--- rpl/lapack/lapack/dlasd6.f 2011/07/22 07:38:08 1.10
+++ rpl/lapack/lapack/dlasd6.f 2011/11/21 20:42:58 1.11
@@ -1,12 +1,323 @@
+*> \brief \b DLASD6
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASD6 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
+* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
+* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK,
+* IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
+* $ NR, SQRE
+* DOUBLE PRECISION ALPHA, BETA, C, S
+* ..
+* .. Array Arguments ..
+* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ),
+* $ PERM( * )
+* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ),
+* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ),
+* $ VF( * ), VL( * ), WORK( * ), Z( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLASD6 computes the SVD of an updated upper bidiagonal matrix B
+*> obtained by merging two smaller ones by appending a row. This
+*> routine is used only for the problem which requires all singular
+*> values and optionally singular vector matrices in factored form.
+*> B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE.
+*> A related subroutine, DLASD1, handles the case in which all singular
+*> values and singular vectors of the bidiagonal matrix are desired.
+*>
+*> DLASD6 computes the SVD as follows:
+*>
+*> ( D1(in) 0 0 0 )
+*> B = U(in) * ( Z1**T a Z2**T b ) * VT(in)
+*> ( 0 0 D2(in) 0 )
+*>
+*> = U(out) * ( D(out) 0) * VT(out)
+*>
+*> where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
+*> with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
+*> elsewhere; and the entry b is empty if SQRE = 0.
+*>
+*> The singular values of B can be computed using D1, D2, the first
+*> components of all the right singular vectors of the lower block, and
+*> the last components of all the right singular vectors of the upper
+*> block. These components are stored and updated in VF and VL,
+*> respectively, in DLASD6. Hence U and VT are not explicitly
+*> referenced.
+*>
+*> The singular values are stored in D. The algorithm consists of two
+*> stages:
+*>
+*> The first stage consists of deflating the size of the problem
+*> when there are multiple singular values or if there is a zero
+*> in the Z vector. For each such occurence the dimension of the
+*> secular equation problem is reduced by one. This stage is
+*> performed by the routine DLASD7.
+*>
+*> The second stage consists of calculating the updated
+*> singular values. This is done by finding the roots of the
+*> secular equation via the routine DLASD4 (as called by DLASD8).
+*> This routine also updates VF and VL and computes the distances
+*> between the updated singular values and the old singular
+*> values.
+*>
+*> DLASD6 is called from DLASDA.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ICOMPQ
+*> \verbatim
+*> ICOMPQ is INTEGER
+*> Specifies whether singular vectors are to be computed in
+*> factored form:
+*> = 0: Compute singular values only.
+*> = 1: Compute singular vectors in factored form as well.
+*> \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,out] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension ( NL+NR+1 ).
+*> On entry D(1:NL,1:NL) contains the singular values of the
+*> upper block, and D(NL+2:N) contains the singular values
+*> of the lower block. On exit D(1:N) contains the singular
+*> values of the modified matrix.
+*> \endverbatim
+*>
+*> \param[in,out] VF
+*> \verbatim
+*> VF is DOUBLE PRECISION array, dimension ( M )
+*> On entry, VF(1:NL+1) contains the first components of all
+*> right singular vectors of the upper block; and VF(NL+2:M)
+*> contains the first components of all right singular vectors
+*> of the lower block. On exit, VF contains the first components
+*> of all right singular vectors of the bidiagonal matrix.
+*> \endverbatim
+*>
+*> \param[in,out] VL
+*> \verbatim
+*> VL is DOUBLE PRECISION array, dimension ( M )
+*> On entry, VL(1:NL+1) contains the last components of all
+*> right singular vectors of the upper block; and VL(NL+2:M)
+*> contains the last components of all right singular vectors of
+*> the lower block. On exit, VL contains the last components of
+*> all right singular vectors of the bidiagonal matrix.
+*> \endverbatim
+*>
+*> \param[in,out] ALPHA
+*> \verbatim
+*> ALPHA is DOUBLE PRECISION
+*> Contains the diagonal element associated with the added row.
+*> \endverbatim
+*>
+*> \param[in,out] BETA
+*> \verbatim
+*> BETA is DOUBLE PRECISION
+*> Contains the off-diagonal element associated with the added
+*> row.
+*> \endverbatim
+*>
+*> \param[out] IDXQ
+*> \verbatim
+*> IDXQ is INTEGER array, dimension ( N )
+*> This contains the permutation which will reintegrate the
+*> subproblem just solved back into sorted order, i.e.
