dlasd3.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 383 行 · 第 1/2 页

      ELSE IF( LDQ.LT.K ) THEN
         INFO = -7
      ELSE IF( LDU.LT.N ) THEN
         INFO = -10
      ELSE IF( LDU2.LT.N ) THEN
         INFO = -12
      ELSE IF( LDVT.LT.M ) THEN
         INFO = -14
      ELSE IF( LDVT2.LT.M ) THEN
         INFO = -16
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.186"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DLASD3.186"></a><a href="dlasd3.f.html#DLASD3.1">DLASD3</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 ) )
         CALL DCOPY( M, VT2( 1, 1 ), LDVT2, VT( 1, 1 ), LDVT )
         IF( Z( 1 ).GT.ZERO ) THEN
            CALL DCOPY( N, U2( 1, 1 ), 1, U( 1, 1 ), 1 )
         ELSE
            DO 10 I = 1, N
               U( I, 1 ) = -U2( I, 1 )
   10       CONTINUE
         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 20 I = 1, K
         DSIGMA( I ) = <a name="DLAMC3.223"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
   20 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Keep a copy of Z.
</span><span class="comment">*</span><span class="comment">
</span>      CALL DCOPY( K, Z, 1, Q, 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.233"></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">     Find the new singular values.
</span><span class="comment">*</span><span class="comment">
</span>      DO 30 J = 1, K
         CALL <a name="DLASD4.239"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>( K, J, DSIGMA, Z, U( 1, J ), RHO, D( J ),
     $                VT( 1, J ), INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        If the zero finder fails, the computation is terminated.
</span><span class="comment">*</span><span class="comment">
</span>         IF( INFO.NE.0 ) THEN
            RETURN
         END IF
   30 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 60 I = 1, K
         Z( I ) = U( I, K )*VT( I, K )
         DO 40 J = 1, I - 1
            Z( I ) = Z( I )*( U( I, J )*VT( I, J ) /
     $               ( DSIGMA( I )-DSIGMA( J ) ) /
     $               ( DSIGMA( I )+DSIGMA( J ) ) )
   40    CONTINUE
         DO 50 J = I, K - 1
            Z( I ) = Z( I )*( U( I, J )*VT( I, J ) /
     $               ( DSIGMA( I )-DSIGMA( J+1 ) ) /
     $               ( DSIGMA( I )+DSIGMA( J+1 ) ) )
   50    CONTINUE
         Z( I ) = SIGN( SQRT( ABS( Z( I ) ) ), Q( I, 1 ) )
   60 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute left singular vectors of the modified diagonal matrix,
</span><span class="comment">*</span><span class="comment">     and store related information for the right singular vectors.
</span><span class="comment">*</span><span class="comment">
</span>      DO 90 I = 1, K
         VT( 1, I ) = Z( 1 ) / U( 1, I ) / VT( 1, I )
         U( 1, I ) = NEGONE
         DO 70 J = 2, K
            VT( J, I ) = Z( J ) / U( J, I ) / VT( J, I )
            U( J, I ) = DSIGMA( J )*VT( J, I )
   70    CONTINUE
         TEMP = DNRM2( K, U( 1, I ), 1 )
         Q( 1, I ) = U( 1, I ) / TEMP
         DO 80 J = 2, K
            JC = IDXC( J )
            Q( J, I ) = U( JC, I ) / TEMP
   80    CONTINUE
   90 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Update the left singular vector matrix.
</span><span class="comment">*</span><span class="comment">
</span>      IF( K.EQ.2 ) THEN
         CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, N, K, K, ONE, U2, LDU2, Q, LDQ, ZERO, U,
     $               LDU )
         GO TO 100
      END IF
      IF( CTOT( 1 ).GT.0 ) THEN
         CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, NL, K, CTOT( 1 ), ONE, U2( 1, 2 ), LDU2,
     $               Q( 2, 1 ), LDQ, ZERO, U( 1, 1 ), LDU )
         IF( CTOT( 3 ).GT.0 ) THEN
            KTEMP = 2 + CTOT( 1 ) + CTOT( 2 )
            CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, NL, K, CTOT( 3 ), ONE, U2( 1, KTEMP ),
     $                  LDU2, Q( KTEMP, 1 ), LDQ, ONE, U( 1, 1 ), LDU )
         END IF
      ELSE IF( CTOT( 3 ).GT.0 ) THEN
         KTEMP = 2 + CTOT( 1 ) + CTOT( 2 )
         CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, NL, K, CTOT( 3 ), ONE, U2( 1, KTEMP ),
     $               LDU2, Q( KTEMP, 1 ), LDQ, ZERO, U( 1, 1 ), LDU )
      ELSE
         CALL <a name="DLACPY.304"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>( <span class="string">'F'</span>, NL, K, U2, LDU2, U, LDU )
      END IF
      CALL DCOPY( K, Q( 1, 1 ), LDQ, U( NLP1, 1 ), LDU )
      KTEMP = 2 + CTOT( 1 )
      CTEMP = CTOT( 2 ) + CTOT( 3 )
      CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, NR, K, CTEMP, ONE, U2( NLP2, KTEMP ), LDU2,
     $            Q( KTEMP, 1 ), LDQ, ZERO, U( NLP2, 1 ), LDU )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Generate the right singular vectors.
</span><span class="comment">*</span><span class="comment">
</span>  100 CONTINUE
      DO 120 I = 1, K
         TEMP = DNRM2( K, VT( 1, I ), 1 )
         Q( I, 1 ) = VT( 1, I ) / TEMP
         DO 110 J = 2, K
            JC = IDXC( J )
            Q( I, J ) = VT( JC, I ) / TEMP
  110    CONTINUE
  120 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Update the right singular vector matrix.
</span><span class="comment">*</span><span class="comment">
</span>      IF( K.EQ.2 ) THEN
         CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, K, M, K, ONE, Q, LDQ, VT2, LDVT2, ZERO,
     $               VT, LDVT )
         RETURN
      END IF
      KTEMP = 1 + CTOT( 1 )
      CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, K, NLP1, KTEMP, ONE, Q( 1, 1 ), LDQ,
     $            VT2( 1, 1 ), LDVT2, ZERO, VT( 1, 1 ), LDVT )
      KTEMP = 2 + CTOT( 1 ) + CTOT( 2 )
      IF( KTEMP.LE.LDVT2 )
     $   CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, K, NLP1, CTOT( 3 ), ONE, Q( 1, KTEMP ),
     $               LDQ, VT2( KTEMP, 1 ), LDVT2, ONE, VT( 1, 1 ),
     $               LDVT )
<span class="comment">*</span><span class="comment">
</span>      KTEMP = CTOT( 1 ) + 1
      NRP1 = NR + SQRE
      IF( KTEMP.GT.1 ) THEN
         DO 130 I = 1, K
            Q( I, KTEMP ) = Q( I, 1 )
  130    CONTINUE
         DO 140 I = NLP2, M
            VT2( KTEMP, I ) = VT2( 1, I )
  140    CONTINUE
      END IF
      CTEMP = 1 + CTOT( 2 ) + CTOT( 3 )
      CALL DGEMM( <span class="string">'N'</span>, <span class="string">'N'</span>, K, NRP1, CTEMP, ONE, Q( 1, KTEMP ), LDQ,
     $            VT2( KTEMP, NLP2 ), LDVT2, ZERO, VT( 1, NLP2 ), LDVT )
<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="DLASD3.356"></a><a href="dlasd3.f.html#DLASD3.1">DLASD3</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

 </body>
</html>