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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