trieige.f

computes the eigenvalues of a symmetric tridiagonal * matrix T. The user may ask for all eigenvalue

         DO 20 J = 1, N - 1
            TMP2 = SQRT( WORK( J ) )
            GU = MAX( GU, D( J )+TMP1+TMP2 )
            GL = MIN( GL, D( J )-TMP1-TMP2 )
            TMP1 = TMP2
   20    CONTINUE
*
         GU = MAX( GU, D( N )+TMP1 )
         GL = MIN( GL, D( N )-TMP1 )
         TNORM = MAX( ABS( GL ), ABS( GU ) )
         GL = GL - FUDGE*TNORM*ULP*N - FUDGE*TWO*PIVMIN
         GU = GU + FUDGE*TNORM*ULP*N + FUDGE*PIVMIN
*
*        Compute Iteration parameters
*
         ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) /
     $           LOG( TWO ) ) + 2
         IF( ABSTOL.LE.ZERO ) THEN
            ATOLI = ULP*TNORM
         ELSE
            ATOLI = ABSTOL
         END IF
*
         WORK( N+1 ) = GL
         WORK( N+2 ) = GL
         WORK( N+3 ) = GU
         WORK( N+4 ) = GU
         WORK( N+5 ) = GL
         WORK( N+6 ) = GU
         IWORK( 1 ) = -1
         IWORK( 2 ) = -1
         IWORK( 3 ) = N + 1
         IWORK( 4 ) = N + 1
         IWORK( 5 ) = IL - 1
         IWORK( 6 ) = IU
*
         CALL SLAEBZ( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN, D, E,
     $                WORK, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT,
     $                IWORK, W, IBLOCK, IINFO )
*
         IF( IWORK( 6 ).EQ.IU ) THEN
            WL = WORK( N+1 )
            WLU = WORK( N+3 )
            NWL = IWORK( 1 )
            WU = WORK( N+4 )
            WUL = WORK( N+2 )
            NWU = IWORK( 4 )
         ELSE
            WL = WORK( N+2 )
            WLU = WORK( N+4 )
            NWL = IWORK( 2 )
            WU = WORK( N+3 )
            WUL = WORK( N+1 )
            NWU = IWORK( 3 )
         END IF
*
         IF( NWL.LT.0 .OR. NWL.GE.N .OR. NWU.LT.1 .OR. NWU.GT.N ) THEN
            INFO = 4
            RETURN
         END IF
      ELSE
*
*        RANGE='A' or 'V' -- Set ATOLI
*
         TNORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
     $           ABS( D( N ) )+ABS( E( N-1 ) ) )
*
         DO 30 J = 2, N - 1
            TNORM = MAX( TNORM, ABS( D( J ) )+ABS( E( J-1 ) )+
     $              ABS( E( J ) ) )
   30    CONTINUE
*
         IF( ABSTOL.LE.ZERO ) THEN
            ATOLI = ULP*TNORM
         ELSE
            ATOLI = ABSTOL
         END IF
*
         IF( IRANGE.EQ.2 ) THEN
            WL = VL
            WU = VU
         ELSE
            WL = ZERO
            WU = ZERO
         END IF
      END IF
*
*     Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
*     NWL accumulates the number of eigenvalues .le. WL,
*     NWU accumulates the number of eigenvalues .le. WU
*
      M = 0
      IEND = 0
      INFO = 0
      NWL = 0
      NWU = 0
*
      DO 70 JB = 1, NSPLIT
         IOFF = IEND
         IBEGIN = IOFF + 1
         IEND = ISPLIT( JB )
         IN = IEND - IOFF
*
         IF( IN.EQ.1 ) THEN
*
*           Special Case -- IN=1
*
            IF( IRANGE.EQ.1 .OR. WL.GE.D( IBEGIN )-PIVMIN )
     $         NWL = NWL + 1
            IF( IRANGE.EQ.1 .OR. WU.GE.D( IBEGIN )-PIVMIN )
     $         NWU = NWU + 1
            IF( IRANGE.EQ.1 .OR. ( WL.LT.D( IBEGIN )-PIVMIN .AND. WU.GE.
     $          D( IBEGIN )-PIVMIN ) ) THEN
               M = M + 1
               W( M ) = D( IBEGIN )
               IBLOCK( M ) = JB
            END IF
         ELSE
*
*           General Case -- IN > 1
*
*           Compute Gershgorin Interval
*           and use it as the initial interval
*
            GU = D( IBEGIN )
            GL = D( IBEGIN )
            TMP1 = ZERO
*
            DO 40 J = IBEGIN, IEND - 1
               TMP2 = ABS( E( J ) )
               GU = MAX( GU, D( J )+TMP1+TMP2 )
               GL = MIN( GL, D( J )-TMP1-TMP2 )
               TMP1 = TMP2
   40       CONTINUE
*
            GU = MAX( GU, D( IEND )+TMP1 )
            GL = MIN( GL, D( IEND )-TMP1 )
            BNORM = MAX( ABS( GL ), ABS( GU ) )
            GL = GL - FUDGE*BNORM*ULP*IN - FUDGE*PIVMIN
            GU = GU + FUDGE*BNORM*ULP*IN + FUDGE*PIVMIN
*
*           Compute ATOLI for the current submatrix
*
            IF( ABSTOL.LE.ZERO ) THEN
               ATOLI = ULP*MAX( ABS( GL ), ABS( GU ) )
            ELSE
               ATOLI = ABSTOL
            END IF
*
            IF( IRANGE.GT.1 ) THEN
               IF( GU.LT.WL ) THEN
                  NWL = NWL + IN
                  NWU = NWU + IN
                  GO TO 70
               END IF
               GL = MAX( GL, WL )
               GU = MIN( GU, WU )
               IF( GL.GE.GU )
     $            GO TO 70
            END IF
*
*           Set Up Initial Interval
*
            WORK( N+1 ) = GL
            WORK( N+IN+1 ) = GU
            CALL SLAEBZ( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
     $                   D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ),
     $                   IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM,
     $                   IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
*
            NWL = NWL + IWORK( 1 )
            NWU = NWU + IWORK( IN+1 )
            IWOFF = M - IWORK( 1 )
*
*           Compute Eigenvalues
*
            ITMAX = INT( ( LOG( GU-GL+PIVMIN )-LOG( PIVMIN ) ) /
     $              LOG( TWO ) ) + 2
            CALL SLAEBZ( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
     $                   D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ),
     $                   IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT,
     $                   IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
*
*           Copy Eigenvalues Into W and IBLOCK
*           Use -JB for block number for unconverged eigenvalues.
