater than tol.

Status Returned

`CUSPARSE_STATUS_SUCCESS`	the operation completed successfully.
`CUSPARSE_STATUS_NOT_INITIALIZED`	the library was not initialized.
`CUSPARSE_STATUS_ALLOC_FAILED`	the resources could not be allocated.
`CUSPARSE_STATUS_INVALID_VALUE`	invalid parameters were passed (`m, n<0`).
`CUSPARSE_STATUS_ARCH_MISMATCH`	the device does not support double precision.
`CUSPARSE_STATUS_EXECUTION_FAILED`	the function failed to launch on the GPU.
`CUSPARSE_STATUS_INTERNAL_ERROR`	an internal operation failed.
`CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED`	the matrix type is not supported.

Appendix A: cuSPARSE Library C++ Example

For sample code reference please see the example code below. It shows an application written in C++ using the cuSPARSE library API. The code performs the following actions:

1. Creates a sparse test matrix in COO format.

2. Creates a sparse and dense vector.

3. Allocates GPU memory and copies the matrix and vectors into it.

4. Initializes the cuSPARSE library.

5. Creates and sets up the matrix descriptor.

6. Converts the matrix from COO to CSR format.

7. Exercises Level 1 routines.

8. Exercises Level 2 routines.

9. Exercises Level 3 routines.

10. Destroys the matrix descriptor.

11. Releases resources allocated for the cuSPARSE library.

//Example: Application using C++ and the CUSPARSE library 
//-------------------------------------------------------
#include <stdio.h>
#include <stdlib.h>
#include <cuda_runtime.h>
#include "cusparse.h"

#define CLEANUP(s)                                   \
do {                                                 \
    printf ("%s\n", s);                              \
    if (yHostPtr)           free(yHostPtr);          \
    if (zHostPtr)           free(zHostPtr);          \
    if (xIndHostPtr)        free(xIndHostPtr);       \
    if (xValHostPtr)        free(xValHostPtr);       \
    if (cooRowIndexHostPtr) free(cooRowIndexHostPtr);\
    if (cooColIndexHostPtr) free(cooColIndexHostPtr);\
    if (cooValHostPtr)      free(cooValHostPtr);     \
    if (y)                  cudaFree(y);             \
    if (z)                  cudaFree(z);             \
    if (xInd)               cudaFree(xInd);          \
    if (xVal)               cudaFree(xVal);          \
    if (csrRowPtr)          cudaFree(csrRowPtr);     \
    if (cooRowIndex)        cudaFree(cooRowIndex);   \
    if (cooColIndex)        cudaFree(cooColIndex);   \
    if (cooVal)             cudaFree(cooVal);        \
    if (descr)              cusparseDestroyMatDescr(descr);\
    if (handle)             cusparseDestroy(handle); \
    cudaDeviceReset();          \
    fflush (stdout);                                 \
} while (0)

int main(){     
    cudaError_t cudaStat1,cudaStat2,cudaStat3,cudaStat4,cudaStat5,cudaStat6;
    cusparseStatus_t status;
    cusparseHandle_t handle=0;
    cusparseMatDescr_t descr=0;
    int *    cooRowIndexHostPtr=0;
    int *    cooColIndexHostPtr=0;    
    double * cooValHostPtr=0;
    int *    cooRowIndex=0;
    int *    cooColIndex=0;    
    double * cooVal=0;
    int *    xIndHostPtr=0;
    double * xValHostPtr=0;
    double * yHostPtr=0;
    int *    xInd=0;
    double * xVal=0;
    double * y=0;  
    int *    csrRowPtr=0;
    double * zHostPtr=0; 
    double * z=0; 
    int      n, nnz, nnz_vector;
    double dzero =0.0;
    double dtwo  =2.0;
    double dthree=3.0;
    double dfive =5.0;

    printf("testing example\n");
    /* create the following sparse test matrix in COO format */
    /* |1.0     2.0 3.0|
       |    4.0        |
       |5.0     6.0 7.0|
       |    8.0     9.0| */
    n=4; nnz=9; 
    cooRowIndexHostPtr = (int *)   malloc(nnz*sizeof(cooRowIndexHostPtr[0])); 
    cooColIndexHostPtr = (int *)   malloc(nnz*sizeof(cooColIndexHostPtr[0])); 
    cooValHostPtr      = (double *)malloc(nnz*sizeof(cooValHostPtr[0])); 
    if ((!cooRowIndexHostPtr) || (!cooColIndexHostPtr) || (!cooValHostPtr)){
        CLEANUP("Host malloc failed (matrix)");
        return 1; 
    }
    cooRowIndexHostPtr[0]=0; cooColIndexHostPtr[0]=0; cooValHostPtr[0]=1.0;  
    cooRowIndexHostPtr[1]=0; cooColIndexHostPtr[1]=2; cooValHostPtr[1]=2.0;  
    cooRowIndexHostPtr[2]=0; cooColIndexHostPtr[2]=3; cooValHostPtr[2]=3.0;  
    cooRowIndexHostPtr[3]=1; cooColIndexHostPtr[3]=1; cooValHostPtr[3]=4.0;  
    cooRowIndexHostPtr[4]=2; cooColIndexHostPtr[4]=0; cooValHostPtr[4]=5.0;  
    cooRowIndexHostPtr[5]=2; cooColIndexHostPtr[5]=2; cooValHostPtr[5]=6.0;
    cooRowIndexHostPtr[6]=2; cooColIndexHostPtr[6]=3; cooValHostPtr[6]=7.0;  
    cooRowIndexHostPtr[7]=3; cooColIndexHostPtr[7]=1; cooValHostPtr[7]=8.0;  
    cooRowIndexHostPtr[8]=3; cooColIndexHostPtr[8]=3; cooValHostPtr[8]=9.0;  
    /*
    //print the matrix
    printf("Input data:\n");
    for (int i=0; i<nnz; i++){        
        printf("cooRowIndexHostPtr[%d]=%d  ",i,cooRowIndexHostPtr[i]);
        printf("cooColIndexHostPtr[%d]=%d  ",i,cooColIndexHostPtr[i]);
        printf("cooValHostPtr[%d]=%f     \n",i,cooValHostPtr[i]);
    }
    */

    /* create a sparse and dense vector */ 
    /* xVal= [100.0 200.0 400.0]   (sparse)
       xInd= [0     1     3    ]
       y   = [10.0 20.0 30.0 40.0 | 50.0 60.0 70.0 80.0] (dense) */
    nnz_vector = 3;
    xIndHostPtr = (int *)   malloc(nnz_vector*sizeof(xIndHostPtr[0])); 
    xValHostPtr = (double *)malloc(nnz_vector*sizeof(xValHostPtr[0])); 
    yHostPtr    = (double *)malloc(2*n       *sizeof(yHostPtr[0]));
    zHostPtr    = (double *)malloc(2*(n+1)   *sizeof(zHostPtr[0]));
    if((!xIndHostPtr) || (!xValHostPtr) || (!yHostPtr) || (!zHostPtr)){
        CLEANUP("Host malloc failed (vectors)");
        return 1; 
    }
    yHostPtr[0] = 10.0;  xIndHostPtr[0]=0; xValHostPtr[0]=100.0; 
    yHostPtr[1] = 20.0;  xIndHostPtr[1]=1; xValHostPtr[1]=200.0;  
    yHostPtr[2] = 30.0;
    yHostPtr[3] = 40.0;  xIndHostPtr[2]=3; xValHostPtr[2]=400.0;  
    yHostPtr[4] = 50.0;
    yHostPtr[5] = 60.0;
    yHostPtr[6] = 70.0;
    yHostPtr[7] = 80.0;
    /*
    //print the vectors
    for (int j=0; j<2; j++){
        for (int i=0; i<n; i++){        
            printf("yHostPtr[%d,%d]=%f\n",i,j,yHostPtr[i+n*j]);
        }
    }
    for (int i=0; i<nnz_vector; i++){        
        printf("xIndHostPtr[%d]=%d  ",i,xIndHostPtr[i]);
        printf("xValHostPtr[%d]=%f\n",i,xValHostPtr[i]);
    }
    */

    /* allocate GPU memory and copy the matrix and vectors into it */
    cudaStat1 = cudaMalloc((void**)&cooRowIndex,nnz*sizeof(cooRowIndex[0])); 
    cudaStat2 = cudaMalloc((void**)&cooColIndex,nnz*sizeof(cooColIndex[0]));
    cudaStat3 = cudaMalloc((void**)&cooVal,     nnz*sizeof(cooVal[0])); 
    cudaStat4 = cudaMalloc((void**)&y,          2*n*sizeof(y[0]));   
    cudaStat5 = cudaMalloc((void**)&xInd,nnz_vector*sizeof(xInd[0])); 
    cudaStat6 = cudaMalloc((void**)&xVal,nnz_vector*sizeof(xVal[0])); 
    if ((cudaStat1 != cudaSuccess) ||
        (cudaStat2 != cudaSuccess) ||
        (cudaStat3 != cudaSuccess) ||
        (cudaStat4 != cudaSuccess) ||
        (cudaStat5 != cudaSuccess) ||
        (cudaStat6 != cudaSuccess)) {
        CLEANUP("Device malloc failed");
        return 1; 
    }    
    cudaStat1 = cudaMemcpy(cooRowIndex, cooRowIndexHostPtr, 
                           (size_t)(nnz*sizeof(cooRowIndex[0])), 
                           cudaMemcpyHostToDevice);
    cudaStat2 = cudaMemcpy(cooColIndex, cooColIndexHostPtr, 
                           (size_t)(nnz*sizeof(cooColIndex[0])), 
                           cudaMemcpyHostToDevice);
    cudaStat3 = cudaMemcpy(cooVal,      cooValHostPtr,      
                           (size_t)(nnz*sizeof(cooVal[0])),      
                           cudaMemcpyHostToDevice);
    cudaStat4 = cudaMemcpy(y,           yHostPtr,           
                           (size_t)(2*n*sizeof(y[0])),           
                           cudaMemcpyHostToDevice);
    cudaStat5 = cudaMemcpy(xInd,        xIndHostPtr,        
                           (size_t)(nnz_vector*sizeof(xInd[0])), 
                           cudaMemcpyHostToDevice);
    cudaStat6 = cudaMemcpy(xVal,        xValHostPtr,        
                           (size_t)(nnz_vector*sizeof(xVal[0])), 
                           cudaMemcpyHostToDevice);
    if ((cudaStat1 != cudaSuccess) ||
        (cudaStat2 != cudaSuccess) ||
        (cudaStat3 != cudaSuccess) ||
        (cudaStat4 != cudaSuccess) ||
        (cudaStat5 != cudaSuccess) ||
        (cudaStat6 != cudaSuccess)) {
        CLEANUP("Memcpy from Host to Device failed");
        return 1;
    }
    
