table of contents
| gemmtr(3) | LAPACK | gemmtr(3) |
NAME¶
gemmtr - gemmtr: general matrix-matrix multiply with triangular output
SYNOPSIS¶
Functions¶
subroutine cgemmtr (uplo, transa, transb, n, k, alpha, a,
lda, b, ldb, beta, c, ldc)
CGEMMTR subroutine dgemmtr (uplo, transa, transb, n, k, alpha,
a, lda, b, ldb, beta, c, ldc)
DGEMMTR subroutine sgemmtr (uplo, transa, transb, n, k, alpha,
a, lda, b, ldb, beta, c, ldc)
SGEMMTR subroutine zgemmtr (uplo, transa, transb, n, k, alpha,
a, lda, b, ldb, beta, c, ldc)
ZGEMMTR
Detailed Description¶
@defgroup hemm {he,sy}mm: Hermitian/symmetric matrix-matrix multiply
@defgroup herk {he,sy}rk: Hermitian/symmetric rank-k update
@defgroup her2k {he,sy}r2k: Hermitian/symmetric rank-2k update
@defgroup trmm trmm: triangular matrix-matrix multiply
@defgroup trsm trsm: triangular matrix-matrix solve
@}
Function Documentation¶
subroutine cgemmtr (character uplo, character transa, character transb, 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)¶
CGEMMTR
Purpose:
!> !> CGEMMTR 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 n by k matrix, op( B ) a k by n matrix and C an n by n matrix. !> Thereby, the routine only accesses and updates the upper or lower !> triangular part of the result matrix C. This behaviour can be used if !> the resulting matrix C is known to be Hermitian or symmetric. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the lower or the upper !> triangular part of C is access and updated. !> !> UPLO = 'L' or 'l', the lower triangular part of C is used. !> !> UPLO = 'U' or 'u', the upper triangular part of C is used. !>
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. !>
N
!> N is INTEGER !> On entry, N specifies the number of rows and columns of !> the matrix C, the number of columns of op(B) and the number !> of rows of op(A). 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 n otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading n 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, n ), 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 n 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 upper or lower triangular part of the matrix !> C is overwritten by the n 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, n ). !>
Author
Martin Koehler
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 19-July-2023. !> Martin Koehler, MPI Magdeburg !>
subroutine dgemmtr (character uplo, character transa, character transb, 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)¶
DGEMMTR
Purpose:
!> !> DGEMMTR 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 n by k matrix, op( B ) a k by n matrix and C an n by n matrix. !> Thereby, the routine only accesses and updates the upper or lower !> triangular part of the result matrix C. This behaviour can be used if !> the resulting matrix C is known to be symmetric. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the lower or the upper !> triangular part of C is access and updated. !> !> UPLO = 'L' or 'l', the lower triangular part of C is used. !> !> UPLO = 'U' or 'u', the upper triangular part of C is used. !>
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. !>
N
!> N is INTEGER !> On entry, N specifies the number of rows and columns of !> the matrix C, the number of columns of op(B) and the number !> of rows of op(A). 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 n otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading n 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, n ), 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 n 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 upper or lower triangular part of the matrix !> C is overwritten by the n 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, n ). !>
Author
Martin Koehler
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 19-July-2023. !> Martin Koehler, MPI Magdeburg !>
subroutine sgemmtr (character uplo, character transa, character transb, 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)¶
SGEMMTR
Purpose:
!> !> SGEMMTR 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 n by k matrix, op( B ) a k by n matrix and C an n by n matrix. !> Thereby, the routine only accesses and updates the upper or lower !> triangular part of the result matrix C. This behaviour can be used if !> the resulting matrix C is known to be symmetric. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the lower or the upper !> triangular part of C is access and updated. !> !> UPLO = 'L' or 'l', the lower triangular part of C is used. !> !> UPLO = 'U' or 'u', the upper triangular part of C is used. !>
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. !>
N
!> N is INTEGER !> On entry, N specifies the number of rows and columns of !> the matrix C, the number of columns of op(B) and the number !> of rows of op(A). 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 n otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading n 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, n ), 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 n 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 upper or lower triangular part of the matrix !> C is overwritten by the n 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, n ). !>
Author
Martin Koehler
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 19-July-2023. !> Martin Koehler, MPI Magdeburg !>
subroutine zgemmtr (character uplo, character transa, character transb, 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)¶
ZGEMMTR
Purpose:
!> !> ZGEMMTR 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 n by k matrix, op( B ) a k by n matrix and C an n by n matrix. !> Thereby, the routine only accesses and updates the upper or lower !> triangular part of the result matrix C. This behaviour can be used if !> the resulting matrix C is known to be Hermitian or symmetric. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the lower or the upper !> triangular part of C is access and updated. !> !> UPLO = 'L' or 'l', the lower triangular part of C is used. !> !> UPLO = 'U' or 'u', the upper triangular part of C is used. !>
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. !>
N
!> N is INTEGER !> On entry, N specifies the number of rows and columns of !> the matrix C, the number of columns of op(B) and the number !> of rows of op(A). 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 n otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading n 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, n ), 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 n 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 upper or lower triangular part of the matrix !> C is overwritten by the n 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, n ). !>
Author
Martin Koehler
Further Details:
!> !> Level 3 Blas routine. !> !> -- Written on 19-July-2023. !> Martin Koehler, MPI Magdeburg !>
Author¶
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