dlasd8.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 278 行 · 第 1/2 页

</span>      IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
         INFO = -1
      ELSE IF( K.LT.1 ) THEN
         INFO = -2
      ELSE IF( LDDIFR.LT.K ) THEN
         INFO = -9
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.129"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DLASD8.129"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( K.EQ.1 ) THEN
         D( 1 ) = ABS( Z( 1 ) )
         DIFL( 1 ) = D( 1 )
         IF( ICOMPQ.EQ.1 ) THEN
            DIFL( 2 ) = ONE
            DIFR( 1, 2 ) = ONE
         END IF
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can
</span><span class="comment">*</span><span class="comment">     be computed with high relative accuracy (barring over/underflow).
</span><span class="comment">*</span><span class="comment">     This is a problem on machines without a guard digit in
</span><span class="comment">*</span><span class="comment">     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
</span><span class="comment">*</span><span class="comment">     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I),
</span><span class="comment">*</span><span class="comment">     which on any of these machines zeros out the bottommost
</span><span class="comment">*</span><span class="comment">     bit of DSIGMA(I) if it is 1; this makes the subsequent
</span><span class="comment">*</span><span class="comment">     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation
</span><span class="comment">*</span><span class="comment">     occurs. On binary machines with a guard digit (almost all
</span><span class="comment">*</span><span class="comment">     machines) it does not change DSIGMA(I) at all. On hexadecimal
</span><span class="comment">*</span><span class="comment">     and decimal machines with a guard digit, it slightly
</span><span class="comment">*</span><span class="comment">     changes the bottommost bits of DSIGMA(I). It does not account
</span><span class="comment">*</span><span class="comment">     for hexadecimal or decimal machines without guard digits
</span><span class="comment">*</span><span class="comment">     (we know of none). We use a subroutine call to compute
</span><span class="comment">*</span><span class="comment">     2*DSIGMA(I) to prevent optimizing compilers from eliminating
</span><span class="comment">*</span><span class="comment">     this code.
</span><span class="comment">*</span><span class="comment">
</span>      DO 10 I = 1, K
         DSIGMA( I ) = <a name="DLAMC3.163"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
   10 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Book keeping.
</span><span class="comment">*</span><span class="comment">
</span>      IWK1 = 1
      IWK2 = IWK1 + K
      IWK3 = IWK2 + K
      IWK2I = IWK2 - 1
      IWK3I = IWK3 - 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Normalize Z.
</span><span class="comment">*</span><span class="comment">
</span>      RHO = DNRM2( K, Z, 1 )
      CALL <a name="DLASCL.177"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, RHO, ONE, K, 1, Z, K, INFO )
      RHO = RHO*RHO
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize WORK(IWK3).
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DLASET.182"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>( <span class="string">'A'</span>, K, 1, ONE, ONE, WORK( IWK3 ), K )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the updated singular values, the arrays DIFL, DIFR,
</span><span class="comment">*</span><span class="comment">     and the updated Z.
</span><span class="comment">*</span><span class="comment">
</span>      DO 40 J = 1, K
         CALL <a name="DLASD4.188"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>( K, J, DSIGMA, Z, WORK( IWK1 ), RHO, D( J ),
     $                WORK( IWK2 ), INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        If the root finder fails, the computation is terminated.
</span><span class="comment">*</span><span class="comment">
</span>         IF( INFO.NE.0 ) THEN
            RETURN
         END IF
         WORK( IWK3I+J ) = WORK( IWK3I+J )*WORK( J )*WORK( IWK2I+J )
         DIFL( J ) = -WORK( J )
         DIFR( J, 1 ) = -WORK( J+1 )
         DO 20 I = 1, J - 1
            WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )*
     $                        WORK( IWK2I+I ) / ( DSIGMA( I )-
     $                        DSIGMA( J ) ) / ( DSIGMA( I )+
     $                        DSIGMA( J ) )
   20    CONTINUE
         DO 30 I = J + 1, K
            WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )*
     $                        WORK( IWK2I+I ) / ( DSIGMA( I )-
     $                        DSIGMA( J ) ) / ( DSIGMA( I )+
     $                        DSIGMA( J ) )
   30    CONTINUE
   40 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute updated Z.
</span><span class="comment">*</span><span class="comment">
</span>      DO 50 I = 1, K
         Z( I ) = SIGN( SQRT( ABS( WORK( IWK3I+I ) ) ), Z( I ) )
   50 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Update VF and VL.
</span><span class="comment">*</span><span class="comment">
</span>      DO 80 J = 1, K
         DIFLJ = DIFL( J )
         DJ = D( J )
         DSIGJ = -DSIGMA( J )
         IF( J.LT.K ) THEN
            DIFRJ = -DIFR( J, 1 )
            DSIGJP = -DSIGMA( J+1 )
         END IF
         WORK( J ) = -Z( J ) / DIFLJ / ( DSIGMA( J )+DJ )
         DO 60 I = 1, J - 1
            WORK( I ) = Z( I ) / ( <a name="DLAMC3.231"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>( DSIGMA( I ), DSIGJ )-DIFLJ )
     $                   / ( DSIGMA( I )+DJ )
   60    CONTINUE
         DO 70 I = J + 1, K
            WORK( I ) = Z( I ) / ( <a name="DLAMC3.235"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>( DSIGMA( I ), DSIGJP )+DIFRJ )
     $                   / ( DSIGMA( I )+DJ )
   70    CONTINUE
         TEMP = DNRM2( K, WORK, 1 )
         WORK( IWK2I+J ) = DDOT( K, WORK, 1, VF, 1 ) / TEMP
         WORK( IWK3I+J ) = DDOT( K, WORK, 1, VL, 1 ) / TEMP
         IF( ICOMPQ.EQ.1 ) THEN
            DIFR( J, 2 ) = TEMP
         END IF
   80 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      CALL DCOPY( K, WORK( IWK2 ), 1, VF, 1 )
      CALL DCOPY( K, WORK( IWK3 ), 1, VL, 1 )
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DLASD8.251"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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