    /* initialize cusparse library */
    status= cusparseCreate(&handle);
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("CUSPARSE Library initialization failed");
        return 1;
    }

    /* create and setup matrix descriptor */ 
    status= cusparseCreateMatDescr(&descr); 
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Matrix descriptor initialization failed");
        return 1;
    }       
    cusparseSetMatType(descr,CUSPARSE_MATRIX_TYPE_GENERAL);
    cusparseSetMatIndexBase(descr,CUSPARSE_INDEX_BASE_ZERO);  
    
    /* exercise conversion routines (convert matrix from COO 2 CSR format) */
    cudaStat1 = cudaMalloc((void**)&csrRowPtr,(n+1)*sizeof(csrRowPtr[0]));
    if (cudaStat1 != cudaSuccess) {
        CLEANUP("Device malloc failed (csrRowPtr)");
        return 1;
    }
    status= cusparseXcoo2csr(handle,cooRowIndex,nnz,n,
                             csrRowPtr,CUSPARSE_INDEX_BASE_ZERO); 
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Conversion from COO to CSR format failed");
        return 1;
    }  
    //csrRowPtr = [0 3 4 7 9] 

    // The following test only works for compute capability 1.3 and above 
    // because it needs double precision.
    int devId;
    cudaDeviceProp prop;
    cudaError_t cudaStat;
    cudaStat = cudaGetDevice(&devId);
    if (cudaSuccess != cudaStat){
        CLEANUP("cudaGetDevice failed");
        printf("Error: cudaStat %d, %s\n", cudaStat, cudaGetErrorString(cudaStat));
        return 1;
    }
    cudaStat = cudaGetDeviceProperties( &prop, devId) ;
    if (cudaSuccess != cudaStat){
        CLEANUP("cudaGetDeviceProperties failed");
        printf("Error: cudaStat %d, %s\n", cudaStat, cudaGetErrorString(cudaStat));
        return 1;
    }
    int cc = 100*prop.major + 10*prop.minor;
    if (cc < 130){
        CLEANUP("waive the test because only sm13 and above are supported\n");
        printf("the device has compute capability %d\n", cc);
        printf("example test WAIVED");
        return 2;
    }

    /* exercise Level 1 routines (scatter vector elements) */
    status= cusparseDsctr(handle, nnz_vector, xVal, xInd, 
                          &y[n], CUSPARSE_INDEX_BASE_ZERO);
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Scatter from sparse to dense vector failed");
        return 1;
    }  
    //y = [10 20 30 40 | 100 200 70 400]

    /* exercise Level 2 routines (csrmv) */
    status= cusparseDcsrmv(handle,CUSPARSE_OPERATION_NON_TRANSPOSE, n, n, nnz,
                           &dtwo, descr, cooVal, csrRowPtr, cooColIndex, 
                           &y[0], &dthree, &y[n]);
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Matrix-vector multiplication failed");
        return 1;
    }    
    //y = [10 20 30 40 | 680 760 1230 2240]
    cudaMemcpy(yHostPtr, y, (size_t)(2*n*sizeof(y[0])), cudaMemcpyDeviceToHost);
    /*
    printf("Intermediate results:\n");
    for (int j=0; j<2; j++){
        for (int i=0; i<n; i++){        
            printf("yHostPtr[%d,%d]=%f\n",i,j,yHostPtr[i+n*j]);
        }
    }
    */

    /* exercise Level 3 routines (csrmm) */
    cudaStat1 = cudaMalloc((void**)&z, 2*(n+1)*sizeof(z[0]));   
    if (cudaStat1 != cudaSuccess) {
        CLEANUP("Device malloc failed (z)");
        return 1;
    }
    cudaStat1 = cudaMemset((void *)z,0, 2*(n+1)*sizeof(z[0]));    
    if (cudaStat1 != cudaSuccess) {
        CLEANUP("Memset on Device failed");
        return 1;
    }
    status= cusparseDcsrmm(handle, CUSPARSE_OPERATION_NON_TRANSPOSE, n, 2, n, 
                           nnz, &dfive, descr, cooVal, csrRowPtr, cooColIndex, 
                           y, n, &dzero, z, n+1);
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Matrix-matrix multiplication failed");
        return 1;
    }  

    /* print final results (z) */
    cudaStat1 = cudaMemcpy(zHostPtr, z, 
                           (size_t)(2*(n+1)*sizeof(z[0])), 
                           cudaMemcpyDeviceToHost);
    if (cudaStat1 != cudaSuccess)  {
        CLEANUP("Memcpy from Device to Host failed");
        return 1;
    } 
    //z = [950 400 2550 2600 0 | 49300 15200 132300 131200 0]
    /*
    printf("Final results:\n");
    for (int j=0; j<2; j++){
        for (int i=0; i<n+1; i++){
            printf("z[%d,%d]=%f\n",i,j,zHostPtr[i+(n+1)*j]);
        }
    }
    */

    /* destroy matrix descriptor */ 
    status = cusparseDestroyMatDescr(descr); 
    descr = 0;
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("Matrix descriptor destruction failed");
        return 1;
    }    

    /* destroy handle */
    status = cusparseDestroy(handle);
    handle = 0;
    if (status != CUSPARSE_STATUS_SUCCESS) {
        CLEANUP("CUSPARSE Library release of resources failed");
        return 1;
    }   

    /* check the results */
    /* Notice that CLEANUP() contains a call to cusparseDestroy(handle) */
    if ((zHostPtr[0] != 950.0)    || 
        (zHostPtr[1] != 400.0)    || 
        (zHostPtr[2] != 2550.0)   || 
        (zHostPtr[3] != 2600.0)   || 
        (zHostPtr[4] != 0.0)      || 
        (zHostPtr[5] != 49300.0)  || 
        (zHostPtr[6] != 15200.0)  || 
        (zHostPtr[7] != 132300.0) || 
        (zHostPtr[8] != 131200.0) || 
        (zHostPtr[9] != 0.0)      ||
        (yHostPtr[0] != 10.0)     || 
        (yHostPtr[1] != 20.0)     || 
        (yHostPtr[2] != 30.0)     || 
        (yHostPtr[3] != 40.0)     || 
        (yHostPtr[4] != 680.0)    || 
        (yHostPtr[5] != 760.0)    || 
        (yHostPtr[6] != 1230.0)   || 
        (yHostPtr[7] != 2240.0)){ 
        CLEANUP("example test FAILED");
        return 1;
    }
    else{
        CLEANUP("example test PASSED");
        return 0;
    }      
}

Appendix B: cuSPARSE Fortran Bindings

The cuSPARSE library is implemented using the C-based CUDA toolchain, and it thus provides a C-style API that makes interfacing to applications written in C or C++ trivial. There are also many applications implemented in Fortran that would benefit from using cuSPARSE, and therefore a cuSPARSE Fortran interface has been developed.

Unfortunately, Fortran-to-C calling conventions are not standardized and differ by platform and toolchain. In particular, differences may exist in the following areas:

Symbol names (capitalization, name decoration)

Argument passing (by value or reference)

Passing of pointer arguments (size of the pointer)

To provide maximum flexibility in addressing those differences, the cuSPARSE Fortran interface is provided in the form of wrapper functions, which are written in C and are located in the file cusparse_fortran.c. This file also contains a few additional wrapper functions (for cudaMalloc(), cudaMemset, and so on) that can be used to allocate memory on the GPU.

The cuSPARSE Fortran wrapper code is provided as an example only and needs to be compiled into an application for it to call the cuSPARSE API functions. Providing this source code allows users to make any changes necessary for a particular platform and toolchain.

The cuSPARSE Fortran wrapper code has been used to demonstrate interoperability with the compilers g95 0.91 (on 32-bit and 64-bit Linux) and g95 0.92 (on 32-bit and 64-bit Mac OS X). In order to use other compilers, users have to make any changes to the wrapper code that may be required.

The direct wrappers, intended for production code, substitute device pointers for vector and matrix arguments in all cuSPARSE functions. To use these interfaces, existing applications need to be modified slightly to allocate and deallocate data structures in GPU memory space (using CUDA_MALLOC() and CUDA_FREE()) and to copy data between GPU and CPU memory spaces (using the CUDA_MEMCPY() routines). The sample wrappers provided in cusparse_fortran.c map device pointers to the OS-dependent type size_t, which is 32 bits wide on 32-bit platforms and 64 bits wide on a 64-bit platforms.

One approach to dealing with index arithmetic on device pointers in Fortran code is to use C-style macros and to use the C preprocessor to expand them. On Linux and Mac OS X, preprocessing can be done by using the option '-cpp' with g95 or gfortran. The function GET_SHIFTED_ADDRESS(), provided with the cuSPARSE Fortran wrappers, can also be used, as shown in example B.

Example B shows the the C++ of example A implemented in Fortran 77 on the host. This example should be compiled with ARCH_64 defined as 1 on a 64-bit OS system and as undefined on a 32-bit OS system. For example, on g95 or gfortran, it can be done directly on the command line using the option -cpp -DARCH_64=1.

