--- rpl/lapack/lapack/dlalsd.f 2010/01/26 15:22:45 1.1.1.1
+++ rpl/lapack/lapack/dlalsd.f 2012/12/14 14:22:33 1.13
@@ -1,10 +1,188 @@
+*> \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLALSD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
+* RANK, WORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ
+* DOUBLE PRECISION RCOND
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLALSD uses the singular value decomposition of A to solve the least
+*> squares problem of finding X to minimize the Euclidean norm of each
+*> column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
+*> are N-by-NRHS. The solution X overwrites B.
+*>
+*> The singular values of A smaller than RCOND times the largest
+*> singular value are treated as zero in solving the least squares
+*> problem; in this case a minimum norm solution is returned.
+*> The actual singular values are returned in D in ascending order.
+*>
+*> This code makes very mild assumptions about floating point
+*> arithmetic. It will work on machines with a guard digit in
+*> add/subtract, or on those binary machines without guard digits
+*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
+*> It could conceivably fail on hexadecimal or decimal machines
+*> without guard digits, but we know of none.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': D and E define an upper bidiagonal matrix.
+*> = 'L': D and E define a lower bidiagonal matrix.
+*> \endverbatim
+*>
+*> \param[in] SMLSIZ
+*> \verbatim
+*> SMLSIZ is INTEGER
+*> The maximum size of the subproblems at the bottom of the
+*> computation tree.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The dimension of the bidiagonal matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of columns of B. NRHS must be at least 1.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (N)
+*> On entry D contains the main diagonal of the bidiagonal
+*> matrix. On exit, if INFO = 0, D contains its singular values.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*> E is DOUBLE PRECISION array, dimension (N-1)
+*> Contains the super-diagonal entries of the bidiagonal matrix.
+*> On exit, E has been destroyed.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*> On input, B contains the right hand sides of the least
+*> squares problem. On output, B contains the solution X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of B in the calling subprogram.
+*> LDB must be at least max(1,N).
+*> \endverbatim
+*>
+*> \param[in] RCOND
+*> \verbatim
+*> RCOND is DOUBLE PRECISION
+*> The singular values of A less than or equal to RCOND times
+*> the largest singular value are treated as zero in solving
+*> the least squares problem. If RCOND is negative,
+*> machine precision is used instead.
+*> For example, if diag(S)*X=B were the least squares problem,
+*> where diag(S) is a diagonal matrix of singular values, the
+*> solution would be X(i) = B(i) / S(i) if S(i) is greater than
+*> RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
+*> RCOND*max(S).
+*> \endverbatim
+*>
+*> \param[out] RANK
+*> \verbatim
+*> RANK is INTEGER
+*> The number of singular values of A greater than RCOND times
+*> the largest singular value.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension at least
+*> (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
+*> where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension at least
+*> (3*N*NLVL + 11*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> > 0: The algorithm failed to compute a singular value while
+*> working on the submatrix lying in rows and columns
+*> INFO/(N+1) through MOD(INFO,N+1).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date September 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
+* =====================================================================
SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, IWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* September 2012
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -16,96 +194,6 @@
DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DLALSD uses the singular value decomposition of A to solve the least
-* squares problem of finding X to minimize the Euclidean norm of each
-* column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
-* are N-by-NRHS. The solution X overwrites B.
-*
-* The singular values of A smaller than RCOND times the largest
-* singular value are treated as zero in solving the least squares
-* problem; in this case a minimum norm solution is returned.
-* The actual singular values are returned in D in ascending order.
-*
-* This code makes very mild assumptions about floating point
-* arithmetic. It will work on machines with a guard digit in
-* add/subtract, or on those binary machines without guard digits
-* which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-* It could conceivably fail on hexadecimal or decimal machines
-* without guard digits, but we know of none.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': D and E define an upper bidiagonal matrix.
-* = 'L': D and E define a lower bidiagonal matrix.
-*
-* SMLSIZ (input) INTEGER
-* The maximum size of the subproblems at the bottom of the
-* computation tree.
-*
-* N (input) INTEGER
-* The dimension of the bidiagonal matrix. N >= 0.
-*
-* NRHS (input) INTEGER
-* The number of columns of B. NRHS must be at least 1.
-*
-* D (input/output) DOUBLE PRECISION array, dimension (N)
-* On entry D contains the main diagonal of the bidiagonal
-* matrix. On exit, if INFO = 0, D contains its singular values.
-*
-* E (input/output) DOUBLE PRECISION array, dimension (N-1)
-* Contains the super-diagonal entries of the bidiagonal matrix.
-* On exit, E has been destroyed.
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
-* On input, B contains the right hand sides of the least
-* squares problem. On output, B contains the solution X.
-*
-* LDB (input) INTEGER
-* The leading dimension of B in the calling subprogram.
-* LDB must be at least max(1,N).
-*
-* RCOND (input) DOUBLE PRECISION
-* The singular values of A less than or equal to RCOND times
-* the largest singular value are treated as zero in solving
-* the least squares problem. If RCOND is negative,
-* machine precision is used instead.
-* For example, if diag(S)*X=B were the least squares problem,
-* where diag(S) is a diagonal matrix of singular values, the
-* solution would be X(i) = B(i) / S(i) if S(i) is greater than
-* RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
-* RCOND*max(S).
-*
-* RANK (output) INTEGER
-* The number of singular values of A greater than RCOND times
-* the largest singular value.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension at least
-* (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
-* where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
-*
-* IWORK (workspace) INTEGER array, dimension at least
-* (3*N*NLVL + 11*N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: The algorithm failed to compute an singular value while
-* working on the submatrix lying in rows and columns
-* INFO/(N+1) through MOD(INFO,N+1).
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ming Gu and Ren-Cang Li, Computer Science Division, University of
-* California at Berkeley, USA
-* Osni Marques, LBNL/NERSC, USA
-*
* =====================================================================
*
* .. Parameters ..