table of contents
| gemm(3) | Library Functions Manual | gemm(3) |
NAME¶
gemm - gemm: general matrix-matrix multiply
SYNOPSIS¶
Functions¶
subroutine CGEMM (transa, transb, m, n, k, alpha, a, lda,
b, ldb, beta, c, ldc)
CGEMM subroutine DGEMM (transa, transb, m, n, k, alpha, a, lda,
b, ldb, beta, c, ldc)
DGEMM subroutine SGEMM (transa, transb, m, n, k, alpha, a, lda,
b, ldb, beta, c, ldc)
SGEMM subroutine ZGEMM (transa, transb, m, n, k, alpha, a, lda,
b, ldb, beta, c, ldc)
ZGEMM
Detailed Description¶
Function Documentation¶
subroutine CGEMM (character transa, character transb, integer m, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)¶
CGEMM
Purpose:
!> !> CGEMM performs one of the matrix-matrix operations !> !> C := alpha*op( A )*op( B ) + beta*C, !> !> where op( X ) is one of !> !> op( X ) = X or op( X ) = X**T or op( X ) = X**H, !> !> alpha and beta are scalars, and A, B and C are matrices, with op( A ) !> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. !>
Parameters
TRANSA
!> TRANSA is CHARACTER*1 !> On entry, TRANSA specifies the form of op( A ) to be used in !> the matrix multiplication as follows: !> !> TRANSA = 'N' or 'n', op( A ) = A. !> !> TRANSA = 'T' or 't', op( A ) = A**T. !> !> TRANSA = 'C' or 'c', op( A ) = A**H. !>
TRANSB
!> TRANSB is CHARACTER*1 !> On entry, TRANSB specifies the form of op( B ) to be used in !> the matrix multiplication as follows: !> !> TRANSB = 'N' or 'n', op( B ) = B. !> !> TRANSB = 'T' or 't', op( B ) = B**T. !> !> TRANSB = 'C' or 'c', op( B ) = B**H. !>
M
!> M is INTEGER !> On entry, M specifies the number of rows of the matrix !> op( A ) and of the matrix C. M must be at least zero. !>
N
!> N is INTEGER !> On entry, N specifies the number of columns of the matrix !> op( B ) and the number of columns of the matrix C. N must be !> at least zero. !>
K
!> K is INTEGER !> On entry, K specifies the number of columns of the matrix !> op( A ) and the number of rows of the matrix op( B ). K must !> be at least zero. !>
ALPHA
!> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !>
A
!> A is COMPLEX array, dimension ( LDA, ka ), where ka is !> k when TRANSA = 'N' or 'n', and is m otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading m by k !> part of the array A must contain the matrix A, otherwise !> the leading k by m part of the array A must contain the !> matrix A. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. When TRANSA = 'N' or 'n' then !> LDA must be at least max( 1, m ), otherwise LDA must be at !> least max( 1, k ). !>
B
!> B is COMPLEX array, dimension ( LDB, kb ), where kb is !> n when TRANSB = 'N' or 'n', and is k otherwise. !> Before entry with TRANSB = 'N' or 'n', the leading k by n !> part of the array B must contain the matrix B, otherwise !> the leading n by k part of the array B must contain the !> matrix B. !>
LDB
!> LDB is INTEGER !> On entry, LDB specifies the first dimension of B as declared !> in the calling (sub) program. When TRANSB = 'N' or 'n' then !> LDB must be at least max( 1, k ), otherwise LDB must be at !> least max( 1, n ). !>
BETA
!> BETA is COMPLEX !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !>
C
!> C is COMPLEX array, dimension ( LDC, N ) !> Before entry, the leading m by n part of the array C must !> contain the matrix C, except when beta is zero, in which !> case C need not be set on entry. !> On exit, the array C is overwritten by the m by n matrix !> ( alpha*op( A )*op( B ) + beta*C ). !>
LDC
!> LDC is INTEGER !> On entry, LDC specifies the first dimension of C as declared !> in the calling (sub) program. LDC must be at least !> max( 1, m ). !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 8-February-1989. !> Jack Dongarra, Argonne National Laboratory. !> Iain Duff, AERE Harwell. !> Jeremy Du Croz, Numerical Algorithms Group Ltd. !> Sven Hammarling, Numerical Algorithms Group Ltd. !>
Definition at line 186 of file cgemm.f.
