zgelsd.f

          SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
         $                   WORK, LWORK, RWORK, IWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
          DOUBLE PRECISION   RCOND
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   RWORK( * ), S( * )
          COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGELSD computes the minimum-norm solution to a real linear least
    *  squares problem:
    *      minimize 2-norm(| b - A*x |)
    *  using the singular value decomposition (SVD) of A. A is an M-by-N
    *  matrix which may be rank-deficient.
    *
    *  Several right hand side vectors b and solution vectors x can be
    *  handled in a single call; they are stored as the columns of the
    *  M-by-NRHS right hand side matrix B and the N-by-NRHS solution
    *  matrix X.
    *
    *  The problem is solved in three steps:
    *  (1) Reduce the coefficient matrix A to bidiagonal form with
    *      Householder tranformations, reducing the original problem
    *      into a "bidiagonal least squares problem" (BLS)
    *  (2) Solve the BLS using a divide and conquer approach.
    *  (3) Apply back all the Householder tranformations to solve
    *      the original least squares problem.
    *
    *  The effective rank of A is determined by treating as zero those
    *  singular values which are less than RCOND times the largest singular
    *  value.
    *
    *  The divide and conquer algorithm 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.
    *
    *  Arguments
    *  =========
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix A. M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix A. N >= 0.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrices B and X. NRHS >= 0.
    *
    *  A       (input) COMPLEX*16 array, dimension (LDA,N)
    *          On entry, the M-by-N matrix A.
    *          On exit, A has been destroyed.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A. LDA >= max(1,M).
    *
    *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
    *          On entry, the M-by-NRHS right hand side matrix B.
    *          On exit, B is overwritten by the N-by-NRHS solution matrix X.
    *          If m >= n and RANK = n, the residual sum-of-squares for
    *          the solution in the i-th column is given by the sum of
    *          squares of the modulus of elements n+1:m in that column.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,M,N).
    *
    *  S       (output) DOUBLE PRECISION array, dimension (min(M,N))
    *          The singular values of A in decreasing order.
    *          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
    *
    *  RCOND   (input) DOUBLE PRECISION
    *          RCOND is used to determine the effective rank of A.
    *          Singular values S(i) <= RCOND*S(1) are treated as zero.
    *          If RCOND < 0, machine precision is used instead.
    *
    *  RANK    (output) INTEGER
    *          The effective rank of A, i.e., the number of singular values
    *          which are greater than RCOND*S(1).
    *
    *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK. LWORK must be at least 1.
    *          The exact minimum amount of workspace needed depends on M,
    *          N and NRHS. As long as LWORK is at least
    *              2*N + N*NRHS
    *          if M is greater than or equal to N or
    *              2*M + M*NRHS
    *          if M is less than N, the code will execute correctly.
    *          For good performance, LWORK should generally be larger.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the array WORK and the
    *          minimum sizes of the arrays RWORK and IWORK, and returns
    *          these values as the first entries of the WORK, RWORK and
    *          IWORK arrays, and no error message related to LWORK is issued
    *          by XERBLA.
    *
    *  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    *          LRWORK >=
    *              10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
    *             (SMLSIZ+1)**2
    *          if M is greater than or equal to N or
    *             10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
    *             (SMLSIZ+1)**2
    *          if M is less than N, the code will execute correctly.
    *          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), and
    *             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
    *          On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK.
    *
    *  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK))
    *          LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),
    *          where MINMN = MIN( M,N ).
    *          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  the algorithm for computing the SVD failed to converge;
    *                if INFO = i, i off-diagonal elements of an intermediate
    *                bidiagonal form did not converge to zero.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Ming Gu and Ren-Cang Li, Computer Science Division, University of
    *       California at Berkeley, USA
    *     Osni Marques, LBNL/NERSC, USA
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE, TWO
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
          COMPLEX*16         CZERO
          PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY
          INTEGER            IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ,
         $                   LDWORK, LIWORK, LRWORK, MAXMN, MAXWRK, MINMN,
         $                   MINWRK, MM, MNTHR, NLVL, NRWORK, NWORK, SMLSIZ
          DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLABAD, DLASCL, DLASET, XERBLA, ZGEBRD, ZGELQF,
         $                   ZGEQRF, ZLACPY, ZLALSD, ZLASCL, ZLASET, ZUNMBR,
         $                   ZUNMLQ, ZUNMQR
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          DOUBLE PRECISION   DLAMCH, ZLANGE
          EXTERNAL           ILAENV, DLAMCH, ZLANGE
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          INT, LOG, MAX, MIN, DBLE
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments.