14.1. Example B, Fortran Application

c     #define ARCH_64 0
c     #define ARCH_64 1

      program cusparse_fortran_example
      implicit none
      integer cuda_malloc
      external cuda_free
      integer cuda_memcpy_c2fort_int
      integer cuda_memcpy_c2fort_real
      integer cuda_memcpy_fort2c_int
      integer cuda_memcpy_fort2c_real
      integer cuda_memset
      integer cusparse_create 
      external cusparse_destroy
      integer cusparse_get_version 
      integer cusparse_create_mat_descr
      external cusparse_destroy_mat_descr
      integer cusparse_set_mat_type 
      integer cusparse_get_mat_type
      integer cusparse_get_mat_fill_mode
      integer cusparse_get_mat_diag_type
      integer cusparse_set_mat_index_base
      integer cusparse_get_mat_index_base
      integer cusparse_xcoo2csr
      integer cusparse_dsctr
      integer cusparse_dcsrmv
      integer cusparse_dcsrmm
      external get_shifted_address
#if ARCH_64      
      integer*8 handle
      integer*8 descrA      
      integer*8 cooRowIndex
      integer*8 cooColIndex    
      integer*8 cooVal
      integer*8 xInd
      integer*8 xVal
      integer*8 y  
      integer*8 z 
      integer*8 csrRowPtr
      integer*8 ynp1  
#else
      integer*4 handle
      integer*4 descrA
      integer*4 cooRowIndex
      integer*4 cooColIndex    
      integer*4 cooVal
      integer*4 xInd
      integer*4 xVal
      integer*4 y  
      integer*4 z 
      integer*4 csrRowPtr
      integer*4 ynp1  
#endif      
      integer status
      integer cudaStat1,cudaStat2,cudaStat3
      integer cudaStat4,cudaStat5,cudaStat6
      integer n, nnz, nnz_vector
      parameter (n=4, nnz=9, nnz_vector=3)
      integer cooRowIndexHostPtr(nnz)
      integer cooColIndexHostPtr(nnz)    
      real*8  cooValHostPtr(nnz)
      integer xIndHostPtr(nnz_vector)
      real*8  xValHostPtr(nnz_vector)
      real*8  yHostPtr(2*n)
      real*8  zHostPtr(2*(n+1)) 
      integer i, j
      integer version, mtype, fmode, dtype, ibase
      real*8  dzero,dtwo,dthree,dfive
      real*8  epsilon


      write(*,*) "testing fortran example"

c     predefined constants (need to be careful with them)
      dzero = 0.0
      dtwo  = 2.0
      dthree= 3.0
      dfive = 5.0
c     create the following sparse test matrix in COO format 
c     (notice one-based indexing)
c     |1.0     2.0 3.0|
c     |    4.0        |
c     |5.0     6.0 7.0|
c     |    8.0     9.0| 
      cooRowIndexHostPtr(1)=1 
      cooColIndexHostPtr(1)=1 
      cooValHostPtr(1)     =1.0  
      cooRowIndexHostPtr(2)=1 
      cooColIndexHostPtr(2)=3 
      cooValHostPtr(2)     =2.0  
      cooRowIndexHostPtr(3)=1 
      cooColIndexHostPtr(3)=4 
      cooValHostPtr(3)     =3.0  
      cooRowIndexHostPtr(4)=2 
      cooColIndexHostPtr(4)=2 
      cooValHostPtr(4)     =4.0  
      cooRowIndexHostPtr(5)=3 
      cooColIndexHostPtr(5)=1 
      cooValHostPtr(5)     =5.0  
      cooRowIndexHostPtr(6)=3 
      cooColIndexHostPtr(6)=3 
      cooValHostPtr(6)     =6.0
      cooRowIndexHostPtr(7)=3 
      cooColIndexHostPtr(7)=4 
      cooValHostPtr(7)     =7.0  
      cooRowIndexHostPtr(8)=4 
      cooColIndexHostPtr(8)=2 
      cooValHostPtr(8)     =8.0  
      cooRowIndexHostPtr(9)=4 
      cooColIndexHostPtr(9)=4 
      cooValHostPtr(9)     =9.0  
c     print the matrix
      write(*,*) "Input data:"
      do i=1,nnz        
         write(*,*) "cooRowIndexHostPtr[",i,"]=",cooRowIndexHostPtr(i)
         write(*,*) "cooColIndexHostPtr[",i,"]=",cooColIndexHostPtr(i)
         write(*,*) "cooValHostPtr[",     i,"]=",cooValHostPtr(i)
      enddo
  
c     create a sparse and dense vector  
c     xVal= [100.0 200.0 400.0]   (sparse)
c     xInd= [0     1     3    ]
c     y   = [10.0 20.0 30.0 40.0 | 50.0 60.0 70.0 80.0] (dense) 
c     (notice one-based indexing)
      yHostPtr(1) = 10.0  
      yHostPtr(2) = 20.0  
      yHostPtr(3) = 30.0
      yHostPtr(4) = 40.0  
      yHostPtr(5) = 50.0
      yHostPtr(6) = 60.0
      yHostPtr(7) = 70.0
      yHostPtr(8) = 80.0
      xIndHostPtr(1)=1 
      xValHostPtr(1)=100.0 
      xIndHostPtr(2)=2 
      xValHostPtr(2)=200.0
      xIndHostPtr(3)=4 
      xValHostPtr(3)=400.0    
c     print the vectors
      do j=1,2
         do i=1,n        
            write(*,*) "yHostPtr[",i,",",j,"]=",yHostPtr(i+n*(j-1))
         enddo
      enddo
      do i=1,nnz_vector        
         write(*,*) "xIndHostPtr[",i,"]=",xIndHostPtr(i)
         write(*,*) "xValHostPtr[",i,"]=",xValHostPtr(i)
      enddo

c     allocate GPU memory and copy the matrix and vectors into it 
c     cudaSuccess=0
c     cudaMemcpyHostToDevice=1
      cudaStat1 = cuda_malloc(cooRowIndex,nnz*4) 
      cudaStat2 = cuda_malloc(cooColIndex,nnz*4)
      cudaStat3 = cuda_malloc(cooVal,     nnz*8) 
      cudaStat4 = cuda_malloc(y,          2*n*8)   
      cudaStat5 = cuda_malloc(xInd,nnz_vector*4) 
      cudaStat6 = cuda_malloc(xVal,nnz_vector*8) 
      if ((cudaStat1 /= 0) .OR. 
     $    (cudaStat2 /= 0) .OR. 
     $    (cudaStat3 /= 0) .OR. 
     $    (cudaStat4 /= 0) .OR. 
     $    (cudaStat5 /= 0) .OR. 
     $    (cudaStat6 /= 0)) then 
         write(*,*) "Device malloc failed"
         write(*,*) "cudaStat1=",cudaStat1
         write(*,*) "cudaStat2=",cudaStat2
         write(*,*) "cudaStat3=",cudaStat3
         write(*,*) "cudaStat4=",cudaStat4
         write(*,*) "cudaStat5=",cudaStat5
         write(*,*) "cudaStat6=",cudaStat6
         stop 2 
      endif    
      cudaStat1 = cuda_memcpy_fort2c_int(cooRowIndex,cooRowIndexHostPtr, 
     $                                   nnz*4,1)        
      cudaStat2 = cuda_memcpy_fort2c_int(cooColIndex,cooColIndexHostPtr, 
     $                                   nnz*4,1)       
      cudaStat3 = cuda_memcpy_fort2c_real(cooVal,    cooValHostPtr,      
     $                                    nnz*8,1)       
      cudaStat4 = cuda_memcpy_fort2c_real(y,      yHostPtr,           
     $                                    2*n*8,1)       
      cudaStat5 = cuda_memcpy_fort2c_int(xInd,       xIndHostPtr,        
     $                                   nnz_vector*4,1) 
      cudaStat6 = cuda_memcpy_fort2c_real(xVal,      xValHostPtr,        
     $                                    nnz_vector*8,1)
      if ((cudaStat1 /= 0) .OR. 
     $    (cudaStat2 /= 0) .OR. 
     $    (cudaStat3 /= 0) .OR. 
     $    (cudaStat4 /= 0) .OR. 
     $    (cudaStat5 /= 0) .OR. 
     $    (cudaStat6 /= 0)) then 
         write(*,*) "Memcpy from Host to Device failed"
         write(*,*) "cudaStat1=",cudaStat1
         write(*,*) "cudaStat2=",cudaStat2
         write(*,*) "cudaStat3=",cudaStat3
         write(*,*) "cudaStat4=",cudaStat4
         write(*,*) "cudaStat5=",cudaStat5
         write(*,*) "cudaStat6=",cudaStat6
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         stop 1
      endif
    
c     initialize cusparse library
c     CUSPARSE_STATUS_SUCCESS=0 
      status = cusparse_create(handle)
      if (status /= 0) then 
         write(*,*) "CUSPARSE Library initialization failed"
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         stop 1
      endif
c     get version
c     CUSPARSE_STATUS_SUCCESS=0
      status = cusparse_get_version(handle,version)
      if (status /= 0) then 
         write(*,*) "CUSPARSE Library initialization failed"
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)   
         call cusparse_destroy(handle)
         stop 1
      endif
      write(*,*) "CUSPARSE Library version",version

c     create and setup the matrix descriptor
c     CUSPARSE_STATUS_SUCCESS=0 
c     CUSPARSE_MATRIX_TYPE_GENERAL=0
c     CUSPARSE_INDEX_BASE_ONE=1  
      status= cusparse_create_mat_descr(descrA) 
      if (status /= 0) then 
         write(*,*) "Creating matrix descriptor failed"
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cusparse_destroy(handle)
         stop 1
      endif  
      status = cusparse_set_mat_type(descrA,0)       
      status = cusparse_set_mat_index_base(descrA,1) 
c     print the matrix descriptor
      mtype = cusparse_get_mat_type(descrA)
      fmode = cusparse_get_mat_fill_mode(descrA) 
      dtype = cusparse_get_mat_diag_type(descrA) 
      ibase = cusparse_get_mat_index_base(descrA) 
      write (*,*) "matrix descriptor:"
      write (*,*) "t=",mtype,"m=",fmode,"d=",dtype,"b=",ibase

c     exercise conversion routines (convert matrix from COO 2 CSR format) 
c     cudaSuccess=0
c     CUSPARSE_STATUS_SUCCESS=0 
c     CUSPARSE_INDEX_BASE_ONE=1
      cudaStat1 = cuda_malloc(csrRowPtr,(n+1)*4)
      if (cudaStat1 /= 0) then  
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Device malloc failed (csrRowPtr)"
         stop 2
      endif
      status= cusparse_xcoo2csr(handle,cooRowIndex,nnz,n,
     $                          csrRowPtr,1)         
      if (status /= 0) then 
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Conversion from COO to CSR format failed"
         stop 1
      endif  
c     csrRowPtr = [0 3 4 7 9] 

