LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlasda.f
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00001 *> \brief \b DLASDA
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLASDA + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasda.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasda.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasda.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
00022 *                          DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
00023 *                          PERM, GIVNUM, C, S, WORK, IWORK, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       INTEGER            ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       INTEGER            GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
00030 *      $                   K( * ), PERM( LDGCOL, * )
00031 *       DOUBLE PRECISION   C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ),
00032 *      $                   E( * ), GIVNUM( LDU, * ), POLES( LDU, * ),
00033 *      $                   S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ),
00034 *      $                   Z( LDU, * )
00035 *       ..
00036 *  
00037 *
00038 *> \par Purpose:
00039 *  =============
00040 *>
00041 *> \verbatim
00042 *>
00043 *> Using a divide and conquer approach, DLASDA computes the singular
00044 *> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
00045 *> B with diagonal D and offdiagonal E, where M = N + SQRE. The
00046 *> algorithm computes the singular values in the SVD B = U * S * VT.
00047 *> The orthogonal matrices U and VT are optionally computed in
00048 *> compact form.
00049 *>
00050 *> A related subroutine, DLASD0, computes the singular values and
00051 *> the singular vectors in explicit form.
00052 *> \endverbatim
00053 *
00054 *  Arguments:
00055 *  ==========
00056 *
00057 *> \param[in] ICOMPQ
00058 *> \verbatim
00059 *>          ICOMPQ is INTEGER
00060 *>         Specifies whether singular vectors are to be computed
00061 *>         in compact form, as follows
00062 *>         = 0: Compute singular values only.
00063 *>         = 1: Compute singular vectors of upper bidiagonal
00064 *>              matrix in compact form.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] SMLSIZ
00068 *> \verbatim
00069 *>          SMLSIZ is INTEGER
00070 *>         The maximum size of the subproblems at the bottom of the
00071 *>         computation tree.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] N
00075 *> \verbatim
00076 *>          N is INTEGER
00077 *>         The row dimension of the upper bidiagonal matrix. This is
00078 *>         also the dimension of the main diagonal array D.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] SQRE
00082 *> \verbatim
00083 *>          SQRE is INTEGER
00084 *>         Specifies the column dimension of the bidiagonal matrix.
00085 *>         = 0: The bidiagonal matrix has column dimension M = N;
00086 *>         = 1: The bidiagonal matrix has column dimension M = N + 1.
00087 *> \endverbatim
00088 *>
00089 *> \param[in,out] D
00090 *> \verbatim
00091 *>          D is DOUBLE PRECISION array, dimension ( N )
00092 *>         On entry D contains the main diagonal of the bidiagonal
00093 *>         matrix. On exit D, if INFO = 0, contains its singular values.
00094 *> \endverbatim
00095 *>
00096 *> \param[in] E
00097 *> \verbatim
00098 *>          E is DOUBLE PRECISION array, dimension ( M-1 )
00099 *>         Contains the subdiagonal entries of the bidiagonal matrix.
00100 *>         On exit, E has been destroyed.
00101 *> \endverbatim
00102 *>
00103 *> \param[out] U
00104 *> \verbatim
00105 *>          U is DOUBLE PRECISION array,
00106 *>         dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
00107 *>         if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
00108 *>         singular vector matrices of all subproblems at the bottom
00109 *>         level.
00110 *> \endverbatim
00111 *>
00112 *> \param[in] LDU
00113 *> \verbatim
00114 *>          LDU is INTEGER, LDU = > N.
00115 *>         The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
00116 *>         GIVNUM, and Z.
00117 *> \endverbatim
00118 *>
00119 *> \param[out] VT
00120 *> \verbatim
00121 *>          VT is DOUBLE PRECISION array,
00122 *>         dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
00123 *>         if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
00124 *>         singular vector matrices of all subproblems at the bottom
00125 *>         level.
00126 *> \endverbatim
00127 *>
00128 *> \param[out] K
00129 *> \verbatim
00130 *>          K is INTEGER array,
00131 *>         dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
00132 *>         If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
00133 *>         secular equation on the computation tree.
