LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slasd0.f
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00001 *> \brief \b SLASD0
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLASD0 + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd0.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
00022 *                          WORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IWORK( * )
00029 *       REAL               D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
00030 *      $                   WORK( * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> Using a divide and conquer approach, SLASD0 computes the singular
00040 *> value decomposition (SVD) of a real upper bidiagonal N-by-M
00041 *> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
00042 *> The algorithm computes orthogonal matrices U and VT such that
00043 *> B = U * S * VT. The singular values S are overwritten on D.
00044 *>
00045 *> A related subroutine, SLASDA, computes only the singular values,
00046 *> and optionally, the singular vectors in compact form.
00047 *> \endverbatim
00048 *
00049 *  Arguments:
00050 *  ==========
00051 *
00052 *> \param[in] N
00053 *> \verbatim
00054 *>          N is INTEGER
00055 *>         On entry, the row dimension of the upper bidiagonal matrix.
00056 *>         This is also the dimension of the main diagonal array D.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] SQRE
00060 *> \verbatim
00061 *>          SQRE is INTEGER
00062 *>         Specifies the column dimension of the bidiagonal matrix.
00063 *>         = 0: The bidiagonal matrix has column dimension M = N;
00064 *>         = 1: The bidiagonal matrix has column dimension M = N+1;
00065 *> \endverbatim
00066 *>
00067 *> \param[in,out] D
00068 *> \verbatim
00069 *>          D is REAL array, dimension (N)
00070 *>         On entry D contains the main diagonal of the bidiagonal
00071 *>         matrix.
00072 *>         On exit D, if INFO = 0, contains its singular values.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] E
00076 *> \verbatim
00077 *>          E is REAL array, dimension (M-1)
00078 *>         Contains the subdiagonal entries of the bidiagonal matrix.
00079 *>         On exit, E has been destroyed.
00080 *> \endverbatim
00081 *>
00082 *> \param[out] U
00083 *> \verbatim
00084 *>          U is REAL array, dimension at least (LDQ, N)
00085 *>         On exit, U contains the left singular vectors.
00086 *> \endverbatim
00087 *>
00088 *> \param[in] LDU
00089 *> \verbatim
00090 *>          LDU is INTEGER
00091 *>         On entry, leading dimension of U.
00092 *> \endverbatim
00093 *>
00094 *> \param[out] VT
00095 *> \verbatim
00096 *>          VT is REAL array, dimension at least (LDVT, M)
00097 *>         On exit, VT**T contains the right singular vectors.
00098 *> \endverbatim
00099 *>
00100 *> \param[in] LDVT
00101 *> \verbatim
00102 *>          LDVT is INTEGER
00103 *>         On entry, leading dimension of VT.
00104 *> \endverbatim
00105 *>
00106 *> \param[in] SMLSIZ
00107 *> \verbatim
00108 *>          SMLSIZ is INTEGER
00109 *>         On entry, maximum size of the subproblems at the
00110 *>         bottom of the computation tree.
00111 *> \endverbatim
00112 *>
00113 *> \param[out] IWORK
00114 *> \verbatim
00115 *>          IWORK is INTEGER array, dimension (8*N)
00116 *> \endverbatim
00117 *>
00118 *> \param[out] WORK
00119 *> \verbatim
00120 *>          WORK is REAL array, dimension (3*M**2+2*M)
00121 *> \endverbatim
00122 *>
00123 *> \param[out] INFO
00124 *> \verbatim
00125 *>          INFO is INTEGER
00126 *>          = 0:  successful exit.
00127 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00128 *>          > 0:  if INFO = 1, a singular value did not converge
00129 *> \endverbatim
00130 *
00131 *  Authors:
00132 *  ========
00133 *
00134 *> \author Univ. of Tennessee 
00135 *> \author Univ. of California Berkeley 
00136 *> \author Univ. of Colorado Denver 
00137 *> \author NAG Ltd. 
00138 *
00139 *> \date November 2011
00140 *
00141 *> \ingroup auxOTHERauxiliary
00142 *
00143 *> \par Contributors:
00144 *  ==================
00145 *>
00146 *>     Ming Gu and Huan Ren, Computer Science Division, University of
00147 *>     California at Berkeley, USA
00148 *>
00149 *  =====================================================================
00150       SUBROUTINE SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
00151      $                   WORK, INFO )
00152 *
00153 *  -- LAPACK auxiliary routine (version 3.4.0) --
00154 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00155 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00156 *     November 2011
00157 *
00158 *     .. Scalar Arguments ..
00159       INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
00160 *     ..
00161 *     .. Array Arguments ..
00162       INTEGER            IWORK( * )
00163       REAL               D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
00164      $                   WORK( * )
00165 *     ..
00166 *
00167 *  =====================================================================
00168 *
00169 *     .. Local Scalars ..