*
            DO 60 J = 1, IOUT
               TMP1 = HALF*( WORK( J+N )+WORK( J+IN+N ) )
*
*              Flag non-convergence.
*
               IF( J.GT.IOUT-IINFO ) THEN
                  NCNVRG = .TRUE.
                  IB = -JB
               ELSE
                  IB = JB
               END IF
               DO 50 JE = IWORK( J ) + 1 + IWOFF,
     $                 IWORK( J+IN ) + IWOFF
                  W( JE ) = TMP1
                  IBLOCK( JE ) = IB
   50          CONTINUE
   60       CONTINUE
*
            M = M + IM
         END IF
   70 CONTINUE
*
*     If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
*     If NWL+1 < IL or NWU > IU, discard extra eigenvalues.
*
      IF( IRANGE.EQ.3 ) THEN
         IM = 0
         IDISCL = IL - 1 - NWL
         IDISCU = NWU - IU
*
         IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN
            DO 80 JE = 1, M
               IF( W( JE ).LE.WLU .AND. IDISCL.GT.0 ) THEN
                  IDISCL = IDISCL - 1
               ELSE IF( W( JE ).GE.WUL .AND. IDISCU.GT.0 ) THEN
                  IDISCU = IDISCU - 1
               ELSE
                  IM = IM + 1
                  W( IM ) = W( JE )
                  IBLOCK( IM ) = IBLOCK( JE )
               END IF
   80       CONTINUE
            M = IM
         END IF
         IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN
*
*           Code to deal with effects of bad arithmetic:
*           Some low eigenvalues to be discarded are not in (WL,WLU],
*           or high eigenvalues to be discarded are not in (WUL,WU]
*           so just kill off the smallest IDISCL/largest IDISCU
*           eigenvalues, by simply finding the smallest/largest
*           eigenvalue(s).
*
*           (If N(w) is monotone non-decreasing, this should never
*               happen.)
*
            IF( IDISCL.GT.0 ) THEN
               WKILL = WU
               for(JDISC = 1;jdisc<= IDISCL;jdisc++){
                  IW = 0
                  for(JE = 1;je<= M;je++){
                     IF( IBLOCK( JE ).NE.0 .AND.
     $                   ( W( JE ).LT.WKILL .OR. IW.EQ.0 ) ) THEN
                        IW = JE
                        WKILL = W( JE )
                     END IF
				  }
                  IBLOCK( IW ) = 0
			   }
            END IF
            IF( IDISCU.GT.0 ) THEN
*
               WKILL = WL
               DO 120 JDISC = 1, IDISCU
                  IW = 0
                  DO 110 JE = 1, M
                     IF( IBLOCK( JE ).NE.0 .AND.
     $                   ( W( JE ).GT.WKILL .OR. IW.EQ.0 ) ) THEN
                        IW = JE
                        WKILL = W( JE )
                     END IF
  110             CONTINUE
                  IBLOCK( IW ) = 0
  120          CONTINUE
            END IF
            IM = 0
            DO 130 JE = 1, M
               IF( IBLOCK( JE ).NE.0 ) THEN
                  IM = IM + 1
                  W( IM ) = W( JE )
                  IBLOCK( IM ) = IBLOCK( JE )
               END IF
  130       CONTINUE
            M = IM
         END IF
         IF( IDISCL.LT.0 .OR. IDISCU.LT.0 ) THEN
            TOOFEW = .TRUE.
         END IF
      END IF
*
*     If ORDER='B', do nothing -- the eigenvalues are already sorted
*        by block.
*     If ORDER='E', sort the eigenvalues from smallest to largest
*
      IF( IORDER.EQ.1 .AND. NSPLIT.GT.1 ) THEN
	     for( JE = 1;je<= M - 1;je++){
            IE = 0
            TMP1 = W( JE )
            for(J = JE + 1;j<= M;j++){
               IF( W( J ).LT.TMP1 ) THEN
                  IE = J
                  TMP1 = W( J )
               END IF
            }
*
            IF( IE.NE.0 ) THEN
               ITMP1 = IBLOCK( IE )
               W( IE ) = W( JE )
               IBLOCK( IE ) = IBLOCK( JE )
               W( JE ) = TMP1
               IBLOCK( JE ) = ITMP1
            END IF
		 }
      END IF
*
      INFO = 0
      IF( NCNVRG )
     $   INFO = INFO + 1
      IF( TOOFEW )
     $   INFO = INFO + 2
      RETURN
*
*     End of SSTEBZ
*
      END