00134 *> \endverbatim
00135 *>
00136 *> \param[out] DIFL
00137 *> \verbatim
00138 *>          DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
00139 *>         where NLVL = floor(log_2 (N/SMLSIZ))).
00140 *> \endverbatim
00141 *>
00142 *> \param[out] DIFR
00143 *> \verbatim
00144 *>          DIFR is DOUBLE PRECISION array,
00145 *>                  dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
00146 *>                  dimension ( N ) if ICOMPQ = 0.
00147 *>         If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
00148 *>         record distances between singular values on the I-th
00149 *>         level and singular values on the (I -1)-th level, and
00150 *>         DIFR(1:N, 2 * I ) contains the normalizing factors for
00151 *>         the right singular vector matrix. See DLASD8 for details.
00152 *> \endverbatim
00153 *>
00154 *> \param[out] Z
00155 *> \verbatim
00156 *>          Z is DOUBLE PRECISION array,
00157 *>                  dimension ( LDU, NLVL ) if ICOMPQ = 1 and
00158 *>                  dimension ( N ) if ICOMPQ = 0.
00159 *>         The first K elements of Z(1, I) contain the components of
00160 *>         the deflation-adjusted updating row vector for subproblems
00161 *>         on the I-th level.
00162 *> \endverbatim
00163 *>
00164 *> \param[out] POLES
00165 *> \verbatim
00166 *>          POLES is DOUBLE PRECISION array,
00167 *>         dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
00168 *>         if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
00169 *>         POLES(1, 2*I) contain  the new and old singular values
00170 *>         involved in the secular equations on the I-th level.
00171 *> \endverbatim
00172 *>
00173 *> \param[out] GIVPTR
00174 *> \verbatim
00175 *>          GIVPTR is INTEGER array,
00176 *>         dimension ( N ) if ICOMPQ = 1, and not referenced if
00177 *>         ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
00178 *>         the number of Givens rotations performed on the I-th
00179 *>         problem on the computation tree.
00180 *> \endverbatim
00181 *>
00182 *> \param[out] GIVCOL
00183 *> \verbatim
00184 *>          GIVCOL is INTEGER array,
00185 *>         dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
00186 *>         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
00187 *>         GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
00188 *>         of Givens rotations performed on the I-th level on the
00189 *>         computation tree.
00190 *> \endverbatim
00191 *>
00192 *> \param[in] LDGCOL
00193 *> \verbatim
00194 *>          LDGCOL is INTEGER, LDGCOL = > N.
00195 *>         The leading dimension of arrays GIVCOL and PERM.
00196 *> \endverbatim
00197 *>
00198 *> \param[out] PERM
00199 *> \verbatim
00200 *>          PERM is INTEGER array,
00201 *>         dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
00202 *>         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
00203 *>         permutations done on the I-th level of the computation tree.
00204 *> \endverbatim
00205 *>
00206 *> \param[out] GIVNUM
00207 *> \verbatim
00208 *>          GIVNUM is DOUBLE PRECISION array,
00209 *>         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
00210 *>         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
00211 *>         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
00212 *>         values of Givens rotations performed on the I-th level on
00213 *>         the computation tree.
00214 *> \endverbatim
00215 *>
00216 *> \param[out] C
00217 *> \verbatim
00218 *>          C is DOUBLE PRECISION array,
00219 *>         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
00220 *>         If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
00221 *>         C( I ) contains the C-value of a Givens rotation related to
00222 *>         the right null space of the I-th subproblem.
00223 *> \endverbatim
00224 *>
00225 *> \param[out] S
00226 *> \verbatim
00227 *>          S is DOUBLE PRECISION array, dimension ( N ) if
00228 *>         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
00229 *>         and the I-th subproblem is not square, on exit, S( I )
00230 *>         contains the S-value of a Givens rotation related to
00231 *>         the right null space of the I-th subproblem.
00232 *> \endverbatim
00233 *>
00234 *> \param[out] WORK
00235 *> \verbatim
00236 *>          WORK is DOUBLE PRECISION array, dimension
00237 *>         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
00238 *> \endverbatim
00239 *>
00240 *> \param[out] IWORK
00241 *> \verbatim
00242 *>          IWORK is INTEGER array.
