zgesdd.f

famous linear algebra library (LAPACK) ports to windows

*              (Rworkspace: 0)
*
               CALL ZLACPY( 'L', M, N, A, LDA, U, LDU )
               CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
     $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
*
*              Perform bidiagonal SVD, computing left singular vectors
*              of bidiagonal matrix in RWORK(IRU) and computing right
*              singular vectors of bidiagonal matrix in RWORK(IRVT)
*              (CWorkspace: need 0)
*              (RWorkspace: need BDSPAC)
*
               IRU = NRWORK
               IRVT = IRU + N*N
               NRWORK = IRVT + N*N
               CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
     $                      N, RWORK( IRVT ), N, DUM, IDUM,
     $                      RWORK( NRWORK ), IWORK, INFO )
*
*              Multiply real matrix RWORK(IRVT) by P**H in VT,
*              storing the result in A, copying to VT
*              (Cworkspace: need 0)
*              (Rworkspace: need 3*N*N)
*
               CALL ZLARCM( N, N, RWORK( IRVT ), N, VT, LDVT, A, LDA,
     $                      RWORK( NRWORK ) )
               CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT )
*
*              Multiply Q in U by real matrix RWORK(IRU), storing the
*              result in A, copying to U
*              (CWorkspace: 0)
*              (Rworkspace: need 3*N*N)
*
               NRWORK = IRVT
               CALL ZLACRM( M, N, U, LDU, RWORK( IRU ), N, A, LDA,
     $                      RWORK( NRWORK ) )
               CALL ZLACPY( 'F', M, N, A, LDA, U, LDU )
            END IF
*
         ELSE
*
*           M .LT. MNTHR2
*
*           Path 6 (M at least N, but not much larger)
*           Reduce to bidiagonal form without QR decomposition
*           Use ZUNMBR to compute singular vectors
*
            IE = 1
            NRWORK = IE + N
            ITAUQ = 1
            ITAUP = ITAUQ + N
            NWORK = ITAUP + N
*
*           Bidiagonalize A
*           (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
*           (RWorkspace: need N)
*
            CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                   WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
     $                   IERR )
            IF( WNTQN ) THEN
*
*              Compute singular values only
*              (Cworkspace: 0)
*              (Rworkspace: need BDSPAN)
*
               CALL DBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
     $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
            ELSE IF( WNTQO ) THEN
               IU = NWORK
               IRU = NRWORK
               IRVT = IRU + N*N
               NRWORK = IRVT + N*N
               IF( LWORK.GE.M*N+3*N ) THEN
*
*                 WORK( IU ) is M by N
*
                  LDWRKU = M
               ELSE
*
*                 WORK( IU ) is LDWRKU by N
*
                  LDWRKU = ( LWORK-3*N ) / N
               END IF
               NWORK = IU + LDWRKU*N
*
*              Perform bidiagonal SVD, computing left singular vectors
*              of bidiagonal matrix in RWORK(IRU) and computing right
*              singular vectors of bidiagonal matrix in RWORK(IRVT)
*              (CWorkspace: need 0)
*              (RWorkspace: need BDSPAC)
*
               CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
     $                      N, RWORK( IRVT ), N, DUM, IDUM,
     $                      RWORK( NRWORK ), IWORK, INFO )
*
*              Copy real matrix RWORK(IRVT) to complex matrix VT
*              Overwrite VT by right singular vectors of A
*              (Cworkspace: need 2*N, prefer N+N*NB)
*              (Rworkspace: need 0)
*
               CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
               CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
     $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
*
               IF( LWORK.GE.M*N+3*N ) THEN
*
*              Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
*              Overwrite WORK(IU) by left singular vectors of A, copying
*              to A
*              (Cworkspace: need M*N+2*N, prefer M*N+N+N*NB)
*              (Rworkspace: need 0)
*
                  CALL ZLASET( 'F', M, N, CZERO, CZERO, WORK( IU ),
     $                         LDWRKU )
                  CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, WORK( IU ),
     $                         LDWRKU )
                  CALL ZUNMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
     $                         WORK( ITAUQ ), WORK( IU ), LDWRKU,
     $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
                  CALL ZLACPY( 'F', M, N, WORK( IU ), LDWRKU, A, LDA )
               ELSE
*
*                 Generate Q in A
*                 (Cworkspace: need 2*N, prefer N+N*NB)
*                 (Rworkspace: need 0)
*
                  CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
     $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
*
*                 Multiply Q in A by real matrix RWORK(IRU), storing the
*                 result in WORK(IU), copying to A
*                 (CWorkspace: need N*N, prefer M*N)
*                 (Rworkspace: need 3*N*N, prefer N*N+2*M*N)
*
                  NRWORK = IRVT
                  DO 30 I = 1, M, LDWRKU
                     CHUNK = MIN( M-I+1, LDWRKU )
                     CALL ZLACRM( CHUNK, N, A( I, 1 ), LDA,
     $                            RWORK( IRU ), N, WORK( IU ), LDWRKU,
     $                            RWORK( NRWORK ) )
                     CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU,
     $                            A( I, 1 ), LDA )
   30             CONTINUE
               END IF
*
            ELSE IF( WNTQS ) THEN
*
*              Perform bidiagonal SVD, computing left singular vectors
*              of bidiagonal matrix in RWORK(IRU) and computing right
*              singular vectors of bidiagonal matrix in RWORK(IRVT)
*              (CWorkspace: need 0)
*              (RWorkspace: need BDSPAC)