c     exercise Level 1 routines (scatter vector elements)
c     CUSPARSE_STATUS_SUCCESS=0  
c     CUSPARSE_INDEX_BASE_ONE=1
      call get_shifted_address(y,n*8,ynp1)
      status= cusparse_dsctr(handle, nnz_vector, xVal, xInd, 
     $                       ynp1, 1)
      if (status /= 0) then 
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Scatter from sparse to dense vector failed"
         stop 1
      endif  
c     y = [10 20 30 40 | 100 200 70 400]

c     exercise Level 2 routines (csrmv) 
c     CUSPARSE_STATUS_SUCCESS=0
c     CUSPARSE_OPERATION_NON_TRANSPOSE=0
      status= cusparse_dcsrmv(handle, 0, n, n, nnz, dtwo,
     $                       descrA, cooVal, csrRowPtr, cooColIndex, 
     $                       y, dthree, ynp1)        
      if (status /= 0) then 
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Matrix-vector multiplication failed"
         stop 1
      endif    
    
c     print intermediate results (y) 
c     y = [10 20 30 40 | 680 760 1230 2240]
c     cudaSuccess=0
c     cudaMemcpyDeviceToHost=2
      cudaStat1 = cuda_memcpy_c2fort_real(yHostPtr, y, 2*n*8, 2) 
      if (cudaStat1 /= 0) then  
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Memcpy from Device to Host failed"
         stop 1
      endif
      write(*,*) "Intermediate results:"
      do j=1,2
         do i=1,n        
             write(*,*) "yHostPtr[",i,",",j,"]=",yHostPtr(i+n*(j-1))
         enddo
      enddo 

c     exercise Level 3 routines (csrmm)
c     cudaSuccess=0 
c     CUSPARSE_STATUS_SUCCESS=0
c     CUSPARSE_OPERATION_NON_TRANSPOSE=0
      cudaStat1 = cuda_malloc(z, 2*(n+1)*8)   
      if (cudaStat1 /= 0) then  
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Device malloc failed (z)"
         stop 2
      endif
      cudaStat1 = cuda_memset(z, 0, 2*(n+1)*8)    
      if (cudaStat1 /= 0) then  
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(z) 
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Memset on Device failed"
         stop 1
      endif
      status= cusparse_dcsrmm(handle, 0, n, 2, n, nnz, dfive, 
     $                        descrA, cooVal, csrRowPtr, cooColIndex, 
     $                        y, n, dzero, z, n+1) 
      if (status /= 0) then     
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(z) 
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Matrix-matrix multiplication failed"
         stop 1
      endif  

c     print final results (z) 
c     cudaSuccess=0
c     cudaMemcpyDeviceToHost=2
      cudaStat1 = cuda_memcpy_c2fort_real(zHostPtr, z, 2*(n+1)*8, 2) 
      if (cudaStat1 /= 0) then 
         call cuda_free(cooRowIndex)
         call cuda_free(cooColIndex)    
         call cuda_free(cooVal)
         call cuda_free(xInd)
         call cuda_free(xVal)
         call cuda_free(y)  
         call cuda_free(z) 
         call cuda_free(csrRowPtr)
         call cusparse_destroy_mat_descr(descrA)
         call cusparse_destroy(handle)
         write(*,*) "Memcpy from Device to Host failed"
         stop 1
      endif 
c     z = [950 400 2550 2600 0 | 49300 15200 132300 131200 0]
      write(*,*) "Final results:"
      do j=1,2
         do i=1,n+1
            write(*,*) "z[",i,",",j,"]=",zHostPtr(i+(n+1)*(j-1))
         enddo
      enddo
    
c     check the results 
      epsilon = 0.00000000000001
      if ((DABS(zHostPtr(1) - 950.0)   .GT. epsilon)  .OR. 
     $    (DABS(zHostPtr(2) - 400.0)   .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(3) - 2550.0)  .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(4) - 2600.0)  .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(5) - 0.0)     .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(6) - 49300.0) .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(7) - 15200.0) .GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(8) - 132300.0).GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(9) - 131200.0).GT. epsilon)  .OR.  
     $    (DABS(zHostPtr(10) - 0.0)    .GT. epsilon)  .OR. 
     $    (DABS(yHostPtr(1) - 10.0)    .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(2) - 20.0)    .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(3) - 30.0)    .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(4) - 40.0)    .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(5) - 680.0)   .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(6) - 760.0)   .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(7) - 1230.0)  .GT. epsilon)  .OR.  
     $    (DABS(yHostPtr(8) - 2240.0)  .GT. epsilon)) then 
          write(*,*) "fortran example test FAILED"
       else
          write(*,*) "fortran example test PASSED"
       endif   
       
c      deallocate GPU memory and exit      
       call cuda_free(cooRowIndex)
       call cuda_free(cooColIndex)    
       call cuda_free(cooVal)
       call cuda_free(xInd)
       call cuda_free(xVal)
       call cuda_free(y)  
       call cuda_free(z) 
       call cuda_free(csrRowPtr)
       call cusparse_destroy_mat_descr(descrA)
       call cusparse_destroy(handle)

       stop 0
       end

15. Appendix C: Examples of sparse matrix vector multiplication

15.1. power method

This chapter provides a simple example in the C programming language of eigenvalue problem

A * x = λ * x

A is a 4x4 sparse matrix,

$A = (\begin{matrix} 1.0 & 0.0 & 2.0 & 3.0 \\ 0.0 & 4.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 6.0 & 7.0 \\ 0.0 & 8.0 & 0.0 & 9.0 \end{matrix})$

The goal is to find the largest eigen-pair by power method. The following code uses csrmv_mp inside the loop of power method.

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include csrmvmp_example.cpp 
 *   g++ -fopenmp -o csrmvmp_example csrmvmp_example.o -L/usr/local/cuda/lib64 -lcublas -lcusparse -lcudart
 *
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cublas_v2.h>
#include <cusparse.h>

void printMatrix(int m, int n, const double*A, int lda, const char* name)
{
    for(int row = 0 ; row < m ; row++){
        for(int col = 0 ; col < n ; col++){
            double Areg = A[row + col*lda];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

int main(int argc, char*argv[])
{
    cublasHandle_t cublasH = NULL;
    cusparseHandle_t cusparseH = NULL;
    cudaStream_t stream = NULL;
    cusparseMatDescr_t descrA = NULL;

    cublasStatus_t cublasStat = CUBLAS_STATUS_SUCCESS;
    cusparseStatus_t cusparseStat = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    cudaError_t cudaStat2 = cudaSuccess;
    cudaError_t cudaStat3 = cudaSuccess;
    cudaError_t cudaStat4 = cudaSuccess;
    cudaError_t cudaStat5 = cudaSuccess;
    const int n = 4;
    const int nnzA = 9;
/* 
 *      |    1     0     2     3   |
 *      |    0     4     0     0   |
 *  A = |    5     0     6     7   |
 *      |    0     8     0     9   |
 *
 * eigevales are { -0.5311, 7.5311, 9.0000, 4.0000 }
 *
 * The largest eigenvaluse is 9 and corresponding eigenvector is
 *
 *      | 0.3029  |
 * v =  |     0   |
 *      | 0.9350  |
 *      | 0.1844  |
 */

prepare matrix A

 
    const int csrRowPtrA[n+1] = { 0, 3, 4, 7, 9 };
    const int csrColIndA[nnzA] = {0, 2, 3, 1, 0, 2, 3, 1, 3 };
    const double csrValA[nnzA] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 };
    const double lambda_exact[n] = { 9.0000, 7.5311, 4.0000, -0.5311 };
    const double x0[n] = {1.0, 2.0, 3.0, 4.0 }; /* initial guess */
    double x[n]; /* numerical eigenvector */

    int *d_csrRowPtrA = NULL;
    int *d_csrColIndA = NULL;
    double *d_csrValA = NULL;

    double *d_x = NULL; /* eigenvector */
    double *d_y = NULL; /* workspace */

    const double tol = 1.e-6;
    const int max_ites = 30;

    const double h_one  = 1.0;
    const double h_zero = 0.0;

    printf("example of csrmv_mp \n");
    printf("tol = %E \n", tol);
    printf("max. iterations = %d \n", max_ites);

    printf("1st eigenvaluse is %f\n", lambda_exact[0] );
    printf("2nd eigenvaluse is %f\n", lambda_exact[1] );

    double alpha = lambda_exact[1]/lambda_exact[0] ;
    printf("convergence rate is %f\n", alpha );

    double est_iterations = log(tol)/log(alpha);
    printf("# of iterations required is %d\n", (int)ceil(est_iterations)  );

/* step 1: create cublas/cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    cublasStat = cublasCreate(&cublasH);
    assert(CUBLAS_STATUS_SUCCESS == cublasStat);

    cublasStat = cublasSetStream(cublasH, stream);
    assert(CUBLAS_STATUS_SUCCESS == cublasStat);

    cusparseStat = cusparseCreate(&cusparseH);
    assert(CUSPARSE_STATUS_SUCCESS == cusparseStat);

    cusparseStat = cusparseSetStream(cusparseH, stream);
    assert(CUSPARSE_STATUS_SUCCESS == cusparseStat);

/* step 2: configuration of matrix A */
    cusparseStat = cusparseCreateMatDescr(&descrA);
    assert(CUSPARSE_STATUS_SUCCESS == cusparseStat);

    cusparseSetMatIndexBase(descrA,CUSPARSE_INDEX_BASE_ZERO);
    cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL );

power method

 
/* step 3: copy A and x0 to device */
    cudaStat1 = cudaMalloc ((void**)&d_csrRowPtrA, sizeof(int) * (n+1) );
    cudaStat2 = cudaMalloc ((void**)&d_csrColIndA, sizeof(int) * nnzA );
    cudaStat3 = cudaMalloc ((void**)&d_csrValA   , sizeof(double) * nnzA );
    cudaStat4 = cudaMalloc ((void**)&d_x         , sizeof(double) * n );
    cudaStat5 = cudaMalloc ((void**)&d_y         , sizeof(double) * n );
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);
    assert(cudaSuccess == cudaStat3);
    assert(cudaSuccess == cudaStat4);
    assert(cudaSuccess == cudaStat5);

    cudaStat1 = cudaMemcpy(d_csrRowPtrA, csrRowPtrA, sizeof(int) * (n+1)   , cudaMemcpyHostToDevice);
    cudaStat2 = cudaMemcpy(d_csrColIndA, csrColIndA, sizeof(int) * nnzA    , cudaMemcpyHostToDevice);
    cudaStat3 = cudaMemcpy(d_csrValA   , csrValA   , sizeof(double) * nnzA , cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);
    assert(cudaSuccess == cudaStat3);


/*
 * step 4: power method
 */
    double lambda = 0.0;
    double lambda_next = 0.0;

/*
 *  4.1: initial guess x0
 */
    cudaStat1 = cudaMemcpy(d_x, x0, sizeof(double) * n, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);

    for(int ite = 0 ; ite < max_ites ; ite++ ){
/*
 *  4.2: normalize vector x
 *      x = x / |x|
 */
        double nrm2_x;
        cublasStat = cublasDnrm2_v2(cublasH,
                                    n,
                                    d_x,
                                    1, // incx,
                                    &nrm2_x  /* host pointer */
                                   );
        assert(CUBLAS_STATUS_SUCCESS == cublasStat);

        double one_over_nrm2_x = 1.0 / nrm2_x;
        cublasStat = cublasDscal_v2( cublasH,
                                     n,
                                     &one_over_nrm2_x,  /* host pointer */
                                     d_x,
                                     1 // incx
                                    );
        assert(CUBLAS_STATUS_SUCCESS == cublasStat);

...

