--- rpl/lapack/lapack/dlasda.f 2011/07/22 07:38:08 1.9
+++ rpl/lapack/lapack/dlasda.f 2011/11/21 20:42:59 1.10
@@ -1,11 +1,283 @@
+*> \brief \b DLASDA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASDA + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
+* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
+* PERM, GIVNUM, C, S, WORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
+* ..
+* .. Array Arguments ..
+* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
+* $ K( * ), PERM( LDGCOL, * )
+* DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ),
+* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ),
+* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ),
+* $ Z( LDU, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Using a divide and conquer approach, DLASDA computes the singular
+*> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
+*> B with diagonal D and offdiagonal E, where M = N + SQRE. The
+*> algorithm computes the singular values in the SVD B = U * S * VT.
+*> The orthogonal matrices U and VT are optionally computed in
+*> compact form.
+*>
+*> A related subroutine, DLASD0, computes the singular values and
+*> the singular vectors in explicit form.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ICOMPQ
+*> \verbatim
+*> ICOMPQ is INTEGER
+*> Specifies whether singular vectors are to be computed
+*> in compact form, as follows
+*> = 0: Compute singular values only.
+*> = 1: Compute singular vectors of upper bidiagonal
+*> matrix in compact form.
+*> \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 row dimension of the upper bidiagonal matrix. This is
+*> also the dimension of the main diagonal array D.
+*> \endverbatim
+*>
+*> \param[in] SQRE
+*> \verbatim
+*> SQRE is INTEGER
+*> Specifies the column dimension of the bidiagonal matrix.
+*> = 0: The bidiagonal matrix has column dimension M = N;
+*> = 1: The bidiagonal matrix has column dimension M = N + 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 D, if INFO = 0, contains its singular values.
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*> E is DOUBLE PRECISION array, dimension ( M-1 )
+*> Contains the subdiagonal entries of the bidiagonal matrix.
+*> On exit, E has been destroyed.
+*> \endverbatim
+*>
+*> \param[out] U
+*> \verbatim
+*> U is DOUBLE PRECISION array,
+*> dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
+*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
+*> singular vector matrices of all subproblems at the bottom
+*> level.
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*> LDU is INTEGER, LDU = > N.
+*> The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
+*> GIVNUM, and Z.
+*> \endverbatim
+*>
+*> \param[out] VT
+*> \verbatim
+*> VT is DOUBLE PRECISION array,
+*> dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
+*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
+*> singular vector matrices of all subproblems at the bottom
+*> level.
+*> \endverbatim
+*>
+*> \param[out] K
+*> \verbatim
+*> K is INTEGER array,
+*> dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
+*> If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
+*> secular equation on the computation tree.
+*> \endverbatim
+*>
+*> \param[out] DIFL
+*> \verbatim
+*> DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
+*> where NLVL = floor(log_2 (N/SMLSIZ))).
+*> \endverbatim
+*>
+*> \param[out] DIFR
+*> \verbatim
+*> DIFR is DOUBLE PRECISION array,
+*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
+*> dimension ( N ) if ICOMPQ = 0.
+*> If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
+*> record distances between singular values on the I-th
+*> level and singular values on the (I -1)-th level, and
+*> DIFR(1:N, 2 * I ) contains the normalizing factors for
+*> the right singular vector matrix. See DLASD8 for details.
+*> \endverbatim
+*>
+*> \param[out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array,
+*> dimension ( LDU, NLVL ) if ICOMPQ = 1 and
+*> dimension ( N ) if ICOMPQ = 0.
+*> The first K elements of Z(1, I) contain the components of
+*> the deflation-adjusted updating row vector for subproblems
+*> on the I-th level.
+*> \endverbatim
+*>
+*> \param[out] POLES
+*> \verbatim
+*> POLES is DOUBLE PRECISION array,
+*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
+*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
+*> POLES(1, 2*I) contain the new and old singular values
+*> involved in the secular equations on the I-th level.
+*> \endverbatim
+*>
+*> \param[out] GIVPTR
+*> \verbatim
+*> GIVPTR is INTEGER array,
+*> dimension ( N ) if ICOMPQ = 1, and not referenced if
+*> ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
+*> the number of Givens rotations performed on the I-th
+*> problem on the computation tree.
+*> \endverbatim
+*>
+*> \param[out] GIVCOL
+*> \verbatim
+*> GIVCOL is INTEGER array,
+*> dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
+*> referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
+*> GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
+*> of Givens rotations performed on the I-th level on the
+*> computation tree.
+*> \endverbatim
+*>
+*> \param[in] LDGCOL
+*> \verbatim
+*> LDGCOL is INTEGER, LDGCOL = > N.
+*> The leading dimension of arrays GIVCOL and PERM.
+*> \endverbatim
+*>
+*> \param[out] PERM
+*> \verbatim
+*> PERM is INTEGER array,
+*> dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
+*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
+*> permutations done on the I-th level of the computation tree.
+*> \endverbatim
+*>
+*> \param[out] GIVNUM
+*> \verbatim
+*> GIVNUM is DOUBLE PRECISION array,
+*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not
+*> referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
+*> GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
+*> values of Givens rotations performed on the I-th level on
+*> the computation tree.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array,
+*> dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
+*> If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
+*> C( I ) contains the C-value of a Givens rotation related to
+*> the right null space of the I-th subproblem.
