gemmtr - gemmtr: general matrix-matrix multiply with triangular output

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@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 @}

subroutinecgemmtr(characteruplo,charactertransa,charactertransb,integern,integerk,complexalpha,complex,dimension(lda,*)a,integerlda,complex,dimension(ldb,*)b,integerldb,complexbeta,complex,dimension(ldc,*)c,integerldc)CGEMMTRPurpose: 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. ParametersUPLO 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 FurtherDetails: Level 3 Blas routine. -- Written on 19-July-2023. Martin Koehler, MPI Magdeburg subroutinedgemmtr(characteruplo,charactertransa,charactertransb,integern,integerk,doubleprecisionalpha,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecisionbeta,doubleprecision,dimension(ldc,*)c,integerldc)DGEMMTRPurpose: 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. ParametersUPLO 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 FurtherDetails: Level 3 Blas routine. -- Written on 19-July-2023. Martin Koehler, MPI Magdeburg subroutinesgemmtr(characteruplo,charactertransa,charactertransb,integern,integerk,realalpha,real,dimension(lda,*)a,integerlda,real,dimension(ldb,*)b,integerldb,realbeta,real,dimension(ldc,*)c,integerldc)SGEMMTRPurpose: 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. ParametersUPLO 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 FurtherDetails: Level 3 Blas routine. -- Written on 19-July-2023. Martin Koehler, MPI Magdeburg subroutinezgemmtr(characteruplo,charactertransa,charactertransb,integern,integerk,complex*16alpha,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldb,*)b,integerldb,complex*16beta,complex*16,dimension(ldc,*)c,integerldc)ZGEMMTRPurpose: 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. ParametersUPLO 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 FurtherDetails: Level 3 Blas routine. -- Written on 19-July-2023. Martin Koehler, MPI Magdeburg

gemmtr - gemmtr: general matrix-matrix multiply with triangular output

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