cgeevx.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 533 行 · 第 1/2 页

            IF( WANTVL ) THEN
               CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
     $                WORK, -1, INFO )
            ELSE IF( WANTVR ) THEN
               CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
     $                WORK, -1, INFO )
            ELSE
               IF( WNTSNN ) THEN
                  CALL CHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
     $                WORK, -1, INFO )
               ELSE
                  CALL CHSEQR( 'S', 'N', N, 1, N, A, LDA, W, VR, LDVR,
     $                WORK, -1, INFO )
               END IF
            END IF
            HSWORK = WORK( 1 )
*
            IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
               MINWRK = 2*N
               IF( .NOT.( WNTSNN .OR. WNTSNE ) )
     $            MINWRK = MAX( MINWRK, N*N + 2*N )
               MAXWRK = MAX( MAXWRK, HSWORK )
               IF( .NOT.( WNTSNN .OR. WNTSNE ) )
     $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
            ELSE
               MINWRK = 2*N
               IF( .NOT.( WNTSNN .OR. WNTSNE ) )
     $            MINWRK = MAX( MINWRK, N*N + 2*N )
               MAXWRK = MAX( MAXWRK, HSWORK )
               MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'CUNGHR',
     $                       ' ', N, 1, N, -1 ) )
               IF( .NOT.( WNTSNN .OR. WNTSNE ) )
     $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
               MAXWRK = MAX( MAXWRK, 2*N )
            END IF
            MAXWRK = MAX( MAXWRK, MINWRK )
         END IF
         WORK( 1 ) = MAXWRK
*
         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -20
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CGEEVX', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Get machine constants
*
      EPS = SLAMCH( 'P' )
      SMLNUM = SLAMCH( 'S' )
      BIGNUM = ONE / SMLNUM
      CALL SLABAD( SMLNUM, BIGNUM )
      SMLNUM = SQRT( SMLNUM ) / EPS
      BIGNUM = ONE / SMLNUM
*
*     Scale A if max element outside range [SMLNUM,BIGNUM]
*
      ICOND = 0
      ANRM = CLANGE( 'M', N, N, A, LDA, DUM )
      SCALEA = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = SMLNUM
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = BIGNUM
      END IF
      IF( SCALEA )
     $   CALL CLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
*
*     Balance the matrix and compute ABNRM
*
      CALL CGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR )
      ABNRM = CLANGE( '1', N, N, A, LDA, DUM )
      IF( SCALEA ) THEN
         DUM( 1 ) = ABNRM
         CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR )
         ABNRM = DUM( 1 )
      END IF
*
*     Reduce to upper Hessenberg form
*     (CWorkspace: need 2*N, prefer N+N*NB)
*     (RWorkspace: none)
*
      ITAU = 1
      IWRK = ITAU + N
      CALL CGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
     $             LWORK-IWRK+1, IERR )
*
      IF( WANTVL ) THEN
*
*        Want left eigenvectors
*        Copy Householder vectors to VL
*
         SIDE = 'L'
         CALL CLACPY( 'L', N, N, A, LDA, VL, LDVL )
*
*        Generate unitary matrix in VL
*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
*        (RWorkspace: none)
*
         CALL CUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
     $                LWORK-IWRK+1, IERR )
*
*        Perform QR iteration, accumulating Schur vectors in VL
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
         IWRK = ITAU
         CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
     $                WORK( IWRK ), LWORK-IWRK+1, INFO )
*
         IF( WANTVR ) THEN
*
*           Want left and right eigenvectors
*           Copy Schur vectors to VR
*
            SIDE = 'B'
            CALL CLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
         END IF
*
      ELSE IF( WANTVR ) THEN
*
*        Want right eigenvectors
*        Copy Householder vectors to VR
*
         SIDE = 'R'
         CALL CLACPY( 'L', N, N, A, LDA, VR, LDVR )
*
*        Generate unitary matrix in VR
*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
*        (RWorkspace: none)
*
         CALL CUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
     $                LWORK-IWRK+1, IERR )
*
*        Perform QR iteration, accumulating Schur vectors in VR
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
         IWRK = ITAU
         CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
     $                WORK( IWRK ), LWORK-IWRK+1, INFO )
*
      ELSE
*
*        Compute eigenvalues only
*        If condition numbers desired, compute Schur form
*
         IF( WNTSNN ) THEN
            JOB = 'E'
         ELSE
            JOB = 'S'
         END IF
*
*        (CWorkspace: need 1, prefer HSWORK (see comments) )
*        (RWorkspace: none)
*
         IWRK = ITAU
         CALL CHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
     $                WORK( IWRK ), LWORK-IWRK+1, INFO )
      END IF
*
*     If INFO > 0 from CHSEQR, then quit
*
      IF( INFO.GT.0 )
     $   GO TO 50
*
      IF( WANTVL .OR. WANTVR ) THEN
*
*        Compute left and/or right eigenvectors
*        (CWorkspace: need 2*N)
*        (RWorkspace: need N)
*
         CALL CTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
     $                N, NOUT, WORK( IWRK ), RWORK, IERR )
      END IF
*
*     Compute condition numbers if desired
*     (CWorkspace: need N*N+2*N unless SENSE = 'E')
*     (RWorkspace: need 2*N unless SENSE = 'E')
*
      IF( .NOT.WNTSNN ) THEN
         CALL CTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
     $                RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, RWORK,
     $                ICOND )
      END IF
*
      IF( WANTVL ) THEN
*
*        Undo balancing of left eigenvectors
*
         CALL CGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL,
     $                IERR )
*
*        Normalize left eigenvectors and make largest component real
*
         DO 20 I = 1, N
            SCL = ONE / SCNRM2( N, VL( 1, I ), 1 )
            CALL CSSCAL( N, SCL, VL( 1, I ), 1 )
            DO 10 K = 1, N
               RWORK( K ) = REAL( VL( K, I ) )**2 +
     $                      AIMAG( VL( K, I ) )**2
   10       CONTINUE
            K = ISAMAX( N, RWORK, 1 )
            TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) )
            CALL CSCAL( N, TMP, VL( 1, I ), 1 )
            VL( K, I ) = CMPLX( REAL( VL( K, I ) ), ZERO )
   20    CONTINUE
      END IF
*
      IF( WANTVR ) THEN
*
*        Undo balancing of right eigenvectors
*
         CALL CGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR,
     $                IERR )
*
*        Normalize right eigenvectors and make largest component real
*
         DO 40 I = 1, N
            SCL = ONE / SCNRM2( N, VR( 1, I ), 1 )
            CALL CSSCAL( N, SCL, VR( 1, I ), 1 )
            DO 30 K = 1, N
               RWORK( K ) = REAL( VR( K, I ) )**2 +
     $                      AIMAG( VR( K, I ) )**2
   30       CONTINUE
            K = ISAMAX( N, RWORK, 1 )
            TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) )
            CALL CSCAL( N, TMP, VR( 1, I ), 1 )
            VR( K, I ) = CMPLX( REAL( VR( K, I ) ), ZERO )
   40    CONTINUE
      END IF
*
*     Undo scaling if necessary
*
   50 CONTINUE
      IF( SCALEA ) THEN
         CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
     $                MAX( N-INFO, 1 ), IERR )
         IF( INFO.EQ.0 ) THEN
            IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 )
     $         CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N,
     $                      IERR )
         ELSE
            CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
         END IF
      END IF
*
      WORK( 1 ) = MAXWRK
      RETURN
*
*     End of CGEEVX
*
      END