    *
          INFO = 0
          MINMN = MIN( M, N )
          MAXMN = MAX( M, N )
          LQUERY = ( LWORK.EQ.-1 )
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, MAXMN ) ) THEN
             INFO = -7
          END IF
    *
    *     Compute workspace.
    *     (Note: Comments in the code beginning "Workspace:" describe the
    *     minimal amount of workspace needed at that point in the code,
    *     as well as the preferred amount for good performance.
    *     NB refers to the optimal block size for the immediately
    *     following subroutine, as returned by ILAENV.)
    *
          IF( INFO.EQ.0 ) THEN
             MINWRK = 1
             MAXWRK = 1
             LIWORK = 1
             LRWORK = 1
             IF( MINMN.GT.0 ) THEN
                SMLSIZ = ILAENV( 9, 'ZGELSD', ' ', 0, 0, 0, 0 )
                MNTHR = ILAENV( 6, 'ZGELSD', ' ', M, N, NRHS, -1 )
                NLVL = MAX( INT( LOG( DBLE( MINMN ) / DBLE( SMLSIZ + 1 ) ) /
         $                  LOG( TWO ) ) + 1, 0 )
                LIWORK = 3*MINMN*NLVL + 11*MINMN
                MM = M
                IF( M.GE.N .AND. M.GE.MNTHR ) THEN
    *
    *              Path 1a - overdetermined, with many more rows than
    *                        columns.
    *
                   MM = N
                   MAXWRK = MAX( MAXWRK, N*ILAENV( 1, 'ZGEQRF', ' ', M, N,
         $                       -1, -1 ) )
                   MAXWRK = MAX( MAXWRK, NRHS*ILAENV( 1, 'ZUNMQR', 'LC', M,
         $                       NRHS, N, -1 ) )
                END IF
                IF( M.GE.N ) THEN
    *
    *              Path 1 - overdetermined or exactly determined.
    *
                   LRWORK = 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
         $                  ( SMLSIZ + 1 )**2
                   MAXWRK = MAX( MAXWRK, 2*N + ( MM + N )*ILAENV( 1,
         $                       'ZGEBRD', ' ', MM, N, -1, -1 ) )
                   MAXWRK = MAX( MAXWRK, 2*N + NRHS*ILAENV( 1, 'ZUNMBR',
         $                       'QLC', MM, NRHS, N, -1 ) )
                   MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1,
         $                       'ZUNMBR', 'PLN', N, NRHS, N, -1 ) )
                   MAXWRK = MAX( MAXWRK, 2*N + N*NRHS )
                   MINWRK = MAX( 2*N + MM, 2*N + N*NRHS )
                END IF
                IF( N.GT.M ) THEN
                   LRWORK = 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
         $                  ( SMLSIZ + 1 )**2
                   IF( N.GE.MNTHR ) THEN
    *
    *                 Path 2a - underdetermined, with many more columns
    *                           than rows.
    *
                      MAXWRK = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1,
         $                     -1 )
                      MAXWRK = MAX( MAXWRK, M*M + 4*M + 2*M*ILAENV( 1,
         $                          'ZGEBRD', ' ', M, M, -1, -1 ) )
                      MAXWRK = MAX( MAXWRK, M*M + 4*M + NRHS*ILAENV( 1,
         $                          'ZUNMBR', 'QLC', M, NRHS, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, M*M + 4*M + ( M - 1 )*ILAENV( 1,
         $                          'ZUNMLQ', 'LC', N, NRHS, M, -1 ) )
                      IF( NRHS.GT.1 ) THEN
                         MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS )
                      ELSE
                         MAXWRK = MAX( MAXWRK, M*M + 2*M )
                      END IF
                      MAXWRK = MAX( MAXWRK, M*M + 4*M + M*NRHS )
                   ELSE
    *
    *                 Path 2 - underdetermined.
