Product of Two General Matrices

Operation	TRANSA	TRANSB	Matrix A	Matrix B
	'N' or 'n'	'N' or 'n'	m x k	k x n
	'T' or 't'	'N' or 'n'	k x m	k x n
	'N' or 'n'	'T' or 't'	m x k	n x k
	'T' or 't'	'T' or 't'	k x m	n x k
	'C' or 'c'	'N' or 'n'	k x m	k x n
	'N' or 'n'	'C' or 'c'	m x k	n x k
	'C' or 'c'	'C' or 'c'	k x m	n x k
	'T' or 't'	'C' or 'c'	k x m	n x k
	'C' or 'c'	'T' or 't'	k x m	n x k

Calling Sequence

CALL DGEMM	(TRANSA, TRANSB, M, N, K, DALPHA, DA, LDA, DB, LDB, DBETA, DC, LDC)
CALL SGEMM	(TRANSA, TRANSB, M, N, K, SALPHA, SA, LDA, SB, LDB, SBETA, SC, LDC)
CALL ZGEMM	(TRANSA, TRANSB, M, N, K, ZALPHA, ZA, LDA, ZB, LDB, ZBETA, ZC, LDC)
CALL CGEMM	(TRANSA, TRANSB, M, N, K, CALPHA, CA, LDA, CB, LDB, CBETA, CC, LDC)
void dgemm	(char transa, char transb, int m, int n, int k, double dalpha, double *da, int lda, double *db, int ldb, double dbeta, double *dc, int ldc)
void sgemm	(char transa, char transb, int m, int n, int k, float salpha, float *sa, int lda, float *sb, int ldb, float sbeta, float *sc, int ldc)
void zgemm	(char transa, char transb, int m, int n, int k, doublecomplex *zalpha, doublecomplex *za, int lda, doublecomplex *zb, int ldb, doublecomplex *zbeta, doublecomplex *zc, int ldc)
void cgemm	(char transa, char transb, int m, int n, int k, complex *calpha, complex *ca, int lda, complex *cb, int ldb, complex *cbeta, complex *cc, int ldc)

Arguments

TRANSA	Indicates how to use the matrix stored in the array A. The legal values for TRANSA are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored in A.
	'T' or 't'	Use the transpose of the matrix stored in A.
	'C' or 'c'	Use the conjugate transpose of the matrix stored in A.
TRANSB	Indicates how to use the matrix stored in the array B. The legal values for TRANSB are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored in B.
	'T' or 't'	Use the transpose of the matrix stored in B.
	'C' or 'c'	Use the conjugate transpose of the matrix stored in B.
M, N, K	Indicate the size of the matrices as shown in the table above. M, N, K 0.
xALPHA	Scalar that scales the input value of the matrix in A.
xA	Two-dimensional array in which one of the input matrices is stored.
LDA	Leading dimension of the array A as specified in the dimension or type statement. LDA max (1,K). If TRANSA = 'N' or 'n', LDA max (1,M).
xB	Two-dimensional array in which one of the input matrices is stored.
LDB	Leading dimension of the array B as specified in the dimension or type statement. LDB max(1,N).
	If TRANSB = 'N' or 'n', LDB max (1,K).
xBETA	Scalar that scales the input value of the matrix stored in C.
xC	An M × N array.
	On entry, an input matrix.
	On exit, the result matrix.
LDC	Leading dimension of the array C as specified in the dimension or type statement. LDC max (1,M).

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER K, LDA, LDB, LDC, M, N

PARAMETER (K = 3)

PARAMETER (M = 3)

PARAMETER (N = 2)

PARAMETER (LDA = M)

PARAMETER (LDB = K)

PARAMETER (LDC = M)

C

DOUBLE PRECISION A(LDA,K), ALPHA, B(LDB,N), BETA, C(LDC,N)

INTEGER I, J

C

EXTERNAL DGEMM

C

C Initialize the arrays A, B, and C to store the matrices A,

C B, and C shown below.

C

C 0 0 1 2 5 100 100

C A = 0 1 0 B = 3 6 C = 100 100

C 1 0 0 4 7 100 100

C

DATA A / 0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.0D0, 0.0D0,

$ 1.0D0, 0.0D0, 0.0D0 /

DATA B / 2.0D0, 3.0D0, 4.0D0, 5.0D0, 6.0D0, 7.0D0 /

DATA C / 6*1.0D2 /

C

PRINT 1000

PRINT 1010, ((A(I,J), J = 1, K), I = 1, M)

PRINT 1020

PRINT 1030, ((B(I,J), J = 1, N), I = 1, K)

PRINT 1040

PRINT 1030, ((C(I,J), J = 1, N), I = 1, M)

ALPHA = 2.0D0

BETA = 3.0D0

CALL DGEMM ('NOT TRANSPOSED A', 'NOT TRANSPOSED B', M, N,

$ K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

PRINT 1050

PRINT 1030, ((C(I,J), J = 1, N), I = 1, M)

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (3(3X, F5.1))

1020 FORMAT (/1X, 'B:')

1030 FORMAT (2(3X, F5.1))

1040 FORMAT (/1X, 'C:')

1050 FORMAT (/1X, 'AB + C')

C

END

Sample Output

A:
0.0 0.0 1.0
0.0 1.0 0.0
1.0 0.0 0.0
B:
2.0 5.0
3.0 6.0
4.0 7.0
C:
100.0 100.0
100.0 100.0
100.0 100.0
AB + C
308.0 314.0
306.0 312.0
304.0 310.0