subroutine DGEMM (character transa, character transb, integer m, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)¶
DGEMM
Purpose:
!> !> DGEMM performs one of the matrix-matrix operations !> !> C := alpha*op( A )*op( B ) + beta*C, !> !> where op( X ) is one of !> !> op( X ) = X or op( X ) = X**T, !> !> alpha and beta are scalars, and A, B and C are matrices, with op( A ) !> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. !>
Parameters
TRANSA
!> TRANSA is CHARACTER*1 !> On entry, TRANSA specifies the form of op( A ) to be used in !> the matrix multiplication as follows: !> !> TRANSA = 'N' or 'n', op( A ) = A. !> !> TRANSA = 'T' or 't', op( A ) = A**T. !> !> TRANSA = 'C' or 'c', op( A ) = A**T. !>
TRANSB
!> TRANSB is CHARACTER*1 !> On entry, TRANSB specifies the form of op( B ) to be used in !> the matrix multiplication as follows: !> !> TRANSB = 'N' or 'n', op( B ) = B. !> !> TRANSB = 'T' or 't', op( B ) = B**T. !> !> TRANSB = 'C' or 'c', op( B ) = B**T. !>
M
!> M is INTEGER !> On entry, M specifies the number of rows of the matrix !> op( A ) and of the matrix C. M must be at least zero. !>
N
!> N is INTEGER !> On entry, N specifies the number of columns of the matrix !> op( B ) and the number of columns of the matrix C. N must be !> at least zero. !>
K
!> K is INTEGER !> On entry, K specifies the number of columns of the matrix !> op( A ) and the number of rows of the matrix op( B ). K must !> be at least zero. !>
ALPHA
!> ALPHA is DOUBLE PRECISION. !> On entry, ALPHA specifies the scalar alpha. !>
A
!> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is !> k when TRANSA = 'N' or 'n', and is m otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading m by k !> part of the array A must contain the matrix A, otherwise !> the leading k by m part of the array A must contain the !> matrix A. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. When TRANSA = 'N' or 'n' then !> LDA must be at least max( 1, m ), otherwise LDA must be at !> least max( 1, k ). !>
B
!> B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is !> n when TRANSB = 'N' or 'n', and is k otherwise. !> Before entry with TRANSB = 'N' or 'n', the leading k by n !> part of the array B must contain the matrix B, otherwise !> the leading n by k part of the array B must contain the !> matrix B. !>
LDB
!> LDB is INTEGER !> On entry, LDB specifies the first dimension of B as declared !> in the calling (sub) program. When TRANSB = 'N' or 'n' then !> LDB must be at least max( 1, k ), otherwise LDB must be at !> least max( 1, n ). !>
BETA
!> BETA is DOUBLE PRECISION. !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !>
C
!> C is DOUBLE PRECISION array, dimension ( LDC, N ) !> Before entry, the leading m by n part of the array C must !> contain the matrix C, except when beta is zero, in which !> case C need not be set on entry. !> On exit, the array C is overwritten by the m by n matrix !> ( alpha*op( A )*op( B ) + beta*C ). !>
LDC
!> LDC is INTEGER !> On entry, LDC specifies the first dimension of C as declared !> in the calling (sub) program. LDC must be at least !> max( 1, m ). !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 8-February-1989. !> Jack Dongarra, Argonne National Laboratory. !> Iain Duff, AERE Harwell. !> Jeremy Du Croz, Numerical Algorithms Group Ltd. !> Sven Hammarling, Numerical Algorithms Group Ltd. !>
Definition at line 186 of file dgemm.f.
subroutine SGEMM (character transa, character transb, integer m, integer n, integer k, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)¶
SGEMM
Purpose:
!> !> SGEMM performs one of the matrix-matrix operations !> !> C := alpha*op( A )*op( B ) + beta*C, !> !> where op( X ) is one of !> !> op( X ) = X or op( X ) = X**T, !> !> alpha and beta are scalars, and A, B and C are matrices, with op( A ) !> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. !>
Parameters
TRANSA
!> TRANSA is CHARACTER*1 !> On entry, TRANSA specifies the form of op( A ) to be used in !> the matrix multiplication as follows: !> !> TRANSA = 'N' or 'n', op( A ) = A. !> !> TRANSA = 'T' or 't', op( A ) = A**T. !> !> TRANSA = 'C' or 'c', op( A ) = A**T. !>
TRANSB
!> TRANSB is CHARACTER*1 !> On entry, TRANSB specifies the form of op( B ) to be used in !> the matrix multiplication as follows: !> !> TRANSB = 'N' or 'n', op( B ) = B. !> !> TRANSB = 'T' or 't', op( B ) = B**T. !> !> TRANSB = 'C' or 'c', op( B ) = B**T. !>
M
!> M is INTEGER !> On entry, M specifies the number of rows of the matrix !> op( A ) and of the matrix C. M must be at least zero. !>
N
!> N is INTEGER !> On entry, N specifies the number of columns of the matrix !> op( B ) and the number of columns of the matrix C. N must be !> at least zero. !>
K
!> K is INTEGER !> On entry, K specifies the number of columns of the matrix !> op( A ) and the number of rows of the matrix op( B ). K must !> be at least zero. !>
ALPHA
!> ALPHA is REAL !> On entry, ALPHA specifies the scalar alpha. !>
A
!> A is REAL array, dimension ( LDA, ka ), where ka is !> k when TRANSA = 'N' or 'n', and is m otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading m by k !> part of the array A must contain the matrix A, otherwise !> the leading k by m part of the array A must contain the !> matrix A. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. When TRANSA = 'N' or 'n' then !> LDA must be at least max( 1, m ), otherwise LDA must be at !> least max( 1, k ). !>
B
!> B is REAL array, dimension ( LDB, kb ), where kb is !> n when TRANSB = 'N' or 'n', and is k otherwise. !> Before entry with TRANSB = 'N' or 'n', the leading k by n !> part of the array B must contain the matrix B, otherwise !> the leading n by k part of the array B must contain the !> matrix B. !>
LDB
!> LDB is INTEGER !> On entry, LDB specifies the first dimension of B as declared !> in the calling (sub) program. When TRANSB = 'N' or 'n' then !> LDB must be at least max( 1, k ), otherwise LDB must be at !> least max( 1, n ). !>
BETA
!> BETA is REAL !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !>
C
!> C is REAL array, dimension ( LDC, N ) !> Before entry, the leading m by n part of the array C must !> contain the matrix C, except when beta is zero, in which !> case C need not be set on entry. !> On exit, the array C is overwritten by the m by n matrix !> ( alpha*op( A )*op( B ) + beta*C ). !>
LDC
!> LDC is INTEGER !> On entry, LDC specifies the first dimension of C as declared !> in the calling (sub) program. LDC must be at least !> max( 1, m ). !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 8-February-1989. !> Jack Dongarra, Argonne National Laboratory. !> Iain Duff, AERE Harwell. !> Jeremy Du Croz, Numerical Algorithms Group Ltd. !> Sven Hammarling, Numerical Algorithms Group Ltd. !>
Definition at line 186 of file sgemm.f.
