dlatbs.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 748 行 · 第 1/4 页

</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute the growth in A' * x = b.
</span><span class="comment">*</span><span class="comment">
</span>         IF( UPPER ) THEN
            JFIRST = 1
            JLAST = N
            JINC = 1
            MAIND = KD + 1
         ELSE
            JFIRST = N
            JLAST = 1
            JINC = -1
            MAIND = 1
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( TSCAL.NE.ONE ) THEN
            GROW = ZERO
            GO TO 80
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( NOUNIT ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           A is non-unit triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute GROW = 1/G(j) and XBND = 1/M(j).
</span><span class="comment">*</span><span class="comment">           Initially, M(0) = max{x(i), i=1,...,n}.
</span><span class="comment">*</span><span class="comment">
</span>            GROW = ONE / MAX( XBND, SMLNUM )
            XBND = GROW
            DO 60 J = JFIRST, JLAST, JINC
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Exit the loop if the growth factor is too small.
</span><span class="comment">*</span><span class="comment">
</span>               IF( GROW.LE.SMLNUM )
     $            GO TO 80
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) )
</span><span class="comment">*</span><span class="comment">
</span>               XJ = ONE + CNORM( J )
               GROW = MIN( GROW, XBND / XJ )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j))
</span><span class="comment">*</span><span class="comment">
</span>               TJJ = ABS( AB( MAIND, J ) )
               IF( XJ.GT.TJJ )
     $            XBND = XBND*( TJJ / XJ )
   60       CONTINUE
            GROW = MIN( GROW, XBND )
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           A is unit triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
</span><span class="comment">*</span><span class="comment">
</span>            GROW = MIN( ONE, ONE / MAX( XBND, SMLNUM ) )
            DO 70 J = JFIRST, JLAST, JINC
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Exit the loop if the growth factor is too small.
</span><span class="comment">*</span><span class="comment">
</span>               IF( GROW.LE.SMLNUM )
     $            GO TO 80
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              G(j) = ( 1 + CNORM(j) )*G(j-1)
</span><span class="comment">*</span><span class="comment">
</span>               XJ = ONE + CNORM( J )
               GROW = GROW / XJ
   70       CONTINUE
         END IF
   80    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use the Level 2 BLAS solve if the reciprocal of the bound on
</span><span class="comment">*</span><span class="comment">        elements of X is not too small.
</span><span class="comment">*</span><span class="comment">
</span>         CALL DTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, X, 1 )
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use a Level 1 BLAS solve, scaling intermediate results.
</span><span class="comment">*</span><span class="comment">
</span>         IF( XMAX.GT.BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Scale X so that its components are less than or equal to
</span><span class="comment">*</span><span class="comment">           BIGNUM in absolute value.
</span><span class="comment">*</span><span class="comment">
</span>            SCALE = BIGNUM / XMAX
            CALL DSCAL( N, SCALE, X, 1 )
            XMAX = BIGNUM
         END IF
<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">           Solve A * x = b
</span><span class="comment">*</span><span class="comment">
</span>            DO 110 J = JFIRST, JLAST, JINC
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute x(j) = b(j) / A(j,j), scaling x if necessary.
</span><span class="comment">*</span><span class="comment">
</span>               XJ = ABS( X( J ) )
               IF( NOUNIT ) THEN
                  TJJS = AB( MAIND, J )*TSCAL
               ELSE
                  TJJS = TSCAL
                  IF( TSCAL.EQ.ONE )
     $               GO TO 100
               END IF
               TJJ = ABS( TJJS )
               IF( TJJ.GT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    abs(A(j,j)) &gt; SMLNUM:
</span><span class="comment">*</span><span class="comment">
</span>                  IF( TJJ.LT.ONE ) THEN
                     IF( XJ.GT.TJJ*BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                          Scale x by 1/b(j).
</span><span class="comment">*</span><span class="comment">
</span>                        REC = ONE / XJ
                        CALL DSCAL( N, REC, X, 1 )
                        SCALE = SCALE*REC
                        XMAX = XMAX*REC
                     END IF
                  END IF
                  X( J ) = X( J ) / TJJS
                  XJ = ABS( X( J ) )
               ELSE IF( TJJ.GT.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    0 &lt; abs(A(j,j)) &lt;= SMLNUM:
</span><span class="comment">*</span><span class="comment">
</span>                  IF( XJ.GT.TJJ*BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                       Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
</span><span class="comment">*</span><span class="comment">                       to avoid overflow when dividing by A(j,j).
</span><span class="comment">*</span><span class="comment">
</span>                     REC = ( TJJ*BIGNUM ) / XJ
                     IF( CNORM( J ).GT.ONE ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                          Scale by 1/CNORM(j) to avoid overflow when
</span><span class="comment">*</span><span class="comment">                          multiplying x(j) times column j.
</span><span class="comment">*</span><span class="comment">
</span>                        REC = REC / CNORM( J )
                     END IF
                     CALL DSCAL( N, REC, X, 1 )
                     SCALE = SCALE*REC
                     XMAX = XMAX*REC
                  END IF
                  X( J ) = X( J ) / TJJS
                  XJ = ABS( X( J ) )
               ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
</span><span class="comment">*</span><span class="comment">                    scale = 0, and compute a solution to A*x = 0.
</span><span class="comment">*</span><span class="comment">
</span>                  DO 90 I = 1, N
                     X( I ) = ZERO
   90             CONTINUE
                  X( J ) = ONE
                  XJ = ONE
                  SCALE = ZERO
                  XMAX = ZERO
               END IF
  100          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Scale x if necessary to avoid overflow when adding a
</span><span class="comment">*</span><span class="comment">              multiple of column j of A.
</span><span class="comment">*</span><span class="comment">
</span>               IF( XJ.GT.ONE ) THEN
                  REC = ONE / XJ
                  IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Scale x by 1/(2*abs(x(j))).
</span><span class="comment">*</span><span class="comment">
</span>                     REC = REC*HALF
                     CALL DSCAL( N, REC, X, 1 )
                     SCALE = SCALE*REC
                  END IF
               ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Scale x by 1/2.
</span><span class="comment">*</span><span class="comment">
</span>                  CALL DSCAL( N, HALF, X, 1 )
                  SCALE = SCALE*HALF
               END IF
<span class="comment">*</span><span class="comment">
</span>               IF( UPPER ) THEN
                  IF( J.GT.1 ) THEN