slasq2.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 473 行 · 第 1/2 页

   30 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      I0 = 1
      N0 = N
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reverse the qd-array, if warranted.
</span><span class="comment">*</span><span class="comment">
</span>      IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN
         IPN4 = 4*( I0+N0 )
         DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4
            TEMP = Z( I4-3 )
            Z( I4-3 ) = Z( IPN4-I4-3 )
            Z( IPN4-I4-3 ) = TEMP
            TEMP = Z( I4-1 )
            Z( I4-1 ) = Z( IPN4-I4-5 )
            Z( IPN4-I4-5 ) = TEMP
   40    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initial split checking via dqd and Li's test.
</span><span class="comment">*</span><span class="comment">
</span>      PP = 0
<span class="comment">*</span><span class="comment">
</span>      DO 80 K = 1, 2
<span class="comment">*</span><span class="comment">
</span>         D = Z( 4*N0+PP-3 )
         DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4
            IF( Z( I4-1 ).LE.TOL2*D ) THEN
               Z( I4-1 ) = -ZERO
               D = Z( I4-3 )
            ELSE
               D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) )
            END IF
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        dqd maps Z to ZZ plus Li's test.
</span><span class="comment">*</span><span class="comment">
</span>         EMIN = Z( 4*I0+PP+1 )
         D = Z( 4*I0+PP-3 )
         DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4
            Z( I4-2*PP-2 ) = D + Z( I4-1 )
            IF( Z( I4-1 ).LE.TOL2*D ) THEN
               Z( I4-1 ) = -ZERO
               Z( I4-2*PP-2 ) = D
               Z( I4-2*PP ) = ZERO
               D = Z( I4+1 )
            ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND.
     $               SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN
               TEMP = Z( I4+1 ) / Z( I4-2*PP-2 )
               Z( I4-2*PP ) = Z( I4-1 )*TEMP
               D = D*TEMP
            ELSE
               Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) )
               D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) )
            END IF
            EMIN = MIN( EMIN, Z( I4-2*PP ) )
   60    CONTINUE 
         Z( 4*N0-PP-2 ) = D
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Now find qmax.
</span><span class="comment">*</span><span class="comment">
</span>         QMAX = Z( 4*I0-PP-2 )
         DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4
            QMAX = MAX( QMAX, Z( I4 ) )
   70    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Prepare for the next iteration on K.
</span><span class="comment">*</span><span class="comment">
</span>         PP = 1 - PP
   80 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialise variables to pass to <a name="SLAZQ3.290"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>
</span><span class="comment">*</span><span class="comment">
</span>      TTYPE = 0
      DMIN1 = ZERO
      DMIN2 = ZERO
      DN    = ZERO
      DN1   = ZERO
      DN2   = ZERO
      TAU   = ZERO
<span class="comment">*</span><span class="comment">
</span>      ITER = 2
      NFAIL = 0
      NDIV = 2*( N0-I0 )
<span class="comment">*</span><span class="comment">
</span>      DO 140 IWHILA = 1, N + 1
         IF( N0.LT.1 ) 
     $      GO TO 150
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        While array unfinished do 
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        E(N0) holds the value of SIGMA when submatrix in I0:N0
</span><span class="comment">*</span><span class="comment">        splits from the rest of the array, but is negated.
</span><span class="comment">*</span><span class="comment">      
</span>         DESIG = ZERO
         IF( N0.EQ.N ) THEN
            SIGMA = ZERO
         ELSE
            SIGMA = -Z( 4*N0-1 )
         END IF
         IF( SIGMA.LT.ZERO ) THEN
            INFO = 1
            RETURN
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find last unreduced submatrix's top index I0, find QMAX and
</span><span class="comment">*</span><span class="comment">        EMIN. Find Gershgorin-type bound if Q's much greater than E's.