+*> D( IDXQ( I = 1, N ) ) will be in ascending order.
+*> \endverbatim
+*>
+*> \param[out] PERM
+*> \verbatim
+*> PERM is INTEGER array, dimension ( N )
+*> The permutations (from deflation and sorting) to be applied
+*> to each block. Not referenced if ICOMPQ = 0.
+*> \endverbatim
+*>
+*> \param[out] GIVPTR
+*> \verbatim
+*> GIVPTR is INTEGER
+*> The number of Givens rotations which took place in this
+*> subproblem. Not referenced if ICOMPQ = 0.
+*> \endverbatim
+*>
+*> \param[out] GIVCOL
+*> \verbatim
+*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
+*> Each pair of numbers indicates a pair of columns to take place
+*> in a Givens rotation. Not referenced if ICOMPQ = 0.
+*> \endverbatim
+*>
+*> \param[in] LDGCOL
+*> \verbatim
+*> LDGCOL is INTEGER
+*> leading dimension of GIVCOL, must be at least N.
+*> \endverbatim
+*>
+*> \param[out] GIVNUM
+*> \verbatim
+*> GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
+*> Each number indicates the C or S value to be used in the
+*> corresponding Givens rotation. Not referenced if ICOMPQ = 0.
+*> \endverbatim
+*>
+*> \param[in] LDGNUM
+*> \verbatim
+*> LDGNUM is INTEGER
+*> The leading dimension of GIVNUM and POLES, must be at least N.
+*> \endverbatim
+*>
+*> \param[out] POLES
+*> \verbatim
+*> POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
+*> On exit, POLES(1,*) is an array containing the new singular
+*> values obtained from solving the secular equation, and
+*> POLES(2,*) is an array containing the poles in the secular
+*> equation. Not referenced if ICOMPQ = 0.
+*> \endverbatim
+*>
+*> \param[out] DIFL
+*> \verbatim
+*> DIFL is DOUBLE PRECISION array, dimension ( N )
+*> On exit, DIFL(I) is the distance between I-th updated
+*> (undeflated) singular value and the I-th (undeflated) old
+*> singular value.
+*> \endverbatim
+*>
+*> \param[out] DIFR
+*> \verbatim
+*> DIFR is DOUBLE PRECISION array,
+*> dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and
+*> dimension ( N ) if ICOMPQ = 0.
+*> On exit, DIFR(I, 1) is the distance between I-th updated
+*> (undeflated) singular value and the I+1-th (undeflated) old
+*> singular value.
+*>
+*> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
+*> normalizing factors for the right singular vector matrix.
+*>
+*> See DLASD8 for details on DIFL and DIFR.
+*> \endverbatim
+*>
+*> \param[out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension ( M )
+*> The first elements of this array contain the components
+*> of the deflation-adjusted updating row vector.
+*> \endverbatim
+*>
+*> \param[out] 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[out] 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[out] 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 ( 4 * M )
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension ( 3 * 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 DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
$ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
$ LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK,
$ IWORK, INFO )
*
-* -- LAPACK auxiliary routine (version 3.3.0) --
+* -- 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..--
-* November 2010
+* November 2011
*
* .. Scalar Arguments ..
INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
@@ -21,185 +332,6 @@
$ VF( * ), VL( * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
-*
-* DLASD6 computes the SVD of an updated upper bidiagonal matrix B
-* obtained by merging two smaller ones by appending a row. This
-* routine is used only for the problem which requires all singular
-* values and optionally singular vector matrices in factored form.
-* B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE.
-* A related subroutine, DLASD1, handles the case in which all singular
-* values and singular vectors of the bidiagonal matrix are desired.
-*
-* DLASD6 computes the SVD as follows:
-*
-* ( D1(in) 0 0 0 )
-* B = U(in) * ( Z1**T a Z2**T b ) * VT(in)
-* ( 0 0 D2(in) 0 )
-*
-* = U(out) * ( D(out) 0) * VT(out)
-*
-* where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
-* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
-* elsewhere; and the entry b is empty if SQRE = 0.
-*
-* The singular values of B can be computed using D1, D2, the first
-* components of all the right singular vectors of the lower block, and
-* the last components of all the right singular vectors of the upper
-* block. These components are stored and updated in VF and VL,
-* respectively, in DLASD6. Hence U and VT are not explicitly
-* referenced.
