hpmv(3)

NAME
hpmv - {hp,sp}mv: Hermitian/symmetric matrix-vector multiply

SYNOPSIS

  Functions

subroutine chpmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
CHPMV
subroutine dspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
DSPMV
subroutine sspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
SSPMV
subroutine zhpmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
ZHPMV
subroutine cspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
subroutine zspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Detailed Description

Function Documentation

  subroutine chpmv (character uplo, integer n, complex alpha, complex, dimension(*) ap, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)

CHPMV

Purpose:

    !>
    !> CHPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n hermitian matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    N

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

    ALPHA

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

    AP

    !>          AP is COMPLEX array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>           Note that the imaginary parts of the diagonal elements need
    !>           not be set and are assumed to be zero.
    !>

    X

    !>          X is COMPLEX array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the n
    !>           element 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 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    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 cspmv (character uplo, integer n, complex alpha, complex, dimension( * ) ap, complex, dimension( * ) x, integer incx, complex beta, complex, dimension( * ) y, integer incy)

CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Purpose:

    !>
    !> CSPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n symmetric matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>
    !>           Unchanged on exit.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>           Unchanged on exit.
    !>

    ALPHA

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

    AP

    !>          AP is COMPLEX array, dimension at least
    !>           ( ( N*( N + 1 ) )/2 ).
    !>           Before entry, with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry, with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>           Unchanged on exit.
    !>

    X

    !>          X is COMPLEX array, dimension at least
    !>           ( 1 + ( N - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the N-
    !>           element vector x.
    !>           Unchanged on exit.
    !>

    INCX

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

    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.
    !>           Unchanged on exit.
    !>

    Y

    !>          Y is COMPLEX array, dimension at least
    !>           ( 1 + ( N - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    INCY

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dspmv (character uplo, integer n, double precision alpha, double precision, dimension(*) ap, double precision, dimension(*) x, integer incx, double precision beta, double precision, dimension(*) y, integer incy)

DSPMV

Purpose:

    !>
    !> DSPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n symmetric matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    N

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

    ALPHA

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

    AP

    !>          AP is DOUBLE PRECISION array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the n
    !>           element 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 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    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 sspmv (character uplo, integer n, real alpha, real, dimension(*) ap, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy)

SSPMV

Purpose:

    !>
    !> SSPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n symmetric matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    N

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

    ALPHA

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

    AP

    !>          AP is REAL array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>

    X

    !>          X is REAL array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the n
    !>           element 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 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    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 zhpmv (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZHPMV

Purpose:

    !>
    !> ZHPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n hermitian matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>

    N

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

    ALPHA

    !>          ALPHA is COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the hermitian matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>           Note that the imaginary parts of the diagonal elements need
    !>           not be set and are assumed to be zero.
    !>

    X

    !>          X is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the n
    !>           element 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 + ( n - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    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 zspmv (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) ap, complex*16, dimension( * ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y, integer incy)

ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Purpose:

    !>
    !> ZSPMV  performs the matrix-vector operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> where alpha and beta are scalars, x and y are n element vectors and
    !> A is an n by n symmetric matrix, supplied in packed form.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the upper or lower
    !>           triangular part of the matrix A is supplied in the packed
    !>           array AP as follows:
    !>
    !>              UPLO = 'U' or 'u'   The upper triangular part of A is
    !>                                  supplied in AP.
    !>
    !>              UPLO = 'L' or 'l'   The lower triangular part of A is
    !>                                  supplied in AP.
    !>
    !>           Unchanged on exit.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>           Unchanged on exit.
    !>

    ALPHA

    !>          ALPHA is COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>           Unchanged on exit.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension at least
    !>           ( ( N*( N + 1 ) )/2 ).
    !>           Before entry, with UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    !>           and a( 2, 2 ) respectively, and so on.
    !>           Before entry, with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular part of the symmetric matrix
    !>           packed sequentially, column by column, so that AP( 1 )
    !>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    !>           and a( 3, 1 ) respectively, and so on.
    !>           Unchanged on exit.
    !>

    X

    !>          X is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( N - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the N-
    !>           element vector x.
    !>           Unchanged on exit.
    !>

    INCX

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

    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.
    !>           Unchanged on exit.
    !>

    Y

    !>          Y is COMPLEX*16 array, dimension at least
    !>           ( 1 + ( N - 1 )*abs( INCY ) ).
    !>           Before entry, the incremented array Y must contain the n
    !>           element vector y. On exit, Y is overwritten by the updated
    !>           vector y.
    !>

    INCY

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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