kml_sparse_?csrsm

Solve a system of triangular matrix equations. One of the matrices is a sparse matrix in the CSR format. The operation is defined as follows:

A * y = alpha * x
A^T * y = alpha * x
A^H * y = alpha * x

x and y are m x n matrices, and A is a sparse matrix (m x m) stored in the CSR format. The non-zero elements of a given row in matrix A must be stored in the same order as they are displayed in the row (from left to right).

Table 1 describes the relationship between layout and sparse matrix indexing.

**Table 1** Relationship between layout and sparse matrix indexing
Sparse matrix indexing	Dense matrix layout
KML_SPARSE_INDEX_BASE_ZERO	KML_SPARSE_LAYOUT_ROW_MAJOR
KML_SPARSE_INDEX_BASE_ONE	KML_SPARSE_LAYOUT_COLUMN_MAJOR

Interface Definition

C interface:

kml_sparse_status_t kml_sparse_scsrsm(const kml_sparse_operation_t opt, const KML_INT m, const KML_INT n, const float alpha, const char *matdescra, const float *val, const KML_INT *indx, const KML_INT *pntrb, const KML_INT *pntre, const float *x, const KML_INT ldx, float *y , const KML_INT ldy);

kml_sparse_status_t kml_sparse_dcsrsm(const kml_sparse_operation_t opt, const KML_INT m, const KML_INT n, const double alpha, const char *matdescra, const double *val, const KML_INT *indx, const KML_INT *pntrb, const KML_INT *pntre,const double *x, const KML_INT ldx, double *y , const KML_INT ldy);

kml_sparse_status_t kml_sparse_ccsrsm(const kml_sparse_operation_t opt, const KML_INT m, const KML_INT n, const KML_Complex8 alpha, const char *matdescra, const KML_Complex8 *val, const KML_INT *indx, const KML_INT *pntrb, const KML_INT *pntre, const KML_Complex8 *x, const KML_INT ldx, KML_Complex8 *y, const KML_INT ldy);

kml_sparse_status_t kml_sparse_zcsrsm(const kml_sparse_operation_t opt, const KML_INT m, const KML_INT n, const KML_Complex16 alpha, const char *matdescra, const KML_Complex16 *val, const KML_INT *indx, const KML_INT *pntrb, const KML_INT *pntre, const KML_Complex16 *x, const KML_INT ldx, KML_Complex16 *y , const KML_INT ldy);

Parameters

Parameter	Type	Description	Input/Output
opt	Enumeration type kml_sparse_operation_t	Indicates whether to transpose. If opt = KML_SPARSE_OPERATION_NON_TRANSPOSE, then A * y = alpha * x. If opt = KML_SPARSE_OPERATION_TRANSPOSE, then A^T * y = alpha * x. If opt = KML_SPARSE_OPERATION_CONJUGATE_TRANSPOSE, then A^H * y = alpha * x.	Input
m	Integer	Number of rows in matrix A. The value range is [1, MAX_KML_INT].	Input
n	Integer	Number of columns in matrix x. The value range is [1, MAX_KML_INT].	Input
alpha	For scsrsm, alpha is of the single-precision floating-point type. For dcsrsm, alpha is of the double-precision floating-point type. For ccsrsm, alpha is a single-precision complex number. For zcsrsm, alpha is a double-precision complex number.	Scalar alpha	Input
matdescra	Char pointer	Matrix operation attribute. For details, see the description of matdescra.	Input
val	For scsrsm, val is a single-precision floating-point array. For dcsrsm, val is a double-precision floating-point array. For ccsrsm, val is a single-precision complex number array. For zcsrsm, val is a double-precision complex number array.	Array values storing non-zero elements of matrix A in the CSR format. The length is pntre[m-1] - pntrb[0].	Input
indx	Integer array	Array columns in the CSR format, which contains the column indices for non-zero elements in matrix A	Input
pntrb	Integer array	Array of length m, containing row indices of matrix A. pntrb[i] - pntrb[0] indicates the subscript of the first non-zero element in row i in the val and indx arrays.	Input
pntre	Integer array	Array of length m, containing row indices of matrix A. pntre[i] - pntrb[0]-1 indicates the subscript of the last non-zero element in row i in the val and indx arrays.	Input
x	For scsrsm, x is a single-precision floating-point array. For dcsrsm, x is a double-precision floating-point array. For ccsrsm, x is a single-precision complex number array. For zcsrsm, x is a double-precision complex number array.	Array value of matrix x	Input
ldx	Integer array	Size of the leading dimension of matrix x for one-based indexing Size of the second dimension of matrix x for zero-based indexing	Input
y	For scsrsm, y is a single-precision floating-point array. For dcsrsm, y is a double-precision floating-point array. For ccsrsm, y is a single-precision complex number array. For zcsrsm, y is a double-precision complex number array.	Array value of matrix y	Input/Output
ldy	Integer array	Size of the leading dimension of matrix y for one-based indexing Size of the second dimension of matrix y for zero-based indexing	Input

Table 2 describes the parameter constraints on matrix x.

**Table 2** Parameter constraints on matrix x
opt	Matrix Scale	Data Layout	Value Range
op(A) = A, A^T, or A^H	m x n	Row-major order	m * ldbMAX_KML_INT
op(A) = A, A^T, or A^H	m x n	Column-major order	ldb * n MAX_KML_INT

Table 3 describes the parameter constraints on matrix y.

**Table 3** Parameter constraints on matrix y
opt	Matrix Scale	Data Layout	Value Range
op(A) = A, A^T, or A^H	m x n	Row-major order	m * ldcMAX_KML_INT
op(A) = A, A^T, or A^H	m x n	Column-major order	ldc * n MAX_KML_INT

The function does not verify the integrity of parameters. Ensure that the elements in pntrb and pntre do not exceed the maximum index value of the input matrix.

Return Value

Function execution status. The enumeration type is kml_sparse_status_t.

Dependencies

C: "kspblas.h"

Fortran: "kspblas.f03"

Examples

C interface:

    kml_sparse_operation_t opt = KML_SPARSE_OPERATION_NON_TRANSPOSE; 
    KML_INT m = 4; 
    KML_INT n = 2; 
    float alpha = 1.0; 
    char *matdescra = "TLNF"; // Triangular matrix with one-based indexing
    float val[9] = {2, -3, 7, 1, -6, 8, -4, 5, 9}; 
    KML_INT indx[9] = {1, 2, 4, 2, 4, 1, 3, 1, 4}; 
    KML_INT pntrb[4] = {1, 4, 6, 8}; 
    KML_INT pntre[4] = {4, 6, 8, 10}; 
    float x[8] = {1, 3, -2, 5, 7, -3, 6, 8}; 
    float y[8] = {0, 0, 0, 0, 0, 0, 0, 0}; 
    KML_INT ldx = 4; 
    KML_INT ldy = 4; 
    kml_sparse_status_t status = kml_sparse_scsrsm(opt, m, n, alpha, matdescra, val, indx, pntrb, pntre, x, ldx, y, ldy); 
    /* 
     *  Output Y: 
     *     0.500000  3.000000  1.500000  0.277778   
3.500000  -3.000000  5.500000  -1.055556 
     * 
     * */

Parent topic: Sparse BLAS Level 2 and Level 3 Functions