 
/*
 *  4.3: y = A*x
 */
        cusparseStat = cusparseDcsrmv_mp(cusparseH,
                                         CUSPARSE_OPERATION_NON_TRANSPOSE,
                                         n,
                                         n,
                                         nnzA,
                                         &h_one,
                                         descrA,
                                         d_csrValA,
                                         d_csrRowPtrA,
                                         d_csrColIndA,
                                         d_x,
                                         &h_zero,
                                         d_y);
        assert(CUSPARSE_STATUS_SUCCESS == cusparseStat);

/*
 *  4.4: lambda = y**T*x
 */
        cublasStat = cublasDdot_v2 ( cublasH,
                                     n,
                                     d_x,
                                     1, // incx,
                                     d_y,
                                     1, // incy,
                                     &lambda_next  /* host pointer */
                                   );
        assert(CUBLAS_STATUS_SUCCESS == cublasStat);

        double lambda_err = fabs( lambda_next - lambda_exact[0] );
        printf("ite %d: lambda = %f, error = %E\n", ite, lambda_next, lambda_err );
/*
 *  4.5: check if converges
 */
        if ( (ite > 0) &&
             fabs( lambda - lambda_next ) < tol
        ){
            break; // converges
        }

/*
 *  4.6: x := y
 *       lambda = lambda_next
 *
 *  so new approximation is (lambda, x), x is not normalized.
 */
        cudaStat1 = cudaMemcpy(d_x, d_y, sizeof(double) * n , cudaMemcpyDeviceToDevice);
        assert(cudaSuccess == cudaStat1);

        lambda = lambda_next;
    }

report largest eigenvalue and eigenvector.

 
/*
 * step 5: report eigen-pair
 */
    cudaStat1 = cudaMemcpy(x, d_x, sizeof(double) * n, cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);

    printf("largest eigenvalue is %E\n", lambda );

    printf("eigenvector = (matlab base-1)\n");
    printMatrix(n, 1, x, n, "V0");
    printf("=====\n");


/* free resources */
    if (d_csrRowPtrA  ) cudaFree(d_csrRowPtrA);
    if (d_csrColIndA  ) cudaFree(d_csrColIndA);
    if (d_csrValA     ) cudaFree(d_csrValA);
    if (d_x           ) cudaFree(d_x);
    if (d_y           ) cudaFree(d_y);

    if (cublasH       ) cublasDestroy(cublasH);
    if (cusparseH     ) cusparseDestroy(cusparseH);
    if (stream        ) cudaStreamDestroy(stream);
    if (descrA        ) cusparseDestroyMatDescr(descrA);

    cudaDeviceReset();

    return 0;
}

16. Appendix D: Examples of sorting

16.1. COO sort

This chapter provides a simple example in the C programming language of sorting of COO format.

A is a 3x3 sparse matrix,

$A = (\begin{matrix} 1.0 & 2.0 & 0.0 \\ 0.0 & 5.0 & 0.0 \\ 0.0 & 8.0 & 0.0 \end{matrix})$

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include coosort.cpp 
 *   g++ -o coosort.cpp coosort.o -L/usr/local/cuda/lib64 -lcusparse -lcudart
 *
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cusparse.h>

int main(int argc, char*argv[])
{
    cusparseHandle_t handle = NULL;
    cudaStream_t stream = NULL;

    cusparseStatus_t status = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    cudaError_t cudaStat2 = cudaSuccess;
    cudaError_t cudaStat3 = cudaSuccess;
    cudaError_t cudaStat4 = cudaSuccess;
    cudaError_t cudaStat5 = cudaSuccess;
    cudaError_t cudaStat6 = cudaSuccess;

/*
 * A is a 3x3 sparse matrix 
 *     | 1 2 0 | 
 * A = | 0 5 0 | 
 *     | 0 8 0 | 
 */
    const int m = 3;
    const int n = 3;
    const int nnz = 4;

#if 0
/* index starts at 0 */
    int h_cooRows[nnz] = {2, 1, 0, 0 };
    int h_cooCols[nnz] = {1, 1, 0, 1 }; 
#else
/* index starts at -2 */
    int h_cooRows[nnz] = {0, -1, -2, -2 };
    int h_cooCols[nnz] = {-1, -1, -2, -1 };
#endif
    double h_cooVals[nnz] = {8.0, 5.0, 1.0, 2.0 };
    int h_P[nnz];

    int *d_cooRows = NULL;
    int *d_cooCols = NULL;
    int *d_P       = NULL;
    double *d_cooVals = NULL;
    double *d_cooVals_sorted = NULL;
    size_t pBufferSizeInBytes = 0;
    void *pBuffer = NULL;

    printf("m = %d, n = %d, nnz=%d \n", m, n, nnz );

...

 
/* step 1: create cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    status = cusparseCreate(&handle);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseSetStream(handle, stream);
    assert(CUSPARSE_STATUS_SUCCESS == status);

/* step 2: allocate buffer */ 
    status = cusparseXcoosort_bufferSizeExt(
        handle,
        m,
        n,
        nnz,
        d_cooRows,
        d_cooCols,
        &pBufferSizeInBytes
    );
    assert( CUSPARSE_STATUS_SUCCESS == status);

    printf("pBufferSizeInBytes = %lld bytes \n", (long long)pBufferSizeInBytes);

    cudaStat1 = cudaMalloc( &d_cooRows, sizeof(int)*nnz);
    cudaStat2 = cudaMalloc( &d_cooCols, sizeof(int)*nnz);
    cudaStat3 = cudaMalloc( &d_P      , sizeof(int)*nnz);
    cudaStat4 = cudaMalloc( &d_cooVals, sizeof(double)*nnz);
    cudaStat5 = cudaMalloc( &d_cooVals_sorted, sizeof(double)*nnz);
    cudaStat6 = cudaMalloc( &pBuffer, sizeof(char)* pBufferSizeInBytes);

    assert( cudaSuccess == cudaStat1 );
    assert( cudaSuccess == cudaStat2 );
    assert( cudaSuccess == cudaStat3 );
    assert( cudaSuccess == cudaStat4 );
    assert( cudaSuccess == cudaStat5 );
    assert( cudaSuccess == cudaStat6 );

    cudaStat1 = cudaMemcpy(d_cooRows, h_cooRows, sizeof(int)*nnz   , cudaMemcpyHostToDevice);
    cudaStat2 = cudaMemcpy(d_cooCols, h_cooCols, sizeof(int)*nnz   , cudaMemcpyHostToDevice);
    cudaStat3 = cudaMemcpy(d_cooVals, h_cooVals, sizeof(double)*nnz, cudaMemcpyHostToDevice);
    cudaStat4 = cudaDeviceSynchronize();
    assert( cudaSuccess == cudaStat1 );
    assert( cudaSuccess == cudaStat2 );
    assert( cudaSuccess == cudaStat3 );
    assert( cudaSuccess == cudaStat4 );

/* step 3: setup permutation vector P to identity */
    status = cusparseCreateIdentityPermutation(
        handle,
        nnz,
        d_P);
    assert( CUSPARSE_STATUS_SUCCESS == status);

...

 
/* step 4: sort COO format by Row */
    status = cusparseXcoosortByRow(
        handle, 
        m, 
        n, 
        nnz, 
        d_cooRows, 
        d_cooCols, 
        d_P, 
        pBuffer
    ); 
    assert( CUSPARSE_STATUS_SUCCESS == status);

/* step 5: gather sorted cooVals */
    status = cusparseDgthr(
        handle, 
        nnz, 
        d_cooVals, 
        d_cooVals_sorted, 
        d_P, 
        CUSPARSE_INDEX_BASE_ZERO
    ); 
    assert( CUSPARSE_STATUS_SUCCESS == status);

    cudaStat1 = cudaDeviceSynchronize(); /* wait until the computation is done */
    cudaStat2 = cudaMemcpy(h_cooRows, d_cooRows, sizeof(int)*nnz   , cudaMemcpyDeviceToHost);
    cudaStat3 = cudaMemcpy(h_cooCols, d_cooCols, sizeof(int)*nnz   , cudaMemcpyDeviceToHost);
    cudaStat4 = cudaMemcpy(h_P,       d_P      , sizeof(int)*nnz   , cudaMemcpyDeviceToHost);
    cudaStat5 = cudaMemcpy(h_cooVals, d_cooVals_sorted, sizeof(double)*nnz, cudaMemcpyDeviceToHost);
    cudaStat6 = cudaDeviceSynchronize();
    assert( cudaSuccess == cudaStat1 );
    assert( cudaSuccess == cudaStat2 );
    assert( cudaSuccess == cudaStat3 );
    assert( cudaSuccess == cudaStat4 );
    assert( cudaSuccess == cudaStat5 );
    assert( cudaSuccess == cudaStat6 );

    printf("sorted coo: \n");
    for(int j = 0 ; j < nnz; j++){
        printf("(%d, %d, %f) \n", h_cooRows[j], h_cooCols[j], h_cooVals[j] );
    }

    for(int j = 0 ; j < nnz; j++){
        printf("P[%d] = %d \n", j, h_P[j] );
    }

/* free resources */
    if (d_cooRows     ) cudaFree(d_cooRows);
    if (d_cooCols     ) cudaFree(d_cooCols);
    if (d_P           ) cudaFree(d_P);
    if (d_cooVals     ) cudaFree(d_cooVals);
    if (d_cooVals_sorted ) cudaFree(d_cooVals_sorted);
    if (pBuffer       ) cudaFree(pBuffer);
    if (handle        ) cusparseDestroy(handle);
    if (stream        ) cudaStreamDestroy(stream);
    cudaDeviceReset();
    return 0;
}

17. Appendix E: Examples of prune

17.1. prune dense to sparse

This section provides a simple example in the C programming language of pruning a dense matrix to a sparse matrix of CSR format.