00170       INTEGER            I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
00171      $                   J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
00172      $                   NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
00173       REAL               ALPHA, BETA
00174 *     ..
00175 *     .. External Subroutines ..
00176       EXTERNAL           SLASD1, SLASDQ, SLASDT, XERBLA
00177 *     ..
00178 *     .. Executable Statements ..
00179 *
00180 *     Test the input parameters.
00181 *
00182       INFO = 0
00183 *
00184       IF( N.LT.0 ) THEN
00185          INFO = -1
00186       ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
00187          INFO = -2
00188       END IF
00189 *
00190       M = N + SQRE
00191 *
00192       IF( LDU.LT.N ) THEN
00193          INFO = -6
00194       ELSE IF( LDVT.LT.M ) THEN
00195          INFO = -8
00196       ELSE IF( SMLSIZ.LT.3 ) THEN
00197          INFO = -9
00198       END IF
00199       IF( INFO.NE.0 ) THEN
00200          CALL XERBLA( 'SLASD0', -INFO )
00201          RETURN
00202       END IF
00203 *
00204 *     If the input matrix is too small, call SLASDQ to find the SVD.
00205 *
00206       IF( N.LE.SMLSIZ ) THEN
00207          CALL SLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U,
00208      $                LDU, WORK, INFO )
00209          RETURN
00210       END IF
00211 *
00212 *     Set up the computation tree.
00213 *
00214       INODE = 1
00215       NDIML = INODE + N
00216       NDIMR = NDIML + N
00217       IDXQ = NDIMR + N
00218       IWK = IDXQ + N
00219       CALL SLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
00220      $             IWORK( NDIMR ), SMLSIZ )
00221 *
00222 *     For the nodes on bottom level of the tree, solve
00223 *     their subproblems by SLASDQ.
00224 *
00225       NDB1 = ( ND+1 ) / 2
00226       NCC = 0
00227       DO 30 I = NDB1, ND
00228 *
00229 *     IC : center row of each node
00230 *     NL : number of rows of left  subproblem
00231 *     NR : number of rows of right subproblem
00232 *     NLF: starting row of the left   subproblem
00233 *     NRF: starting row of the right  subproblem
00234 *
00235          I1 = I - 1
00236          IC = IWORK( INODE+I1 )
00237          NL = IWORK( NDIML+I1 )
00238          NLP1 = NL + 1
00239          NR = IWORK( NDIMR+I1 )
00240          NRP1 = NR + 1
00241          NLF = IC - NL
00242          NRF = IC + 1
00243          SQREI = 1
00244          CALL SLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ),
00245      $                VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU,
00246      $                U( NLF, NLF ), LDU, WORK, INFO )
00247          IF( INFO.NE.0 ) THEN
00248             RETURN
00249          END IF
00250          ITEMP = IDXQ + NLF - 2
00251          DO 10 J = 1, NL
00252             IWORK( ITEMP+J ) = J
00253    10    CONTINUE
00254          IF( I.EQ.ND ) THEN
00255             SQREI = SQRE
00256          ELSE
00257             SQREI = 1
00258          END IF
00259          NRP1 = NR + SQREI
00260          CALL SLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ),
00261      $                VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU,
00262      $                U( NRF, NRF ), LDU, WORK, INFO )
00263          IF( INFO.NE.0 ) THEN
00264             RETURN
00265          END IF
00266          ITEMP = IDXQ + IC
00267          DO 20 J = 1, NR
00268             IWORK( ITEMP+J-1 ) = J
00269    20    CONTINUE
00270    30 CONTINUE
00271 *
00272 *     Now conquer each subproblem bottom-up.
00273 *
00274       DO 50 LVL = NLVL, 1, -1
00275 *
00276 *        Find the first node LF and last node LL on the
00277 *        current level LVL.
00278 *
00279          IF( LVL.EQ.1 ) THEN
00280             LF = 1
00281             LL = 1
00282          ELSE
00283             LF = 2**( LVL-1 )
00284             LL = 2*LF - 1
00285          END IF
00286          DO 40 I = LF, LL
00287             IM1 = I - 1
00288             IC = IWORK( INODE+IM1 )
00289             NL = IWORK( NDIML+IM1 )
00290             NR = IWORK( NDIMR+IM1 )
00291             NLF = IC - NL
00292             IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN
00293                SQREI = SQRE
00294             ELSE
00295                SQREI = 1
00296             END IF
00297             IDXQC = IDXQ + NLF - 1
00298             ALPHA = D( IC )
00299             BETA = E( IC )
00300             CALL SLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA,
00301      $                   U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT,
00302      $                   IWORK( IDXQC ), IWORK( IWK ), WORK, INFO )
00303             IF( INFO.NE.0 ) THEN
00304                RETURN
00305             END IF
00306    40    CONTINUE
00307    50 CONTINUE
00308 *
00309       RETURN
00310 *
00311 *     End of SLASD0
00312 *
00313       END
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