zgegv.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 602 行 · 第 1/2 页

      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Get machine constants
*
      EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
      SAFMIN = DLAMCH( 'S' )
      SAFMIN = SAFMIN + SAFMIN
      SAFMAX = ONE / SAFMIN
*
*     Scale A
*
      ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
      ANRM1 = ANRM
      ANRM2 = ONE
      IF( ANRM.LT.ONE ) THEN
         IF( SAFMAX*ANRM.LT.ONE ) THEN
            ANRM1 = SAFMIN
            ANRM2 = SAFMAX*ANRM
         END IF
      END IF
*
      IF( ANRM.GT.ZERO ) THEN
         CALL ZLASCL( 'G', -1, -1, ANRM, ONE, N, N, A, LDA, IINFO )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 10
            RETURN
         END IF
      END IF
*
*     Scale B
*
      BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
      BNRM1 = BNRM
      BNRM2 = ONE
      IF( BNRM.LT.ONE ) THEN
         IF( SAFMAX*BNRM.LT.ONE ) THEN
            BNRM1 = SAFMIN
            BNRM2 = SAFMAX*BNRM
         END IF
      END IF
*
      IF( BNRM.GT.ZERO ) THEN
         CALL ZLASCL( 'G', -1, -1, BNRM, ONE, N, N, B, LDB, IINFO )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 10
            RETURN
         END IF
      END IF
*
*     Permute the matrix to make it more nearly triangular
*     Also "balance" the matrix.
*
      ILEFT = 1
      IRIGHT = N + 1
      IRWORK = IRIGHT + N
      CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
     $             RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 1
         GO TO 80
      END IF
*
*     Reduce B to triangular form, and initialize VL and/or VR
*
      IROWS = IHI + 1 - ILO
      IF( ILV ) THEN
         ICOLS = N + 1 - ILO
      ELSE
         ICOLS = IROWS
      END IF
      ITAU = 1
      IWORK = ITAU + IROWS
      CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
     $             WORK( IWORK ), LWORK+1-IWORK, IINFO )
      IF( IINFO.GE.0 )
     $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 2
         GO TO 80
      END IF
*
      CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
     $             LWORK+1-IWORK, IINFO )
      IF( IINFO.GE.0 )
     $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 3
         GO TO 80
      END IF
*
      IF( ILVL ) THEN
         CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
         CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
     $                VL( ILO+1, ILO ), LDVL )
         CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
     $                WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
     $                IINFO )
         IF( IINFO.GE.0 )
     $      LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 4
            GO TO 80
         END IF
      END IF
*
      IF( ILVR )
     $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
*
*     Reduce to generalized Hessenberg form
*
      IF( ILV ) THEN
*
*        Eigenvectors requested -- work on whole matrix.
*
         CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
     $                LDVL, VR, LDVR, IINFO )
      ELSE
         CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
     $                B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IINFO )
      END IF
      IF( IINFO.NE.0 ) THEN
         INFO = N + 5
         GO TO 80
      END IF
*
*     Perform QZ algorithm
*
      IWORK = ITAU
      IF( ILV ) THEN
         CHTEMP = 'S'
      ELSE
         CHTEMP = 'E'
      END IF
      CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
     $             ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWORK ),
     $             LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
      IF( IINFO.GE.0 )
     $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
      IF( IINFO.NE.0 ) THEN
         IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
            INFO = IINFO
         ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
            INFO = IINFO - N
         ELSE
            INFO = N + 6
         END IF
         GO TO 80
      END IF
*
      IF( ILV ) THEN
*
*        Compute Eigenvectors
*
         IF( ILVL ) THEN
            IF( ILVR ) THEN
               CHTEMP = 'B'
            ELSE
               CHTEMP = 'L'
            END IF
         ELSE
            CHTEMP = 'R'
         END IF
*
         CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL, LDVL,
     $                VR, LDVR, N, IN, WORK( IWORK ), RWORK( IRWORK ),
     $                IINFO )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 7
            GO TO 80
         END IF
*
*        Undo balancing on VL and VR, rescale
*
         IF( ILVL ) THEN
            CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
     $                   RWORK( IRIGHT ), N, VL, LDVL, IINFO )
            IF( IINFO.NE.0 ) THEN
               INFO = N + 8
               GO TO 80
            END IF
            DO 30 JC = 1, N
               TEMP = ZERO
               DO 10 JR = 1, N
                  TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
   10          CONTINUE
               IF( TEMP.LT.SAFMIN )
     $            GO TO 30
               TEMP = ONE / TEMP
               DO 20 JR = 1, N
                  VL( JR, JC ) = VL( JR, JC )*TEMP
   20          CONTINUE
   30       CONTINUE
         END IF
         IF( ILVR ) THEN
            CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
     $                   RWORK( IRIGHT ), N, VR, LDVR, IINFO )
            IF( IINFO.NE.0 ) THEN
               INFO = N + 9
               GO TO 80
            END IF
            DO 60 JC = 1, N
               TEMP = ZERO
               DO 40 JR = 1, N
                  TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
   40          CONTINUE
               IF( TEMP.LT.SAFMIN )
     $            GO TO 60
               TEMP = ONE / TEMP
               DO 50 JR = 1, N
                  VR( JR, JC ) = VR( JR, JC )*TEMP
   50          CONTINUE
   60       CONTINUE
         END IF
*
*        End of eigenvector calculation
*
      END IF
*
*     Undo scaling in alpha, beta
*
*     Note: this does not give the alpha and beta for the unscaled
*     problem.