A is a 4x4 dense matrix,

$A = (\begin{matrix} 1.0 & 0.0 & 2.0 & -3.0 \\ 0.0 & 4.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 6.0 & 7.0 \\ 0.0 & 8.0 & 0.0 & 9.0 \end{matrix})$

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include prunedense_example.cpp 
 *   g++ -o prunedense_example.cpp prunedense_example.o -L/usr/local/cuda/lib64 -lcusparse -lcudart
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cusparse.h>

void printMatrix(int m, int n, const float*A, int lda, const char* name)
{
    for(int row = 0 ; row < m ; row++){
        for(int col = 0 ; col < n ; col++){
            float Areg = A[row + col*lda];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

void printCsr(
    int m,
    int n,
    int nnz,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const char* name)
{
    const int base = (cusparseGetMatIndexBase(descrA) != CUSPARSE_INDEX_BASE_ONE)? 0:1 ;

    printf("matrix %s is %d-by-%d, nnz=%d, base=%d\n", name, m, n, nnz, base);
    for(int row = 0 ; row < m ; row++){
        const int start = csrRowPtrA[row  ] - base;
        const int end   = csrRowPtrA[row+1] - base;
        for(int colidx = start ; colidx < end ; colidx++){
            const int col = csrColIndA[colidx] - base;
            const float Areg = csrValA[colidx];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

int main(int argc, char*argv[])
{
    cusparseHandle_t handle = NULL;
    cudaStream_t stream = NULL;
    cusparseMatDescr_t descrC = NULL;

...

 
    cusparseStatus_t status = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    cudaError_t cudaStat2 = cudaSuccess;
    cudaError_t cudaStat3 = cudaSuccess;
    cudaError_t cudaStat4 = cudaSuccess;
    cudaError_t cudaStat5 = cudaSuccess;
    const int m = 4;
    const int n = 4;
    const int lda = m;
/* 
 *      |    1     0     2     -3  |
 *      |    0     4     0     0   |
 *  A = |    5     0     6     7   |
 *      |    0     8     0     9   |
 *
 */
    const float A[lda*n] = {1, 0, 5, 0, 0, 4, 0, 8, 2, 0, 6, 0, -3, 0, 7, 9};
    int* csrRowPtrC = NULL;
    int* csrColIndC = NULL;
    float* csrValC  = NULL;

    float *d_A = NULL;
    int *d_csrRowPtrC = NULL;
    int *d_csrColIndC = NULL;
    float *d_csrValC = NULL;

    size_t lworkInBytes = 0;
    char *d_work = NULL;

    int nnzC = 0;

    float threshold = 4.1; /* remove Aij <= 4.1 */
//    float threshold = 0; /* remove zeros */

    printf("example of pruneDense2csr \n");

    printf("prune |A(i,j)| <= threshold \n");
    printf("threshold = %E \n", threshold);

    printMatrix(m, n, A, lda, "A");

/* step 1: create cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    status = cusparseCreate(&handle);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseSetStream(handle, stream);
    assert(CUSPARSE_STATUS_SUCCESS == status);

...

 
/* step 2: configuration of matrix C */
    status = cusparseCreateMatDescr(&descrC);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    cusparseSetMatIndexBase(descrC,CUSPARSE_INDEX_BASE_ZERO);
    cusparseSetMatType(descrC, CUSPARSE_MATRIX_TYPE_GENERAL );

    cudaStat1 = cudaMalloc ((void**)&d_A         , sizeof(float)*lda*n );
    cudaStat2 = cudaMalloc ((void**)&d_csrRowPtrC, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);

/* step 3: query workspace */
    cudaStat1 = cudaMemcpy(d_A, A, sizeof(float)*lda*n, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);

    status = cusparseSpruneDense2csr_bufferSizeExt(
        handle,
        m,
        n,
        d_A,
        lda,
        &threshold,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        &lworkInBytes);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    printf("lworkInBytes (prune) = %lld \n", (long long)lworkInBytes);

    if (NULL != d_work) { cudaFree(d_work); }
    cudaStat1 = cudaMalloc((void**)&d_work, lworkInBytes);
    assert(cudaSuccess == cudaStat1);

/* step 4: compute csrRowPtrC and nnzC */
    status = cusparseSpruneDense2csrNnz(
        handle,
        m,
        n,
        d_A,
        lda,
        &threshold,
        descrC,
        d_csrRowPtrC,
        &nnzC, /* host */
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

    printf("nnzC = %d\n", nnzC);
    if (0 == nnzC ){
        printf("C is empty \n");
        return 0;
    }

...

/* step 5: compute csrColIndC and csrValC */
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndC, sizeof(int  ) * nnzC );
    cudaStat2 = cudaMalloc ((void**)&d_csrValC   , sizeof(float) * nnzC );
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);

    status = cusparseSpruneDense2csr(
        handle,
        m,
        n,
        d_A,
        lda,
        &threshold,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

/* step 6: output C */
    csrRowPtrC = (int*  )malloc(sizeof(int  )*(m+1));
    csrColIndC = (int*  )malloc(sizeof(int  )*nnzC);
    csrValC    = (float*)malloc(sizeof(float)*nnzC);
    assert( NULL != csrRowPtrC);
    assert( NULL != csrColIndC);
    assert( NULL != csrValC);

    cudaStat1 = cudaMemcpy(csrRowPtrC, d_csrRowPtrC, sizeof(int  )*(m+1), cudaMemcpyDeviceToHost);
    cudaStat2 = cudaMemcpy(csrColIndC, d_csrColIndC, sizeof(int  )*nnzC , cudaMemcpyDeviceToHost);
    cudaStat3 = cudaMemcpy(csrValC   , d_csrValC   , sizeof(float)*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);
    assert(cudaSuccess == cudaStat3);

    printCsr(m, n, nnzC, descrC, csrValC, csrRowPtrC, csrColIndC, "C");

/* free resources */
    if (d_A           ) cudaFree(d_A);
    if (d_csrRowPtrC  ) cudaFree(d_csrRowPtrC);
    if (d_csrColIndC  ) cudaFree(d_csrColIndC);
    if (d_csrValC     ) cudaFree(d_csrValC);

    if (csrRowPtrC  ) free(csrRowPtrC);
    if (csrColIndC  ) free(csrColIndC);
    if (csrValC     ) free(csrValC);

    if (handle        ) cusparseDestroy(handle);
    if (stream        ) cudaStreamDestroy(stream);
    if (descrC        ) cusparseDestroyMatDescr(descrC);

    cudaDeviceReset();
    return 0;
}

17.2. prune sparse to sparse

This section provides a simple example in the C programming language of pruning a sparse matrix to a sparse matrix of CSR format.

A is a 4x4 sparse matrix,

$A = (\begin{matrix} 1.0 & 0.0 & 2.0 & -3.0 \\ 0.0 & 4.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 6.0 & 7.0 \\ 0.0 & 8.0 & 0.0 & 9.0 \end{matrix})$

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include prunecsr_example.cpp 
 *   g++ -o prunecsr_example.cpp prunecsr_example.o -L/usr/local/cuda/lib64 -lcusparse -lcudart
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cusparse.h>

void printCsr(
    int m,
    int n,
    int nnz,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const char* name)
{
    const int base = (cusparseGetMatIndexBase(descrA) != CUSPARSE_INDEX_BASE_ONE)? 0:1 ;

    printf("matrix %s is %d-by-%d, nnz=%d, base=%d, output base-1\n", name, m, n, nnz, base);
    for(int row = 0 ; row < m ; row++){
        const int start = csrRowPtrA[row  ] - base;
        const int end   = csrRowPtrA[row+1] - base;
        for(int colidx = start ; colidx < end ; colidx++){
            const int col = csrColIndA[colidx] - base;
            const float Areg = csrValA[colidx];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

int main(int argc, char*argv[])
{
    cusparseHandle_t handle = NULL;
    cudaStream_t stream = NULL;
    cusparseMatDescr_t descrA = NULL;
    cusparseMatDescr_t descrC = NULL;

    cusparseStatus_t status = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    const int m = 4;
    const int n = 4;
    const int nnzA = 9;
/* 
 *      |    1     0     2     -3  |
 *      |    0     4     0     0   |
 *  A = |    5     0     6     7   |
 *      |    0     8     0     9   |
 *
 */

...

 
    const int csrRowPtrA[m+1] = { 1, 4, 5, 8, 10};
    const int csrColIndA[nnzA] = { 1, 3, 4, 2, 1, 3, 4, 2, 4};
    const float csrValA[nnzA] = {1, 2, -3, 4, 5, 6, 7, 8, 9};

    int* csrRowPtrC = NULL;
    int* csrColIndC = NULL;
    float* csrValC  = NULL;

    int *d_csrRowPtrA = NULL;
    int *d_csrColIndA = NULL;
    float *d_csrValA = NULL;

    int *d_csrRowPtrC = NULL;
    int *d_csrColIndC = NULL;
    float *d_csrValC = NULL;

    size_t lworkInBytes = 0;
    char *d_work = NULL;

    int nnzC = 0;

    float threshold = 4.1; /* remove Aij <= 4.1 */
//    float threshold = 0; /* remove zeros */

    printf("example of pruneCsr2csr \n");

    printf("prune |A(i,j)| <= threshold \n");
    printf("threshold = %E \n", threshold);

/* step 1: create cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    status = cusparseCreate(&handle);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseSetStream(handle, stream);
    assert(CUSPARSE_STATUS_SUCCESS == status);