00243 *>         Dimension must be at least (7 * N).
00244 *> \endverbatim
00245 *>
00246 *> \param[out] INFO
00247 *> \verbatim
00248 *>          INFO is INTEGER
00249 *>          = 0:  successful exit.
00250 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00251 *>          > 0:  if INFO = 1, a singular value did not converge
00252 *> \endverbatim
00253 *
00254 *  Authors:
00255 *  ========
00256 *
00257 *> \author Univ. of Tennessee 
00258 *> \author Univ. of California Berkeley 
00259 *> \author Univ. of Colorado Denver 
00260 *> \author NAG Ltd. 
00261 *
00262 *> \date November 2011
00263 *
00264 *> \ingroup auxOTHERauxiliary
00265 *
00266 *> \par Contributors:
00267 *  ==================
00268 *>
00269 *>     Ming Gu and Huan Ren, Computer Science Division, University of
00270 *>     California at Berkeley, USA
00271 *>
00272 *  =====================================================================
00273       SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
00274      $                   DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
00275      $                   PERM, GIVNUM, C, S, WORK, IWORK, INFO )
00276 *
00277 *  -- LAPACK auxiliary routine (version 3.4.0) --
00278 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00279 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00280 *     November 2011
00281 *
00282 *     .. Scalar Arguments ..
00283       INTEGER            ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
00284 *     ..
00285 *     .. Array Arguments ..
00286       INTEGER            GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
00287      $                   K( * ), PERM( LDGCOL, * )
00288       DOUBLE PRECISION   C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ),
00289      $                   E( * ), GIVNUM( LDU, * ), POLES( LDU, * ),
00290      $                   S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ),
00291      $                   Z( LDU, * )
00292 *     ..
00293 *
00294 *  =====================================================================
00295 *
00296 *     .. Parameters ..
00297       DOUBLE PRECISION   ZERO, ONE
00298       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00299 *     ..
00300 *     .. Local Scalars ..
00301       INTEGER            I, I1, IC, IDXQ, IDXQI, IM1, INODE, ITEMP, IWK,
00302      $                   J, LF, LL, LVL, LVL2, M, NCC, ND, NDB1, NDIML,
00303      $                   NDIMR, NL, NLF, NLP1, NLVL, NR, NRF, NRP1, NRU,
00304      $                   NWORK1, NWORK2, SMLSZP, SQREI, VF, VFI, VL, VLI
00305       DOUBLE PRECISION   ALPHA, BETA
00306 *     ..
00307 *     .. External Subroutines ..
00308       EXTERNAL           DCOPY, DLASD6, DLASDQ, DLASDT, DLASET, XERBLA
00309 *     ..
00310 *     .. Executable Statements ..
00311 *
00312 *     Test the input parameters.
00313 *
00314       INFO = 0
00315 *
00316       IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
00317          INFO = -1
00318       ELSE IF( SMLSIZ.LT.3 ) THEN
00319          INFO = -2
00320       ELSE IF( N.LT.0 ) THEN
00321          INFO = -3
00322       ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
00323          INFO = -4
00324       ELSE IF( LDU.LT.( N+SQRE ) ) THEN
00325          INFO = -8
00326       ELSE IF( LDGCOL.LT.N ) THEN
00327          INFO = -17
00328       END IF
00329       IF( INFO.NE.0 ) THEN
00330          CALL XERBLA( 'DLASDA', -INFO )
00331          RETURN
00332       END IF
00333 *
00334       M = N + SQRE
00335 *
00336 *     If the input matrix is too small, call DLASDQ to find the SVD.
00337 *
00338       IF( N.LE.SMLSIZ ) THEN
00339          IF( ICOMPQ.EQ.0 ) THEN
00340             CALL DLASDQ( 'U', SQRE, N, 0, 0, 0, D, E, VT, LDU, U, LDU,
00341      $                   U, LDU, WORK, INFO )
00342          ELSE
00343             CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDU, U, LDU,
00344      $                   U, LDU, WORK, INFO )
00345          END IF
00346          RETURN
00347       END IF
00348 *
00349 *     Book-keeping and  set up the computation tree.