    *
                      MAXWRK = 2*M + ( N + M )*ILAENV( 1, 'ZGEBRD', ' ', M,
         $                     N, -1, -1 )
                      MAXWRK = MAX( MAXWRK, 2*M + NRHS*ILAENV( 1, 'ZUNMBR',
         $                          'QLC', M, NRHS, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M + M*ILAENV( 1, 'ZUNMBR',
         $                          'PLN', N, NRHS, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M + M*NRHS )
                   END IF
                   MINWRK = MAX( 2*M + N, 2*M + M*NRHS )
                END IF
             END IF
             MINWRK = MIN( MINWRK, MAXWRK )
             WORK( 1 ) = MAXWRK
             IWORK( 1 ) = LIWORK
             RWORK( 1 ) = LRWORK
    *
             IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                INFO = -12
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGELSD', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF( M.EQ.0 .OR. N.EQ.0 ) THEN
             RANK = 0
             RETURN
          END IF
    *
    *     Get machine parameters.
    *
          EPS = DLAMCH( 'P' )
          SFMIN = DLAMCH( 'S' )
          SMLNUM = SFMIN / EPS
          BIGNUM = ONE / SMLNUM
          CALL DLABAD( SMLNUM, BIGNUM )
    *
    *     Scale A if max entry outside range [SMLNUM,BIGNUM].
    *
          ANRM = ZLANGE( 'M', M, N, A, LDA, RWORK )
          IASCL = 0
          IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
    *
    *        Scale matrix norm up to SMLNUM
    *
             CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
             IASCL = 1
          ELSE IF( ANRM.GT.BIGNUM ) THEN
    *
    *        Scale matrix norm down to BIGNUM.
    *
             CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
             IASCL = 2
          ELSE IF( ANRM.EQ.ZERO ) THEN
    *
    *        Matrix all zero. Return zero solution.
    *
             CALL ZLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB )
             CALL DLASET( 'F', MINMN, 1, ZERO, ZERO, S, 1 )
             RANK = 0
             GO TO 10
          END IF
    *
    *     Scale B if max entry outside range [SMLNUM,BIGNUM].
    *
          BNRM = ZLANGE( 'M', M, NRHS, B, LDB, RWORK )
          IBSCL = 0
          IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
    *
    *        Scale matrix norm up to SMLNUM.
    *
             CALL ZLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
             IBSCL = 1
          ELSE IF( BNRM.GT.BIGNUM ) THEN
    *
    *        Scale matrix norm down to BIGNUM.
    *
             CALL ZLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
             IBSCL = 2
          END IF
    *
    *     If M < N make sure B(M+1:N,:) = 0
    *
          IF( M.LT.N )
         $   CALL ZLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB )
    *
    *     Overdetermined case.
    *
          IF( M.GE.N ) THEN
    *
    *        Path 1 - overdetermined or exactly determined.
    *
             MM = M
             IF( M.GE.MNTHR ) THEN
    *
    *           Path 1a - overdetermined, with many more rows than columns
    *
                MM = N
                ITAU = 1
                NWORK = ITAU + N
    *
    *           Compute A=Q*R.
    *           (RWorkspace: need N)
    *           (CWorkspace: need N, prefer N*NB)
    *
                CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                   LWORK-NWORK+1, INFO )
    *
    *           Multiply B by transpose(Q).
    *           (RWorkspace: need N)
    *           (CWorkspace: need NRHS, prefer NRHS*NB)
    *
                CALL ZUNMQR( 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAU ), B,
         $                   LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
    *           Zero out below R.
    *
                IF( N.GT.1 ) THEN
                   CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
         $                      LDA )
                END IF
             END IF
    *
             ITAUQ = 1
             ITAUP = ITAUQ + N
             NWORK = ITAUP + N
             IE = 1
             NRWORK = IE + N
    *
    *        Bidiagonalize R in A.
    *        (RWorkspace: need N)
    *        (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB)
    *
             CALL ZGEBRD( MM, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                INFO )
    *
    *        Multiply B by transpose of left bidiagonalizing vectors of R.
    *        (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB)
    *
             CALL ZUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, WORK( ITAUQ ),
         $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
    *        Solve the bidiagonal least squares problem.
    *
             CALL ZLALSD( 'U', SMLSIZ, N, NRHS, S, RWORK( IE ), B, LDB,
         $                RCOND, RANK, WORK( NWORK ), RWORK( NRWORK ),
         $                IWORK, INFO )
             IF( INFO.NE.0 ) THEN
                GO TO 10
             END IF
    *
    *        Multiply B by right bidiagonalizing vectors of R.
    *
             CALL ZUNMBR( 'P', 'L', 'N', N, NRHS, N, A, LDA, WORK( ITAUP ),
         $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
          ELSE IF( N.GE.MNTHR .AND. LWORK.GE.4*M+M*M+
         $         MAX( M, 2*M-4, NRHS, N-3*M ) ) THEN
    *
    *        Path 2a - underdetermined, with many more columns than rows
    *        and sufficient workspace for an efficient algorithm.
