version 1.8, 2011/07/22 07:38:20
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version 1.10, 2011/11/21 22:19:56
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*> \brief \b ZSPR |
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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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*> \htmlonly |
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*> Download ZSPR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspr.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspr.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspr.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INCX, N |
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* COMPLEX*16 ALPHA |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 AP( * ), X( * ) |
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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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*> ZSPR performs the symmetric rank 1 operation |
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*> |
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*> A := alpha*x*x**H + A, |
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*> |
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*> where alpha is a complex scalar, x is an n element vector and A is an |
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*> 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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*> |
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*> Unchanged on exit. |
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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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*> Unchanged on exit. |
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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 COMPLEX*16 |
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*> On entry, ALPHA specifies the scalar alpha. |
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*> Unchanged on exit. |
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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 COMPLEX*16 array, 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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*> \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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*> Unchanged on exit. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AP |
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*> \verbatim |
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*> AP is COMPLEX*16 array, 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. On exit, the array |
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*> AP is overwritten by the upper triangular part of the |
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*> updated matrix. |
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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. On exit, the array |
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*> AP is overwritten by the lower triangular part of the |
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*> updated matrix. |
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*> Note that the imaginary parts of the diagonal elements need |
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*> not be set, they are assumed to be zero, and on exit they |
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*> are set to 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 complex16OTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP ) |
SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 AP( * ), X( * ) |
COMPLEX*16 AP( * ), X( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSPR performs the symmetric rank 1 operation |
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* |
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* A := alpha*x*x**H + A, |
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* |
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* where alpha is a complex scalar, x is an n element vector and A is an |
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* 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 (input) 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 (input) 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 (input) COMPLEX*16 |
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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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* X (input) COMPLEX*16 array, 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 (input) 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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* AP (input/output) COMPLEX*16 array, 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. On exit, the array |
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* AP is overwritten by the upper triangular part of the |
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* updated matrix. |
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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. On exit, the array |
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* AP is overwritten by the lower triangular part of the |
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* updated matrix. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set, they are assumed to be zero, and on exit they |
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* are set to zero. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |