--- rpl/lapack/lapack/dbdsdc.f 2011/07/22 07:38:04 1.9 +++ rpl/lapack/lapack/dbdsdc.f 2011/11/21 20:42:49 1.10 @@ -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 3.3.1) -- +* -- 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..-- -* -- April 2011 -- +* 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**T 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 a 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.