00350 *
00351       INODE = 1
00352       NDIML = INODE + N
00353       NDIMR = NDIML + N
00354       IDXQ = NDIMR + N
00355       IWK = IDXQ + N
00356 *
00357       NCC = 0
00358       NRU = 0
00359 *
00360       SMLSZP = SMLSIZ + 1
00361       VF = 1
00362       VL = VF + M
00363       NWORK1 = VL + M
00364       NWORK2 = NWORK1 + SMLSZP*SMLSZP
00365 *
00366       CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
00367      $             IWORK( NDIMR ), SMLSIZ )
00368 *
00369 *     for the nodes on bottom level of the tree, solve
00370 *     their subproblems by DLASDQ.
00371 *
00372       NDB1 = ( ND+1 ) / 2
00373       DO 30 I = NDB1, ND
00374 *
00375 *        IC : center row of each node
00376 *        NL : number of rows of left  subproblem
00377 *        NR : number of rows of right subproblem
00378 *        NLF: starting row of the left   subproblem
00379 *        NRF: starting row of the right  subproblem
00380 *
00381          I1 = I - 1
00382          IC = IWORK( INODE+I1 )
00383          NL = IWORK( NDIML+I1 )
00384          NLP1 = NL + 1
00385          NR = IWORK( NDIMR+I1 )
00386          NLF = IC - NL
00387          NRF = IC + 1
00388          IDXQI = IDXQ + NLF - 2
00389          VFI = VF + NLF - 1
00390          VLI = VL + NLF - 1
00391          SQREI = 1
00392          IF( ICOMPQ.EQ.0 ) THEN
00393             CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, WORK( NWORK1 ),
00394      $                   SMLSZP )
00395             CALL DLASDQ( 'U', SQREI, NL, NLP1, NRU, NCC, D( NLF ),
00396      $                   E( NLF ), WORK( NWORK1 ), SMLSZP,
00397      $                   WORK( NWORK2 ), NL, WORK( NWORK2 ), NL,
00398      $                   WORK( NWORK2 ), INFO )
00399             ITEMP = NWORK1 + NL*SMLSZP
00400             CALL DCOPY( NLP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 )
00401             CALL DCOPY( NLP1, WORK( ITEMP ), 1, WORK( VLI ), 1 )
00402          ELSE
00403             CALL DLASET( 'A', NL, NL, ZERO, ONE, U( NLF, 1 ), LDU )
00404             CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, VT( NLF, 1 ), LDU )
00405             CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ),
00406      $                   E( NLF ), VT( NLF, 1 ), LDU, U( NLF, 1 ), LDU,
00407      $                   U( NLF, 1 ), LDU, WORK( NWORK1 ), INFO )
00408             CALL DCOPY( NLP1, VT( NLF, 1 ), 1, WORK( VFI ), 1 )
00409             CALL DCOPY( NLP1, VT( NLF, NLP1 ), 1, WORK( VLI ), 1 )
00410          END IF
00411          IF( INFO.NE.0 ) THEN
00412             RETURN
00413          END IF
00414          DO 10 J = 1, NL
00415             IWORK( IDXQI+J ) = J
00416    10    CONTINUE
00417          IF( ( I.EQ.ND ) .AND. ( SQRE.EQ.0 ) ) THEN
00418             SQREI = 0
00419          ELSE
00420             SQREI = 1
00421          END IF
00422          IDXQI = IDXQI + NLP1
00423          VFI = VFI + NLP1
00424          VLI = VLI + NLP1
00425          NRP1 = NR + SQREI
00426          IF( ICOMPQ.EQ.0 ) THEN
00427             CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, WORK( NWORK1 ),
00428      $                   SMLSZP )
00429             CALL DLASDQ( 'U', SQREI, NR, NRP1, NRU, NCC, D( NRF ),
00430      $                   E( NRF ), WORK( NWORK1 ), SMLSZP,
00431      $                   WORK( NWORK2 ), NR, WORK( NWORK2 ), NR,
00432      $                   WORK( NWORK2 ), INFO )
00433             ITEMP = NWORK1 + ( NRP1-1 )*SMLSZP
