LAPACK 3.3.1 Linear Algebra PACKage

# dlasd0.f

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```00001       SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
00002      \$                   WORK, INFO )
00003 *
00004 *  -- LAPACK auxiliary routine (version 3.2.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     June 2010
00008 *
00009 *     .. Scalar Arguments ..
00010       INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
00011 *     ..
00012 *     .. Array Arguments ..
00013       INTEGER            IWORK( * )
00014       DOUBLE PRECISION   D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
00015      \$                   WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  Using a divide and conquer approach, DLASD0 computes the singular
00022 *  value decomposition (SVD) of a real upper bidiagonal N-by-M
00023 *  matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
00024 *  The algorithm computes orthogonal matrices U and VT such that
00025 *  B = U * S * VT. The singular values S are overwritten on D.
00026 *
00027 *  A related subroutine, DLASDA, computes only the singular values,
00028 *  and optionally, the singular vectors in compact form.
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  N      (input) INTEGER
00034 *         On entry, the row dimension of the upper bidiagonal matrix.
00035 *         This is also the dimension of the main diagonal array D.
00036 *
00037 *  SQRE   (input) INTEGER
00038 *         Specifies the column dimension of the bidiagonal matrix.
00039 *         = 0: The bidiagonal matrix has column dimension M = N;
00040 *         = 1: The bidiagonal matrix has column dimension M = N+1;
00041 *
00042 *  D      (input/output) DOUBLE PRECISION array, dimension (N)
00043 *         On entry D contains the main diagonal of the bidiagonal
00044 *         matrix.
00045 *         On exit D, if INFO = 0, contains its singular values.
00046 *
00047 *  E      (input) DOUBLE PRECISION array, dimension (M-1)
00048 *         Contains the subdiagonal entries of the bidiagonal matrix.
00049 *         On exit, E has been destroyed.
00050 *
00051 *  U      (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
00052 *         On exit, U contains the left singular vectors.
00053 *
00054 *  LDU    (input) INTEGER
00055 *         On entry, leading dimension of U.
00056 *
00057 *  VT     (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
00058 *         On exit, VT**T contains the right singular vectors.
00059 *
00060 *  LDVT   (input) INTEGER
00061 *         On entry, leading dimension of VT.
00062 *
00063 *  SMLSIZ (input) INTEGER
00064 *         On entry, maximum size of the subproblems at the
00065 *         bottom of the computation tree.
00066 *
00067 *  IWORK  (workspace) INTEGER work array.
00068 *         Dimension must be at least (8 * N)
00069 *
00070 *  WORK   (workspace) DOUBLE PRECISION work array.
00071 *         Dimension must be at least (3 * M**2 + 2 * M)
00072 *
00073 *  INFO   (output) INTEGER
00074 *          = 0:  successful exit.
00075 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00076 *          > 0:  if INFO = 1, a singular value did not converge
00077 *
00078 *  Further Details
00079 *  ===============
00080 *
00081 *  Based on contributions by
00082 *     Ming Gu and Huan Ren, Computer Science Division, University of
00083 *     California at Berkeley, USA
00084 *
00085 *  =====================================================================
00086 *
00087 *     .. Local Scalars ..
00088       INTEGER            I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
00089      \$                   J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
00090      \$                   NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
00091       DOUBLE PRECISION   ALPHA, BETA
00092 *     ..
00093 *     .. External Subroutines ..
00094       EXTERNAL           DLASD1, DLASDQ, DLASDT, XERBLA
00095 *     ..
00096 *     .. Executable Statements ..
00097 *
00098 *     Test the input parameters.
00099 *
00100       INFO = 0
00101 *
00102       IF( N.LT.0 ) THEN
00103          INFO = -1
00104       ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
00105          INFO = -2
00106       END IF
00107 *
00108       M = N + SQRE
00109 *
00110       IF( LDU.LT.N ) THEN
00111          INFO = -6
00112       ELSE IF( LDVT.LT.M ) THEN
00113          INFO = -8
00114       ELSE IF( SMLSIZ.LT.3 ) THEN
00115          INFO = -9
00116       END IF
00117       IF( INFO.NE.0 ) THEN
00118          CALL XERBLA( 'DLASD0', -INFO )
00119          RETURN
00120       END IF
00121 *
00122 *     If the input matrix is too small, call DLASDQ to find the SVD.
