dlasd4.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 915 行 · 第 1/4 页

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         ERRETM = ABS( ERRETM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Evaluate PHI and the derivative DPHI
</span><span class="comment">*</span><span class="comment">
</span>         DPHI = ZERO
         PHI = ZERO
         DO 190 J = N, IIP1, -1
            TEMP = Z( J ) / ( WORK( J )*DELTA( J ) )
            PHI = PHI + Z( J )*TEMP
            DPHI = DPHI + TEMP*TEMP
            ERRETM = ERRETM + PHI
  190    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
         DW = DPSI + DPHI + TEMP*TEMP
         TEMP = Z( II )*TEMP
         W = RHOINV + PHI + PSI + TEMP
         ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
     $            THREE*ABS( TEMP ) + ABS( TAU )*DW
<span class="comment">*</span><span class="comment">
</span>         IF( W.LE.ZERO ) THEN
            SG2LB = MAX( SG2LB, TAU )
         ELSE
            SG2UB = MIN( SG2UB, TAU )
         END IF
<span class="comment">*</span><span class="comment">
</span>         SWTCH = .FALSE.
         IF( ORGATI ) THEN
            IF( -W.GT.ABS( PREW ) / TEN )
     $         SWTCH = .TRUE.
         ELSE
            IF( W.GT.ABS( PREW ) / TEN )
     $         SWTCH = .TRUE.
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Main loop to update the values of the array   DELTA and WORK
</span><span class="comment">*</span><span class="comment">
</span>         ITER = NITER + 1
<span class="comment">*</span><span class="comment">
</span>         DO 230 NITER = ITER, MAXIT
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Test for convergence
</span><span class="comment">*</span><span class="comment">
</span>            IF( ABS( W ).LE.EPS*ERRETM ) THEN
               GO TO 240
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Calculate the new step
</span><span class="comment">*</span><span class="comment">
</span>            IF( .NOT.SWTCH3 ) THEN
               DTIPSQ = WORK( IP1 )*DELTA( IP1 )
               DTISQ = WORK( I )*DELTA( I )
               IF( .NOT.SWTCH ) THEN
                  IF( ORGATI ) THEN
                     C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2
                  ELSE
                     C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2
                  END IF
               ELSE
                  TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
                  IF( ORGATI ) THEN
                     DPSI = DPSI + TEMP*TEMP
                  ELSE
                     DPHI = DPHI + TEMP*TEMP
                  END IF
                  C = W - DTISQ*DPSI - DTIPSQ*DPHI
               END IF
               A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
               B = DTIPSQ*DTISQ*W
               IF( C.EQ.ZERO ) THEN
                  IF( A.EQ.ZERO ) THEN
                     IF( .NOT.SWTCH ) THEN
                        IF( ORGATI ) THEN
                           A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*
     $                         ( DPSI+DPHI )
                        ELSE
                           A = Z( IP1 )*Z( IP1 ) +
     $                         DTISQ*DTISQ*( DPSI+DPHI )
                        END IF
                     ELSE
                        A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI
                     END IF
                  END IF
                  ETA = B / A
               ELSE IF( A.LE.ZERO ) THEN
                  ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
               ELSE
                  ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
               END IF
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Interpolation using THREE most relevant poles
</span><span class="comment">*</span><span class="comment">
</span>               DTIIM = WORK( IIM1 )*DELTA( IIM1 )
               DTIIP = WORK( IIP1 )*DELTA( IIP1 )
               TEMP = RHOINV + PSI + PHI
               IF( SWTCH ) THEN
                  C = TEMP - DTIIM*DPSI - DTIIP*DPHI
                  ZZ( 1 ) = DTIIM*DTIIM*DPSI
                  ZZ( 3 ) = DTIIP*DTIIP*DPHI
               ELSE
                  IF( ORGATI ) THEN
                     TEMP1 = Z( IIM1 ) / DTIIM
                     TEMP1 = TEMP1*TEMP1
                     TEMP2 = ( D( IIM1 )-D( IIP1 ) )*
     $                       ( D( IIM1 )+D( IIP1 ) )*TEMP1
                     C = TEMP - DTIIP*( DPSI+DPHI ) - TEMP2
                     ZZ( 1 ) = Z( IIM1 )*Z( IIM1 )
                     IF( DPSI.LT.TEMP1 ) THEN
                        ZZ( 3 ) = DTIIP*DTIIP*DPHI
                     ELSE
