gemv(3)

NAME
gemv - gemv: general matrix-vector multiply

SYNOPSIS

  Functions

subroutine cgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
CGEMV
subroutine dgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
DGEMV
subroutine sgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
SGEMV
subroutine zgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV

Detailed Description

Function Documentation

  subroutine cgemv (character trans, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)

CGEMV

Purpose:

    !>
    !> CGEMV performs one of the matrix-vector operations
    !>
    !>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
    !>
    !>    y := alpha*A**H*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are vectors and A is an
    !> m by n matrix.
    !>

Parameters
    TRANS

    !>          TRANS is CHARACTER*1
    !>           On entry, TRANS specifies the operation to be performed as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
    !>
    !>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
    !>
    !>              TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.
    !>

    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is COMPLEX
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    A

    !>          A is COMPLEX array, dimension ( LDA, N )
    !>           Before entry, the leading m by n part of the array A must
    !>           contain the matrix of coefficients.
    !>

    LDA

    !>          LDA is INTEGER
    !>           On entry, LDA specifies the first dimension of A as declared
    !>           in the calling (sub) program. LDA must be at least
    !>           max( 1, m ).
    !>

    X

    !>          X is COMPLEX array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
    !>           Before entry, the incremented array X must contain the
    !>           vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    BETA

    !>          BETA is COMPLEX
    !>           On entry, BETA specifies the scalar beta. When BETA is
    !>           supplied as zero then Y need not be set on input.
    !>

    Y

    !>          Y is COMPLEX array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
    !>           Before entry with BETA non-zero, the incremented array Y
    !>           must contain the vector y. On exit, Y is overwritten by the
    !>           updated vector y.
    !>           If either m or n is zero, then Y not referenced and the function
    !>           performs a quick return.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Level 2 Blas routine.
    !>  The vector and matrix arguments are not referenced when N = 0, or M = 0
    !>
    !>  -- Written on 22-October-1986.
    !>     Jack Dongarra, Argonne National Lab.
    !>     Jeremy Du Croz, Nag Central Office.
    !>     Sven Hammarling, Nag Central Office.
    !>     Richard Hanson, Sandia National Labs.
    !>

  subroutine dgemv (character trans, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx, double precision beta, double precision, dimension(*) y, integer incy)

DGEMV

Purpose:

    !>
    !> DGEMV  performs one of the matrix-vector operations
    !>
    !>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are vectors and A is an
    !> m by n matrix.
    !>

Parameters
    TRANS

    !>          TRANS is CHARACTER*1
    !>           On entry, TRANS specifies the operation to be performed as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
    !>
    !>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
    !>
    !>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
    !>

    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N 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, N )
    !>           Before entry, the leading m by n part of the array A must
    !>           contain the matrix of coefficients.
    !>

    LDA

    !>          LDA is INTEGER
    !>           On entry, LDA specifies the first dimension of A as declared
    !>           in the calling (sub) program. LDA must be at least
    !>           max( 1, m ).
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
    !>           Before entry, the incremented array X must contain the
    !>           vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    BETA

    !>          BETA is DOUBLE PRECISION.
    !>           On entry, BETA specifies the scalar beta. When BETA is
    !>           supplied as zero then Y need not be set on input.
    !>

    Y

    !>          Y is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
    !>           Before entry with BETA non-zero, the incremented array Y
    !>           must contain the vector y. On exit, Y is overwritten by the
    !>           updated vector y.
    !>           If either m or n is zero, then Y not referenced and the function
    !>           performs a quick return.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Level 2 Blas routine.
    !>  The vector and matrix arguments are not referenced when N = 0, or M = 0
    !>
    !>  -- Written on 22-October-1986.
    !>     Jack Dongarra, Argonne National Lab.
    !>     Jeremy Du Croz, Nag Central Office.
    !>     Sven Hammarling, Nag Central Office.
    !>     Richard Hanson, Sandia National Labs.
    !>

  subroutine sgemv (character trans, integer m, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy)

SGEMV

Purpose:

    !>
    !> SGEMV  performs one of the matrix-vector operations
    !>
    !>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are vectors and A is an
    !> m by n matrix.
    !>

Parameters
    TRANS

    !>          TRANS is CHARACTER*1
    !>           On entry, TRANS specifies the operation to be performed as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
    !>
    !>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
    !>
    !>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
    !>

    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N must be at least zero.
    !>

    ALPHA

    !>          ALPHA is REAL
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    A

    !>          A is REAL array, dimension ( LDA, N )
    !>           Before entry, the leading m by n part of the array A must
    !>           contain the matrix of coefficients.
    !>

    LDA

    !>          LDA is INTEGER
    !>           On entry, LDA specifies the first dimension of A as declared
    !>           in the calling (sub) program. LDA must be at least
    !>           max( 1, m ).
    !>

    X

    !>          X is REAL array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
    !>           Before entry, the incremented array X must contain the
    !>           vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    BETA

    !>          BETA is REAL
    !>           On entry, BETA specifies the scalar beta. When BETA is
    !>           supplied as zero then Y need not be set on input.
    !>

    Y

    !>          Y is REAL array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
    !>           Before entry with BETA non-zero, the incremented array Y
    !>           must contain the vector y. On exit, Y is overwritten by the
    !>           updated vector y.
    !>           If either m or n is zero, then Y not referenced and the function
    !>           performs a quick return.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Level 2 Blas routine.
    !>  The vector and matrix arguments are not referenced when N = 0, or M = 0
    !>
    !>  -- Written on 22-October-1986.
    !>     Jack Dongarra, Argonne National Lab.
    !>     Jeremy Du Croz, Nag Central Office.
    !>     Sven Hammarling, Nag Central Office.
    !>     Richard Hanson, Sandia National Labs.
    !>

  subroutine zgemv (character trans, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZGEMV

Purpose:

    !>
    !> ZGEMV  performs one of the matrix-vector operations
    !>
    !>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
    !>
    !>    y := alpha*A**H*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are vectors and A is an
    !> m by n matrix.
    !>

Parameters
    TRANS

    !>          TRANS is CHARACTER*1
    !>           On entry, TRANS specifies the operation to be performed as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
    !>
    !>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
    !>
    !>              TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.
    !>

    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the number of columns of the matrix A.
    !>           N 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, N )
    !>           Before entry, the leading m by n part of the array A must
    !>           contain the matrix of coefficients.
    !>

    LDA

    !>          LDA is INTEGER
    !>           On entry, LDA specifies the first dimension of A as declared
    !>           in the calling (sub) program. LDA must be at least
    !>           max( 1, m ).
    !>

    X

    !>          X is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
    !>           Before entry, the incremented array X must contain the
    !>           vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    BETA

    !>          BETA is COMPLEX*16
    !>           On entry, BETA specifies the scalar beta. When BETA is
    !>           supplied as zero then Y need not be set on input.
    !>

    Y

    !>          Y is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
    !>           and at least
    !>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
    !>           Before entry with BETA non-zero, the incremented array Y
    !>           must contain the vector y. On exit, Y is overwritten by the
    !>           updated vector y.
    !>           If either m or n is zero, then Y not referenced and the function
    !>           performs a quick return.
    !>

    INCY

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Level 2 Blas routine.
    !>  The vector and matrix arguments are not referenced when N = 0, or M = 0
    !>
    !>  -- Written on 22-October-1986.
    !>     Jack Dongarra, Argonne National Lab.
    !>     Jeremy Du Croz, Nag Central Office.
    !>     Sven Hammarling, Nag Central Office.
    !>     Richard Hanson, Sandia National Labs.
    !>

Author

Generated automatically by Doxygen for LAPACK from the source code.