Provided by: liblapack-doc_3.12.1-4_all 
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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