ssyevr.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 563 行 · 第 1/2 页

      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, 'SSYTRD', UPLO, N, -1, -1, -1 )
         NB = MAX( NB, ILAENV( 1, 'SORMTR', UPLO, N, -1, -1, -1 ) )
         LWKOPT = MAX( ( NB+1 )*N, LWMIN )
         WORK( 1 ) = LWKOPT
         IWORK( 1 ) = LIWMIN
*
         IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -18
         ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -20
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SSYEVR', -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 ) = 26
         IF( ALLEIG .OR. INDEIG ) THEN
            M = 1
            W( 1 ) = A( 1, 1 )
         ELSE
            IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN
               M = 1
               W( 1 ) = 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 = SLANSY( 'M', UPLO, N, A, LDA, WORK )
      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 SSCAL( N-J+1, SIGMA, A( J, J ), 1 )
   10       CONTINUE
         ELSE
            DO 20 J = 1, N
               CALL SSCAL( 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 SSTEMR fail.

*     WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the
*     elementary reflectors used in SSYTRD.
      INDTAU = 1
*     WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries.
      INDD = INDTAU + N
*     WORK(INDE:INDE+N-1) stores the off-diagonal entries of the
*     tridiagonal matrix from SSYTRD.
      INDE = INDD + N
*     WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over
*     -written by SSTEMR (the SSTERF path copies the diagonal to W).
      INDDD = INDE + N
*     WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over
*     -written while computing the eigenvalues in SSTERF and SSTEMR.
      INDEE = INDDD + N
*     INDWK is the starting offset of the left-over workspace, and
*     LLWORK is the remaining workspace size.
      INDWK = INDEE + N
      LLWORK = LWORK - INDWK + 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 SSYTRD to reduce symmetric matrix to tridiagonal form.
*
      CALL SSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ),
     $             WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO )
*
*     If all eigenvalues are desired
*     then call SSTERF or SSTEMR and SORMTR.
*
      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, WORK( INDD ), 1, W, 1 )
            CALL SCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
            CALL SSTERF( N, W, WORK( INDEE ), INFO )
         ELSE
            CALL SCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
            CALL SCOPY( N, WORK( INDD ), 1, WORK( INDDD ), 1 )
*
            IF (ABSTOL .LE. TWO*N*EPS) THEN
               TRYRAC = .TRUE.
            ELSE
               TRYRAC = .FALSE.
            END IF
            CALL SSTEMR( JOBZ, 'A', N, WORK( INDDD ), WORK( INDEE ),
     $                   VL, VU, IL, IU, M, W, Z, LDZ, N, ISUPPZ,
     $                   TRYRAC, WORK( INDWK ), LWORK, IWORK, LIWORK,
     $                   INFO )
*
*
*
*        Apply orthogonal matrix used in reduction to tridiagonal
*        form to eigenvectors returned by SSTEIN.
*
            IF( WANTZ .AND. INFO.EQ.0 ) THEN
               INDWKN = INDE
               LLWRKN = LWORK - INDWKN + 1
               CALL SORMTR( 'L', UPLO, 'N', N, M, A, LDA,
     $                      WORK( INDTAU ), Z, LDZ, WORK( INDWKN ),
     $                      LLWRKN, IINFO )
            END IF
         END IF
*
*
         IF( INFO.EQ.0 ) THEN
*           Everything worked.  Skip SSTEBZ/SSTEIN.  IWORK(:) are
*           undefined.
            M = N
            GO TO 30
         END IF
         INFO = 0
      END IF
*
*     Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN.
*     Also call SSTEBZ and SSTEIN if SSTEMR fails.
*
      IF( WANTZ ) THEN
         ORDER = 'B'
      ELSE
         ORDER = 'E'
      END IF

      CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
     $             WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
     $             IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWK ),
     $             IWORK( INDIWO ), INFO )
*
      IF( WANTZ ) THEN
         CALL SSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
     $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
     $                WORK( INDWK ), IWORK( INDIWO ), IWORK( INDIFL ),
     $                INFO )
*
*        Apply orthogonal matrix used in reduction to tridiagonal
*        form to eigenvectors returned by SSTEIN.
*
         INDWKN = INDE
         LLWRKN = LWORK - INDWKN + 1
         CALL SORMTR( '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.
*
*  Jump here if SSTEMR/SSTEIN succeeded.
   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.  Note: We do not sort the IFAIL portion of IWORK.
*     It may not be initialized (if SSTEMR/SSTEIN succeeded), and we do
*     not return this detailed information to the user.
*
      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
               W( I ) = W( J )
               W( J ) = TMP1
               CALL SSWAP( 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
      IWORK( 1 ) = LIWMIN
*
      RETURN
*
*     End of SSYEVR
*
      END