--- rpl/lapack/lapack/zlaic1.f 2011/07/22 07:38:17 1.8
+++ rpl/lapack/lapack/zlaic1.f 2011/11/21 20:43:15 1.9
@@ -1,9 +1,144 @@
+*> \brief \b ZLAIC1
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAIC1 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
+*
+* .. Scalar Arguments ..
+* INTEGER J, JOB
+* DOUBLE PRECISION SEST, SESTPR
+* COMPLEX*16 C, GAMMA, S
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 W( J ), X( J )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZLAIC1 applies one step of incremental condition estimation in
+*> its simplest version:
+*>
+*> Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
+*> lower triangular matrix L, such that
+*> twonorm(L*x) = sest
+*> Then ZLAIC1 computes sestpr, s, c such that
+*> the vector
+*> [ s*x ]
+*> xhat = [ c ]
+*> is an approximate singular vector of
+*> [ L 0 ]
+*> Lhat = [ w**H gamma ]
+*> in the sense that
+*> twonorm(Lhat*xhat) = sestpr.
+*>
+*> Depending on JOB, an estimate for the largest or smallest singular
+*> value is computed.
+*>
+*> Note that [s c]**H and sestpr**2 is an eigenpair of the system
+*>
+*> diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]
+*> [ conjg(gamma) ]
+*>
+*> where alpha = x**H * w.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOB
+*> \verbatim
+*> JOB is INTEGER
+*> = 1: an estimate for the largest singular value is computed.
+*> = 2: an estimate for the smallest singular value is computed.
+*> \endverbatim
+*>
+*> \param[in] J
+*> \verbatim
+*> J is INTEGER
+*> Length of X and W
+*> \endverbatim
+*>
+*> \param[in] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (J)
+*> The j-vector x.
+*> \endverbatim
+*>
+*> \param[in] SEST
+*> \verbatim
+*> SEST is DOUBLE PRECISION
+*> Estimated singular value of j by j matrix L
+*> \endverbatim
+*>
+*> \param[in] W
+*> \verbatim
+*> W is COMPLEX*16 array, dimension (J)
+*> The j-vector w.
+*> \endverbatim
+*>
+*> \param[in] GAMMA
+*> \verbatim
+*> GAMMA is COMPLEX*16
+*> The diagonal element gamma.
+*> \endverbatim
+*>
+*> \param[out] SESTPR
+*> \verbatim
+*> SESTPR is DOUBLE PRECISION
+*> Estimated singular value of (j+1) by (j+1) matrix Lhat.
+*> \endverbatim
+*>
+*> \param[out] S
+*> \verbatim
+*> S is COMPLEX*16
+*> Sine needed in forming xhat.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is COMPLEX*16
+*> Cosine needed in forming xhat.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERauxiliary
+*
+* =====================================================================
SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
-* -- LAPACK auxiliary routine (version 3.3.1) --
+* -- 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..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
INTEGER J, JOB
@@ -14,66 +149,6 @@
COMPLEX*16 W( J ), X( J )
* ..
*
-* Purpose
-* =======
-*
-* ZLAIC1 applies one step of incremental condition estimation in
-* its simplest version:
-*
-* Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
-* lower triangular matrix L, such that
-* twonorm(L*x) = sest
-* Then ZLAIC1 computes sestpr, s, c such that
-* the vector
-* [ s*x ]
-* xhat = [ c ]
-* is an approximate singular vector of
-* [ L 0 ]
-* Lhat = [ w**H gamma ]
-* in the sense that
-* twonorm(Lhat*xhat) = sestpr.
-*
-* Depending on JOB, an estimate for the largest or smallest singular
-* value is computed.
-*
-* Note that [s c]**H and sestpr**2 is an eigenpair of the system
-*
-* diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]
-* [ conjg(gamma) ]
-*
-* where alpha = x**H * w.
-*
-* Arguments
-* =========
-*
-* JOB (input) INTEGER
-* = 1: an estimate for the largest singular value is computed.
-* = 2: an estimate for the smallest singular value is computed.
-*
-* J (input) INTEGER
-* Length of X and W
-*
-* X (input) COMPLEX*16 array, dimension (J)
-* The j-vector x.
-*
-* SEST (input) DOUBLE PRECISION
-* Estimated singular value of j by j matrix L
-*
-* W (input) COMPLEX*16 array, dimension (J)
-* The j-vector w.
-*
-* GAMMA (input) COMPLEX*16
-* The diagonal element gamma.
-*
-* SESTPR (output) DOUBLE PRECISION
-* Estimated singular value of (j+1) by (j+1) matrix Lhat.
-*
-* S (output) COMPLEX*16
-* Sine needed in forming xhat.
-*
-* C (output) COMPLEX*16
-* Cosine needed in forming xhat.
-*
* =====================================================================
*
* .. Parameters ..