subroutine ZGEMM (character transa, character transb, integer m, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)¶
ZGEMM
Purpose:
!> !> ZGEMM performs one of the matrix-matrix operations !> !> C := alpha*op( A )*op( B ) + beta*C, !> !> where op( X ) is one of !> !> op( X ) = X or op( X ) = X**T or op( X ) = X**H, !> !> alpha and beta are scalars, and A, B and C are matrices, with op( A ) !> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. !>
Parameters
TRANSA
!> TRANSA is CHARACTER*1 !> On entry, TRANSA specifies the form of op( A ) to be used in !> the matrix multiplication as follows: !> !> TRANSA = 'N' or 'n', op( A ) = A. !> !> TRANSA = 'T' or 't', op( A ) = A**T. !> !> TRANSA = 'C' or 'c', op( A ) = A**H. !>
TRANSB
!> TRANSB is CHARACTER*1 !> On entry, TRANSB specifies the form of op( B ) to be used in !> the matrix multiplication as follows: !> !> TRANSB = 'N' or 'n', op( B ) = B. !> !> TRANSB = 'T' or 't', op( B ) = B**T. !> !> TRANSB = 'C' or 'c', op( B ) = B**H. !>
M
!> M is INTEGER !> On entry, M specifies the number of rows of the matrix !> op( A ) and of the matrix C. M must be at least zero. !>
N
!> N is INTEGER !> On entry, N specifies the number of columns of the matrix !> op( B ) and the number of columns of the matrix C. N must be !> at least zero. !>
K
!> K is INTEGER !> On entry, K specifies the number of columns of the matrix !> op( A ) and the number of rows of the matrix op( B ). K must !> be at least zero. !>
ALPHA
!> ALPHA is COMPLEX*16 !> On entry, ALPHA specifies the scalar alpha. !>
A
!> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is !> k when TRANSA = 'N' or 'n', and is m otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading m by k !> part of the array A must contain the matrix A, otherwise !> the leading k by m part of the array A must contain the !> matrix A. !>
LDA
!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. When TRANSA = 'N' or 'n' then !> LDA must be at least max( 1, m ), otherwise LDA must be at !> least max( 1, k ). !>
B
!> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is !> n when TRANSB = 'N' or 'n', and is k otherwise. !> Before entry with TRANSB = 'N' or 'n', the leading k by n !> part of the array B must contain the matrix B, otherwise !> the leading n by k part of the array B must contain the !> matrix B. !>
LDB
!> LDB is INTEGER !> On entry, LDB specifies the first dimension of B as declared !> in the calling (sub) program. When TRANSB = 'N' or 'n' then !> LDB must be at least max( 1, k ), otherwise LDB must be at !> least max( 1, n ). !>
BETA
!> BETA is COMPLEX*16 !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !>
C
!> C is COMPLEX*16 array, dimension ( LDC, N ) !> Before entry, the leading m by n part of the array C must !> contain the matrix C, except when beta is zero, in which !> case C need not be set on entry. !> On exit, the array C is overwritten by the m by n matrix !> ( alpha*op( A )*op( B ) + beta*C ). !>
LDC
!> LDC is INTEGER !> On entry, LDC specifies the first dimension of C as declared !> in the calling (sub) program. LDC must be at least !> max( 1, m ). !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 8-February-1989. !> Jack Dongarra, Argonne National Laboratory. !> Iain Duff, AERE Harwell. !> Jeremy Du Croz, Numerical Algorithms Group Ltd. !> Sven Hammarling, Numerical Algorithms Group Ltd. !>
Definition at line 186 of file zgemm.f.
Author¶
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