cgtrfs.f.html

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         DO 10 J = 1, NRHS
            FERR( J ) = ZERO
            BERR( J ) = ZERO
   10    CONTINUE
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( NOTRAN ) THEN
         TRANSN = <span class="string">'N'</span>
         TRANST = <span class="string">'C'</span>
      ELSE
         TRANSN = <span class="string">'C'</span>
         TRANST = <span class="string">'N'</span>
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     NZ = maximum number of nonzero elements in each row of A, plus 1
</span><span class="comment">*</span><span class="comment">
</span>      NZ = 4
      EPS = <a name="SLAMCH.199"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Epsilon'</span> )
      SAFMIN = <a name="SLAMCH.200"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> )
      SAFE1 = NZ*SAFMIN
      SAFE2 = SAFE1 / EPS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Do for each right hand side
</span><span class="comment">*</span><span class="comment">
</span>      DO 110 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span>         COUNT = 1
         LSTRES = THREE
   20    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Loop until stopping criterion is satisfied.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute residual R = B - op(A) * X,
</span><span class="comment">*</span><span class="comment">        where op(A) = A, A**T, or A**H, depending on TRANS.
</span><span class="comment">*</span><span class="comment">
</span>         CALL CCOPY( N, B( 1, J ), 1, WORK, 1 )
         CALL <a name="CLAGTM.218"></a><a href="clagtm.f.html#CLAGTM.1">CLAGTM</a>( TRANS, N, 1, -ONE, DL, D, DU, X( 1, J ), LDX, ONE,
     $                WORK, N )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute abs(op(A))*abs(x) + abs(b) for use in the backward
</span><span class="comment">*</span><span class="comment">        error bound.
</span><span class="comment">*</span><span class="comment">
</span>         IF( NOTRAN ) THEN
            IF( N.EQ.1 ) THEN
               RWORK( 1 ) = CABS1( B( 1, J ) ) +
     $                      CABS1( D( 1 ) )*CABS1( X( 1, J ) )
            ELSE
               RWORK( 1 ) = CABS1( B( 1, J ) ) +
     $                      CABS1( D( 1 ) )*CABS1( X( 1, J ) ) +
     $                      CABS1( DU( 1 ) )*CABS1( X( 2, J ) )
               DO 30 I = 2, N - 1
                  RWORK( I ) = CABS1( B( I, J ) ) +
     $                         CABS1( DL( I-1 ) )*CABS1( X( I-1, J ) ) +
     $                         CABS1( D( I ) )*CABS1( X( I, J ) ) +
     $                         CABS1( DU( I ) )*CABS1( X( I+1, J ) )
   30          CONTINUE
               RWORK( N ) = CABS1( B( N, J ) ) +
     $                      CABS1( DL( N-1 ) )*CABS1( X( N-1, J ) ) +
     $                      CABS1( D( N ) )*CABS1( X( N, J ) )
            END IF
         ELSE
            IF( N.EQ.1 ) THEN
               RWORK( 1 ) = CABS1( B( 1, J ) ) +
     $                      CABS1( D( 1 ) )*CABS1( X( 1, J ) )
            ELSE
               RWORK( 1 ) = CABS1( B( 1, J ) ) +
     $                      CABS1( D( 1 ) )*CABS1( X( 1, J ) ) +
     $                      CABS1( DL( 1 ) )*CABS1( X( 2, J ) )
               DO 40 I = 2, N - 1
                  RWORK( I ) = CABS1( B( I, J ) ) +
     $                         CABS1( DU( I-1 ) )*CABS1( X( I-1, J ) ) +
     $                         CABS1( D( I ) )*CABS1( X( I, J ) ) +
     $                         CABS1( DL( I ) )*CABS1( X( I+1, J ) )
   40          CONTINUE
               RWORK( N ) = CABS1( B( N, J ) ) +
     $                      CABS1( DU( N-1 ) )*CABS1( X( N-1, J ) ) +
     $                      CABS1( D( N ) )*CABS1( X( N, J ) )
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute componentwise relative backward error from formula
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        where abs(Z) is the componentwise absolute value of the matrix
</span><span class="comment">*</span><span class="comment">        or vector Z.  If the i-th component of the denominator is less
</span><span class="comment">*</span><span class="comment">        than SAFE2, then SAFE1 is added to the i-th components of the
</span><span class="comment">*</span><span class="comment">        numerator and denominator before dividing.
