zlahef.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 672 行 · 第 1/3 页

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         ELSE
            COLMAX = ZERO
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Column K is zero: set INFO and continue
</span><span class="comment">*</span><span class="comment">
</span>            IF( INFO.EQ.0 )
     $         INFO = K
            KP = K
            A( K, K ) = DBLE( A( K, K ) )
         ELSE
            IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              no interchange, use 1-by-1 pivot block
</span><span class="comment">*</span><span class="comment">
</span>               KP = K
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Copy column IMAX to column K+1 of W and update it
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 )
               CALL <a name="ZLACGV.453"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( IMAX-K, W( K, K+1 ), 1 )
               W( IMAX, K+1 ) = DBLE( A( IMAX, IMAX ) )
               IF( IMAX.LT.N )
     $            CALL ZCOPY( N-IMAX, A( IMAX+1, IMAX ), 1,
     $                        W( IMAX+1, K+1 ), 1 )
               CALL ZGEMV( <span class="string">'No transpose'</span>, N-K+1, K-1, -CONE, A( K, 1 ),
     $                     LDA, W( IMAX, 1 ), LDW, CONE, W( K, K+1 ),
     $                     1 )
               W( IMAX, K+1 ) = DBLE( W( IMAX, K+1 ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              JMAX is the column-index of the largest off-diagonal
</span><span class="comment">*</span><span class="comment">              element in row IMAX, and ROWMAX is its absolute value
</span><span class="comment">*</span><span class="comment">
</span>               JMAX = K - 1 + IZAMAX( IMAX-K, W( K, K+1 ), 1 )
               ROWMAX = CABS1( W( JMAX, K+1 ) )
               IF( IMAX.LT.N ) THEN
                  JMAX = IMAX + IZAMAX( N-IMAX, W( IMAX+1, K+1 ), 1 )
                  ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, K+1 ) ) )
               END IF
<span class="comment">*</span><span class="comment">
</span>               IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 no interchange, use 1-by-1 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = K
               ELSE IF( ABS( DBLE( W( IMAX, K+1 ) ) ).GE.ALPHA*ROWMAX )
     $                   THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 interchange rows and columns K and IMAX, use 1-by-1
</span><span class="comment">*</span><span class="comment">                 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = IMAX
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 copy column K+1 of W to column K
</span><span class="comment">*</span><span class="comment">
</span>                  CALL ZCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
               ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 interchange rows and columns K+1 and IMAX, use 2-by-2
</span><span class="comment">*</span><span class="comment">                 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = IMAX
                  KSTEP = 2
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span>            KK = K + KSTEP - 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Updated column KP is already stored in column KK of W
</span><span class="comment">*</span><span class="comment">
</span>            IF( KP.NE.KK ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Copy non-updated column KK to column KP
</span><span class="comment">*</span><span class="comment">
</span>               A( KP, KP ) = DBLE( A( KK, KK ) )
               CALL ZCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
     $                     LDA )
               CALL <a name="ZLACGV.510"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( KP-KK-1, A( KP, KK+1 ), LDA )
               IF( KP.LT.N )
     $            CALL ZCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Interchange rows KK and KP in first KK columns of A and W
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZSWAP( KK-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
               CALL ZSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
            END IF
<span class="comment">*</span><span class="comment">
</span>            IF( KSTEP.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              1-by-1 pivot block D(k): column k of W now holds
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W(k) = L(k)*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where L(k) is the k-th column of L
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Store L(k) in column k of A
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
               IF( K.LT.N ) THEN
                  R1 = ONE / DBLE( A( K, K ) )
                  CALL ZDSCAL( N-K, R1, A( K+1, K ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Conjugate W(k)
</span><span class="comment">*</span><span class="comment">
</span>                  CALL <a name="ZLACGV.537"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-K, W( K+1, K ), 1 )
               END IF
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              2-by-2 pivot block D(k): columns k and k+1 of W now hold
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where L(k) and L(k+1) are the k-th and (k+1)-th columns
</span><span class="comment">*</span><span class="comment">              of L
</span><span class="comment">*</span><span class="comment">
</span>               IF( K.LT.N-1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Store L(k) and L(k+1) in columns k and k+1 of A
</span><span class="comment">*</span><span class="comment">
</span>                  D21 = W( K+1, K )
                  D11 = W( K+1, K+1 ) / D21
                  D22 = W( K, K ) / DCONJG( D21 )
                  T = ONE / ( DBLE( D11*D22 )-ONE )
                  D21 = T / D21
                  DO 80 J = K + 2, N
                     A( J, K ) = DCONJG( D21 )*
     $                           ( D11*W( J, K )-W( J, K+1 ) )
                     A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) )
   80             CONTINUE
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Copy D(k) to A
</span><span class="comment">*</span><span class="comment">
</span>               A( K, K ) = W( K, K )
               A( K+1, K ) = W( K+1, K )
               A( K+1, K+1 ) = W( K+1, K+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Conjugate W(k) and W(k+1)
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLACGV.572"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-K, W( K+1, K ), 1 )
               CALL <a name="ZLACGV.573"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-K-1, W( K+2, K+1 ), 1 )
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Store details of the interchanges in IPIV
</span><span class="comment">*</span><span class="comment">
</span>         IF( KSTEP.EQ.1 ) THEN
            IPIV( K ) = KP
         ELSE
            IPIV( K ) = -KP
            IPIV( K+1 ) = -KP
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Increase K and return to the start of the main loop
</span><span class="comment">*</span><span class="comment">
</span>         K = K + KSTEP
         GO TO 70
<span class="comment">*</span><span class="comment">
</span>   90    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Update the lower triangle of A22 (= A(k:n,k:n)) as
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        A22 := A22 - L21*D*L21' = A22 - L21*W'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        computing blocks of NB columns at a time (note that conjg(W) is
</span><span class="comment">*</span><span class="comment">        actually stored)
</span><span class="comment">*</span><span class="comment">
</span>         DO 110 J = K, N, NB
            JB = MIN( NB, N-J+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update the lower triangle of the diagonal block
</span><span class="comment">*</span><span class="comment">
</span>            DO 100 JJ = J, J + JB - 1
               A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
               CALL ZGEMV( <span class="string">'No transpose'</span>, J+JB-JJ, K-1, -CONE,
     $                     A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, CONE,
     $                     A( JJ, JJ ), 1 )
               A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
  100       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update the rectangular subdiagonal block
</span><span class="comment">*</span><span class="comment">
</span>            IF( J+JB.LE.N )
     $         CALL ZGEMM( <span class="string">'No transpose'</span>, <span class="string">'Transpose'</span>, N-J-JB+1, JB,
     $                     K-1, -CONE, A( J+JB, 1 ), LDA, W( J, 1 ),
     $                     LDW, CONE, A( J+JB, J ), LDA )
  110    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Put L21 in standard form by partially undoing the interchanges
</span><span class="comment">*</span><span class="comment">        in columns 1:k-1
</span><span class="comment">*</span><span class="comment">
</span>         J = K - 1
  120    CONTINUE
         JJ = J
         JP = IPIV( J )
         IF( JP.LT.0 ) THEN
            JP = -JP
            J = J - 1
         END IF
         J = J - 1
         IF( JP.NE.JJ .AND. J.GE.1 )
     $      CALL ZSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
         IF( J.GE.1 )
     $      GO TO 120
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Set KB to the number of columns factorized
</span><span class="comment">*</span><span class="comment">
</span>         KB = K - 1
<span class="comment">*</span><span class="comment">
</span>      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZLAHEF.645"></a><a href="zlahef.f.html#ZLAHEF.1">ZLAHEF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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