zgelss.f

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         CALL ZUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNMBR ) = TIMNG( UNMBR ) + ( T2-T1 )
*
*        Generate right bidiagonalizing vectors of R in A
*        (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 )
         OPCNT( UNGBR ) = OPCNT( UNGBR ) +
     $                    DOPLA2( 'ZUNGBR', 'P', N, N, N, 0, NB )
         T1 = DSECND( )
         CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNGBR ) = TIMNG( UNGBR ) + ( T2-T1 )
         IRWORK = IE + N
*
*        Perform bidiagonal QR iteration
*          multiply B by transpose of left singular vectors
*          compute right singular vectors in A
*        (CWorkspace: none)
*        (RWorkspace: need BDSPAC)
*
         OPS = 0
         T1 = DSECND( )
         CALL ZBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
     $                1, B, LDB, RWORK( IRWORK ), INFO )
         T2 = DSECND( )
         TIMNG( BDSQR ) = TIMNG( BDSQR ) + ( T2-T1 )
         OPCNT( BDSQR ) = OPCNT( BDSQR ) + OPS
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO ) THEN
            OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
            THR = MAX( EPS*S( 1 ), SFMIN )
         END IF
         RANK = 0
         DO 10 I = 1, N
            IF( S( I ).GT.THR ) THEN
               OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*NRHS+3 )
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   10    CONTINUE
*
*        Multiply B by right singular vectors
*        (CWorkspace: need N, prefer N*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
            OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                      DOPBL3( 'ZGEMM ', N, NRHS, N )
            T1 = DSECND( )
            CALL ZGEMM( 'C', 'N', N, NRHS, N, CONE, A, LDA, B, LDB,
     $                  CZERO, WORK, LDB )
            T2 = DSECND( )
            TIMNG( GEMM ) = TIMNG( GEMM ) + ( T2-T1 )
            CALL ZLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = LWORK / N
            DO 20 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                         DOPBL3( 'ZGEMM ', N, BL, N )
               T1 = DSECND( )
               CALL ZGEMM( 'C', 'N', N, BL, N, CONE, A, LDA, B( 1, I ),
     $                     LDB, CZERO, WORK, N )
               T2 = DSECND( )
               TIMNG( GEMM ) = TIMNG( GEMM ) + ( T2-T1 )
               CALL ZLACPY( 'G', N, BL, WORK, N, B( 1, I ), LDB )
   20       CONTINUE
         ELSE
            OPCNT( GEMV ) = OPCNT( GEMV ) +
     $                      DOPBL2( 'ZGEMV ', N, N, 0, 0 )
            T1 = DSECND( )
            CALL ZGEMV( 'C', N, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
            T2 = DSECND( )
            TIMNG( GEMV ) = TIMNG( GEMV ) + ( T2-T1 )
            CALL ZCOPY( N, WORK, 1, B, 1 )
         END IF
*
      ELSE IF( N.GE.MNTHR .AND. LWORK.GE.3*M+M*M+MAX( M, NRHS, N-2*M ) )
     $          THEN
*
*        Underdetermined case, M much less than N
*
*        Path 2a - underdetermined, with many more columns than rows
*        and sufficient workspace for an efficient algorithm
*
         LDWORK = M
         IF( LWORK.GE.3*M+M*LDA+MAX( M, NRHS, N-2*M ) )
     $      LDWORK = LDA
         ITAU = 1
         IWORK = M + 1
*
*        Compute A=L*Q
*        (CWorkspace: need 2*M, prefer M+M*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
         OPCNT( GELQF ) = OPCNT( GELQF ) +
     $                    DOPLA( 'ZGELQF', M, N, 0, 0, NB )
         T1 = DSECND( )
         CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( GELQF ) = TIMNG( GELQF ) + ( T2-T1 )
         IL = IWORK
*
*        Copy L to WORK(IL), zeroing out above it
*
         CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK )
         CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, WORK( IL+LDWORK ),
     $                LDWORK )
         IE = 1
         ITAUQ = IL + LDWORK*M
         ITAUP = ITAUQ + M
         IWORK = ITAUP + M
*
*        Bidiagonalize L in WORK(IL)
*        (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
*        (RWorkspace: need M)
*
         NB = ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 )
         OPCNT( GEBRD ) = OPCNT( GEBRD ) +
     $                    DOPLA( 'ZGEBRD', M, M, 0, 0, NB )
         T1 = DSECND( )
         CALL ZGEBRD( M, M, WORK( IL ), LDWORK, S, RWORK( IE ),