*
*     Un-scaling is limited to avoid underflow in alpha and beta
*     if they are significant.
*
      DO 70 JC = 1, N
         ABSAR = ABS( DBLE( ALPHA( JC ) ) )
         ABSAI = ABS( DIMAG( ALPHA( JC ) ) )
         ABSB = ABS( DBLE( BETA( JC ) ) )
         SALFAR = ANRM*DBLE( ALPHA( JC ) )
         SALFAI = ANRM*DIMAG( ALPHA( JC ) )
         SBETA = BNRM*DBLE( BETA( JC ) )
         ILIMIT = .FALSE.
         SCALE = ONE
*
*        Check for significant underflow in imaginary part of ALPHA
*
         IF( ABS( SALFAI ).LT.SAFMIN .AND. ABSAI.GE.
     $       MAX( SAFMIN, EPS*ABSAR, EPS*ABSB ) ) THEN
            ILIMIT = .TRUE.
            SCALE = ( SAFMIN / ANRM1 ) / MAX( SAFMIN, ANRM2*ABSAI )
         END IF
*
*        Check for significant underflow in real part of ALPHA
*
         IF( ABS( SALFAR ).LT.SAFMIN .AND. ABSAR.GE.
     $       MAX( SAFMIN, EPS*ABSAI, EPS*ABSB ) ) THEN
            ILIMIT = .TRUE.
            SCALE = MAX( SCALE, ( SAFMIN / ANRM1 ) /
     $              MAX( SAFMIN, ANRM2*ABSAR ) )
         END IF
*
*        Check for significant underflow in BETA
*
         IF( ABS( SBETA ).LT.SAFMIN .AND. ABSB.GE.
     $       MAX( SAFMIN, EPS*ABSAR, EPS*ABSAI ) ) THEN
            ILIMIT = .TRUE.
            SCALE = MAX( SCALE, ( SAFMIN / BNRM1 ) /
     $              MAX( SAFMIN, BNRM2*ABSB ) )
         END IF
*
*        Check for possible overflow when limiting scaling
*
         IF( ILIMIT ) THEN
            TEMP = ( SCALE*SAFMIN )*MAX( ABS( SALFAR ), ABS( SALFAI ),
     $             ABS( SBETA ) )
            IF( TEMP.GT.ONE )
     $         SCALE = SCALE / TEMP
            IF( SCALE.LT.ONE )
     $         ILIMIT = .FALSE.
         END IF
*
*        Recompute un-scaled ALPHA, BETA if necessary.
*
         IF( ILIMIT ) THEN
            SALFAR = ( SCALE*DBLE( ALPHA( JC ) ) )*ANRM
            SALFAI = ( SCALE*DIMAG( ALPHA( JC ) ) )*ANRM
            SBETA = ( SCALE*BETA( JC ) )*BNRM
         END IF
         ALPHA( JC ) = DCMPLX( SALFAR, SALFAI )
         BETA( JC ) = SBETA
   70 CONTINUE
*
   80 CONTINUE
      WORK( 1 ) = LWKOPT
*
      RETURN
*
*     End of ZGEGV
*
      END