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?symm

Compute the product of a symmetric real matrix and a matrix.

That is, or .

alpha and beta are multiplication coefficients, A is a symmetric matrix, and B and C are m*n general matrices.

Interface Definition

C interface:

void cblas_ssymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const BLASINT M, const BLASINT N, const float alpha, const float *A, const BLASINT lda, const float *B, const BLASINT ldb, const float beta, float *C, const BLASINT ldc);

void cblas_dsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const BLASINT M, const BLASINT N, const double alpha, const double *A, const BLASINT lda, const double *B, const BLASINT ldb, const double beta, double *C, const BLASINT ldc);

void cblas_csymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const BLASINT M, const BLASINT N, const void *alpha, const void *A, const BLASINT lda, const void *B, const BLASINT ldb, const void *beta, void *C, const BLASINT ldc);

void cblas_zsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const BLASINT M, const BLASINT N, const void *alpha, const void *A, const BLASINT lda, const void *B, const BLASINT ldb, const void *beta, void *C, const BLASINT ldc);

Fortran interface:

CALL SSYMM(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL DSYMM(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL CSYMM(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL ZSYMM(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

Parameters

Parameter

Type

Description

Input/Output

order

Enumeration type CBLAS_ORDER

Indicates whether the matrix is in row- or column-major order.

Input

Side

Enumeration type CBLAS_SIDE

Indicates whether symmetric matrix A is on the left or right of matrix B.

  • If Side = CblasLeft, .
  • If Side = CblasRight, .

Input

Uplo

Enumeration type CBLAS_UPLO

Indicates whether to use the upper triangle or lower triangle of matrix A.

  • If Uplo = CblasUpper, the upper triangular part of A is used.
  • If Uplo = CblasLower, the lower triangular part of A is used.

Input

M

Integer

Number of rows of matrix C.

  • A*B indicates the number of rows of matrix A.
  • B*A indicates the number of rows of matrix B.

Input

N

Integer

Number of columns of matrix C.

  • A*B indicates the number of columns of matrix B.
  • B*A indicates the number of columns of matrix A.

Input

alpha
  • Single-precision floating-point type for ssymm
  • Double-precision floating-point type for dsymm
  • Single-precision complex type for csymm
  • Double-precision complex type for zsymm

Multiplication coefficient.

Input

A
  • Single-precision floating-point type for ssymm
  • Double-precision floating-point type for dsymm
  • Single-precision complex type for csymm
  • Double-precision complex type for zsymm

Matrix A (lda, ka).

If Side = CblasLeft, ka = m; otherwise, ka = n.

Input

lda

Integer

If Side = CblasLeft, lda is at least max(1, m); otherwise, lda is at least max(1, n).

Input

B
  • Single-precision floating-point type for ssymm
  • Double-precision floating-point type for dsymm
  • Single-precision complex type for csymm
  • Double-precision complex type for zsymm

Matrix B (ldb, n).

Input

ldb

Integer
  • If the matrix is column store, ldb must be at least max(1, m).
  • If the matrix is row store, ldb must be at least max(1, n).

Input

beta
  • Single-precision floating-point type for ssymm
  • Double-precision floating-point type for dsymm
  • Single-precision complex type for csymm
  • Double-precision complex type for zsymm

Multiplication coefficient.

Input

C
  • Single-precision floating-point type for ssymm
  • Double-precision floating-point type for dsymm
  • Single-precision complex type for csymm
  • Double-precision complex type for zsymm

Matrix C.

Input/Output

ldc

Integer
  • If the matrix is column store, ldc must be at least max(1, m).
  • If the matrix is row store, ldc must be at least max(1, n).

