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version 1.5, 2010/08/13 21:03:40 version 1.16, 2023/08/07 08:38:43
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   *> \brief \b DSPMV
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
   *
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION ALPHA,BETA
   *       INTEGER INCX,INCY,N
   *       CHARACTER UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION AP(*),X(*),Y(*)
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION.
   *>           On entry, ALPHA specifies the scalar alpha.
   *> \endverbatim
   *>
   *> \param[in] AP
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in,out] Y
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] INCY
   *> \verbatim
   *>          INCY is INTEGER
   *>           On entry, INCY specifies the increment for the elements of
   *>           Y. INCY must not be zero.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup double_blas_level2
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  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.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)        SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
   *
   *  -- Reference BLAS level2 routine --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION ALPHA,BETA        DOUBLE PRECISION ALPHA,BETA
       INTEGER INCX,INCY,N        INTEGER INCX,INCY,N
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       DOUBLE PRECISION AP(*),X(*),Y(*)        DOUBLE PRECISION AP(*),X(*),Y(*)
 *     ..  *     ..
 *  *
 *  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   - 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      - INTEGER.  
 *           On entry, N specifies the order of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  ALPHA  - DOUBLE PRECISION.  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  AP     - DOUBLE PRECISION array of 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      - DOUBLE PRECISION array of 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   - INTEGER.  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  
 *  BETA   - DOUBLE PRECISION.  
 *           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      - DOUBLE PRECISION array of 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   - INTEGER.  
 *           On entry, INCY specifies the increment for the elements of  
 *           Y. INCY must not be zero.  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 2 Blas routine.  
 *  
 *  -- 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *  *
       RETURN        RETURN
 *  *
 *     End of DSPMV .  *     End of DSPMV
 *  *
       END        END
Removed from v.1.5  
changed lines
  Added in v.1.16

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