Man page - gemm(3)

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Manual

gemm

NAME
SYNOPSIS
Functions
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)
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, integerldc)
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)
subroutine zgemm (character transa, character transb, integer m, integer n,integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integerlda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta,complex*16, dimension(ldc,*) c, integer ldc)
Author

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.

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, integerldc)

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.

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.

subroutine zgemm (character transa, character transb, integer m, integer n,integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integerlda, 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.

Author

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