dspmv

NAME

dspmv - perform the matrix-vector operation y := alpha*A*x + beta*y

SYNOPSIS 

  SUBROUTINE DSPMV( UPLO, N, ALPHA, A, X, INCX, BETA, Y, INCY)
  CHARACTER * 1 UPLO
  INTEGER N, INCX, INCY
  DOUBLE PRECISION ALPHA, BETA
  DOUBLE PRECISION A(*), X(*), Y(*)
 
  SUBROUTINE DSPMV_64( UPLO, N, ALPHA, A, X, INCX, BETA, Y, INCY)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INCX, INCY
  DOUBLE PRECISION ALPHA, BETA
  DOUBLE PRECISION A(*), X(*), Y(*)

F95 INTERFACE 

  SUBROUTINE SPMV( UPLO, N, ALPHA, A, X, [INCX], BETA, Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, INCX, INCY
  REAL(8) :: ALPHA, BETA
  REAL(8), DIMENSION(:) :: A, X, Y
 
  SUBROUTINE SPMV_64( UPLO, N, ALPHA, A, X, [INCX], BETA, Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, INCX, INCY
  REAL(8) :: ALPHA, BETA
  REAL(8), DIMENSION(:) :: A, X, Y

C INTERFACE

#include <sunperf.h>

void dspmv(char uplo, int n, double alpha, double *a, double *x, int incx, double beta, double *y, int incy);

void dspmv_64(char uplo, long n, double alpha, double *a, double *x, long incx, double beta, double *y, long incy);

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.

ARGUMENTS

* UPLO (input)
On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array A as follows:

UPLO = 'U' or 'u' The upper triangular part of A is supplied in A.

UPLO = 'L' or 'l' The lower triangular part of A is supplied in A.

Unchanged on exit.

* N (input)
On entry, N specifies the order of the matrix A. N >= 0. Unchanged on exit.

* ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

* A (input)
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array A must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array A must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Unchanged on exit.

* X (input)
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit.

* INCX (input)
On entry, INCX specifies the increment for the elements of X. INCX <> 0. Unchanged on exit.

* BETA (input)
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 (input/output)
( 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 (input)
On entry, INCY specifies the increment for the elements of Y. INCY <> 0. Unchanged on exit.