*> \brief <b> ZGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZGELSD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelsd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelsd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelsd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, RWORK, IWORK, INFO )
*
* .. 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( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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 transformations, 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 transformations 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrices B and X. NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit, A has been destroyed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M,N).
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is 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)).
*> \endverbatim
*>
*> \param[in] RCOND
*> \verbatim
*> RCOND is 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.
*> \endverbatim
*>
*> \param[out] RANK
*> \verbatim
*> RANK is INTEGER
*> The effective rank of A, i.e., the number of singular values
*> which are greater than RCOND*S(1).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is 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.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
*> LRWORK >=
*> 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
*> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
*> if M is greater than or equal to N or
*> 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
*> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
*> 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.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is 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.
*> \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 for computing the SVD failed to converge;
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2017
*
*> \ingroup complex16GEsolve
*
*> \par Contributors:
* ==================
*>
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
*> California at Berkeley, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*
* =====================================================================
SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
$ WORK, LWORK, RWORK, IWORK, INFO )
*
* -- LAPACK driver routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. 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( * )
* ..
*
* =====================================================================
*
* .. 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 +
$ MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
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 +
$ MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
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 )
! XXX: Ensure the Path 2a case below is triggered. The workspace
! calculation should use queries for all routines eventually.
MAXWRK = MAX( MAXWRK,
$ 4*M+M*M+MAX( M, 2*M-4, NRHS, N-3*M ) )
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