/* step 2: configuration of matrix A and C */
    status = cusparseCreateMatDescr(&descrA);
    assert(CUSPARSE_STATUS_SUCCESS == status);
/* A is base-1*/
    cusparseSetMatIndexBase(descrA,CUSPARSE_INDEX_BASE_ONE);
    cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL );

    status = cusparseCreateMatDescr(&descrC);
    assert(CUSPARSE_STATUS_SUCCESS == status);
/* C is base-0 */
    cusparseSetMatIndexBase(descrC,CUSPARSE_INDEX_BASE_ZERO);
    cusparseSetMatType(descrC, CUSPARSE_MATRIX_TYPE_GENERAL );

    printCsr(m, n, nnzA, descrA, csrValA, csrRowPtrA, csrColIndA, "A");

...

 
    cudaStat1 = cudaMalloc ((void**)&d_csrRowPtrA, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndA, sizeof(int)*nnzA );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrValA   , sizeof(float)*nnzA );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrRowPtrC, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);

    cudaStat1 = cudaMemcpy(d_csrRowPtrA, csrRowPtrA, sizeof(int)*(m+1), cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(d_csrColIndA, csrColIndA, sizeof(int)*nnzA, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(d_csrValA   , csrValA   , sizeof(float)*nnzA, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);

/* step 3: query workspace */
    status = cusparseSpruneCsr2csr_bufferSizeExt(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        &threshold,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        &lworkInBytes);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    printf("lworkInBytes (prune) = %lld \n", (long long)lworkInBytes);

    if (NULL != d_work) { cudaFree(d_work); }
    cudaStat1 = cudaMalloc((void**)&d_work, lworkInBytes);
    assert(cudaSuccess == cudaStat1);

/* step 4: compute csrRowPtrC and nnzC */
    status = cusparseSpruneCsr2csrNnz(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        &threshold,
        descrC,
        d_csrRowPtrC,
        &nnzC, /* host */
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

...

    printf("nnzC = %d\n", nnzC);
    if (0 == nnzC ){
        printf("C is empty \n");
        return 0;
    }
/* step 5: compute csrColIndC and csrValC */
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndC, sizeof(int  ) * nnzC );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrValC   , sizeof(float) * nnzC );
    assert(cudaSuccess == cudaStat1);

    status = cusparseSpruneCsr2csr(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        &threshold,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

/* step 6: output C */
    csrRowPtrC = (int*  )malloc(sizeof(int  )*(m+1));
    csrColIndC = (int*  )malloc(sizeof(int  )*nnzC);
    csrValC    = (float*)malloc(sizeof(float)*nnzC);
    assert( NULL != csrRowPtrC);
    assert( NULL != csrColIndC);
    assert( NULL != csrValC);
    cudaStat1 = cudaMemcpy(csrRowPtrC, d_csrRowPtrC, sizeof(int  )*(m+1), cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(csrColIndC, d_csrColIndC, sizeof(int  )*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(csrValC   , d_csrValC   , sizeof(float)*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    printCsr(m, n, nnzC, descrC, csrValC, csrRowPtrC, csrColIndC, "C");
/* free resources */
    if (d_csrRowPtrA  ) cudaFree(d_csrRowPtrA);
    if (d_csrColIndA  ) cudaFree(d_csrColIndA);
    if (d_csrValA     ) cudaFree(d_csrValA);
    if (d_csrRowPtrC  ) cudaFree(d_csrRowPtrC);
    if (d_csrColIndC  ) cudaFree(d_csrColIndC);
    if (d_csrValC     ) cudaFree(d_csrValC);
    if (csrRowPtrC  ) free(csrRowPtrC);
    if (csrColIndC  ) free(csrColIndC);
    if (csrValC     ) free(csrValC);
    if (handle        ) cusparseDestroy(handle);
    if (stream        ) cudaStreamDestroy(stream);
    if (descrA        ) cusparseDestroyMatDescr(descrA);
    if (descrC        ) cusparseDestroyMatDescr(descrC);
    cudaDeviceReset();
    return 0;
}

17.3. prune dense to sparse by percentage

This section provides a simple example in the C programming language of pruning a dense matrix to a sparse matrix by percentage.

A is a 4x4 dense matrix,

$A = (\begin{matrix} 1.0 & 0.0 & 2.0 & -3.0 \\ 0.0 & 4.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 6.0 & 7.0 \\ 0.0 & 8.0 & 0.0 & 9.0 \end{matrix})$

The percentage is 50, which means to prune 50 percent of the dense matrix. The matrix has 16 elements, so 8 out of 16 must be pruned out. Therefore 7 zeros are pruned out, and value 1.0 is also out because it is the smallest among 9 nonzero elements.

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include prunedense2csrbyP.cpp
 *   g++ -o prunedense2csrbyP.cpp prunedense2csrbyP.o -L/usr/local/cuda/lib64 -lcusparse -lcudart
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cusparse.h>

void printMatrix(int m, int n, const float*A, int lda, const char* name)
{
    for(int row = 0 ; row < m ; row++){
        for(int col = 0 ; col < n ; col++){
            float Areg = A[row + col*lda];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

void printCsr(
    int m,
    int n,
    int nnz,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const char* name)
{
    const int base = (cusparseGetMatIndexBase(descrA) != CUSPARSE_INDEX_BASE_ONE)? 0:1 ;

    printf("matrix %s is %d-by-%d, nnz=%d, base=%d, output base-1\n", name, m, n, nnz, base);
    for(int row = 0 ; row < m ; row++){
        const int start = csrRowPtrA[row  ] - base;
        const int end   = csrRowPtrA[row+1] - base;
        for(int colidx = start ; colidx < end ; colidx++){
            const int col = csrColIndA[colidx] - base;
            const float Areg = csrValA[colidx];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

int main(int argc, char*argv[])
{
    cusparseHandle_t handle = NULL;
    cudaStream_t stream = NULL;
    cusparseMatDescr_t descrC = NULL;
    pruneInfo_t info = NULL;

    cusparseStatus_t status = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    cudaError_t cudaStat2 = cudaSuccess;
    cudaError_t cudaStat3 = cudaSuccess;
    cudaError_t cudaStat4 = cudaSuccess;
    cudaError_t cudaStat5 = cudaSuccess;
    const int m = 4;
    const int n = 4;
    const int lda = m;

...

 
/* 
 *      |    1     0     2     -3  |
 *      |    0     4     0     0   |
 *  A = |    5     0     6     7   |
 *      |    0     8     0     9   |
 *
 */
    const float A[lda*n] = {1, 0, 5, 0, 0, 4, 0, 8, 2, 0, 6, 0, -3, 0, 7, 9};
    int* csrRowPtrC = NULL;
    int* csrColIndC = NULL;
    float* csrValC  = NULL;

    float *d_A = NULL;
    int *d_csrRowPtrC = NULL;
    int *d_csrColIndC = NULL;
    float *d_csrValC = NULL;

    size_t lworkInBytes = 0;
    char *d_work = NULL;

    int nnzC = 0;

    float percentage = 50; /* 50% of nnz */

    printf("example of pruneDense2csrByPercentage \n");

    printf("prune out %.1f percentage of A \n", percentage);

    printMatrix(m, n, A, lda, "A");

/* step 1: create cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    status = cusparseCreate(&handle);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseSetStream(handle, stream);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseCreatePruneInfo(&info);
    assert(CUSPARSE_STATUS_SUCCESS == status);

/* step 2: configuration of matrix C */
    status = cusparseCreateMatDescr(&descrC);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    cusparseSetMatIndexBase(descrC,CUSPARSE_INDEX_BASE_ZERO);
    cusparseSetMatType(descrC, CUSPARSE_MATRIX_TYPE_GENERAL );

    cudaStat1 = cudaMalloc ((void**)&d_A         , sizeof(float)*lda*n );
    cudaStat2 = cudaMalloc ((void**)&d_csrRowPtrC, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);

    cudaStat1 = cudaMemcpy(d_A, A, sizeof(float)*lda*n, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);

...

 
/* step 3: query workspace */
    status = cusparseSpruneDense2csrByPercentage_bufferSizeExt(
        handle,
        m,
        n,
        d_A,
        lda,
        percentage,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        info,
        &lworkInBytes);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    printf("lworkInBytes = %lld \n", (long long)lworkInBytes);

    if (NULL != d_work) { cudaFree(d_work); }
    cudaStat1 = cudaMalloc((void**)&d_work, lworkInBytes);
    assert(cudaSuccess == cudaStat1);

/* step 4: compute csrRowPtrC and nnzC */
    status = cusparseSpruneDense2csrNnzByPercentage(
        handle,
        m,
        n,
        d_A,
        lda,
        percentage,
        descrC,
        d_csrRowPtrC,
        &nnzC, /* host */
        info,
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

    printf("nnzC = %d\n", nnzC);
    if (0 == nnzC ){
        printf("C is empty \n");
        return 0;
    }

/* step 5: compute csrColIndC and csrValC */
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndC, sizeof(int  ) * nnzC );
    cudaStat2 = cudaMalloc ((void**)&d_csrValC   , sizeof(float) * nnzC );
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);

...

    status = cusparseSpruneDense2csrByPercentage(
        handle,
        m,
        n,
        d_A,
        lda,
        percentage,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        info,
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

/* step 7: output C */
    csrRowPtrC = (int*  )malloc(sizeof(int  )*(m+1));
    csrColIndC = (int*  )malloc(sizeof(int  )*nnzC);
    csrValC    = (float*)malloc(sizeof(float)*nnzC);
    assert( NULL != csrRowPtrC);
    assert( NULL != csrColIndC);
    assert( NULL != csrValC);

    cudaStat1 = cudaMemcpy(csrRowPtrC, d_csrRowPtrC, sizeof(int  )*(m+1), cudaMemcpyDeviceToHost);
    cudaStat2 = cudaMemcpy(csrColIndC, d_csrColIndC, sizeof(int  )*nnzC , cudaMemcpyDeviceToHost);
    cudaStat3 = cudaMemcpy(csrValC   , d_csrValC   , sizeof(float)*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    assert(cudaSuccess == cudaStat2);
    assert(cudaSuccess == cudaStat3);

    printCsr(m, n, nnzC, descrC, csrValC, csrRowPtrC, csrColIndC, "C");

/* free resources */
    if (d_A         ) cudaFree(d_A);
    if (d_csrRowPtrC) cudaFree(d_csrRowPtrC);
    if (d_csrColIndC) cudaFree(d_csrColIndC);
    if (d_csrValC   ) cudaFree(d_csrValC);

    if (csrRowPtrC  ) free(csrRowPtrC);
    if (csrColIndC  ) free(csrColIndC);
    if (csrValC     ) free(csrValC);

    if (handle      ) cusparseDestroy(handle);
    if (stream      ) cudaStreamDestroy(stream);
    if (descrC      ) cusparseDestroyMatDescr(descrC);
    if (info        ) cusparseDestroyPruneInfo(info);

    cudaDeviceReset();

    return 0;
}

17.4. prune sparse to sparse by percentage

This section provides a simple example in the C programming language of pruning a sparse matrix to a sparse matrix by percentage.

