--- rpl/lapack/lapack/dlals0.f 2010/01/26 15:22:46 1.1.1.1
+++ rpl/lapack/lapack/dlals0.f 2015/11/26 11:44:17 1.14
@@ -1,11 +1,277 @@
+*> \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLALS0 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
+* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
+* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL,
+* $ LDGNUM, NL, NR, NRHS, SQRE
+* DOUBLE PRECISION C, S
+* ..
+* .. Array Arguments ..
+* INTEGER GIVCOL( LDGCOL, * ), PERM( * )
+* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ),
+* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ),
+* $ POLES( LDGNUM, * ), WORK( * ), Z( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLALS0 applies back the multiplying factors of either the left or the
+*> right singular vector matrix of a diagonal matrix appended by a row
+*> to the right hand side matrix B in solving the least squares problem
+*> using the divide-and-conquer SVD approach.
+*>
+*> For the left singular vector matrix, three types of orthogonal
+*> matrices are involved:
+*>
+*> (1L) Givens rotations: the number of such rotations is GIVPTR; the
+*> pairs of columns/rows they were applied to are stored in GIVCOL;
+*> and the C- and S-values of these rotations are stored in GIVNUM.
+*>
+*> (2L) Permutation. The (NL+1)-st row of B is to be moved to the first
+*> row, and for J=2:N, PERM(J)-th row of B is to be moved to the
+*> J-th row.
+*>
+*> (3L) The left singular vector matrix of the remaining matrix.
+*>
+*> For the right singular vector matrix, four types of orthogonal
+*> matrices are involved:
+*>
+*> (1R) The right singular vector matrix of the remaining matrix.
+*>
+*> (2R) If SQRE = 1, one extra Givens rotation to generate the right
+*> null space.
+*>
+*> (3R) The inverse transformation of (2L).
+*>
+*> (4R) The inverse transformation of (1L).
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ICOMPQ
+*> \verbatim
+*> ICOMPQ is INTEGER
+*> Specifies whether singular vectors are to be computed in
+*> factored form:
+*> = 0: Left singular vector matrix.
+*> = 1: Right singular vector matrix.
+*> \endverbatim
+*>
+*> \param[in] NL
+*> \verbatim
+*> NL is INTEGER
+*> The row dimension of the upper block. NL >= 1.
+*> \endverbatim
+*>
+*> \param[in] NR
+*> \verbatim
+*> NR is INTEGER
+*> The row dimension of the lower block. NR >= 1.
+*> \endverbatim
+*>
+*> \param[in] SQRE
+*> \verbatim
+*> SQRE is INTEGER
+*> = 0: the lower block is an NR-by-NR square matrix.
+*> = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
+*>
+*> The bidiagonal matrix has row dimension N = NL + NR + 1,
+*> and column dimension M = N + SQRE.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of columns of B and BX. NRHS must be at least 1.
+*> \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 in rows 1 through M. On output, B contains
+*> the solution X in rows 1 through N.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of B. LDB must be at least
+*> max(1,MAX( M, N ) ).
+*> \endverbatim
+*>
+*> \param[out] BX
+*> \verbatim
+*> BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS )
+*> \endverbatim
+*>
+*> \param[in] LDBX
+*> \verbatim
+*> LDBX is INTEGER
+*> The leading dimension of BX.
+*> \endverbatim
+*>
+*> \param[in] PERM
+*> \verbatim
+*> PERM is INTEGER array, dimension ( N )
+*> The permutations (from deflation and sorting) applied
+*> to the two blocks.
+*> \endverbatim
+*>
+*> \param[in] GIVPTR
+*> \verbatim
+*> GIVPTR is INTEGER
+*> The number of Givens rotations which took place in this
+*> subproblem.
+*> \endverbatim
+*>
+*> \param[in] GIVCOL
+*> \verbatim
+*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
+*> Each pair of numbers indicates a pair of rows/columns
+*> involved in a Givens rotation.
+*> \endverbatim
+*>
+*> \param[in] LDGCOL
+*> \verbatim
+*> LDGCOL is INTEGER
+*> The leading dimension of GIVCOL, must be at least N.
+*> \endverbatim
+*>
+*> \param[in] GIVNUM
+*> \verbatim
+*> GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
+*> Each number indicates the C or S value used in the
+*> corresponding Givens rotation.
+*> \endverbatim
+*>
+*> \param[in] LDGNUM
+*> \verbatim
+*> LDGNUM is INTEGER
+*> The leading dimension of arrays DIFR, POLES and
+*> GIVNUM, must be at least K.
+*> \endverbatim
+*>
+*> \param[in] POLES
+*> \verbatim
+*> POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
+*> On entry, POLES(1:K, 1) contains the new singular
+*> values obtained from solving the secular equation, and
+*> POLES(1:K, 2) is an array containing the poles in the secular
+*> equation.
+*> \endverbatim
+*>
+*> \param[in] DIFL
+*> \verbatim
+*> DIFL is DOUBLE PRECISION array, dimension ( K ).
+*> On entry, DIFL(I) is the distance between I-th updated
+*> (undeflated) singular value and the I-th (undeflated) old
+*> singular value.
+*> \endverbatim
+*>
+*> \param[in] DIFR
+*> \verbatim
+*> DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ).
+*> On entry, DIFR(I, 1) contains the distances between I-th
+*> updated (undeflated) singular value and the I+1-th
+*> (undeflated) old singular value. And DIFR(I, 2) is the
+*> normalizing factor for the I-th right singular vector.
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension ( K )
+*> Contain the components of the deflation-adjusted updating row
+*> vector.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> Contains the dimension of the non-deflated matrix,
+*> This is the order of the related secular equation. 1 <= K <=N.
