zlahef.f.html

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

                  CALL ZGEMV( <span class="string">'No transpose'</span>, K, N-K, -CONE,
     $                        A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
     $                        CONE, W( 1, KW-1 ), 1 )
                  W( IMAX, KW-1 ) = DBLE( W( IMAX, KW-1 ) )
               END IF
<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 = IMAX + IZAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 )
               ROWMAX = CABS1( W( JMAX, KW-1 ) )
               IF( IMAX.GT.1 ) THEN
                  JMAX = IZAMAX( IMAX-1, W( 1, KW-1 ), 1 )
                  ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, KW-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, KW-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 KW-1 of W to column KW
</span><span class="comment">*</span><span class="comment">
</span>                  CALL ZCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 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
            KKW = NB + KK - N
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Updated column KP is already stored in column KKW 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( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
     $                     LDA )
               CALL <a name="ZLACGV.260"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( KK-1-KP, A( KP, KP+1 ), LDA )
               CALL ZCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Interchange rows KK and KP in last KK columns of A and W
</span><span class="comment">*</span><span class="comment">
</span>               IF( KK.LT.N )
     $            CALL ZSWAP( N-KK, A( KK, KK+1 ), LDA, A( KP, KK+1 ),
     $                        LDA )
               CALL ZSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
     $                     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 KW of W now holds
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W(k) = U(k)*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where U(k) is the k-th column of U
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Store U(k) in column k of A
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
               R1 = ONE / DBLE( A( K, K ) )
               CALL ZDSCAL( K-1, R1, A( 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.288"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( K-1, W( 1, KW ), 1 )
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              2-by-2 pivot block D(k): columns KW and KW-1 of W now
</span><span class="comment">*</span><span class="comment">              hold
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where U(k) and U(k-1) are the k-th and (k-1)-th columns
</span><span class="comment">*</span><span class="comment">              of U
</span><span class="comment">*</span><span class="comment">
</span>               IF( K.GT.2 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Store U(k) and U(k-1) in columns k and k-1 of A
</span><span class="comment">*</span><span class="comment">
</span>                  D21 = W( K-1, KW )
                  D11 = W( K, KW ) / DCONJG( D21 )
                  D22 = W( K-1, KW-1 ) / D21
                  T = ONE / ( DBLE( D11*D22 )-ONE )
                  D21 = T / D21
                  DO 20 J = 1, K - 2
                     A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
                     A( J, K ) = DCONJG( D21 )*
     $                           ( D22*W( J, KW )-W( J, KW-1 ) )
   20             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-1, K-1 ) = W( K-1, KW-1 )
               A( K-1, K ) = W( K-1, KW )
               A( K, K ) = W( K, KW )
<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.323"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( K-1, W( 1, KW ), 1 )
               CALL <a name="ZLACGV.324"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( K-2, W( 1, KW-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">        Decrease K and return to the start of the main loop
</span><span class="comment">*</span><span class="comment">
</span>         K = K - KSTEP
         GO TO 10
<span class="comment">*</span><span class="comment">
</span>   30    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Update the upper triangle of A11 (= A(1:k,1:k)) as
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        A11 := A11 - U12*D*U12' = A11 - U12*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 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
            JB = MIN( NB, K-J+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update the upper triangle of the diagonal block
</span><span class="comment">*</span><span class="comment">
</span>            DO 40 JJ = J, J + JB - 1
               A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
               CALL ZGEMV( <span class="string">'No transpose'</span>, JJ-J+1, N-K, -CONE,
     $                     A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, CONE,
     $                     A( J, JJ ), 1 )
               A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
   40       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update the rectangular superdiagonal block
</span><span class="comment">*</span><span class="comment">
</span>            CALL ZGEMM( <span class="string">'No transpose'</span>, <span class="string">'Transpose'</span>, J-1, JB, N-K,
     $                  -CONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
     $                  CONE, A( 1, J ), LDA )
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Put U12 in standard form by partially undoing the interchanges
</span><span class="comment">*</span><span class="comment">        in columns k+1:n
</span><span class="comment">*</span><span class="comment">
</span>         J = K + 1
   60    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.LE.N )
     $      CALL ZSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
         IF( J.LE.N )
     $      GO TO 60
<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 = N - K
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Factorize the leading columns of A using the lower triangle
</span><span class="comment">*</span><span class="comment">        of A and working forwards, and compute the matrix W = L21*D
</span><span class="comment">*</span><span class="comment">        for use in updating A22 (note that conjg(W) is actually stored)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        K is the main loop index, increasing from 1 in steps of 1 or 2
</span><span class="comment">*</span><span class="comment">
</span>         K = 1
   70    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Exit from loop
</span><span class="comment">*</span><span class="comment">
</span>         IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
     $      GO TO 90
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Copy column K of A to column K of W and update it
</span><span class="comment">*</span><span class="comment">
</span>         W( K, K ) = DBLE( A( K, K ) )
         IF( K.LT.N )
     $      CALL ZCOPY( N-K, A( K+1, K ), 1, W( K+1, K ), 1 )
         CALL ZGEMV( <span class="string">'No transpose'</span>, N-K+1, K-1, -CONE, A( K, 1 ), LDA,
     $               W( K, 1 ), LDW, CONE, W( K, K ), 1 )
         W( K, K ) = DBLE( W( K, K ) )
<span class="comment">*</span><span class="comment">
</span>         KSTEP = 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Determine rows and columns to be interchanged and whether
</span><span class="comment">*</span><span class="comment">        a 1-by-1 or 2-by-2 pivot block will be used
</span><span class="comment">*</span><span class="comment">
</span>         ABSAKK = ABS( DBLE( W( K, K ) ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        IMAX is the row-index of the largest off-diagonal element in
</span><span class="comment">*</span><span class="comment">        column K, and COLMAX is its absolute value
</span><span class="comment">*</span><span class="comment">
</span>         IF( K.LT.N ) THEN
            IMAX = K + IZAMAX( N-K, W( K+1, K ), 1 )
            COLMAX = CABS1( W( IMAX, K ) )