zlatrd.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 304 行 · 第 1/2 页

</span><span class="comment">*</span><span class="comment">  an element of the original matrix that is unchanged, and vi denotes
</span><span class="comment">*</span><span class="comment">  an element of the vector defining H(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         ZERO, ONE, HALF
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
     $                   ONE = ( 1.0D+0, 0.0D+0 ),
     $                   HALF = ( 0.5D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, IW
      COMPLEX*16         ALPHA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           ZAXPY, ZGEMV, ZHEMV, <a name="ZLACGV.150"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>, <a name="ZLARFG.150"></a><a href="zlarfg.f.html#ZLARFG.1">ZLARFG</a>, ZSCAL
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.153"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      COMPLEX*16         ZDOTC
      EXTERNAL           <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, ZDOTC
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          DBLE, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.LE.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.167"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Reduce last NB columns of upper triangle
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = N, N - NB + 1, -1
            IW = I - N + NB
            IF( I.LT.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Update A(1:i,i)
</span><span class="comment">*</span><span class="comment">
</span>               A( I, I ) = DBLE( A( I, I ) )
               CALL <a name="ZLACGV.178"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-I, W( I, IW+1 ), LDW )
               CALL ZGEMV( <span class="string">'No transpose'</span>, I, N-I, -ONE, A( 1, I+1 ),
     $                     LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 )
               CALL <a name="ZLACGV.181"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-I, W( I, IW+1 ), LDW )
               CALL <a name="ZLACGV.182"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-I, A( I, I+1 ), LDA )
               CALL ZGEMV( <span class="string">'No transpose'</span>, I, N-I, -ONE, W( 1, IW+1 ),
     $                     LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 )
               CALL <a name="ZLACGV.185"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( N-I, A( I, I+1 ), LDA )
               A( I, I ) = DBLE( A( I, I ) )
            END IF
            IF( I.GT.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Generate elementary reflector H(i) to annihilate
</span><span class="comment">*</span><span class="comment">              A(1:i-2,i)
</span><span class="comment">*</span><span class="comment">
</span>               ALPHA = A( I-1, I )
               CALL <a name="ZLARFG.194"></a><a href="zlarfg.f.html#ZLARFG.1">ZLARFG</a>( I-1, ALPHA, A( 1, I ), 1, TAU( I-1 ) )
               E( I-1 ) = ALPHA
               A( I-1, I ) = ONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute W(1:i-1,i)
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZHEMV( <span class="string">'Upper'</span>, I-1, ONE, A, LDA, A( 1, I ), 1,
     $                     ZERO, W( 1, IW ), 1 )
               IF( I.LT.N ) THEN
                  CALL ZGEMV( <span class="string">'Conjugate transpose'</span>, I-1, N-I, ONE,
     $                        W( 1, IW+1 ), LDW, A( 1, I ), 1, ZERO,
     $                        W( I+1, IW ), 1 )
                  CALL ZGEMV( <span class="string">'No transpose'</span>, I-1, N-I, -ONE,
     $                        A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE,
     $                        W( 1, IW ), 1 )
                  CALL ZGEMV( <span class="string">'Conjugate transpose'</span>, I-1, N-I, ONE,
     $                        A( 1, I+1 ), LDA, A( 1, I ), 1, ZERO,
     $                        W( I+1, IW ), 1 )
                  CALL ZGEMV( <span class="string">'No transpose'</span>, I-1, N-I, -ONE,
     $                        W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE,
     $                        W( 1, IW ), 1 )
               END IF
               CALL ZSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 )
               ALPHA = -HALF*TAU( I-1 )*ZDOTC( I-1, W( 1, IW ), 1,
     $                 A( 1, I ), 1 )
               CALL ZAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 )
            END IF
<span class="comment">*</span><span class="comment">
</span>   10    CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Reduce first NB columns of lower triangle
</span><span class="comment">*</span><span class="comment">
</span>         DO 20 I = 1, NB
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update A(i:n,i)
</span><span class="comment">*</span><span class="comment">
</span>            A( I, I ) = DBLE( A( I, I ) )
            CALL <a name="ZLACGV.232"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( I-1, W( I, 1 ), LDW )
            CALL ZGEMV( <span class="string">'No transpose'</span>, N-I+1, I-1, -ONE, A( I, 1 ),
     $                  LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 )
            CALL <a name="ZLACGV.235"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( I-1, W( I, 1 ), LDW )
            CALL <a name="ZLACGV.236"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( I-1, A( I, 1 ), LDA )
            CALL ZGEMV( <span class="string">'No transpose'</span>, N-I+1, I-1, -ONE, W( I, 1 ),
     $                  LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 )
            CALL <a name="ZLACGV.239"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( I-1, A( I, 1 ), LDA )
            A( I, I ) = DBLE( A( I, I ) )
            IF( I.LT.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Generate elementary reflector H(i) to annihilate
</span><span class="comment">*</span><span class="comment">              A(i+2:n,i)
</span><span class="comment">*</span><span class="comment">
</span>               ALPHA = A( I+1, I )
               CALL <a name="ZLARFG.247"></a><a href="zlarfg.f.html#ZLARFG.1">ZLARFG</a>( N-I, ALPHA, A( MIN( I+2, N ), I ), 1,
     $                      TAU( I ) )
               E( I ) = ALPHA
               A( I+1, I ) = ONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute W(i+1:n,i)
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZHEMV( <span class="string">'Lower'</span>, N-I, ONE, A( I+1, I+1 ), LDA,
     $                     A( I+1, I ), 1, ZERO, W( I+1, I ), 1 )
               CALL ZGEMV( <span class="string">'Conjugate transpose'</span>, N-I, I-1, ONE,
     $                     W( I+1, 1 ), LDW, A( I+1, I ), 1, ZERO,
     $                     W( 1, I ), 1 )
               CALL ZGEMV( <span class="string">'No transpose'</span>, N-I, I-1, -ONE, A( I+1, 1 ),
     $                     LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 )
               CALL ZGEMV( <span class="string">'Conjugate transpose'</span>, N-I, I-1, ONE,
     $                     A( I+1, 1 ), LDA, A( I+1, I ), 1, ZERO,
     $                     W( 1, I ), 1 )
               CALL ZGEMV( <span class="string">'No transpose'</span>, N-I, I-1, -ONE, W( I+1, 1 ),
     $                     LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 )
               CALL ZSCAL( N-I, TAU( I ), W( I+1, I ), 1 )
               ALPHA = -HALF*TAU( I )*ZDOTC( N-I, W( I+1, I ), 1,
     $                 A( I+1, I ), 1 )
               CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 )
            END IF
<span class="comment">*</span><span class="comment">
</span>   20    CONTINUE
      END IF
<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="ZLATRD.277"></a><a href="zlatrd.f.html#ZLATRD.1">ZLATRD</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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