</span><span class="comment">*</span><span class="comment">
</span>         EMAX = ZERO 
         IF( N0.GT.I0 ) THEN
            EMIN = ABS( Z( 4*N0-5 ) )
         ELSE
            EMIN = ZERO
         END IF
         QMIN = Z( 4*N0-3 )
         QMAX = QMIN
         DO 90 I4 = 4*N0, 8, -4
            IF( Z( I4-5 ).LE.ZERO )
     $         GO TO 100
            IF( QMIN.GE.FOUR*EMAX ) THEN
               QMIN = MIN( QMIN, Z( I4-3 ) )
               EMAX = MAX( EMAX, Z( I4-5 ) )
            END IF
            QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) )
            EMIN = MIN( EMIN, Z( I4-5 ) )
   90    CONTINUE
         I4 = 4 
<span class="comment">*</span><span class="comment">
</span>  100    CONTINUE
         I0 = I4 / 4
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Store EMIN for passing to <a name="SLAZQ3.350"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>.
</span><span class="comment">*</span><span class="comment">
</span>         Z( 4*N0-1 ) = EMIN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Put -(initial shift) into DMIN.
</span><span class="comment">*</span><span class="comment">
</span>         DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Now I0:N0 is unreduced. PP = 0 for ping, PP = 1 for pong.
</span><span class="comment">*</span><span class="comment">
</span>         PP = 0 
<span class="comment">*</span><span class="comment">
</span>         NBIG = 30*( N0-I0+1 )
         DO 120 IWHILB = 1, NBIG
            IF( I0.GT.N0 ) 
     $         GO TO 130
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           While submatrix unfinished take a good dqds step.
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="SLAZQ3.369"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
     $                   ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
     $                   DN2, TAU )
<span class="comment">*</span><span class="comment">
</span>            PP = 1 - PP
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           When EMIN is very small check for splits.
</span><span class="comment">*</span><span class="comment">
</span>            IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN
               IF( Z( 4*N0 ).LE.TOL2*QMAX .OR.
     $             Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN
                  SPLT = I0 - 1
                  QMAX = Z( 4*I0-3 )
                  EMIN = Z( 4*I0-1 )
                  OLDEMN = Z( 4*I0 )
                  DO 110 I4 = 4*I0, 4*( N0-3 ), 4
                     IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR.
     $                   Z( I4-1 ).LE.TOL2*SIGMA ) THEN
                        Z( I4-1 ) = -SIGMA
                        SPLT = I4 / 4
                        QMAX = ZERO
                        EMIN = Z( I4+3 )
                        OLDEMN = Z( I4+4 )
                     ELSE
                        QMAX = MAX( QMAX, Z( I4+1 ) )
                        EMIN = MIN( EMIN, Z( I4-1 ) )
                        OLDEMN = MIN( OLDEMN, Z( I4 ) )
                     END IF
  110             CONTINUE
                  Z( 4*N0-1 ) = EMIN
                  Z( 4*N0 ) = OLDEMN
                  I0 = SPLT + 1
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span>  120    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         INFO = 2
         RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        end IWHILB
</span><span class="comment">*</span><span class="comment">
</span>  130    CONTINUE
<span class="comment">*</span><span class="comment">
</span>  140 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      INFO = 3
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     end IWHILA   
</span><span class="comment">*</span><span class="comment">
</span>  150 CONTINUE
<span class="comment">*</span><span class="comment">      
</span><span class="comment">*</span><span class="comment">     Move q's to the front.
</span><span class="comment">*</span><span class="comment">      
</span>      DO 160 K = 2, N
         Z( K ) = Z( 4*K-3 )
  160 CONTINUE
<span class="comment">*</span><span class="comment">      
</span><span class="comment">*</span><span class="comment">     Sort and compute sum of eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SLASRT.430"></a><a href="slasrt.f.html#SLASRT.1">SLASRT</a>( <span class="string">'D'</span>, N, Z, IINFO )
<span class="comment">*</span><span class="comment">
</span>      E = ZERO
      DO 170 K = N, 1, -1
         E = E + Z( K )
  170 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Store trace, sum(eigenvalues) and information on performance.
</span><span class="comment">*</span><span class="comment">
</span>      Z( 2*N+1 ) = TRACE 
      Z( 2*N+2 ) = E
      Z( 2*N+3 ) = REAL( ITER )
      Z( 2*N+4 ) = REAL( NDIV ) / REAL( N**2 )
      Z( 2*N+5 ) = HUNDRD*NFAIL / REAL( ITER )
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLASQ2.446"></a><a href="slasq2.f.html#SLASQ2.1">SLASQ2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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