Input

Dependency

#include "kblas.h"

C interface:

    int m = 3, n = 6, lda = 4, ldb =3, ldc = 5; 
    float alpha = 2.0, beta = 2.0; 
    /** 
     *                   | 4.0    .     .  | 
     *    A(4 * 3)    =  | 3.0   4.0    .  | 
     *                   | 6.0  -7.0  -1.0 | 
     *                   |  .     .     .  | 
     * 
     *                    | -1.0  -3.0   2.0   2.0  -1.0    8.0 | 
     *     B(3 * 6)    =  | 2.0   3.0   0.0   4.0   2.0    -2.0 | 
     *                    | 11.0  -2.0  -21.0  -1.0  -1.0   5.0 | 
     * 
     *                    |  3.0   2.0  -1.0  3.0   -1.0  -11.0| 
     *                    |  9.0  13.0  5.0   5.0   3.0   -5.0 | 
     *     C(5 * 6)    =  | -1.0  -6.0  -3.0  3.0   -1.0   32.0| 
     *                    |   .     .    .     .     .      .  | 
     *                    |   .     .    .     .     .      .  | 
     */ 
    float a[12] = {4.0, 3.0, 6.0, 0, 
                   3.0, 4.0, -7.0, 0, 
                   6.0, -7.0, -1.0, 0}; 
    float b[18] = {-1.0, 2.0, 11.0, 
                   -3.0, 3.0, -2.0, 
                   2.0, 0, -21.0, 
                   2.0, 4.0, -1.0, 
                   -1.0, 2.0, -1.0, 
                   8.0, -2.0, 5.0};   
    float c[30] = {6.0, 9.0, -1.0, 0, 0, 
                   2.0, 13.0, -6.0, 0, 0, 
                   -1.0, 5.0, -3.0, 0, 0, 
                   3.0, 5.0, 3.0, 0, 0, 
                   -1.0, 3.0, -1.0, 0, 0, 
                   -11.0, -5.0, 32.0, 0, 0}; 
 
    cblas_ssymm(CblasColMajor,CblasLeft,CblasLower, m, n, alpha, a, lda, b, ldb, beta, c, ldc); 
    /** 
     * Output C 
     *                   |  148.0  -26.0 -238.0  34.0  -10.0  90.0 | 
     *                   | -126.0   60.0  316.0  68.0  30.0  -48.0 | 
     *    C(5 * 6)    =  | -64.0   -86.0  60.0  -24.0  -40.0  178.0| 
     *                   |   .      .      .      .     .      .   | 
     *                   |   .      .      .      .     .      .   | 
     * 
     */

Fortran interface:

      INTEGER :: M=3, N=6 
      INTEGER :: LDA=4, LDB=3, LDC=5 
      REAL(4) :: ALPHA=2.0, BETA=2.0 
      REAL(4) :: A(4, 3), B(3,6), C(5, 6) 
      DATA A/4.0, 3.0, 6.0, 0, 
     $       3.0, 4.0, -7.0, 0, 
     $       6.0, -7.0, -1.0, 0/ 
      DATA B/-1.0, 2.0, 11.0, 
     $       -3.0, 3.0, -2.0, 
     $       2.0, 0, -21.0, 
     $       2.0, 4.0, -1.0, 
     $       -1.0, 2.0, -1.0, 
     $       8.0, -2.0, 5.0/ 
      DATA C/6.0, 9.0, -1.0, 0, 0, 
     $       2.0, 13.0, -6.0, 0, 0, 
     $       -1.0, 5.0, -3.0, 0, 0, 
     $       3.0, 5.0, 3.0, 0, 0, 
     $       -1.0, 3.0, -1.0, 0, 0, 
     $       -11.0, -5.0, 32.0, 0, 0/ 
      EXTERNAL SSYMM 
      CALL SSYMM('L', 'L', M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC) 
 
*     Output C 
*                       |  148.0  -26.0 -238.0  34.0  -10.0  90.0 | 
*                       | -126.0   60.0  316.0  68.0  30.0  -48.0 | 
*        C(5 * 6)    =  | -64.0   -86.0  60.0  -24.0  -40.0  178.0| 
*                       |   .      .      .      .     .      .   | 
*                       |   .      .      .      .     .      .   |