                        ZZ( 3 ) = DTIIP*DTIIP*( ( DPSI-TEMP1 )+DPHI )
                     END IF
                  ELSE
                     TEMP1 = Z( IIP1 ) / DTIIP
                     TEMP1 = TEMP1*TEMP1
                     TEMP2 = ( D( IIP1 )-D( IIM1 ) )*
     $                       ( D( IIM1 )+D( IIP1 ) )*TEMP1
                     C = TEMP - DTIIM*( DPSI+DPHI ) - TEMP2
                     IF( DPHI.LT.TEMP1 ) THEN
                        ZZ( 1 ) = DTIIM*DTIIM*DPSI
                     ELSE
                        ZZ( 1 ) = DTIIM*DTIIM*( DPSI+( DPHI-TEMP1 ) )
                     END IF
                     ZZ( 3 ) = Z( IIP1 )*Z( IIP1 )
                  END IF
               END IF
               DD( 1 ) = DTIIM
               DD( 2 ) = DELTA( II )*WORK( II )
               DD( 3 ) = DTIIP
               CALL <a name="DLAED6.799"></a><a href="dlaed6.f.html#DLAED6.1">DLAED6</a>( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
               IF( INFO.NE.0 )
     $            GO TO 240
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Note, eta should be positive if w is negative, and
</span><span class="comment">*</span><span class="comment">           eta should be negative otherwise. However,
</span><span class="comment">*</span><span class="comment">           if for some reason caused by roundoff, eta*w &gt; 0,
</span><span class="comment">*</span><span class="comment">           we simply use one Newton step instead. This way
</span><span class="comment">*</span><span class="comment">           will guarantee eta*w &lt; 0.
</span><span class="comment">*</span><span class="comment">
</span>            IF( W*ETA.GE.ZERO )
     $         ETA = -W / DW
            IF( ORGATI ) THEN
               TEMP1 = WORK( I )*DELTA( I )
               TEMP = ETA - TEMP1
            ELSE
               TEMP1 = WORK( IP1 )*DELTA( IP1 )
               TEMP = ETA - TEMP1
            END IF
            IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN
               IF( W.LT.ZERO ) THEN
                  ETA = ( SG2UB-TAU ) / TWO
               ELSE
                  ETA = ( SG2LB-TAU ) / TWO
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span>            TAU = TAU + ETA
            ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
<span class="comment">*</span><span class="comment">
</span>            SIGMA = SIGMA + ETA
            DO 200 J = 1, N
               WORK( J ) = WORK( J ) + ETA
               DELTA( J ) = DELTA( J ) - ETA
  200       CONTINUE
<span class="comment">*</span><span class="comment">
</span>            PREW = W
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Evaluate PSI and the derivative DPSI
</span><span class="comment">*</span><span class="comment">
</span>            DPSI = ZERO
            PSI = ZERO
            ERRETM = ZERO
            DO 210 J = 1, IIM1
               TEMP = Z( J ) / ( WORK( J )*DELTA( J ) )
               PSI = PSI + Z( J )*TEMP
               DPSI = DPSI + TEMP*TEMP
               ERRETM = ERRETM + PSI
  210       CONTINUE
            ERRETM = ABS( ERRETM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Evaluate PHI and the derivative DPHI
</span><span class="comment">*</span><span class="comment">
</span>            DPHI = ZERO
            PHI = ZERO
            DO 220 J = N, IIP1, -1
               TEMP = Z( J ) / ( WORK( J )*DELTA( J ) )
               PHI = PHI + Z( J )*TEMP
               DPHI = DPHI + TEMP*TEMP
               ERRETM = ERRETM + PHI
  220       CONTINUE
<span class="comment">*</span><span class="comment">
</span>            TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
            DW = DPSI + DPHI + TEMP*TEMP
            TEMP = Z( II )*TEMP
            W = RHOINV + PHI + PSI + TEMP
            ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
     $               THREE*ABS( TEMP ) + ABS( TAU )*DW
            IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN )
     $         SWTCH = .NOT.SWTCH
<span class="comment">*</span><span class="comment">
</span>            IF( W.LE.ZERO ) THEN
               SG2LB = MAX( SG2LB, TAU )
            ELSE
               SG2UB = MIN( SG2UB, TAU )
            END IF
<span class="comment">*</span><span class="comment">
</span>  230    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Return with INFO = 1, NITER = MAXIT and not converged
</span><span class="comment">*</span><span class="comment">
</span>         INFO = 1
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span>  240 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DLASD4.888"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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