     $                WORK( ITAUQ ), WORK( ITAUP ), WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( GEBRD ) = TIMNG( GEBRD ) + ( T2-T1 )
*
*        Multiply B by transpose of left bidiagonalizing vectors of L
*        (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNMBR', 'QLC', M, NRHS, M, -1 )
         OPCNT( UNMBR ) = OPCNT( UNMBR ) +
     $                    DOPLA2( 'ZUNMBR', 'QLC', M, NRHS, M, 0, NB )
         T1 = DSECND( )
         CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, M, WORK( IL ), LDWORK,
     $                WORK( ITAUQ ), B, LDB, WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNMBR ) = TIMNG( UNMBR ) + ( T2-T1 )
*
*        Generate right bidiagonalizing vectors of R in WORK(IL)
*        (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 )
         OPCNT( UNGBR ) = OPCNT( UNGBR ) +
     $                    DOPLA2( 'ZUNGBR', 'P', M, M, M, 0, NB )
         T1 = DSECND( )
         CALL ZUNGBR( 'P', M, M, M, WORK( IL ), LDWORK, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNGBR ) = TIMNG( UNGBR ) + ( T2-T1 )
         IRWORK = IE + M
*
*        Perform bidiagonal QR iteration, computing right singular
*        vectors of L in WORK(IL) and multiplying B by transpose of
*        left singular vectors
*        (CWorkspace: need M*M)
*        (RWorkspace: need BDSPAC)
*
         OPS = 0
         T1 = DSECND( )
         CALL ZBDSQR( 'U', M, M, 0, NRHS, S, RWORK( IE ), WORK( IL ),
     $                LDWORK, A, LDA, B, LDB, RWORK( IRWORK ), INFO )
         T2 = DSECND( )
         TIMNG( BDSQR ) = TIMNG( BDSQR ) + ( T2-T1 )
         OPCNT( BDSQR ) = OPCNT( BDSQR ) + OPS
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO ) THEN
            OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
            THR = MAX( EPS*S( 1 ), SFMIN )
         END IF
         RANK = 0
         DO 30 I = 1, M
            IF( S( I ).GT.THR ) THEN
               OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*NRHS+3 )
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   30    CONTINUE
         IWORK = IL + M*LDWORK
*
*        Multiply B by right singular vectors of L in WORK(IL)
*        (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN
            OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                      DOPBL3( 'ZGEMM ', M, NRHS, M )
            CALL ZGEMM( 'C', 'N', M, NRHS, M, CONE, WORK( IL ), LDWORK,
     $                  B, LDB, CZERO, WORK( IWORK ), LDB )
            CALL ZLACPY( 'G', M, NRHS, WORK( IWORK ), LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = ( LWORK-IWORK+1 ) / M
            DO 40 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                         DOPBL3( 'ZGEMM ', M, BL, M )
               T1 = DSECND( )
               CALL ZGEMM( 'C', 'N', M, BL, M, CONE, WORK( IL ), LDWORK,
     $                     B( 1, I ), LDB, CZERO, WORK( IWORK ), N )
               T2 = DSECND( )
               TIMNG( GEMM ) = TIMNG( GEMM ) + ( T2-T1 )
               CALL ZLACPY( 'G', M, BL, WORK( IWORK ), N, B( 1, I ),
     $                      LDB )
   40       CONTINUE
         ELSE
            OPCNT( GEMV ) = OPCNT( GEMV ) +
     $                      DOPBL2( 'ZGEMV ', M, M, 0, 0 )
            T1 = DSECND( )
            CALL ZGEMV( 'C', M, M, CONE, WORK( IL ), LDWORK, B( 1, 1 ),
     $                  1, CZERO, WORK( IWORK ), 1 )
            T2 = DSECND( )
            TIMNG( GEMV ) = TIMNG( GEMV ) + ( T2-T1 )
            CALL ZCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 )
         END IF
*
*        Zero out below first M rows of B
*
         CALL ZLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB )
         IWORK = ITAU + M
*
*        Multiply transpose(Q) by B
*        (CWorkspace: need M+NRHS, prefer M+NHRS*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNMLQ', 'LC', N, NRHS, M, -1 )
         OPCNT( UNMLQ ) = OPCNT( UNMLQ ) +
     $                    DOPLA( 'ZUNMLQ', N, NRHS, M, 0, NB )
         T1 = DSECND( )
         CALL ZUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, WORK( ITAU ), B,
     $                LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNMLQ ) = TIMNG( UNMLQ ) + ( T2-T1 )
*
      ELSE
*
*        Path 2 - remaining underdetermined cases
*
         IE = 1
         ITAUQ = 1
         ITAUP = ITAUQ + M
         IWORK = ITAUP + M
*
*        Bidiagonalize A
*        (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB)