00434             CALL DCOPY( NRP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 )
00435             CALL DCOPY( NRP1, WORK( ITEMP ), 1, WORK( VLI ), 1 )
00436          ELSE
00437             CALL DLASET( 'A', NR, NR, ZERO, ONE, U( NRF, 1 ), LDU )
00438             CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, VT( NRF, 1 ), LDU )
00439             CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ),
00440      $                   E( NRF ), VT( NRF, 1 ), LDU, U( NRF, 1 ), LDU,
00441      $                   U( NRF, 1 ), LDU, WORK( NWORK1 ), INFO )
00442             CALL DCOPY( NRP1, VT( NRF, 1 ), 1, WORK( VFI ), 1 )
00443             CALL DCOPY( NRP1, VT( NRF, NRP1 ), 1, WORK( VLI ), 1 )
00444          END IF
00445          IF( INFO.NE.0 ) THEN
00446             RETURN
00447          END IF
00448          DO 20 J = 1, NR
00449             IWORK( IDXQI+J ) = J
00450    20    CONTINUE
00451    30 CONTINUE
00452 *
00453 *     Now conquer each subproblem bottom-up.
00454 *
00455       J = 2**NLVL
00456       DO 50 LVL = NLVL, 1, -1
00457          LVL2 = LVL*2 - 1
00458 *
00459 *        Find the first node LF and last node LL on
00460 *        the current level LVL.
00461 *
00462          IF( LVL.EQ.1 ) THEN
00463             LF = 1
00464             LL = 1
00465          ELSE
00466             LF = 2**( LVL-1 )
00467             LL = 2*LF - 1
00468          END IF
00469          DO 40 I = LF, LL
00470             IM1 = I - 1
00471             IC = IWORK( INODE+IM1 )
00472             NL = IWORK( NDIML+IM1 )
00473             NR = IWORK( NDIMR+IM1 )
00474             NLF = IC - NL
00475             NRF = IC + 1
00476             IF( I.EQ.LL ) THEN
00477                SQREI = SQRE
00478             ELSE
00479                SQREI = 1
00480             END IF
00481             VFI = VF + NLF - 1
00482             VLI = VL + NLF - 1
00483             IDXQI = IDXQ + NLF - 1
00484             ALPHA = D( IC )
00485             BETA = E( IC )
00486             IF( ICOMPQ.EQ.0 ) THEN
00487                CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ),
00488      $                      WORK( VFI ), WORK( VLI ), ALPHA, BETA,
00489      $                      IWORK( IDXQI ), PERM, GIVPTR( 1 ), GIVCOL,
00490      $                      LDGCOL, GIVNUM, LDU, POLES, DIFL, DIFR, Z,
00491      $                      K( 1 ), C( 1 ), S( 1 ), WORK( NWORK1 ),
00492      $                      IWORK( IWK ), INFO )
00493             ELSE
00494                J = J - 1
00495                CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ),
00496      $                      WORK( VFI ), WORK( VLI ), ALPHA, BETA,
00497      $                      IWORK( IDXQI ), PERM( NLF, LVL ),
00498      $                      GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL,
00499      $                      GIVNUM( NLF, LVL2 ), LDU,
00500      $                      POLES( NLF, LVL2 ), DIFL( NLF, LVL ),
00501      $                      DIFR( NLF, LVL2 ), Z( NLF, LVL ), K( J ),
00502      $                      C( J ), S( J ), WORK( NWORK1 ),
00503      $                      IWORK( IWK ), INFO )
00504             END IF
00505             IF( INFO.NE.0 ) THEN
00506                RETURN
00507             END IF
00508    40    CONTINUE
00509    50 CONTINUE
00510 *
00511       RETURN
00512 *
00513 *     End of DLASDA
00514 *
00515       END
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