cheevr.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 589 行 · 第 1/2 页

         INFO = -1
      ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
         INFO = -2
      ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE
         IF( VALEIG ) THEN
            IF( N.GT.0 .AND. VU.LE.VL )
     $         INFO = -8
         ELSE IF( INDEIG ) THEN
            IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
               INFO = -9
            ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
               INFO = -10
            END IF
         END IF
      END IF
      IF( INFO.EQ.0 ) THEN
         IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
            INFO = -15
         END IF
      END IF
*
      IF( INFO.EQ.0 ) THEN
         NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
         NB = MAX( NB, ILAENV( 1, 'CUNMTR', UPLO, N, -1, -1, -1 ) )
         LWKOPT = MAX( ( NB+1 )*N, LWMIN )
         WORK( 1 ) = LWKOPT
         RWORK( 1 ) = LRWMIN
         IWORK( 1 ) = LIWMIN
*
         IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -18
         ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -20
         ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -22
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CHEEVR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      M = 0
      IF( N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      IF( N.EQ.1 ) THEN
         WORK( 1 ) = 2
         IF( ALLEIG .OR. INDEIG ) THEN
            M = 1
            W( 1 ) = REAL( A( 1, 1 ) )
         ELSE
            IF( VL.LT.REAL( A( 1, 1 ) ) .AND. VU.GE.REAL( A( 1, 1 ) ) )
     $           THEN
               M = 1
               W( 1 ) = REAL( A( 1, 1 ) )
            END IF
         END IF
         IF( WANTZ )
     $      Z( 1, 1 ) = ONE
         RETURN
      END IF
*
*     Get machine constants.
*
      SAFMIN = SLAMCH( 'Safe minimum' )
      EPS = SLAMCH( 'Precision' )
      SMLNUM = SAFMIN / EPS
      BIGNUM = ONE / SMLNUM
      RMIN = SQRT( SMLNUM )
      RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
*
*     Scale matrix to allowable range, if necessary.
*
      ISCALE = 0
      ABSTLL = ABSTOL
      IF (VALEIG) THEN
         VLL = VL
         VUU = VU
      END IF
      ANRM = CLANSY( 'M', UPLO, N, A, LDA, RWORK )
      IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
         ISCALE = 1
         SIGMA = RMIN / ANRM
      ELSE IF( ANRM.GT.RMAX ) THEN
         ISCALE = 1
         SIGMA = RMAX / ANRM
      END IF
      IF( ISCALE.EQ.1 ) THEN
         IF( LOWER ) THEN
            DO 10 J = 1, N
               CALL CSSCAL( N-J+1, SIGMA, A( J, J ), 1 )
   10       CONTINUE
         ELSE
            DO 20 J = 1, N
               CALL CSSCAL( J, SIGMA, A( 1, J ), 1 )
   20       CONTINUE
         END IF
         IF( ABSTOL.GT.0 )
     $      ABSTLL = ABSTOL*SIGMA
         IF( VALEIG ) THEN
            VLL = VL*SIGMA
            VUU = VU*SIGMA
         END IF
      END IF

*     Initialize indices into workspaces.  Note: The IWORK indices are
*     used only if SSTERF or CSTEMR fail.

*     WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the
*     elementary reflectors used in CHETRD.
      INDTAU = 1
*     INDWK is the starting offset of the remaining complex workspace,
*     and LLWORK is the remaining complex workspace size.
      INDWK = INDTAU + N
      LLWORK = LWORK - INDWK + 1

*     RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal
*     entries.
      INDRD = 1
*     RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the
*     tridiagonal matrix from CHETRD.
      INDRE = INDRD + N
*     RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over
*     -written by CSTEMR (the SSTERF path copies the diagonal to W).
      INDRDD = INDRE + N
*     RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over
*     -written while computing the eigenvalues in SSTERF and CSTEMR.
      INDREE = INDRDD + N
*     INDRWK is the starting offset of the left-over real workspace, and
*     LLRWORK is the remaining workspace size.
      INDRWK = INDREE + N
      LLRWORK = LRWORK - INDRWK + 1

*     IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and
*     stores the block indices of each of the M<=N eigenvalues.
      INDIBL = 1
*     IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and
*     stores the starting and finishing indices of each block.
      INDISP = INDIBL + N
*     IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors
*     that corresponding to eigenvectors that fail to converge in
*     SSTEIN.  This information is discarded; if any fail, the driver
*     returns INFO > 0.
      INDIFL = INDISP + N
*     INDIWO is the offset of the remaining integer workspace.
      INDIWO = INDISP + N

