?gemm

Compute the product of a general matrix and a matrix.

That is, $\text{[math]}$ .

The value of op(X) may be $\text{[math]}$ . alpha and beta are multiplication coefficients; op(A) is an m*k matrix; op(B) is a k*n matrix, and C is an m*n matrix.

Interface Definition

C interface:

void cblas_sgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const BLASINT M, const BLASINT N, const BLASINT K, 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_dgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const BLASINT M, const BLASINT N, const BLASINT K, 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_cgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const BLASINT M, const BLASINT N, const BLASINT K, 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_zgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const BLASINT M, const BLASINT N, const BLASINT K, 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 SGEMM(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL DGEMM(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL CGEMM(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL ZGEMM(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

Parameters

Parameter	Type	Description	Input/Output
order	Enumeration type CBLAS_ORDER	Whether the matrix is in row- or column-major order.	Input
TransA	Enumeration type CBLAS_TRANSPOSE	Whether matrix A is non-transposed, transposed, or conjugated. If TransA = CblasNoTrans, . If TransA = CblasTrans, . If TransA = CblasConjTrans, $\text{[math]}$ . If TransA = CblasConjTrans, $\text{[math]}$ .	Input
TransB	Enumeration type CBLAS_TRANSPOSE	Whether matrix B is non-transposed, transposed, or conjugated. If TransB = CblasNoTrans, . If TransB = CblasTrans, . If TransB = CblasConjTrans, $\text{[math]}$ . If TransB = CblasConjTrans, .	Input
M	Integer	Number of rows in matrices op(A) and C.	Input
N	Integer	Number of columns in matrices op(B) and C.	Input
K	Integer	Number of columns in matrix op(A) and number of rows in matrix op(B).	Input
alpha	Single-precision floating-point type for sgemm Double-precision floating-point type for dgemm Single-precision complex type for cgemm Double-precision complex type for zgemm	Multiplication coefficient.	Input
A	Single-precision floating-point type for sgemm Double-precision floating-point type for dgemm Single-precision complex type for cgemm Double-precision complex type for zgemm	Matrix A.	Input
lda	Integer	For a column-store matrix with TransA = CblasNoTrans, lda must be at least max(1, m); otherwise, lda must be at least max(1, k). For a row-store matrix with TransA = CblasNoTrans, lda must be at least max(1, k); otherwise, lda must be at least max(1, m).	Input
B	Single-precision floating-point type for sgemm Double-precision floating-point type for dgemm Single-precision complex type for cgemm Double-precision complex type for zgemm	Matrix B.	Input
ldb	Integer	For a column-store matrix with TransB = CblasNoTrans, ldb must be at least max(1, k); otherwise, ldb must be at least max(1, n). For a row-store matrix with TransB = CblasNoTrans, ldb must be at least max(1, n); otherwise, ldb must be at least max(1, k).	Input
beta	Single-precision floating-point type for sgemm Double-precision floating-point type for dgemm Single-precision complex type for cgemm Double-precision complex type for zgemm	Multiplication coefficient.	Input
C	Single-precision floating-point type for sgemm Double-precision floating-point type for dgemm Single-precision complex type for cgemm Double-precision complex type for zgemm	Matrix C.	Input/Output
ldc	Integer	For a column-store matrix, ldc must be at least max(1, m); otherwise, ldc must be at least max(1, n).	Input

Dependency

#include "kblas.h"

Examples

C interface:

    int m = 4, k = 3, n = 4, lda = 4, ldb = 3, ldc = 4; 
    float alpha = 1.0, beta = 2.0; 
     /* 
     * A: 
     *     0.340188,       0.411647,       -0.222225, 
     *     -0.105617,      -0.302449,      0.053970, 
     *     0.283099,       -0.164777,      -0.022603, 
     *     0.298440,       0.268230,       0.128871, 
     * B: 
     *     -0.135216,      0.416195,       -0.358397,      -0.257113, 
     *     0.013401,       0.135712,       0.106969,       -0.362768, 
     *     0.452230,       0.217297,       -0.483699,      0.304177, 
     * C: 
     *     -0.343321,      0.498924,       0.112640,       -0.006417, 
     *     -0.099056,      -0.281743,      -0.203968,      0.472775, 
     *     -0.370210,      0.012932,       0.137552,       -0.207483, 
     *     -0.391191,      0.339112,       0.024287,       0.271358, 
     */ 
    float a[12] = {0.340188, -0.105617, 0.283099, 
                    0.298440, 0.411647, -0.302449, 
                    -0.164777, 0.268230, -0.222225, 
                    0.053970, -0.022603, 0.128871}; 
    float b[12] = {-0.135216, 0.013401, 0.452230, 0.416195, 
                    0.135712, 0.217297, -0.358397, 0.106969, 
                    -0.483699, -0.257113, -0.362768, 0.304177}; 
    float c[16] = {-0.343321, -0.099056, -0.370210, -0.391191, 
                    0.498924, -0.281743, 0.012932, 0.339112, 
                    0.112640, -0.203968, 0.137552, 0.024287, 
                    -0.006417, 0.472775, -0.207483, 0.271358}; 
 
    cblas_sgemm(CblasColMajor,CblasNoTrans,CblasNoTrans, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc); 
    /* 
     * Output C: 
     *     -0.827621       1.147010        0.254881        -0.317229 
     *     -0.163476       -0.636762       -0.428542       1.098841 
     *     -0.791128       0.116416        0.166949        -0.434854 
     *     -0.760862       0.866839        -0.092028       0.407877 
     * 
     */

Fortran interface:

      INTEGER :: M=4, K=3, N=4 
      INTEGER :: LDA=4, LDB=3, LDC=4 
      REAL(4) :: ALPHA=1.0, BETA=2.0 
      REAL(4) :: A(12), B(12), C(16) 
      DATA A/0.340188, -0.105617, 0.283099, 
     $       0.298440, 0.411647, -0.302449, 
     $       -0.164777, 0.268230, -0.222225, 
     $       0.053970, -0.022603, 0.128871/ 
      DATA B/-0.135216, 0.013401, 0.452230, 0.416195, 
     $       0.135712, 0.217297, -0.358397, 0.106969, 
     $       -0.483699, -0.257113, -0.362768, 0.304177/ 
      DATA C/-0.343321, -0.099056, -0.370210, -0.391191, 
     $       0.498924, -0.281743, 0.012932, 0.339112, 
     $       0.112640, -0.203968, 0.137552, 0.024287, 
     $       -0.006417, 0.472775, -0.207483, 0.271358/ 
      EXTERNAL SGEMM 
      CALL SGEMM('N', 'N', M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, 
     $          LDC) 
*     Output C: 
*         -0.827621       1.147010        0.254881        -0.317229 
*         -0.163476       -0.636762       -0.428542       1.098841 
*         -0.791128       0.116416        0.166949        -0.434854 
*         -0.760862       0.866839        -0.092028       0.407877

Parent topic: KML_BLAS Level 3 Functions