ctbrfs.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 422 行 · 第 1/2 页

</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 = KD + 2
      EPS = <a name="SLAMCH.196"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Epsilon'</span> )
      SAFMIN = <a name="SLAMCH.197"></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 250 J = 1, NRHS
<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, X( 1, J ), 1, WORK, 1 )
         CALL CTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 )
         CALL CAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 )
<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>         DO 20 I = 1, N
            RWORK( I ) = CABS1( B( I, J ) )
   20    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         IF( NOTRAN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute abs(A)*abs(X) + abs(B).
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               IF( NOUNIT ) THEN
                  DO 40 K = 1, N
                     XK = CABS1( X( K, J ) )
                     DO 30 I = MAX( 1, K-KD ), K
                        RWORK( I ) = RWORK( I ) +
     $                               CABS1( AB( KD+1+I-K, K ) )*XK
   30                CONTINUE
   40             CONTINUE
               ELSE
                  DO 60 K = 1, N
                     XK = CABS1( X( K, J ) )
                     DO 50 I = MAX( 1, K-KD ), K - 1
                        RWORK( I ) = RWORK( I ) +
     $                               CABS1( AB( KD+1+I-K, K ) )*XK
   50                CONTINUE
                     RWORK( K ) = RWORK( K ) + XK
   60             CONTINUE
               END IF
            ELSE
               IF( NOUNIT ) THEN
                  DO 80 K = 1, N
                     XK = CABS1( X( K, J ) )
                     DO 70 I = K, MIN( N, K+KD )
                        RWORK( I ) = RWORK( I ) +
     $                               CABS1( AB( 1+I-K, K ) )*XK
   70                CONTINUE
   80             CONTINUE
               ELSE
                  DO 100 K = 1, N
                     XK = CABS1( X( K, J ) )
                     DO 90 I = K + 1, MIN( N, K+KD )
                        RWORK( I ) = RWORK( I ) +
     $                               CABS1( AB( 1+I-K, K ) )*XK
   90                CONTINUE
                     RWORK( K ) = RWORK( K ) + XK
  100             CONTINUE
               END IF
            END IF
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute abs(A**H)*abs(X) + abs(B).
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               IF( NOUNIT ) THEN
                  DO 120 K = 1, N
                     S = ZERO
                     DO 110 I = MAX( 1, K-KD ), K
                        S = S + CABS1( AB( KD+1+I-K, K ) )*
     $                      CABS1( X( I, J ) )
  110                CONTINUE
                     RWORK( K ) = RWORK( K ) + S
  120             CONTINUE
               ELSE
                  DO 140 K = 1, N
                     S = CABS1( X( K, J ) )
                     DO 130 I = MAX( 1, K-KD ), K - 1
                        S = S + CABS1( AB( KD+1+I-K, K ) )*
     $                      CABS1( X( I, J ) )
  130                CONTINUE
                     RWORK( K ) = RWORK( K ) + S
  140             CONTINUE
               END IF
            ELSE
               IF( NOUNIT ) THEN
                  DO 160 K = 1, N
                     S = ZERO
                     DO 150 I = K, MIN( N, K+KD )
                        S = S + CABS1( AB( 1+I-K, K ) )*
     $                      CABS1( X( I, J ) )
  150                CONTINUE
                     RWORK( K ) = RWORK( K ) + S
  160             CONTINUE
               ELSE
                  DO 180 K = 1, N
                     S = CABS1( X( K, J ) )
                     DO 170 I = K + 1, MIN( N, K+KD )
                        S = S + CABS1( AB( 1+I-K, K ) )*
     $                      CABS1( X( I, J ) )
  170                CONTINUE
                     RWORK( K ) = RWORK( K ) + S
  180             CONTINUE
               END IF
            END IF
         END IF
         S = ZERO
         DO 190 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
  190    CONTINUE
         BERR( J ) = S
<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="CLACN2.343"></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 200 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
  200    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         KASE = 0
  210    CONTINUE
         CALL <a name="CLACN2.358"></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 CTBSV( UPLO, TRANST, DIAG, N, KD, AB, LDAB, WORK,
     $                     1 )
               DO 220 I = 1, N
                  WORK( I ) = RWORK( I )*WORK( I )
  220          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 230 I = 1, N
                  WORK( I ) = RWORK( I )*WORK( I )
  230          CONTINUE
               CALL CTBSV( UPLO, TRANSN, DIAG, N, KD, AB, LDAB, WORK,
     $                     1 )
            END IF
            GO TO 210
         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 240 I = 1, N
            LSTRES = MAX( LSTRES, CABS1( X( I, J ) ) )
  240    CONTINUE
         IF( LSTRES.NE.ZERO )
     $      FERR( J ) = FERR( J ) / LSTRES
<span class="comment">*</span><span class="comment">
</span>  250 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="CTBRFS.395"></a><a href="ctbrfs.f.html#CTBRFS.1">CTBRFS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

 </body>
</html>