--- rpl/lapack/lapack/dbdsdc.f 2010/01/26 15:22:45 1.1
+++ rpl/lapack/lapack/dbdsdc.f 2011/11/21 22:19:26 1.11
@@ -1,10 +1,214 @@
+*> \brief \b DBDSDC
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DBDSDC + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
+* WORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER COMPQ, UPLO
+* INTEGER INFO, LDU, LDVT, N
+* ..
+* .. Array Arguments ..
+* INTEGER IQ( * ), IWORK( * )
+* DOUBLE PRECISION D( * ), E( * ), Q( * ), U( LDU, * ),
+* $ VT( LDVT, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DBDSDC computes the singular value decomposition (SVD) of a real
+*> N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,
+*> using a divide and conquer method, where S is a diagonal matrix
+*> with non-negative diagonal elements (the singular values of B), and
+*> U and VT are orthogonal matrices of left and right singular vectors,
+*> respectively. DBDSDC can be used to compute all singular values,
+*> and optionally, singular vectors or singular vectors in compact form.
+*>
+*> 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 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. See DLASD3 for details.
+*>
+*> The code currently calls DLASDQ if singular values only are desired.
+*> However, it can be slightly modified to compute singular values
+*> using the divide and conquer method.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': B is upper bidiagonal.
+*> = 'L': B is lower bidiagonal.
+*> \endverbatim
+*>
+*> \param[in] COMPQ
+*> \verbatim
+*> COMPQ is CHARACTER*1
+*> Specifies whether singular vectors are to be computed
+*> as follows:
+*> = 'N': Compute singular values only;
+*> = 'P': Compute singular values and compute singular
+*> vectors in compact form;
+*> = 'I': Compute singular values and singular vectors.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (N)
+*> On entry, the n diagonal elements of the bidiagonal matrix B.
+*> On exit, if INFO=0, the singular values of B.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*> E is DOUBLE PRECISION array, dimension (N-1)
+*> On entry, the elements of E contain the offdiagonal
+*> elements of the bidiagonal matrix whose SVD is desired.
+*> On exit, E has been destroyed.
+*> \endverbatim
+*>
+*> \param[out] U
+*> \verbatim
+*> U is DOUBLE PRECISION array, dimension (LDU,N)
+*> If COMPQ = 'I', then:
+*> On exit, if INFO = 0, U contains the left singular vectors
+*> of the bidiagonal matrix.
+*> For other values of COMPQ, U is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*> LDU is INTEGER
+*> The leading dimension of the array U. LDU >= 1.
+*> If singular vectors are desired, then LDU >= max( 1, N ).
+*> \endverbatim
+*>
+*> \param[out] VT
+*> \verbatim
+*> VT is DOUBLE PRECISION array, dimension (LDVT,N)
+*> If COMPQ = 'I', then:
+*> On exit, if INFO = 0, VT**T contains the right singular
+*> vectors of the bidiagonal matrix.
+*> For other values of COMPQ, VT is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDVT
+*> \verbatim
+*> LDVT is INTEGER
+*> The leading dimension of the array VT. LDVT >= 1.
+*> If singular vectors are desired, then LDVT >= max( 1, N ).
+*> \endverbatim
+*>
+*> \param[out] Q
+*> \verbatim
+*> Q is DOUBLE PRECISION array, dimension (LDQ)
+*> If COMPQ = 'P', then:
+*> On exit, if INFO = 0, Q and IQ contain the left
+*> and right singular vectors in a compact form,
+*> requiring O(N log N) space instead of 2*N**2.
+*> In particular, Q contains all the DOUBLE PRECISION data in
+*> LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
+*> words of memory, where 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).
+*> For other values of COMPQ, Q is not referenced.
+*> \endverbatim
+*>
+*> \param[out] IQ
+*> \verbatim
+*> IQ is INTEGER array, dimension (LDIQ)
+*> If COMPQ = 'P', then:
+*> On exit, if INFO = 0, Q and IQ contain the left
+*> and right singular vectors in a compact form,
+*> requiring O(N log N) space instead of 2*N**2.
+*> In particular, IQ contains all INTEGER data in
+*> LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
+*> words of memory, where 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).
+*> For other values of COMPQ, IQ is not referenced.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> If COMPQ = 'N' then LWORK >= (4 * N).
+*> If COMPQ = 'P' then LWORK >= (6 * N).
+*> If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (8*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.
+*> The update process of divide and conquer failed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ming Gu and Huan Ren, Computer Science Division, University of
+*> California at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
$ WORK, IWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational 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 ..
