zgesvd.f

famous linear algebra library (LAPACK) ports to windows

               ELSE IF( WNTUA .AND. WNTVO ) THEN
*
*                 Path 8 (M much larger than N, JOBU='A', JOBVT='O')
*
                  WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M,
     $                    M, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+2*N*
     $                    ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+N*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+( N-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
                  MAXWRK = 2*N*N + WRKBL
                  MINWRK = 2*N + M
               ELSE IF( WNTUA .AND. WNTVAS ) THEN
*
*                 Path 9 (M much larger than N, JOBU='A', JOBVT='S' or
*                 'A')
*
                  WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M,
     $                    M, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+2*N*
     $                    ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+N*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+( N-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
                  MAXWRK = N*N + WRKBL
                  MINWRK = 2*N + M
               END IF
            ELSE
*
*              Path 10 (M at least N, but not much larger)
*
               MAXWRK = 2*N + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
     $                  -1, -1 )
               IF( WNTUS .OR. WNTUO )
     $            MAXWRK = MAX( MAXWRK, 2*N+N*
     $                     ILAENV( 1, 'ZUNGBR', 'Q', M, N, N, -1 ) )
               IF( WNTUA )
     $            MAXWRK = MAX( MAXWRK, 2*N+M*
     $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) )
               IF( .NOT.WNTVN )
     $            MAXWRK = MAX( MAXWRK, 2*N+( N-1 )*
     $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
               MINWRK = 2*N + M
            END IF
         ELSE IF( MINMN.GT.0 ) THEN
*
*           Space needed for ZBDSQR is BDSPAC = 5*M
*
            MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 )
            IF( N.GE.MNTHR ) THEN
               IF( WNTVN ) THEN
*
*                 Path 1t(N much larger than M, JOBVT='N')
*
                  MAXWRK = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1,
     $                     -1 )
                  MAXWRK = MAX( MAXWRK, 2*M+2*M*
     $                     ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  IF( WNTUO .OR. WNTUAS )
     $               MAXWRK = MAX( MAXWRK, 2*M+M*
     $                        ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MINWRK = 3*M
               ELSE IF( WNTVO .AND. WNTUN ) THEN
*
*                 Path 2t(N much larger than M, JOBU='N', JOBVT='O')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  MAXWRK = MAX( M*M+WRKBL, M*M+M*N )
                  MINWRK = 2*M + N
               ELSE IF( WNTVO .AND. WNTUAS ) THEN
*
*                 Path 3t(N much larger than M, JOBU='S' or 'A',
*                 JOBVT='O')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+M*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MAXWRK = MAX( M*M+WRKBL, M*M+M*N )
                  MINWRK = 2*M + N
               ELSE IF( WNTVS .AND. WNTUN ) THEN
*
*                 Path 4t(N much larger than M, JOBU='N', JOBVT='S')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  MAXWRK = M*M + WRKBL
                  MINWRK = 2*M + N
               ELSE IF( WNTVS .AND. WNTUO ) THEN
*
*                 Path 5t(N much larger than M, JOBU='O', JOBVT='S')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+M*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MAXWRK = 2*M*M + WRKBL
                  MINWRK = 2*M + N
               ELSE IF( WNTVS .AND. WNTUAS ) THEN
*
*                 Path 6t(N much larger than M, JOBU='S' or 'A',
*                 JOBVT='S')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+M*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MAXWRK = M*M + WRKBL
                  MINWRK = 2*M + N
               ELSE IF( WNTVA .AND. WNTUN ) THEN
*
*                 Path 7t(N much larger than M, JOBU='N', JOBVT='A')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  MAXWRK = M*M + WRKBL
                  MINWRK = 2*M + N
               ELSE IF( WNTVA .AND. WNTUO ) THEN
*
*                 Path 8t(N much larger than M, JOBU='O', JOBVT='A')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+M*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MAXWRK = 2*M*M + WRKBL
                  MINWRK = 2*M + N
               ELSE IF( WNTVA .AND. WNTUAS ) THEN
*
*                 Path 9t(N much larger than M, JOBU='S' or 'A',
*                 JOBVT='A')
*
                  WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N,
