--- rpl/lapack/lapack/dlasd4.f 2010/01/26 15:22:46 1.1
+++ rpl/lapack/lapack/dlasd4.f 2011/11/21 20:42:58 1.10
@@ -1,9 +1,162 @@
+*> \brief \b DLASD4
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASD4 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER I, INFO, N
+* DOUBLE PRECISION RHO, SIGMA
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * )
+* ..
+*
+*
+*> \par 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:
+* ==========
+*
+*> \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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( N )
+*> The components of the updating vector.
+*> \endverbatim
+*>
+*> \param[out] DELTA
+*> \verbatim
+*> DELTA is DOUBLE PRECISION 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 DOUBLE PRECISION
+*> The scalar in the symmetric updating formula.
+*> \endverbatim
+*>
+*> \param[out] SIGMA
+*> \verbatim
+*> SIGMA is DOUBLE PRECISION
+*> The computed sigma_I, the I-th updated eigenvalue.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION 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
+*
+*> \par Internal Parameters:
+* =========================
+*>
+*> \verbatim
+*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
+*> whether D(i) or D(i+1) is treated as the origin.
+*>
+*> ORGATI = .true. origin at i
+*> ORGATI = .false. origin at i+1
+*>
+*> Logical variable SWTCH3 (switch-for-3-poles?) is for noting
+*> if we are working with THREE poles!
+*>
+*> MAXIT is the maximum number of iterations allowed for each
+*> eigenvalue.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
-* -- LAPACK auxiliary routine (version 3.2) --
+* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
INTEGER I, INFO, N
@@ -13,89 +166,11 @@
DOUBLE PRECISION 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.
-*
-* 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) DOUBLE PRECISION array, dimension ( N )
-* The original eigenvalues. It is assumed that they are in
-* order, 0 <= D(I) < D(J) for I < J.
-*
-* Z (input) DOUBLE PRECISION array, dimension ( N )
-* The components of the updating vector.
-*
-* DELTA (output) DOUBLE PRECISION 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) DOUBLE PRECISION
-* The scalar in the symmetric updating formula.
-*
-* SIGMA (output) DOUBLE PRECISION
-* The computed sigma_I, the I-th updated eigenvalue.
-*
-* WORK (workspace) DOUBLE PRECISION 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
-* ===================
-*
-* Logical variable ORGATI (origin-at-i?) is used for distinguishing
-* whether D(i) or D(i+1) is treated as the origin.
-*
-* ORGATI = .true. origin at i
-* ORGATI = .false. origin at i+1
-*
-* Logical variable SWTCH3 (switch-for-3-poles?) is for noting
-* if we are working with THREE poles!
-*
-* MAXIT is the maximum number of iterations allowed for each
-* eigenvalue.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ren-Cang Li, Computer Science Division, University of California
-* at Berkeley, USA
-*
* =====================================================================
*
* .. Parameters ..
INTEGER MAXIT
- PARAMETER ( MAXIT = 20 )
+ PARAMETER ( MAXIT = 64 )
DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
$ THREE = 3.0D+0, FOUR = 4.0D+0, EIGHT = 8.0D+0,