sggesx.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 677 行 · 第 1/2 页

      ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
         INFO = -16
      ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
         INFO = -18
      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
         IF( N.GT.0) THEN
            MINWRK = MAX( 8*N, 6*N + 16 )
            MAXWRK = MINWRK - N +
     $               N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 )
            MAXWRK = MAX( MAXWRK, MINWRK - N +
     $               N*ILAENV( 1, 'SORMQR', ' ', N, 1, N, -1 ) )
            IF( ILVSL ) THEN
               MAXWRK = MAX( MAXWRK, MINWRK - N +
     $                  N*ILAENV( 1, 'SORGQR', ' ', N, 1, N, -1 ) )
            END IF
            LWRK = MAXWRK
            IF( IJOB.GE.1 )
     $         LWRK = MAX( LWRK, N*N/2 )
         ELSE
            MINWRK = 1
            MAXWRK = 1
            LWRK   = 1
         END IF
         WORK( 1 ) = LWRK
         IF( WANTSN .OR. N.EQ.0 ) THEN
            LIWMIN = 1
         ELSE
            LIWMIN = N + 6
         END IF
         IWORK( 1 ) = LIWMIN
*
         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -22
         ELSE IF( LIWORK.LT.LIWMIN  .AND. .NOT.LQUERY ) THEN
            INFO = -24
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SGGESX', -INFO )
         RETURN
      ELSE IF (LQUERY) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         SDIM = 0
         RETURN
      END IF
*
*     Get machine constants
*
      EPS = SLAMCH( 'P' )
      SAFMIN = SLAMCH( 'S' )
      SAFMAX = ONE / SAFMIN
      CALL SLABAD( SAFMIN, SAFMAX )
      SMLNUM = SQRT( SAFMIN ) / EPS
      BIGNUM = ONE / SMLNUM
*
*     Scale A if max element outside range [SMLNUM,BIGNUM]
*
      ANRM = SLANGE( 'M', N, N, A, LDA, WORK )
      ILASCL = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         ANRMTO = SMLNUM
         ILASCL = .TRUE.
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         ANRMTO = BIGNUM
         ILASCL = .TRUE.
      END IF
      IF( ILASCL )
     $   CALL SLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
*
*     Scale B if max element outside range [SMLNUM,BIGNUM]
*
      BNRM = SLANGE( 'M', N, N, B, LDB, WORK )
      ILBSCL = .FALSE.
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
         BNRMTO = SMLNUM
         ILBSCL = .TRUE.
      ELSE IF( BNRM.GT.BIGNUM ) THEN
         BNRMTO = BIGNUM
         ILBSCL = .TRUE.
      END IF
      IF( ILBSCL )
     $   CALL SLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
*
*     Permute the matrix to make it more nearly triangular
*     (Workspace: need 6*N + 2*N for permutation parameters)
*
      ILEFT = 1
      IRIGHT = N + 1
      IWRK = IRIGHT + N
      CALL SGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
     $             WORK( IRIGHT ), WORK( IWRK ), IERR )
*
*     Reduce B to triangular form (QR decomposition of B)
*     (Workspace: need N, prefer N*NB)
*
      IROWS = IHI + 1 - ILO
      ICOLS = N + 1 - ILO
      ITAU = IWRK
      IWRK = ITAU + IROWS
      CALL SGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
*
*     Apply the orthogonal transformation to matrix A
*     (Workspace: need N, prefer N*NB)
*
      CALL SORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
     $             LWORK+1-IWRK, IERR )
*
*     Initialize VSL
*     (Workspace: need N, prefer N*NB)
*
      IF( ILVSL ) THEN
         CALL SLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL )
         IF( IROWS.GT.1 ) THEN
            CALL SLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
     $                   VSL( ILO+1, ILO ), LDVSL )
         END IF
         CALL SORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
     $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
      END IF
*
*     Initialize VSR
*
      IF( ILVSR )
     $   CALL SLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR )
*
*     Reduce to generalized Hessenberg form
*     (Workspace: none needed)
*
      CALL SGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
     $             LDVSL, VSR, LDVSR, IERR )
*
      SDIM = 0
*
*     Perform QZ algorithm, computing Schur vectors if desired
*     (Workspace: need N)
*
      IWRK = ITAU
      CALL SHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
     $             ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
      IF( IERR.NE.0 ) THEN
         IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
            INFO = IERR
         ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
            INFO = IERR - N
         ELSE
            INFO = N + 1
         END IF
         GO TO 50
      END IF
*
*     Sort eigenvalues ALPHA/BETA and compute the reciprocal of
*     condition number(s)
*     (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) )
*                 otherwise, need 8*(N+1) )
*
      IF( WANTST ) THEN
*
*        Undo scaling on eigenvalues before SELCTGing
*
         IF( ILASCL ) THEN
            CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N,
     $                   IERR )
            CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N,
     $                   IERR )
         END IF
         IF( ILBSCL )
     $      CALL SLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
*
*        Select eigenvalues
*
         DO 10 I = 1, N
            BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
   10    CONTINUE
*
*        Reorder eigenvalues, transform Generalized Schur vectors, and
*        compute reciprocal condition numbers
*
         CALL STGSEN( IJOB, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
     $                ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
     $                SDIM, PL, PR, DIF, WORK( IWRK ), LWORK-IWRK+1,
     $                IWORK, LIWORK, IERR )
*
         IF( IJOB.GE.1 )
     $      MAXWRK = MAX( MAXWRK, 2*SDIM*( N-SDIM ) )
         IF( IERR.EQ.-22 ) THEN
*
*            not enough real workspace
*
            INFO = -22
         ELSE
            IF( IJOB.EQ.1 .OR. IJOB.EQ.4 ) THEN
               RCONDE( 1 ) = PL
               RCONDE( 2 ) = PR
            END IF
            IF( IJOB.EQ.2 .OR. IJOB.EQ.4 ) THEN
               RCONDV( 1 ) = DIF( 1 )
               RCONDV( 2 ) = DIF( 2 )
            END IF
            IF( IERR.EQ.1 )
     $         INFO = N + 3
         END IF
*
      END IF
*
*     Apply permutation to VSL and VSR
*     (Workspace: none needed)
*
      IF( ILVSL )
     $   CALL SGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ),
     $                WORK( IRIGHT ), N, VSL, LDVSL, IERR )
*
      IF( ILVSR )
     $   CALL SGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ),
     $                WORK( IRIGHT ), N, VSR, LDVSR, IERR )
*
*     Check if unscaling would cause over/underflow, if so, rescale
*     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of
*     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I)
*
      IF( ILASCL ) THEN  
         DO 20 I = 1, N  
            IF( ALPHAI( I ).NE.ZERO ) THEN
               IF( ( ALPHAR( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) .OR.
     $             ( SAFMIN / ALPHAR( I ) ).GT.( ANRM / ANRMTO ) )        
     $            THEN
                  WORK( 1 ) = ABS( A( I, I ) / ALPHAR( I ) )
                  BETA( I ) = BETA( I )*WORK( 1 )
                  ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                  ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
               ELSE IF( ( ALPHAI( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) 
     $            .OR. ( SAFMIN / ALPHAI( I ) ).GT.( ANRM / ANRMTO ) )
     $            THEN
                  WORK( 1 ) = ABS( A( I, I+1 ) / ALPHAI( I ) )
                  BETA( I ) = BETA( I )*WORK( 1 )
                  ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                  ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
               END IF
            END IF
   20    CONTINUE
      END IF 
*
      IF( ILBSCL ) THEN 
         DO 25 I = 1, N
            IF( ALPHAI( I ).NE.ZERO ) THEN
               IF( ( BETA( I ) / SAFMAX ).GT.( BNRMTO / BNRM ) .OR.
     $             ( SAFMIN / BETA( I ) ).GT.( BNRM / BNRMTO ) ) THEN
                  WORK( 1 ) = ABS( B( I, I ) / BETA( I ) )
                  BETA( I ) = BETA( I )*WORK( 1 )
                  ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
                  ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
               END IF 
            END IF 
   25    CONTINUE
      END IF 
*
*     Undo scaling
*
      IF( ILASCL ) THEN
         CALL SLASCL( 'H', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
         CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
         CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
      END IF
*
      IF( ILBSCL ) THEN
         CALL SLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
         CALL SLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
      END IF
*
      IF( WANTST ) THEN
*
*        Check if reordering is correct
*
         LASTSL = .TRUE.
         LST2SL = .TRUE.
         SDIM = 0
         IP = 0
         DO 40 I = 1, N
            CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
            IF( ALPHAI( I ).EQ.ZERO ) THEN
               IF( CURSL )
     $            SDIM = SDIM + 1
               IP = 0
               IF( CURSL .AND. .NOT.LASTSL )
     $            INFO = N + 2
            ELSE
               IF( IP.EQ.1 ) THEN
*
*                 Last eigenvalue of conjugate pair
*
                  CURSL = CURSL .OR. LASTSL
                  LASTSL = CURSL
                  IF( CURSL )
     $               SDIM = SDIM + 2
                  IP = -1
                  IF( CURSL .AND. .NOT.LST2SL )
     $               INFO = N + 2
               ELSE
*
*                 First eigenvalue of conjugate pair
*
                  IP = 1
               END IF
            END IF
            LST2SL = LASTSL
            LASTSL = CURSL
   40    CONTINUE
*
      END IF
*
   50 CONTINUE
*
      WORK( 1 ) = MAXWRK
      IWORK( 1 ) = LIWMIN
*
      RETURN
*
*     End of SGGESX
*
      END