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kml_sparse_?csrsv

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

A * y = alpha * x, AT * y = alpha * x, or AH * y = alpha * x

x and y are vectors, and A is a sparse matrix (m * m) 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).

Interface Definition

C interface:

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

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

kml_sparse_status_t kml_sparse_ccsrsv(const kml_sparse_operation_t opt, const KML_INT m, 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, KML_Complex8 *y);

kml_sparse_status_t kml_sparse_zcsrsv(const kml_sparse_operation_t opt, const KML_INT m, 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, KML_Complex16 *y);

Fortran interface:

RES = KML_SPARSE_SCSRSV(OPT, M, ALPHA, MATDESCRA, VAL, INDX, PNTRB, PNTRE, X, Y);

RES = KML_SPARSE_DCSRSV(OPT, M, ALPHA, MATDESCRA, VAL, INDX, PNTRB, PNTRE, X, Y);

RES = KML_SPARSE_CCSRSV(OPT, M, ALPHA, MATDESCRA, VAL, INDX, PNTRB, PNTRE, X, Y);

RES = KML_SPARSE_ZCSRSV(OPT, M, ALPHA, MATDESCRA, VAL, INDX, PNTRB, PNTRE, X, Y);

Parameters

Parameter

Type

Description

Input/Output

opt

Enumeration type kml_sparse_operation_t

Operation on matrix A.

  • If opt=KML_SPARSE_OPERATION_NON_TRANSPOSE, then A * y = alpha * x.
  • If opt=KML_SPARSE_OPERATION_TRANSPOSE, then AT * y = alpha * x.
  • If opt=KML_SPARSE_OPERATION_CONJUGATE_TRANSPOSE, then AH * y = alpha * x.

Input

m

Integer

Number of rows in matrix A. The value range is [1, MAX_KML_INT].

Input

alpha
  • For scsrsv, alpha is of single-precision floating-point type.
  • For dcsrsv, alpha is of double-precision floating-point type.
  • For ccsrsv, alpha is a single-precision complex number.
  • For zcsrsv, alpha is a double-precision complex number.

Coefficient

Input

matdescra

Char pointer

Matrix operation attribute. For details, see the description of matdescra.

Input

val
  • For scsrsv, val is a single-precision floating-point array.
  • For dcsrsv, val is a double-precision floating-point array.
  • For ccsrsv, val is a single-precision complex number array.
  • For zcsrsv, val is a double-precision complex number array.

Non-zero elements in matrix A

Input

indx

Integer array

indx[i] indicates the column number of the ith element of the val array 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 scsrsv, x is a single-precision floating-point array.
  • For dcsrsv, x is a double-precision floating-point array.
  • For ccsrsv, x is a single-precision complex number array.
  • For zcsrsv, x is a double-precision complex number array.

Vector x

Input

y
  • For scsrsv, y is a single-precision floating-point array.
  • For dcsrsv, y is a double-precision floating-point array.
  • For ccsrsv, y is a single-precision complex number array.
  • For zcsrsv, y is a double-precision complex number array.

Vector y.

This parameter is output after update.

Input/Output
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; 
    float alpha = 1.0; 
    char *matdescra = "TLNF"; // General 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[4] = {1, 3, -2, 5}; 
    float y[4] = {0, 0, 0, 0}; 
    kml_sparse_status_t status = kml_sparse_scsrsv(opt, m, alpha, matdescra, val, indx, pntrb, pntre, x, y); 
    /* 
     *  Output Y: 
     *     0.500000   3.000000   1.500000   0.277778 
     * 
     */

Fortran interface:

    INTEGER(C_INT) :: OPT = KML_SPARSE_OPERATION_NON_TRANSPOSE 
    INTEGER(C_INT) :: M = 4 
    REAL(C_FLOAT) :: ALPHA = 1.0 
    CHARACTER(KIND=C_CHAR, LEN=4) :: MATDESCRA = "TLNF" ! General matrix with one-based indexing
    REAL(C_FLOAT) :: VAL(9), X(4), Y(4) 
    INTEGER(C_INT) :: INDX(9), PNTRB(4),PNTRE(4) 
    INTEGER(C_INT) :: STATUS  
    DATA VAL /2, -3, 7, 1, -6, 8, -4, 5, 9/ 
    DATA INDX /1, 2, 4, 2, 4, 1, 3, 1, 4/ 
    DATA PNTRB /1, 4, 6, 8/ 
    DATA PNTRE/4, 6, 8, 10/ 
    DATA X/1, 3, -2, 5/ 
    DATA Y/0, 0, 0, 0/ 
    STATUS = KML_SPARSE_SCSRSV(OPT, M, ALPHA, MATDESCRA, VAL, INDX, PNTRB, PNTRE, X, Y); 
    ! 
    !  OUTPUT Y: 
    !     0.500000   3.000000   1.500000   0.277778 
    !