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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
committerjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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- SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
-*
-* -- LAPACK auxiliary routine (version 3.3.1) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
-*
-* .. Scalar Arguments ..
- INTEGER I, INFO, N
- REAL RHO, SIGMA
-* ..
-* .. Array Arguments ..
- REAL D( * ), DELTA( * ), WORK( * ), Z( * )
-* ..
-*
+*> \brief \b SLASD4
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER I, INFO, N
+* REAL RHO, SIGMA
+* ..
+* .. Array Arguments ..
+* REAL D( * ), DELTA( * ), WORK( * ), Z( * )
+* ..
+*
* Purpose
* =======
*
-* This subroutine computes the square root of the I-th updated
-* eigenvalue of a positive symmetric rank-one modification to
-* a positive diagonal matrix whose entries are given as the squares
-* of the corresponding entries in the array d, and that
-*
-* 0 <= D(i) < D(j) for i < j
-*
-* and that RHO > 0. This is arranged by the calling routine, and is
-* no loss in generality. The rank-one modified system is thus
-*
-* diag( D ) * diag( D ) + RHO * Z * Z_transpose.
-*
-* where we assume the Euclidean norm of Z is 1.
-*
-* The method consists of approximating the rational functions in the
-* secular equation by simpler interpolating rational functions.
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> This subroutine computes the square root of the I-th updated
+*> eigenvalue of a positive symmetric rank-one modification to
+*> a positive diagonal matrix whose entries are given as the squares
+*> of the corresponding entries in the array d, and that
+*>
+*> 0 <= D(i) < D(j) for i < j
+*>
+*> and that RHO > 0. This is arranged by the calling routine, and is
+*> no loss in generality. The rank-one modified system is thus
+*>
+*> diag( D ) * diag( D ) + RHO * Z * Z_transpose.
+*>
+*> where we assume the Euclidean norm of Z is 1.
+*>
+*> The method consists of approximating the rational functions in the
+*> secular equation by simpler interpolating rational functions.
+*>
+*>\endverbatim
*
* Arguments
* =========
*
-* N (input) INTEGER
-* The length of all arrays.
-*
-* I (input) INTEGER
-* The index of the eigenvalue to be computed. 1 <= I <= N.
-*
-* D (input) REAL array, dimension ( N )
-* The original eigenvalues. It is assumed that they are in
-* order, 0 <= D(I) < D(J) for I < J.
-*
-* Z (input) REAL array, dimension (N)
-* The components of the updating vector.
-*
-* DELTA (output) REAL array, dimension (N)
-* If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th
-* component. If N = 1, then DELTA(1) = 1. The vector DELTA
-* contains the information necessary to construct the
-* (singular) eigenvectors.
-*
-* RHO (input) REAL
-* The scalar in the symmetric updating formula.
-*
-* SIGMA (output) REAL
-* The computed sigma_I, the I-th updated eigenvalue.
-*
-* WORK (workspace) REAL array, dimension (N)
-* If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th
-* component. If N = 1, then WORK( 1 ) = 1.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* > 0: if INFO = 1, the updating process failed.
-*
-* Internal Parameters
-* ===================
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The length of all arrays.
+*> \endverbatim
+*>
+*> \param[in] I
+*> \verbatim
+*> I is INTEGER
+*> The index of the eigenvalue to be computed. 1 <= I <= N.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is REAL array, dimension ( N )
+*> The original eigenvalues. It is assumed that they are in
+*> order, 0 <= D(I) < D(J) for I < J.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*> Z is REAL array, dimension (N)
+*> The components of the updating vector.
+*> \endverbatim
+*>
+*> \param[out] DELTA
+*> \verbatim
+*> DELTA is REAL array, dimension (N)
+*> If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th
+*> component. If N = 1, then DELTA(1) = 1. The vector DELTA
+*> contains the information necessary to construct the
+*> (singular) eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] RHO
+*> \verbatim
+*> RHO is REAL
+*> The scalar in the symmetric updating formula.
+*> \endverbatim
+*>
+*> \param[out] SIGMA
+*> \verbatim
+*> SIGMA is REAL
+*> The computed sigma_I, the I-th updated eigenvalue.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (N)
+*> If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th
+*> component. If N = 1, then WORK( 1 ) = 1.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> > 0: if INFO = 1, the updating process failed.
+*> \endverbatim
+*> \verbatim
+*> Internal Parameters
+*> ===================
+*> \endverbatim
+*> \verbatim
+*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
+*> whether D(i) or D(i+1) is treated as the origin.
+*> \endverbatim
+*> \verbatim
+*> ORGATI = .true. origin at i
+*> ORGATI = .false. origin at i+1
+*> \endverbatim
+*> \verbatim
+*> Logical variable SWTCH3 (switch-for-3-poles?) is for noting
+*> if we are working with THREE poles!
+*> \endverbatim
+*> \verbatim
+*> MAXIT is the maximum number of iterations allowed for each
+*> eigenvalue.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* Logical variable ORGATI (origin-at-i?) is used for distinguishing
-* whether D(i) or D(i+1) is treated as the origin.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* ORGATI = .true. origin at i
-* ORGATI = .false. origin at i+1
+*> \date November 2011
*
-* Logical variable SWTCH3 (switch-for-3-poles?) is for noting
-* if we are working with THREE poles!
+*> \ingroup auxOTHERauxiliary
*
-* MAXIT is the maximum number of iterations allowed for each
-* eigenvalue.
*
* Further Details
* ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*> Based on contributions by
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
-* Based on contributions by
-* Ren-Cang Li, Computer Science Division, University of California
-* at Berkeley, USA
+* -- LAPACK auxiliary routine (version 3.3.1) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
+*
+* .. Scalar Arguments ..
+ INTEGER I, INFO, N
+ REAL RHO, SIGMA
+* ..
+* .. Array Arguments ..
+ REAL D( * ), DELTA( * ), WORK( * ), Z( * )
+* ..
*
* =====================================================================
*