CHARACTER COMPQ, UPLO
@@ -16,119 +220,6 @@
$ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DBDSDC computes the singular value decomposition (SVD) of a real
-* N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,
-* using a divide and conquer method, where S is a diagonal matrix
-* with non-negative diagonal elements (the singular values of B), and
-* U and VT are orthogonal matrices of left and right singular vectors,
-* respectively. DBDSDC can be used to compute all singular values,
-* and optionally, singular vectors or singular vectors in compact form.
-*
-* 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 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. See DLASD3 for details.
-*
-* The code currently calls DLASDQ if singular values only are desired.
-* However, it can be slightly modified to compute singular values
-* using the divide and conquer method.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': B is upper bidiagonal.
-* = 'L': B is lower bidiagonal.
-*
-* COMPQ (input) CHARACTER*1
-* Specifies whether singular vectors are to be computed
-* as follows:
-* = 'N': Compute singular values only;
-* = 'P': Compute singular values and compute singular
-* vectors in compact form;
-* = 'I': Compute singular values and singular vectors.
-*
-* N (input) INTEGER
-* The order of the matrix B. N >= 0.
-*
-* D (input/output) DOUBLE PRECISION array, dimension (N)
-* On entry, the n diagonal elements of the bidiagonal matrix B.
-* On exit, if INFO=0, the singular values of B.
-*
-* E (input/output) DOUBLE PRECISION array, dimension (N-1)
-* On entry, the elements of E contain the offdiagonal
-* elements of the bidiagonal matrix whose SVD is desired.
-* On exit, E has been destroyed.
-*
-* U (output) DOUBLE PRECISION array, dimension (LDU,N)
-* If COMPQ = 'I', then:
-* On exit, if INFO = 0, U contains the left singular vectors
-* of the bidiagonal matrix.
-* For other values of COMPQ, U is not referenced.
-*
-* LDU (input) INTEGER
-* The leading dimension of the array U. LDU >= 1.
-* If singular vectors are desired, then LDU >= max( 1, N ).
-*
-* VT (output) DOUBLE PRECISION array, dimension (LDVT,N)
-* If COMPQ = 'I', then:
-* On exit, if INFO = 0, VT' contains the right singular
-* vectors of the bidiagonal matrix.
-* For other values of COMPQ, VT is not referenced.
-*
-* LDVT (input) INTEGER
-* The leading dimension of the array VT. LDVT >= 1.
-* If singular vectors are desired, then LDVT >= max( 1, N ).
-*
-* Q (output) DOUBLE PRECISION array, dimension (LDQ)
-* If COMPQ = 'P', then:
-* On exit, if INFO = 0, Q and IQ contain the left
-* and right singular vectors in a compact form,
-* requiring O(N log N) space instead of 2*N**2.
-* In particular, Q contains all the DOUBLE PRECISION data in
-* LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
-* words of memory, where 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).
-* For other values of COMPQ, Q is not referenced.
-*
-* IQ (output) INTEGER array, dimension (LDIQ)
-* If COMPQ = 'P', then:
-* On exit, if INFO = 0, Q and IQ contain the left
-* and right singular vectors in a compact form,
-* requiring O(N log N) space instead of 2*N**2.
-* In particular, IQ contains all INTEGER data in
-* LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
-* words of memory, where 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).
-* For other values of COMPQ, IQ is not referenced.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* If COMPQ = 'N' then LWORK >= (4 * N).
-* If COMPQ = 'P' then LWORK >= (6 * N).
-* If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).
-*
-* IWORK (workspace) INTEGER array, dimension (8*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.
-* The update process of divide and conquer failed.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ming Gu and Huan Ren, Computer Science Division, University of
-* California at Berkeley, USA
-*
* =====================================================================
* Changed dimension statement in comment describing E from (N) to
* (N-1). Sven, 17 Feb 05.
@@ -287,7 +378,7 @@
CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, IERR )
CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, NM1, 1, E, NM1, IERR )
*
- EPS = DLAMCH( 'Epsilon' )
+ EPS = (0.9D+0)*DLAMCH( 'Epsilon' )
*
MLVL = INT( LOG( DBLE( N ) / DBLE( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1
SMLSZP = SMLSIZ + 1
@@ -368,9 +459,9 @@
$ Q( START+( IC+QSTART-2 )*N ),
$ Q( START+( IS+QSTART-2 )*N ),
$ WORK( WSTART ), IWORK, INFO )
- IF( INFO.NE.0 ) THEN
- RETURN
- END IF
+ END IF
+ IF( INFO.NE.0 ) THEN
+ RETURN
END IF
START = I + 1
END IF