-*
-* The singular values are stored in D. The algorithm consists of two
-* stages:
-*
-* The first stage consists of deflating the size of the problem
-* when there are multiple singular values or if there is a zero
-* in the Z vector. For each such occurence the dimension of the
-* secular equation problem is reduced by one. This stage is
-* performed by the routine DLASD7.
-*
-* The second stage consists of calculating the updated
-* singular values. This is done by finding the roots of the
-* secular equation via the routine DLASD4 (as called by DLASD8).
-* This routine also updates VF and VL and computes the distances
-* between the updated singular values and the old singular
-* values.
-*
-* DLASD6 is called from DLASDA.
-*
-* Arguments
-* =========
-*
-* ICOMPQ (input) INTEGER
-* Specifies whether singular vectors are to be computed in
-* factored form:
-* = 0: Compute singular values only.
-* = 1: Compute singular vectors in factored form as well.
-*
-* 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.
-*
-* D (input/output) DOUBLE PRECISION array, dimension ( NL+NR+1 ).
-* On entry D(1:NL,1:NL) contains the singular values of the
-* upper block, and D(NL+2:N) contains the singular values
-* of the lower block. On exit D(1:N) contains the singular
-* values of the modified matrix.
-*
-* VF (input/output) DOUBLE PRECISION array, dimension ( M )
-* On entry, VF(1:NL+1) contains the first components of all
-* right singular vectors of the upper block; and VF(NL+2:M)
-* contains the first components of all right singular vectors
-* of the lower block. On exit, VF contains the first components
-* of all right singular vectors of the bidiagonal matrix.
-*
-* VL (input/output) DOUBLE PRECISION array, dimension ( M )
-* On entry, VL(1:NL+1) contains the last components of all
-* right singular vectors of the upper block; and VL(NL+2:M)
-* contains the last components of all right singular vectors of
-* the lower block. On exit, VL contains the last components of
-* all right singular vectors of the bidiagonal matrix.
-*
-* ALPHA (input/output) DOUBLE PRECISION
-* Contains the diagonal element associated with the added row.
-*
-* BETA (input/output) DOUBLE PRECISION
-* Contains the off-diagonal element associated with the added
-* row.
-*
-* IDXQ (output) INTEGER array, dimension ( N )
-* This contains the permutation which will reintegrate the
-* subproblem just solved back into sorted order, i.e.
-* D( IDXQ( I = 1, N ) ) will be in ascending order.
-*
-* PERM (output) INTEGER array, dimension ( N )
-* The permutations (from deflation and sorting) to be applied
-* to each block. Not referenced if ICOMPQ = 0.
-*
-* GIVPTR (output) INTEGER
-* The number of Givens rotations which took place in this
-* subproblem. Not referenced if ICOMPQ = 0.
-*
-* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 )
-* Each pair of numbers indicates a pair of columns to take place
-* in a Givens rotation. Not referenced if ICOMPQ = 0.
-*
-* LDGCOL (input) INTEGER
-* leading dimension of GIVCOL, must be at least N.
-*
-* GIVNUM (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
-* Each number indicates the C or S value to be used in the
-* corresponding Givens rotation. Not referenced if ICOMPQ = 0.
-*
-* LDGNUM (input) INTEGER
-* The leading dimension of GIVNUM and POLES, must be at least N.
-*
-* POLES (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
-* On exit, POLES(1,*) is an array containing the new singular
-* values obtained from solving the secular equation, and
-* POLES(2,*) is an array containing the poles in the secular
-* equation. Not referenced if ICOMPQ = 0.
-*
-* DIFL (output) DOUBLE PRECISION array, dimension ( N )
-* On exit, DIFL(I) is the distance between I-th updated
-* (undeflated) singular value and the I-th (undeflated) old
-* singular value.
-*
-* DIFR (output) DOUBLE PRECISION array,
-* dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and
-* dimension ( N ) if ICOMPQ = 0.
-* On exit, DIFR(I, 1) is the distance between I-th updated
-* (undeflated) singular value and the I+1-th (undeflated) old
-* singular value.
-*
-* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
-* normalizing factors for the right singular vector matrix.
-*
-* See DLASD8 for details on DIFL and DIFR.
-*
-* Z (output) DOUBLE PRECISION array, dimension ( M )
-* The first elements of this array contain the components
-* of the deflation-adjusted updating row vector.
-*
-* K (output) INTEGER
-* Contains the dimension of the non-deflated matrix,
-* This is the order of the related secular equation. 1 <= K <=N.
-*
-* C (output) 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 (output) 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 ( 4 * M )
-*
-* IWORK (workspace) INTEGER array, dimension ( 3 * 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 ..