</span><span class="comment">*</span><span class="comment">
</span>         S = ZERO
         DO 50 I = 1, N
            IF( RWORK( I ).GT.SAFE2 ) THEN
               S = MAX( S, CABS1( WORK( I ) ) / RWORK( I ) )
            ELSE
               S = MAX( S, ( CABS1( WORK( I ) )+SAFE1 ) /
     $             ( RWORK( I )+SAFE1 ) )
            END IF
   50    CONTINUE
         BERR( J ) = S
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Test stopping criterion. Continue iterating if
</span><span class="comment">*</span><span class="comment">           1) The residual BERR(J) is larger than machine epsilon, and
</span><span class="comment">*</span><span class="comment">           2) BERR(J) decreased by at least a factor of 2 during the
</span><span class="comment">*</span><span class="comment">              last iteration, and
</span><span class="comment">*</span><span class="comment">           3) At most ITMAX iterations tried.
</span><span class="comment">*</span><span class="comment">
</span>         IF( BERR( J ).GT.EPS .AND. TWO*BERR( J ).LE.LSTRES .AND.
     $       COUNT.LE.ITMAX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update solution and try again.
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="CGTTRS.293"></a><a href="cgttrs.f.html#CGTTRS.1">CGTTRS</a>( TRANS, N, 1, DLF, DF, DUF, DU2, IPIV, WORK, N,
     $                   INFO )
            CALL CAXPY( N, CMPLX( ONE ), WORK, 1, X( 1, J ), 1 )
            LSTRES = BERR( J )
            COUNT = COUNT + 1
            GO TO 20
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Bound error from formula
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        norm(X - XTRUE) / norm(X) .le. FERR =
</span><span class="comment">*</span><span class="comment">        norm( abs(inv(op(A)))*
</span><span class="comment">*</span><span class="comment">           ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        where
</span><span class="comment">*</span><span class="comment">          norm(Z) is the magnitude of the largest component of Z
</span><span class="comment">*</span><span class="comment">          inv(op(A)) is the inverse of op(A)
</span><span class="comment">*</span><span class="comment">          abs(Z) is the componentwise absolute value of the matrix or
</span><span class="comment">*</span><span class="comment">             vector Z
</span><span class="comment">*</span><span class="comment">          NZ is the maximum number of nonzeros in any row of A, plus 1
</span><span class="comment">*</span><span class="comment">          EPS is machine epsilon
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
</span><span class="comment">*</span><span class="comment">        is incremented by SAFE1 if the i-th component of
</span><span class="comment">*</span><span class="comment">        abs(op(A))*abs(X) + abs(B) is less than SAFE2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use <a name="CLACN2.319"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a> to estimate the infinity-norm of the matrix
</span><span class="comment">*</span><span class="comment">           inv(op(A)) * diag(W),
</span><span class="comment">*</span><span class="comment">        where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) )))
</span><span class="comment">*</span><span class="comment">
</span>         DO 60 I = 1, N
            IF( RWORK( I ).GT.SAFE2 ) THEN
               RWORK( I ) = CABS1( WORK( I ) ) + NZ*EPS*RWORK( I )
            ELSE
               RWORK( I ) = CABS1( WORK( I ) ) + NZ*EPS*RWORK( I ) +
     $                      SAFE1
            END IF
   60    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         KASE = 0
   70    CONTINUE
         CALL <a name="CLACN2.334"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>( N, WORK( N+1 ), WORK, FERR( J ), KASE, ISAVE )
         IF( KASE.NE.0 ) THEN
            IF( KASE.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Multiply by diag(W)*inv(op(A)**H).
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="CGTTRS.340"></a><a href="cgttrs.f.html#CGTTRS.1">CGTTRS</a>( TRANST, N, 1, DLF, DF, DUF, DU2, IPIV, WORK,
     $                      N, INFO )
               DO 80 I = 1, N
                  WORK( I ) = RWORK( I )*WORK( I )
   80          CONTINUE
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Multiply by inv(op(A))*diag(W).
</span><span class="comment">*</span><span class="comment">
</span>               DO 90 I = 1, N
                  WORK( I ) = RWORK( I )*WORK( I )
   90          CONTINUE
               CALL <a name="CGTTRS.352"></a><a href="cgttrs.f.html#CGTTRS.1">CGTTRS</a>( TRANSN, N, 1, DLF, DF, DUF, DU2, IPIV, WORK,
     $                      N, INFO )
            END IF
            GO TO 70
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Normalize error.
</span><span class="comment">*</span><span class="comment">
</span>         LSTRES = ZERO
         DO 100 I = 1, N
            LSTRES = MAX( LSTRES, CABS1( X( I, J ) ) )
  100    CONTINUE
         IF( LSTRES.NE.ZERO )
     $      FERR( J ) = FERR( J ) / LSTRES
<span class="comment">*</span><span class="comment">
</span>  110 CONTINUE
<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="CGTRFS.371"></a><a href="cgtrfs.f.html#CGTRFS.1">CGTRFS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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