00123 *
00124       IF( N.LE.SMLSIZ ) THEN
00125          CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U,
00126      \$                LDU, WORK, INFO )
00127          RETURN
00128       END IF
00129 *
00130 *     Set up the computation tree.
00131 *
00132       INODE = 1
00133       NDIML = INODE + N
00134       NDIMR = NDIML + N
00135       IDXQ = NDIMR + N
00136       IWK = IDXQ + N
00137       CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
00138      \$             IWORK( NDIMR ), SMLSIZ )
00139 *
00140 *     For the nodes on bottom level of the tree, solve
00141 *     their subproblems by DLASDQ.
00142 *
00143       NDB1 = ( ND+1 ) / 2
00144       NCC = 0
00145       DO 30 I = NDB1, ND
00146 *
00147 *     IC : center row of each node
00148 *     NL : number of rows of left  subproblem
00149 *     NR : number of rows of right subproblem
00150 *     NLF: starting row of the left   subproblem
00151 *     NRF: starting row of the right  subproblem
00152 *
00153          I1 = I - 1
00154          IC = IWORK( INODE+I1 )
00155          NL = IWORK( NDIML+I1 )
00156          NLP1 = NL + 1
00157          NR = IWORK( NDIMR+I1 )
00158          NRP1 = NR + 1
00159          NLF = IC - NL
00160          NRF = IC + 1
00161          SQREI = 1
00162          CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ),
00163      \$                VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU,
00164      \$                U( NLF, NLF ), LDU, WORK, INFO )
00165          IF( INFO.NE.0 ) THEN
00166             RETURN
00167          END IF
00168          ITEMP = IDXQ + NLF - 2
00169          DO 10 J = 1, NL
00170             IWORK( ITEMP+J ) = J
00171    10    CONTINUE
00172          IF( I.EQ.ND ) THEN
00173             SQREI = SQRE
00174          ELSE
00175             SQREI = 1
00176          END IF
00177          NRP1 = NR + SQREI
00178          CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ),
00179      \$                VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU,
00180      \$                U( NRF, NRF ), LDU, WORK, INFO )
00181          IF( INFO.NE.0 ) THEN
00182             RETURN
00183          END IF
00184          ITEMP = IDXQ + IC
00185          DO 20 J = 1, NR
00186             IWORK( ITEMP+J-1 ) = J
00187    20    CONTINUE
00188    30 CONTINUE
00189 *
00190 *     Now conquer each subproblem bottom-up.
00191 *
00192       DO 50 LVL = NLVL, 1, -1
00193 *
00194 *        Find the first node LF and last node LL on the
00195 *        current level LVL.
00196 *
00197          IF( LVL.EQ.1 ) THEN
00198             LF = 1
00199             LL = 1
00200          ELSE
00201             LF = 2**( LVL-1 )
00202             LL = 2*LF - 1
00203          END IF
00204          DO 40 I = LF, LL
00205             IM1 = I - 1
00206             IC = IWORK( INODE+IM1 )
00207             NL = IWORK( NDIML+IM1 )
00208             NR = IWORK( NDIMR+IM1 )
00209             NLF = IC - NL
00210             IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN
00211                SQREI = SQRE
00212             ELSE
00213                SQREI = 1
00214             END IF
00215             IDXQC = IDXQ + NLF - 1
00216             ALPHA = D( IC )
00217             BETA = E( IC )
00218             CALL DLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA,
00219      \$                   U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT,
00220      \$                   IWORK( IDXQC ), IWORK( IWK ), WORK, INFO )
00221             IF( INFO.NE.0 ) THEN
00222                RETURN
00223             END IF
00224    40    CONTINUE
00225    50 CONTINUE
00226 *
00227       RETURN
00228 *
00229 *     End of DLASD0
00230 *
00231       END
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