*        (RWorkspace: need N)
*
         NB = ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 )
         OPCNT( GEBRD ) = OPCNT( GEBRD ) +
     $                    DOPLA( 'ZGEBRD', M, N, 0, 0, NB )
         T1 = DSECND( )
         CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
     $                INFO )
         T2 = DSECND( )
         TIMNG( GEBRD ) = TIMNG( GEBRD ) + ( T2-T1 )
*
*        Multiply B by transpose of left bidiagonalizing vectors
*        (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNMBR', 'QLC', M, NRHS, N, -1 )
         OPCNT( UNMBR ) = OPCNT( UNMBR ) +
     $                    DOPLA2( 'ZUNMBR', 'QLC', M, NRHS, N, 0, NB )
         T1 = DSECND( )
         CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNMBR ) = TIMNG( UNMBR ) + ( T2-T1 )
*
*        Generate right bidiagonalizing vectors in A
*        (CWorkspace: need 3*M, prefer 2*M+M*NB)
*        (RWorkspace: none)
*
         NB = ILAENV( 1, 'ZUNGBR', 'P', M, N, M, -1 )
         OPCNT( UNGBR ) = OPCNT( UNGBR ) +
     $                    DOPLA2( 'ZUNGBR', 'P', M, N, M, 0, NB )
         T1 = DSECND( )
         CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         T2 = DSECND( )
         TIMNG( UNGBR ) = TIMNG( UNGBR ) + ( T2-T1 )
         IRWORK = IE + M
*
*        Perform bidiagonal QR iteration,
*           computing right singular vectors of A in A and
*           multiplying B by transpose of left singular vectors
*        (CWorkspace: none)
*        (RWorkspace: need BDSPAC)
*
         OPS = 0
         T1 = DSECND( )
         CALL ZBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
     $                1, B, LDB, RWORK( IRWORK ), INFO )
         T2 = DSECND( )
         TIMNG( BDSQR ) = TIMNG( BDSQR ) + ( T2-T1 )
         OPCNT( BDSQR ) = OPCNT( BDSQR ) + OPS
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO ) THEN
            OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 1 )
            THR = MAX( EPS*S( 1 ), SFMIN )
         END IF
         RANK = 0
         DO 50 I = 1, M
            IF( S( I ).GT.THR ) THEN
               OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*NRHS+3 )
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   50    CONTINUE
*
*        Multiply B by right singular vectors of A
*        (CWorkspace: need N, prefer N*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
            OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                      DOPBL3( 'ZGEMM ', N, NRHS, M )
            T1 = DSECND( )
            CALL ZGEMM( 'C', 'N', N, NRHS, M, CONE, A, LDA, B, LDB,
     $                  CZERO, WORK, LDB )
            T2 = DSECND( )
            TIMNG( GEMM ) = TIMNG( GEMM ) + ( T2-T1 )
            CALL ZLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = LWORK / N
            DO 60 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               OPCNT( GEMM ) = OPCNT( GEMM ) +
     $                         DOPBL3( 'ZGEMM ', N, BL, N )
               T1 = DSECND( )
               CALL ZGEMM( 'C', 'N', N, BL, M, CONE, A, LDA, B( 1, I ),
     $                     LDB, CZERO, WORK, N )
               T2 = DSECND( )
               TIMNG( GEMM ) = TIMNG( GEMM ) + ( T2-T1 )
               CALL ZLACPY( 'F', N, BL, WORK, N, B( 1, I ), LDB )
   60       CONTINUE
         ELSE
            OPCNT( GELSS ) = OPCNT( GELSS ) +
     $                       DOPBL2( 'ZGEMV ', M, N, 0, 0 )
            T1 = DSECND( )
            CALL ZGEMV( 'C', M, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
            T2 = DSECND( )
            TIMNG( GEMV ) = TIMNG( GEMV ) + ( T2-T1 )
            CALL ZCOPY( N, WORK, 1, B, 1 )
         END IF
      END IF
*
*     Undo scaling
*
      IF( IASCL.EQ.1 ) THEN
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*( N*NRHS+MINMN ) )
         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
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*( N*NRHS+MINMN ) )
         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
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*N*NRHS )
         CALL ZLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
      ELSE IF( IBSCL.EQ.2 ) THEN
         OPCNT( GELSS ) = OPCNT( GELSS ) + DBLE( 6*N*NRHS )
         CALL ZLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
      END IF
   70 CONTINUE
      WORK( 1 ) = MAXWRK
      RETURN
*
*     End of ZGELSS
*
      END