*
               IRU = NRWORK
               IRVT = IRU + N*N
               NRWORK = IRVT + N*N
               CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
     $                      N, RWORK( IRVT ), N, DUM, IDUM,
     $                      RWORK( NRWORK ), IWORK, INFO )
*
*              Copy real matrix RWORK(IRU) to complex matrix U
*              Overwrite U by left singular vectors of A
*              (CWorkspace: need 3*N, prefer 2*N+N*NB)
*              (RWorkspace: 0)
*
               CALL ZLASET( 'F', M, N, CZERO, CZERO, U, LDU )
               CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, U, LDU )
               CALL ZUNMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
     $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
*
*              Copy real matrix RWORK(IRVT) to complex matrix VT
*              Overwrite VT by right singular vectors of A
*              (CWorkspace: need 3*N, prefer 2*N+N*NB)
*              (RWorkspace: 0)
*
               CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
               CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
     $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
            ELSE
*
*              Perform bidiagonal SVD, computing left singular vectors
*              of bidiagonal matrix in RWORK(IRU) and computing right
*              singular vectors of bidiagonal matrix in RWORK(IRVT)
*              (CWorkspace: need 0)
*              (RWorkspace: need BDSPAC)
*
               IRU = NRWORK
               IRVT = IRU + N*N
               NRWORK = IRVT + N*N
               CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
     $                      N, RWORK( IRVT ), N, DUM, IDUM,
     $                      RWORK( NRWORK ), IWORK, INFO )
*
*              Set the right corner of U to identity matrix
*
               CALL ZLASET( 'F', M, M, CZERO, CZERO, U, LDU )
               IF( M.GT.N ) THEN
                  CALL ZLASET( 'F', M-N, M-N, CZERO, CONE,
     $                         U( N+1, N+1 ), LDU )
               END IF
*
*              Copy real matrix RWORK(IRU) to complex matrix U
*              Overwrite U by left singular vectors of A
*              (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
*              (RWorkspace: 0)
*
               CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, U, LDU )
               CALL ZUNMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
     $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
*
*              Copy real matrix RWORK(IRVT) to complex matrix VT
*              Overwrite VT by right singular vectors of A
*              (CWorkspace: need 3*N, prefer 2*N+N*NB)
*              (RWorkspace: 0)
*
               CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
               CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
     $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
            END IF
*
         END IF
*
      ELSE
*
*        A has more columns than rows. If A has sufficiently more
*        columns than rows, first reduce using the LQ decomposition (if
*        sufficient workspace available)
*
         IF( N.GE.MNTHR1 ) THEN
*
            IF( WNTQN ) THEN
*
*              Path 1t (N much larger than M, JOBZ='N')
*              No singular vectors to be computed
*
               ITAU = 1
               NWORK = ITAU + M
*
*              Compute A=L*Q
*              (CWorkspace: need 2*M, prefer M+M*NB)
*              (RWorkspace: 0)
*
               CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
*
*              Zero out above L
*
               CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, A( 1, 2 ),
     $                      LDA )
               IE = 1
               ITAUQ = 1
               ITAUP = ITAUQ + M
               NWORK = ITAUP + M
*
*              Bidiagonalize L in A
*              (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
*              (RWorkspace: need M)
*
               CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                      WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
     $                      IERR )
               NRWORK = IE + M
*
*              Perform bidiagonal SVD, compute singular values only
*              (CWorkspace: 0)
*              (RWorkspace: need BDSPAN)
*
               CALL DBDSDC( 'U', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
     $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
*
            ELSE IF( WNTQO ) THEN
*
*              Path 2t (N much larger than M, JOBZ='O')
*              M right singular vectors to be overwritten on A and
*              M left singular vectors to be computed in U
*
               IVT = 1
               LDWKVT = M
*
*              WORK(IVT) is M by M
*
               IL = IVT + LDWKVT*M
               IF( LWORK.GE.M*N+M*M+3*M ) THEN
*
*                 WORK(IL) M by N
*
                  LDWRKL = M
                  CHUNK = N
               ELSE
*
*                 WORK(IL) is M by CHUNK
*
                  LDWRKL = M
                  CHUNK = ( LWORK-M*M-3*M ) / M
               END IF
               ITAU = IL + LDWRKL*CHUNK
               NWORK = ITAU + M
*
*              Compute A=L*Q
*              (CWorkspace: need 2*M, prefer M+M*NB)
*              (RWorkspace: 0)
*
               CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
*
*              Copy L to WORK(IL), zeroing about above it
*
               CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWRKL )
               CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO,
     $                      WORK( IL+LDWRKL ), LDWRKL )
*
*              Generate Q in A
*              (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
*              (RWorkspace: 0)
*
               CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
     $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
               IE = 1
               ITAUQ = ITAU
               ITAUP = ITAUQ + M
               NWORK = ITAUP + M
*