--- rpl/lapack/lapack/dgelsd.f 2010/08/06 15:32:23 1.4
+++ rpl/lapack/lapack/dgelsd.f 2012/08/22 09:48:13 1.11
@@ -1,10 +1,218 @@
+*> \brief DGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGELSD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
+* WORK, LWORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
+* DOUBLE PRECISION RCOND
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGELSD computes the minimum-norm solution to a real linear least
+*> squares problem:
+*> minimize 2-norm(| b - A*x |)
+*> using the singular value decomposition (SVD) of A. A is an M-by-N
+*> matrix which may be rank-deficient.
+*>
+*> Several right hand side vectors b and solution vectors x can be
+*> handled in a single call; they are stored as the columns of the
+*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
+*> matrix X.
+*>
+*> The problem is solved in three steps:
+*> (1) Reduce the coefficient matrix A to bidiagonal form with
+*> Householder transformations, reducing the original problem
+*> into a "bidiagonal least squares problem" (BLS)
+*> (2) Solve the BLS using a divide and conquer approach.
+*> (3) Apply back all the Householder tranformations to solve
+*> the original least squares problem.
+*>
+*> The effective rank of A is determined by treating as zero those
+*> singular values which are less than RCOND times the largest singular
+*> value.
+*>
+*> The divide and conquer algorithm 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 X-MP, Cray Y-MP, 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] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrices B and X. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the M-by-N matrix A.
+*> On exit, A has been destroyed.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*> On entry, the M-by-NRHS right hand side matrix B.
+*> On exit, B is overwritten by the N-by-NRHS solution
+*> matrix X. If m >= n and RANK = n, the residual
+*> sum-of-squares for the solution in the i-th column is given
+*> by the sum of squares of elements n+1:m in that column.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,max(M,N)).
+*> \endverbatim
+*>
+*> \param[out] S
+*> \verbatim
+*> S is DOUBLE PRECISION array, dimension (min(M,N))
+*> The singular values of A in decreasing order.
+*> The condition number of A in the 2-norm = S(1)/S(min(m,n)).
+*> \endverbatim
+*>
+*> \param[in] RCOND
+*> \verbatim
+*> RCOND is DOUBLE PRECISION
+*> RCOND is used to determine the effective rank of A.
+*> Singular values S(i) <= RCOND*S(1) are treated as zero.
+*> If RCOND < 0, machine precision is used instead.
+*> \endverbatim
+*>
+*> \param[out] RANK
+*> \verbatim
+*> RANK is INTEGER
+*> The effective rank of A, i.e., the number of singular values
+*> which are greater than RCOND*S(1).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK must be at least 1.
+*> The exact minimum amount of workspace needed depends on M,
+*> N and NRHS. As long as LWORK is at least
+*> 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
+*> if M is greater than or equal to N or
+*> 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
+*> if M is less than N, the code will execute correctly.
+*> SMLSIZ is returned by ILAENV and is equal to the maximum
+*> size of the subproblems at the bottom of the computation
+*> tree (usually about 25), and
+*> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*> For good performance, LWORK should generally be larger.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
+*> LIWORK >= max(1, 3 * MINMN * NLVL + 11 * MINMN),
+*> where MINMN = MIN( M,N ).
+*> On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
+*> \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 for computing the SVD failed to converge;
+*> if INFO = i, i off-diagonal elements of an intermediate
+*> bidiagonal form did not converge to zero.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleGEsolve
+*
+*> \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 DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
$ WORK, LWORK, IWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver 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 INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -15,123 +223,6 @@
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGELSD computes the minimum-norm solution to a real linear least
-* squares problem:
-* minimize 2-norm(| b - A*x |)
-* using the singular value decomposition (SVD) of A. A is an M-by-N
-* matrix which may be rank-deficient.
-*
-* Several right hand side vectors b and solution vectors x can be
-* handled in a single call; they are stored as the columns of the
-* M-by-NRHS right hand side matrix B and the N-by-NRHS solution
-* matrix X.