*
*     Call CHETRD to reduce Hermitian matrix to tridiagonal form.
*
      CALL CHETRD( UPLO, N, A, LDA, RWORK( INDRD ), RWORK( INDRE ),
     $             WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO )
*
*     If all eigenvalues are desired
*     then call SSTERF or CSTEMR and CUNMTR.
*
      TEST = .FALSE.
      IF( INDEIG ) THEN
         IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
            TEST = .TRUE.
         END IF
      END IF
      IF( ( ALLEIG.OR.TEST ) .AND. ( IEEEOK.EQ.1 ) ) THEN
         IF( .NOT.WANTZ ) THEN
            CALL SCOPY( N, RWORK( INDRD ), 1, W, 1 )
            CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 )
            CALL SSTERF( N, W, RWORK( INDREE ), INFO )
         ELSE
            CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 )
            CALL SCOPY( N, RWORK( INDRD ), 1, RWORK( INDRDD ), 1 )
*
            IF (ABSTOL .LE. TWO*N*EPS) THEN
               TRYRAC = .TRUE.
            ELSE
               TRYRAC = .FALSE.
            END IF
            CALL CSTEMR( JOBZ, 'A', N, RWORK( INDRDD ),
     $                   RWORK( INDREE ), VL, VU, IL, IU, M, W,
     $                   Z, LDZ, N, ISUPPZ, TRYRAC,
     $                   RWORK( INDRWK ), LLRWORK,
     $                   IWORK, LIWORK, INFO )
*
*           Apply unitary matrix used in reduction to tridiagonal
*           form to eigenvectors returned by CSTEIN.
*
            IF( WANTZ .AND. INFO.EQ.0 ) THEN
               INDWKN = INDWK
               LLWRKN = LWORK - INDWKN + 1
               CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA,
     $                      WORK( INDTAU ), Z, LDZ, WORK( INDWKN ),
     $                      LLWRKN, IINFO )
            END IF
         END IF
*
*
         IF( INFO.EQ.0 ) THEN
            M = N
            GO TO 30
         END IF
         INFO = 0
      END IF
*
*     Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN.
*     Also call SSTEBZ and CSTEIN if CSTEMR fails.
*
      IF( WANTZ ) THEN
         ORDER = 'B'
      ELSE
         ORDER = 'E'
      END IF

      CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
     $             RWORK( INDRD ), RWORK( INDRE ), M, NSPLIT, W,
     $             IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
     $             IWORK( INDIWO ), INFO )
*
      IF( WANTZ ) THEN
         CALL CSTEIN( N, RWORK( INDRD ), RWORK( INDRE ), M, W,
     $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
     $                RWORK( INDRWK ), IWORK( INDIWO ), IWORK( INDIFL ),
     $                INFO )
*
*        Apply unitary matrix used in reduction to tridiagonal
*        form to eigenvectors returned by CSTEIN.
*
         INDWKN = INDWK
         LLWRKN = LWORK - INDWKN + 1
         CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
     $                LDZ, WORK( INDWKN ), LLWRKN, IINFO )
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
   30 CONTINUE
      IF( ISCALE.EQ.1 ) THEN
         IF( INFO.EQ.0 ) THEN
            IMAX = M
         ELSE
            IMAX = INFO - 1
         END IF
         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
      END IF
*
*     If eigenvalues are not in order, then sort them, along with
*     eigenvectors.
*
      IF( WANTZ ) THEN
         DO 50 J = 1, M - 1
            I = 0
            TMP1 = W( J )
            DO 40 JJ = J + 1, M
               IF( W( JJ ).LT.TMP1 ) THEN
                  I = JJ
                  TMP1 = W( JJ )
               END IF
   40       CONTINUE
*
            IF( I.NE.0 ) THEN
               ITMP1 = IWORK( INDIBL+I-1 )
               W( I ) = W( J )
               IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
               W( J ) = TMP1
               IWORK( INDIBL+J-1 ) = ITMP1
               CALL CSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
            END IF
   50    CONTINUE
      END IF
*
*     Set WORK(1) to optimal workspace size.
*
      WORK( 1 ) = LWKOPT
      RWORK( 1 ) = LRWMIN
      IWORK( 1 ) = LIWMIN
*
      RETURN
*
*     End of CHEEVR
*
      END