+*> \endverbatim
+*>
+*> \param[out] S
+*> \verbatim
+*> S is DOUBLE PRECISION array, dimension ( N ) if
+*> ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
+*> and the I-th subproblem is not square, on exit, S( I )
+*> contains the S-value of a Givens rotation related to
+*> the right null space of the I-th subproblem.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension
+*> (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array.
+*> Dimension must be at least (7 * 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: if INFO = 1, a singular value did not converge
+*> \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:
+* ==================
+*>
+*> Ming Gu and Huan Ren, Computer Science Division, University of
+*> California at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
$ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
$ PERM, GIVNUM, C, S, WORK, IWORK, INFO )
*
-* -- LAPACK auxiliary routine (version 3.2.2) --
+* -- 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..--
-* June 2010
+* November 2011
*
* .. Scalar Arguments ..
INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
@@ -19,154 +291,6 @@
$ Z( LDU, * )
* ..
*
-* Purpose
-* =======
-*
-* Using a divide and conquer approach, DLASDA computes the singular
-* value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
-* B with diagonal D and offdiagonal E, where M = N + SQRE. The
-* algorithm computes the singular values in the SVD B = U * S * VT.
-* The orthogonal matrices U and VT are optionally computed in
-* compact form.
-*
-* A related subroutine, DLASD0, computes the singular values and
-* the singular vectors in explicit form.
-*
-* Arguments
-* =========
-*
-* ICOMPQ (input) INTEGER
-* Specifies whether singular vectors are to be computed
-* in compact form, as follows
-* = 0: Compute singular values only.
-* = 1: Compute singular vectors of upper bidiagonal
-* matrix in compact form.
-*
-* SMLSIZ (input) INTEGER
-* The maximum size of the subproblems at the bottom of the
-* computation tree.
-*
-* N (input) INTEGER
-* The row dimension of the upper bidiagonal matrix. This is
-* also the dimension of the main diagonal array D.
-*
-* SQRE (input) INTEGER
-* Specifies the column dimension of the bidiagonal matrix.
-* = 0: The bidiagonal matrix has column dimension M = N;
-* = 1: The bidiagonal matrix has column dimension M = N + 1.
-*
-* D (input/output) DOUBLE PRECISION array, dimension ( N )
-* On entry D contains the main diagonal of the bidiagonal
-* matrix. On exit D, if INFO = 0, contains its singular values.
-*
-* E (input) DOUBLE PRECISION array, dimension ( M-1 )
-* Contains the subdiagonal entries of the bidiagonal matrix.
-* On exit, E has been destroyed.
-*
-* U (output) DOUBLE PRECISION array,
-* dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
-* if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
-* singular vector matrices of all subproblems at the bottom
-* level.
-*
-* LDU (input) INTEGER, LDU = > N.
-* The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
-* GIVNUM, and Z.
-*
-* VT (output) DOUBLE PRECISION array,
-* dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
-* if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
-* singular vector matrices of all subproblems at the bottom
-* level.
-*
-* K (output) INTEGER array,
-* dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
-* If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
-* secular equation on the computation tree.
-*
-* DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
-* where NLVL = floor(log_2 (N/SMLSIZ))).
-*
-* DIFR (output) DOUBLE PRECISION array,
-* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
-* dimension ( N ) if ICOMPQ = 0.
-* If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
-* record distances between singular values on the I-th
-* level and singular values on the (I -1)-th level, and
-* DIFR(1:N, 2 * I ) contains the normalizing factors for
-* the right singular vector matrix. See DLASD8 for details.
-*
-* Z (output) DOUBLE PRECISION array,
-* dimension ( LDU, NLVL ) if ICOMPQ = 1 and
-* dimension ( N ) if ICOMPQ = 0.
-* The first K elements of Z(1, I) contain the components of
-* the deflation-adjusted updating row vector for subproblems
-* on the I-th level.
-*
-* POLES (output) DOUBLE PRECISION array,
-* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
-* if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
-* POLES(1, 2*I) contain the new and old singular values
-* involved in the secular equations on the I-th level.
-*
-* GIVPTR (output) INTEGER array,
-* dimension ( N ) if ICOMPQ = 1, and not referenced if
-* ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
-* the number of Givens rotations performed on the I-th
-* problem on the computation tree.
-*
-* GIVCOL (output) INTEGER array,
-* dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
-* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
-* GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
-* of Givens rotations performed on the I-th level on the
-* computation tree.
-*
-* LDGCOL (input) INTEGER, LDGCOL = > N.
-* The leading dimension of arrays GIVCOL and PERM.
-*
-* PERM (output) INTEGER array,
-* dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
-* if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
-* permutations done on the I-th level of the computation tree.
-*
-* GIVNUM (output) DOUBLE PRECISION array,
-* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not
-* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
-* GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
-* values of Givens rotations performed on the I-th level on
-* the computation tree.
-*
-* C (output) DOUBLE PRECISION array,
-* dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
-* If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
-* C( I ) contains the C-value of a Givens rotation related to
-* the right null space of the I-th subproblem.
-*
-* S (output) DOUBLE PRECISION array, dimension ( N ) if
-* ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
-* and the I-th subproblem is not square, on exit, S( I )
-* contains the S-value of a Givens rotation related to
-* the right null space of the I-th subproblem.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension
-* (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
-*
-* IWORK (workspace) INTEGER array.
-* Dimension must be at least (7 * N).
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: if INFO = 1, a singular value did not converge
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ming Gu and Huan Ren, Computer Science Division, University of
-* California at Berkeley, USA
-*
* =====================================================================
*
* .. Parameters ..