+*> \endverbatim
+*>
+*> \param[in] C
+*> \verbatim
+*> C is DOUBLE PRECISION
+*> C contains garbage if SQRE =0 and the C-value of a Givens
+*> rotation related to the right null space if SQRE = 1.
+*> \endverbatim
+*>
+*> \param[in] S
+*> \verbatim
+*> S is DOUBLE PRECISION
+*> S contains garbage if SQRE =0 and the S-value of a Givens
+*> rotation related to the right null space if SQRE = 1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension ( K )
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \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 DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
$ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
$ POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.6.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2015
*
* .. Scalar Arguments ..
INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL,
@@ -19,148 +285,6 @@
$ POLES( LDGNUM, * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
-*
-* DLALS0 applies back the multiplying factors of either the left or the
-* right singular vector matrix of a diagonal matrix appended by a row
-* to the right hand side matrix B in solving the least squares problem
-* using the divide-and-conquer SVD approach.
-*
-* For the left singular vector matrix, three types of orthogonal
-* matrices are involved:
-*
-* (1L) Givens rotations: the number of such rotations is GIVPTR; the
-* pairs of columns/rows they were applied to are stored in GIVCOL;
-* and the C- and S-values of these rotations are stored in GIVNUM.
-*
-* (2L) Permutation. The (NL+1)-st row of B is to be moved to the first
-* row, and for J=2:N, PERM(J)-th row of B is to be moved to the
-* J-th row.
-*
-* (3L) The left singular vector matrix of the remaining matrix.
-*
-* For the right singular vector matrix, four types of orthogonal
-* matrices are involved:
-*
-* (1R) The right singular vector matrix of the remaining matrix.
-*
-* (2R) If SQRE = 1, one extra Givens rotation to generate the right
-* null space.
-*
-* (3R) The inverse transformation of (2L).
-*
-* (4R) The inverse transformation of (1L).
-*
-* Arguments
-* =========
-*
-* ICOMPQ (input) INTEGER
-* Specifies whether singular vectors are to be computed in
-* factored form:
-* = 0: Left singular vector matrix.
-* = 1: Right singular vector matrix.
-*
-* NL (input) INTEGER
-* The row dimension of the upper block. NL >= 1.
-*
-* NR (input) INTEGER
-* The row dimension of the lower block. NR >= 1.
-*
-* SQRE (input) INTEGER
-* = 0: the lower block is an NR-by-NR square matrix.
-* = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
-*
-* The bidiagonal matrix has row dimension N = NL + NR + 1,
-* and column dimension M = N + SQRE.
-*
-* NRHS (input) INTEGER
-* The number of columns of B and BX. NRHS must be at least 1.
-*
-* B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS )
-* On input, B contains the right hand sides of the least
-* squares problem in rows 1 through M. On output, B contains
-* the solution X in rows 1 through N.
-*
-* LDB (input) INTEGER
-* The leading dimension of B. LDB must be at least
-* max(1,MAX( M, N ) ).
-*
-* BX (workspace) DOUBLE PRECISION array, dimension ( LDBX, NRHS )
-*
-* LDBX (input) INTEGER
-* The leading dimension of BX.
-*
-* PERM (input) INTEGER array, dimension ( N )
-* The permutations (from deflation and sorting) applied
-* to the two blocks.
-*
-* GIVPTR (input) INTEGER
-* The number of Givens rotations which took place in this
-* subproblem.
-*
-* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 )
-* Each pair of numbers indicates a pair of rows/columns
-* involved in a Givens rotation.
-*
-* LDGCOL (input) INTEGER
-* The leading dimension of GIVCOL, must be at least N.
-*
-* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
-* Each number indicates the C or S value used in the
-* corresponding Givens rotation.
-*
-* LDGNUM (input) INTEGER
-* The leading dimension of arrays DIFR, POLES and
-* GIVNUM, must be at least K.
-*
-* POLES (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
-* On entry, POLES(1:K, 1) contains the new singular
-* values obtained from solving the secular equation, and
-* POLES(1:K, 2) is an array containing the poles in the secular
-* equation.
-*
-* DIFL (input) DOUBLE PRECISION array, dimension ( K ).
-* On entry, DIFL(I) is the distance between I-th updated
-* (undeflated) singular value and the I-th (undeflated) old
-* singular value.
-*
-* DIFR (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ).
-* On entry, DIFR(I, 1) contains the distances between I-th
-* updated (undeflated) singular value and the I+1-th
-* (undeflated) old singular value. And DIFR(I, 2) is the
-* normalizing factor for the I-th right singular vector.
-*
-* Z (input) DOUBLE PRECISION array, dimension ( K )
-* Contain the components of the deflation-adjusted updating row
-* vector.
-*
-* K (input) INTEGER
-* Contains the dimension of the non-deflated matrix,
-* This is the order of the related secular equation. 1 <= K <=N.
-*
-* C (input) DOUBLE PRECISION
-* C contains garbage if SQRE =0 and the C-value of a Givens
-* rotation related to the right null space if SQRE = 1.
-*
-* S (input) DOUBLE PRECISION
-* S contains garbage if SQRE =0 and the S-value of a Givens
-* rotation related to the right null space if SQRE = 1.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension ( K )
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* 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 ..
@@ -187,6 +311,7 @@
* Test the input parameters.
*
INFO = 0
+ N = NL + NR + 1
*
IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
INFO = -1
@@ -196,11 +321,7 @@
INFO = -3
ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
INFO = -4
- END IF
-*
- N = NL + NR + 1
-*
- IF( NRHS.LT.1 ) THEN
+ ELSE IF( NRHS.LT.1 ) THEN
INFO = -5
ELSE IF( LDB.LT.N ) THEN
INFO = -7