-*
-* The problem is solved in three steps:
-* (1) Reduce the coefficient matrix A to bidiagonal form with
-* Householder transformations, reducing the original problem
-* into a "bidiagonal least squares problem" (BLS)
-* (2) Solve the BLS using a divide and conquer approach.
-* (3) Apply back all the Householder tranformations to solve
-* the original least squares problem.
-*
-* The effective rank of A is determined by treating as zero those
-* singular values which are less than RCOND times the largest singular
-* value.
-*
-* The divide and conquer algorithm 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 X-MP, Cray Y-MP, Cray C-90, or
-* Cray-2. It could conceivably fail on hexadecimal or decimal machines
-* without guard digits, but we know of none.
-*
-* Arguments
-* =========
-*
-* M (input) INTEGER
-* The number of rows of A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of A. N >= 0.
-*
-* NRHS (input) INTEGER
-* The number of right hand sides, i.e., the number of columns
-* of the matrices B and X. NRHS >= 0.
-*
-* A (input) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the M-by-N matrix A.
-* On exit, A has been destroyed.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
-* On entry, the M-by-NRHS right hand side matrix B.
-* On exit, B is overwritten by the N-by-NRHS solution
-* matrix X. If m >= n and RANK = n, the residual
-* sum-of-squares for the solution in the i-th column is given
-* by the sum of squares of elements n+1:m in that column.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,max(M,N)).
-*
-* S (output) DOUBLE PRECISION array, dimension (min(M,N))
-* The singular values of A in decreasing order.
-* The condition number of A in the 2-norm = S(1)/S(min(m,n)).
-*
-* RCOND (input) DOUBLE PRECISION
-* RCOND is used to determine the effective rank of A.
-* Singular values S(i) <= RCOND*S(1) are treated as zero.
-* If RCOND < 0, machine precision is used instead.
-*
-* RANK (output) INTEGER
-* The effective rank of A, i.e., the number of singular values
-* which are greater than RCOND*S(1).
-*
-* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK must be at least 1.
-* The exact minimum amount of workspace needed depends on M,
-* N and NRHS. As long as LWORK is at least
-* 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
-* if M is greater than or equal to N or
-* 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
-* if M is less than N, the code will execute correctly.
-* SMLSIZ is returned by ILAENV and is equal to the maximum
-* size of the subproblems at the bottom of the computation
-* tree (usually about 25), and
-* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
-* For good performance, LWORK should generally be larger.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK))
-* LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
-* where MINMN = MIN( M,N ).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: the algorithm for computing the SVD failed to converge;
-* if INFO = i, i off-diagonal elements of an intermediate
-* bidiagonal form did not converge to zero.
-*
-* 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 ..
@@ -141,8 +232,8 @@
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ,
- $ LDWORK, MAXMN, MAXWRK, MINMN, MINWRK, MM,
- $ MNTHR, NLVL, NWORK, SMLSIZ, WLALSD
+ $ LDWORK, LIWORK, MAXMN, MAXWRK, MINMN, MINWRK,
+ $ MM, MNTHR, NLVL, NWORK, SMLSIZ, WLALSD
DOUBLE PRECISION ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM
* ..
* .. External Subroutines ..
@@ -188,12 +279,14 @@
* following subroutine, as returned by ILAENV.)
*
MINWRK = 1
+ LIWORK = 1
MINMN = MAX( 1, MINMN )
NLVL = MAX( INT( LOG( DBLE( MINMN ) / DBLE( SMLSIZ+1 ) ) /
$ LOG( TWO ) ) + 1, 0 )
*
IF( INFO.EQ.0 ) THEN
MAXWRK = 0
+ LIWORK = 3*MINMN*NLVL + 11*MINMN
MM = M
IF( M.GE.N .AND. M.GE.MNTHR ) THEN
*
@@ -261,6 +354,8 @@
END IF
MINWRK = MIN( MINWRK, MAXWRK )
WORK( 1 ) = MAXWRK
+ IWORK( 1 ) = LIWORK
+
IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
@@ -526,6 +621,7 @@
*
10 CONTINUE
WORK( 1 ) = MAXWRK
+ IWORK( 1 ) = LIWORK
RETURN
*
* End of DGELSD