    *
             LDWORK = M
             IF( LWORK.GE.MAX( 4*M+M*LDA+MAX( M, 2*M-4, NRHS, N-3*M ),
         $       M*LDA+M+M*NRHS ) )LDWORK = LDA
             ITAU = 1
             NWORK = M + 1
    *
    *        Compute A=L*Q.
    *        (CWorkspace: need 2*M, prefer M+M*NB)
    *
             CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                LWORK-NWORK+1, INFO )
             IL = NWORK
    *
    *        Copy L to WORK(IL), zeroing out above its diagonal.
    *
             CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK )
             CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, WORK( IL+LDWORK ),
         $                LDWORK )
             ITAUQ = IL + LDWORK*M
             ITAUP = ITAUQ + M
             NWORK = ITAUP + M
             IE = 1
             NRWORK = IE + M
    *
    *        Bidiagonalize L in WORK(IL).
    *        (RWorkspace: need M)
    *        (CWorkspace: need M*M+4*M, prefer M*M+4*M+2*M*NB)
    *
             CALL ZGEBRD( M, M, WORK( IL ), LDWORK, S, RWORK( IE ),
         $                WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
         $                LWORK-NWORK+1, INFO )
    *
    *        Multiply B by transpose of left bidiagonalizing vectors of L.
    *        (CWorkspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB)
    *
             CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, M, WORK( IL ), LDWORK,
         $                WORK( ITAUQ ), B, LDB, WORK( NWORK ),
         $                LWORK-NWORK+1, INFO )
    *
    *        Solve the bidiagonal least squares problem.
    *
             CALL ZLALSD( 'U', SMLSIZ, M, NRHS, S, RWORK( IE ), B, LDB,
         $                RCOND, RANK, WORK( NWORK ), RWORK( NRWORK ),
         $                IWORK, INFO )
             IF( INFO.NE.0 ) THEN
                GO TO 10
             END IF
    *
    *        Multiply B by right bidiagonalizing vectors of L.
    *
             CALL ZUNMBR( 'P', 'L', 'N', M, NRHS, M, WORK( IL ), LDWORK,
         $                WORK( ITAUP ), B, LDB, WORK( NWORK ),
         $                LWORK-NWORK+1, INFO )
    *
    *        Zero out below first M rows of B.
    *
             CALL ZLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB )
             NWORK = ITAU + M
    *
    *        Multiply transpose(Q) by B.
    *        (CWorkspace: need NRHS, prefer NRHS*NB)
    *
             CALL ZUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, WORK( ITAU ), B,
         $                LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
          ELSE
    *
    *        Path 2 - remaining underdetermined cases.
    *
             ITAUQ = 1
             ITAUP = ITAUQ + M
             NWORK = ITAUP + M
             IE = 1
             NRWORK = IE + M
    *
    *        Bidiagonalize A.
    *        (RWorkspace: need M)
    *        (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
    *
             CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                INFO )
    *
    *        Multiply B by transpose of left bidiagonalizing vectors.
    *        (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB)
    *
             CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAUQ ),
         $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
    *        Solve the bidiagonal least squares problem.
    *
             CALL ZLALSD( 'L', SMLSIZ, M, NRHS, S, RWORK( IE ), B, LDB,
         $                RCOND, RANK, WORK( NWORK ), RWORK( NRWORK ),
         $                IWORK, INFO )
             IF( INFO.NE.0 ) THEN
                GO TO 10
             END IF
    *
    *        Multiply B by right bidiagonalizing vectors of A.
    *
             CALL ZUNMBR( 'P', 'L', 'N', N, NRHS, M, A, LDA, WORK( ITAUP ),
         $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
    *
          END IF
    *
    *     Undo scaling.
    *
          IF( IASCL.EQ.1 ) THEN
             CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
             CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
         $                INFO )
          ELSE IF( IASCL.EQ.2 ) THEN
             CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
             CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
         $                INFO )
          END IF
          IF( IBSCL.EQ.1 ) THEN
             CALL ZLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
          ELSE IF( IBSCL.EQ.2 ) THEN
             CALL ZLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
          END IF
    *
       10 CONTINUE
          WORK( 1 ) = MAXWRK
          IWORK( 1 ) = LIWORK
          RWORK( 1 ) = LRWORK
          RETURN
    *
    *     End of ZGELSD
    *
          END