A is a 4x4 sparse matrix,

$A = (\begin{matrix} 1.0 & 0.0 & 2.0 & -3.0 \\ 0.0 & 4.0 & 0.0 & 0.0 \\ 5.0 & 0.0 & 6.0 & 7.0 \\ 0.0 & 8.0 & 0.0 & 9.0 \end{matrix})$

The percentage is 20, which means to prune 20 percent of the nonzeros. The sparse matrix has 9 nonzero elements, so 1.4 elements must be pruned out. The function removes 1.0 and 2.0 which are first two smallest numbers of nonzeros.

...

 
/*
 * How to compile (assume cuda is installed at /usr/local/cuda/)
 *   nvcc -c -I/usr/local/cuda/include prunecsr2csrByP.cpp 
 *   g++ -o prunecsr2csrByP.cpp prunecsr2csrByP.o -L/usr/local/cuda/lib64 -lcusparse -lcudart
 */
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <cusparse.h>

void printCsr(
    int m,
    int n,
    int nnz,
    const cusparseMatDescr_t descrA,
    const float *csrValA,
    const int *csrRowPtrA,
    const int *csrColIndA,
    const char* name)
{
    const int base = (cusparseGetMatIndexBase(descrA) != CUSPARSE_INDEX_BASE_ONE)? 0:1 ;

    printf("matrix %s is %d-by-%d, nnz=%d, base=%d, output base-1\n", name, m, n, nnz, base);
    for(int row = 0 ; row < m ; row++){
        const int start = csrRowPtrA[row  ] - base;
        const int end   = csrRowPtrA[row+1] - base;
        for(int colidx = start ; colidx < end ; colidx++){
            const int col = csrColIndA[colidx] - base;
            const float Areg = csrValA[colidx];
            printf("%s(%d,%d) = %f\n", name, row+1, col+1, Areg);
        }
    }
}

int main(int argc, char*argv[])
{
    cusparseHandle_t handle = NULL;
    cudaStream_t stream = NULL;
    cusparseMatDescr_t descrA = NULL;
    cusparseMatDescr_t descrC = NULL;
    pruneInfo_t info = NULL;

    cusparseStatus_t status = CUSPARSE_STATUS_SUCCESS;
    cudaError_t cudaStat1 = cudaSuccess;
    const int m = 4;
    const int n = 4;
    const int nnzA = 9;
/* 
 *      |    1     0     2     -3  |
 *      |    0     4     0     0   |
 *  A = |    5     0     6     7   |
 *      |    0     8     0     9   |
 *
 */

...

 
    const int csrRowPtrA[m+1] = { 1, 4, 5, 8, 10};
    const int csrColIndA[nnzA] = { 1, 3, 4, 2, 1, 3, 4, 2, 4};
    const float csrValA[nnzA] = {1, 2, -3, 4, 5, 6, 7, 8, 9};

    int* csrRowPtrC = NULL;
    int* csrColIndC = NULL;
    float* csrValC  = NULL;

    int *d_csrRowPtrA = NULL;
    int *d_csrColIndA = NULL;
    float *d_csrValA = NULL;

    int *d_csrRowPtrC = NULL;
    int *d_csrColIndC = NULL;
    float *d_csrValC = NULL;

    size_t lworkInBytes = 0;
    char *d_work = NULL;

    int nnzC = 0;

    float percentage = 20; /* remove 20% of nonzeros */

    printf("example of pruneCsr2csrByPercentage \n");

    printf("prune %.1f percent of nonzeros \n", percentage);

/* step 1: create cusparse handle, bind a stream */
    cudaStat1 = cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking);
    assert(cudaSuccess == cudaStat1);

    status = cusparseCreate(&handle);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseSetStream(handle, stream);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    status = cusparseCreatePruneInfo(&info);
    assert(CUSPARSE_STATUS_SUCCESS == status);

/* step 2: configuration of matrix C */
    status = cusparseCreateMatDescr(&descrA);
    assert(CUSPARSE_STATUS_SUCCESS == status);
/* A is base-1*/
    cusparseSetMatIndexBase(descrA,CUSPARSE_INDEX_BASE_ONE);
    cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL );

    status = cusparseCreateMatDescr(&descrC);
    assert(CUSPARSE_STATUS_SUCCESS == status);
/* C is base-0 */
    cusparseSetMatIndexBase(descrC,CUSPARSE_INDEX_BASE_ZERO);
    cusparseSetMatType(descrC, CUSPARSE_MATRIX_TYPE_GENERAL );

    printCsr(m, n, nnzA, descrA, csrValA, csrRowPtrA, csrColIndA, "A");

...

 
    cudaStat1 = cudaMalloc ((void**)&d_csrRowPtrA, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndA, sizeof(int)*nnzA );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrValA   , sizeof(float)*nnzA );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrRowPtrC, sizeof(int)*(m+1) );
    assert(cudaSuccess == cudaStat1);

    cudaStat1 = cudaMemcpy(d_csrRowPtrA, csrRowPtrA, sizeof(int)*(m+1), cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(d_csrColIndA, csrColIndA, sizeof(int)*nnzA, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(d_csrValA   , csrValA   , sizeof(float)*nnzA, cudaMemcpyHostToDevice);
    assert(cudaSuccess == cudaStat1);

/* step 3: query workspace */
    status = cusparseSpruneCsr2csrByPercentage_bufferSizeExt(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        percentage,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        info,
        &lworkInBytes);
    assert(CUSPARSE_STATUS_SUCCESS == status);

    printf("lworkInBytes = %lld \n", (long long)lworkInBytes);

    if (NULL != d_work) { cudaFree(d_work); }
    cudaStat1 = cudaMalloc((void**)&d_work, lworkInBytes);
    assert(cudaSuccess == cudaStat1);

/* step 4: compute csrRowPtrC and nnzC */
    status = cusparseSpruneCsr2csrNnzByPercentage(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        percentage,
        descrC,
        d_csrRowPtrC,
        &nnzC, /* host */
        info,
        d_work);

...

    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

    printf("nnzC = %d\n", nnzC);
    if (0 == nnzC ){
        printf("C is empty \n");
        return 0;
    }

/* step 5: compute csrColIndC and csrValC */
    cudaStat1 = cudaMalloc ((void**)&d_csrColIndC, sizeof(int  ) * nnzC );
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMalloc ((void**)&d_csrValC   , sizeof(float) * nnzC );
    assert(cudaSuccess == cudaStat1);

    status = cusparseSpruneCsr2csrByPercentage(
        handle,
        m,
        n,
        nnzA,
        descrA,
        d_csrValA,
        d_csrRowPtrA,
        d_csrColIndA,
        percentage,
        descrC,
        d_csrValC,
        d_csrRowPtrC,
        d_csrColIndC,
        info,
        d_work);
    assert(CUSPARSE_STATUS_SUCCESS == status);
    cudaStat1 = cudaDeviceSynchronize();
    assert(cudaSuccess == cudaStat1);

/* step 6: output C */
    csrRowPtrC = (int*  )malloc(sizeof(int  )*(m+1));
    csrColIndC = (int*  )malloc(sizeof(int  )*nnzC);
    csrValC    = (float*)malloc(sizeof(float)*nnzC);
    assert( NULL != csrRowPtrC);
    assert( NULL != csrColIndC);
    assert( NULL != csrValC);

    cudaStat1 = cudaMemcpy(csrRowPtrC, d_csrRowPtrC, sizeof(int  )*(m+1), cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(csrColIndC, d_csrColIndC, sizeof(int  )*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);
    cudaStat1 = cudaMemcpy(csrValC   , d_csrValC   , sizeof(float)*nnzC , cudaMemcpyDeviceToHost);
    assert(cudaSuccess == cudaStat1);

    printCsr(m, n, nnzC, descrC, csrValC, csrRowPtrC, csrColIndC, "C");

...

/* free resources */
    if (d_csrRowPtrA) cudaFree(d_csrRowPtrA);
    if (d_csrColIndA) cudaFree(d_csrColIndA);
    if (d_csrValA   ) cudaFree(d_csrValA);
    if (d_csrRowPtrC) cudaFree(d_csrRowPtrC);
    if (d_csrColIndC) cudaFree(d_csrColIndC);
    if (d_csrValC   ) cudaFree(d_csrValC);

    if (csrRowPtrC  ) free(csrRowPtrC);
    if (csrColIndC  ) free(csrColIndC);
    if (csrValC     ) free(csrValC);

    if (handle      ) cusparseDestroy(handle);
    if (stream      ) cudaStreamDestroy(stream);
    if (descrA      ) cusparseDestroyMatDescr(descrA);
    if (descrC      ) cusparseDestroyMatDescr(descrC);
    if (info        ) cusparseDestroyPruneInfo(info);

    cudaDeviceReset();

    return 0;
}

Appendix F: Acknowledgements

NVIDIA would like to thank the following individuals and institutions for their contributions:

The cusparse<t>gtsv implementation is derived from a version developed by Li-Wen Chang from the University of Illinois.

19. Bibliography

[1] N. Bell and M. Garland, “Implementing Sparse Matrix-Vector Multiplication on Throughput-Oriented Processors”, Supercomputing, 2009.

[2] R. Grimes, D. Kincaid, and D. Young, “ITPACK 2.0 User’s Guide”, Technical Report CNA-150, Center for Numerical Analysis, University of Texas, 1979.

[3] M. Naumov, “Incomplete-LU and Cholesky Preconditioned Iterative Methods Using cuSPARSE and cuBLAS”, Technical Report and White Paper, 2011.

Notices

Notice

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This product includes software developed by the Syncro Soft SRL (http://www.sync.ro/).