version 1.2, 2010/04/21 13:45:09
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version 1.11, 2014/01/27 09:28:12
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*> \brief \b DSPMV |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION ALPHA,BETA |
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* INTEGER INCX,INCY,N |
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* CHARACTER UPLO |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AP(*),X(*),Y(*) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DSPMV performs the matrix-vector operation |
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*> |
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*> y := alpha*A*x + beta*y, |
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*> |
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*> where alpha and beta are scalars, x and y are n element vectors and |
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*> A is an n by n symmetric matrix, supplied in packed form. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> On entry, UPLO specifies whether the upper or lower |
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*> triangular part of the matrix A is supplied in the packed |
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*> array AP as follows: |
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*> |
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*> UPLO = 'U' or 'u' The upper triangular part of A is |
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*> supplied in AP. |
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*> |
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*> UPLO = 'L' or 'l' The lower triangular part of A is |
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*> supplied in AP. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> On entry, N specifies the order of the matrix A. |
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*> N must be at least zero. |
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*> \endverbatim |
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*> |
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*> \param[in] ALPHA |
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*> \verbatim |
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*> ALPHA is DOUBLE PRECISION. |
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*> On entry, ALPHA specifies the scalar alpha. |
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*> \endverbatim |
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*> |
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*> \param[in] AP |
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*> \verbatim |
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*> AP is DOUBLE PRECISION array of DIMENSION at least |
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*> ( ( n*( n + 1 ) )/2 ). |
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*> Before entry with UPLO = 'U' or 'u', the array AP must |
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*> contain the upper triangular part of the symmetric matrix |
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*> packed sequentially, column by column, so that AP( 1 ) |
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*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) |
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*> and a( 2, 2 ) respectively, and so on. |
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*> Before entry with UPLO = 'L' or 'l', the array AP must |
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*> contain the lower triangular part of the symmetric matrix |
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*> packed sequentially, column by column, so that AP( 1 ) |
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*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) |
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*> and a( 3, 1 ) respectively, and so on. |
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*> \endverbatim |
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*> |
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*> \param[in] X |
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*> \verbatim |
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*> X is DOUBLE PRECISION array of dimension at least |
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*> ( 1 + ( n - 1 )*abs( INCX ) ). |
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*> Before entry, the incremented array X must contain the n |
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*> element vector x. |
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*> \endverbatim |
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*> |
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*> \param[in] INCX |
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*> \verbatim |
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*> INCX is INTEGER |
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*> On entry, INCX specifies the increment for the elements of |
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*> X. INCX must not be zero. |
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*> \endverbatim |
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*> |
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*> \param[in] BETA |
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*> \verbatim |
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*> BETA is DOUBLE PRECISION. |
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*> On entry, BETA specifies the scalar beta. When BETA is |
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*> supplied as zero then Y need not be set on input. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Y |
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*> \verbatim |
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*> Y is DOUBLE PRECISION array of dimension at least |
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*> ( 1 + ( n - 1 )*abs( INCY ) ). |
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*> Before entry, the incremented array Y must contain the n |
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*> element vector y. On exit, Y is overwritten by the updated |
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*> vector y. |
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*> \endverbatim |
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*> |
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*> \param[in] INCY |
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*> \verbatim |
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*> INCY is INTEGER |
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*> On entry, INCY specifies the increment for the elements of |
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*> Y. INCY must not be zero. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup double_blas_level2 |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Level 2 Blas routine. |
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*> The vector and matrix arguments are not referenced when N = 0, or M = 0 |
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*> |
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*> -- Written on 22-October-1986. |
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*> Jack Dongarra, Argonne National Lab. |
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*> Jeremy Du Croz, Nag Central Office. |
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*> Sven Hammarling, Nag Central Office. |
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*> Richard Hanson, Sandia National Labs. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) |
SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) |
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* |
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* -- Reference BLAS level2 routine (version 3.4.0) -- |
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
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* |
* .. 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 |
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* ======= |
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* |
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* DSPMV performs the matrix-vector operation |
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* |
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* y := alpha*A*x + beta*y, |
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* |
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* where alpha and beta are scalars, x and y are n element vectors and |
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* A is an n by n symmetric matrix, supplied in packed form. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the matrix A is supplied in the packed |
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* array AP as follows: |
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* |
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* UPLO = 'U' or 'u' The upper triangular part of A is |
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* supplied in AP. |
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* |
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* UPLO = 'L' or 'l' The lower triangular part of A is |
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* supplied in AP. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix A. |
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* N must be at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION. |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* AP - DOUBLE PRECISION array of DIMENSION at least |
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* ( ( n*( n + 1 ) )/2 ). |
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* Before entry with UPLO = 'U' or 'u', the array AP must |
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* contain the upper triangular part of the symmetric matrix |
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* packed sequentially, column by column, so that AP( 1 ) |
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) |
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* and a( 2, 2 ) respectively, and so on. |
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* Before entry with UPLO = 'L' or 'l', the array AP must |
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* contain the lower triangular part of the symmetric matrix |
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* packed sequentially, column by column, so that AP( 1 ) |
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) |
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* and a( 3, 1 ) respectively, and so on. |
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* Unchanged on exit. |
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* |
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* X - DOUBLE PRECISION array of dimension at least |
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* ( 1 + ( n - 1 )*abs( INCX ) ). |
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* Before entry, the incremented array X must contain the n |
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* element vector x. |
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* Unchanged on exit. |
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* |
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* INCX - INTEGER. |
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* On entry, INCX specifies the increment for the elements of |
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* X. INCX must not be zero. |
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* Unchanged on exit. |
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* |
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* BETA - DOUBLE PRECISION. |
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* On entry, BETA specifies the scalar beta. When BETA is |
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* supplied as zero then Y need not be set on input. |
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* Unchanged on exit. |
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* |
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* Y - DOUBLE PRECISION array of dimension at least |
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* ( 1 + ( n - 1 )*abs( INCY ) ). |
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* Before entry, the incremented array Y must contain the n |
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* element vector y. On exit, Y is overwritten by the updated |
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* vector y. |
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* |
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* INCY - INTEGER. |
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* On entry, INCY specifies the increment for the elements of |
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* Y. INCY must not be zero. |
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* Unchanged on exit. |
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* |
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* Further Details |
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* =============== |
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* |
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* Level 2 Blas routine. |
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* |
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* -- Written on 22-October-1986. |
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* Jack Dongarra, Argonne National Lab. |
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* Jeremy Du Croz, Nag Central Office. |
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* Sven Hammarling, Nag Central Office. |
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* Richard Hanson, Sandia National Labs. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |