hpmv - Man Page

{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.

Definition at line 148 of file chpmv.f.

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.

Definition at line 150 of file cspmv.f.

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.

Definition at line 146 of file dspmv.f.

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.

Definition at line 146 of file sspmv.f.

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.

Definition at line 148 of file zhpmv.f.

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.

Definition at line 150 of file zspmv.f.

Author

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