     $                    N, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+2*M*
     $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+( M-1 )*
     $                    ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) )
                  WRKBL = MAX( WRKBL, 2*M+M*
     $                    ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
                  MAXWRK = M*M + WRKBL
                  MINWRK = 2*M + N
               END IF
            ELSE
*
*              Path 10t(N greater than M, but not much larger)
*
               MAXWRK = 2*M + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
     $                  -1, -1 )
               IF( WNTVS .OR. WNTVO )
     $            MAXWRK = MAX( MAXWRK, 2*M+M*
     $                     ILAENV( 1, 'ZUNGBR', 'P', M, N, M, -1 ) )
               IF( WNTVA )
     $            MAXWRK = MAX( MAXWRK, 2*M+N*
     $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, M, -1 ) )
               IF( .NOT.WNTUN )
     $            MAXWRK = MAX( MAXWRK, 2*M+( M-1 )*
     $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) )
               MINWRK = 2*M + N
            END IF
         END IF
         MAXWRK = MAX( MAXWRK, MINWRK )
         WORK( 1 ) = MAXWRK
*
         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -13
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZGESVD', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
         RETURN
      END IF
*
*     Get machine constants
*
      EPS = DLAMCH( 'P' )
      SMLNUM = SQRT( DLAMCH( 'S' ) ) / EPS
      BIGNUM = ONE / SMLNUM
*
*     Scale A if max element outside range [SMLNUM,BIGNUM]
*
      ANRM = ZLANGE( 'M', M, N, A, LDA, DUM )
      ISCL = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         ISCL = 1
         CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR )
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         ISCL = 1
         CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR )
      END IF
*
      IF( M.GE.N ) THEN
*
*        A has at least as many rows as columns. If A has sufficiently
*        more rows than columns, first reduce using the QR
*        decomposition (if sufficient workspace available)
*
         IF( M.GE.MNTHR ) THEN
*
            IF( WNTUN ) THEN
*
*              Path 1 (M much larger than N, JOBU='N')
*              No left singular vectors to be computed
*
               ITAU = 1
               IWORK = ITAU + N
*
*              Compute A=Q*R
*              (CWorkspace: need 2*N, prefer N+N*NB)
*              (RWorkspace: need 0)
*
               CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
     $                      LWORK-IWORK+1, IERR )
*
*              Zero out below R
*
               CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
     $                      LDA )
               IE = 1
               ITAUQ = 1
               ITAUP = ITAUQ + N
               IWORK = ITAUP + N
*
*              Bidiagonalize R in A
*              (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
*              (RWorkspace: need N)
*
               CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                      WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
     $                      IERR )
               NCVT = 0
               IF( WNTVO .OR. WNTVAS ) THEN
*
*                 If right singular vectors desired, generate P'.
*                 (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
*                 (RWorkspace: 0)
*
                  CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
     $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                  NCVT = N
               END IF
               IRWORK = IE + N
*
*              Perform bidiagonal QR iteration, computing right
*              singular vectors of A in A if desired
*              (CWorkspace: 0)
*              (RWorkspace: need BDSPAC)
*
               CALL ZBDSQR( 'U', N, NCVT, 0, 0, S, RWORK( IE ), A, LDA,
     $                      CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO )
*
*              If right singular vectors desired in VT, copy them there
*
               IF( WNTVAS )
     $            CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT )
*
            ELSE IF( WNTUO .AND. WNTVN ) THEN
*
*              Path 2 (M much larger than N, JOBU='O', JOBVT='N')
*              N left singular vectors to be overwritten on A and
*              no right singular vectors to be computed
*
               IF( LWORK.GE.N*N+3*N ) THEN
*
*                 Sufficient workspace for a fast algorithm
*
                  IR = 1
                  IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*N ) THEN
*
*                    WORK(IU) is LDA by N, WORK(IR) is LDA by N
*