ssytd2.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 272 行 · 第 1/2 页

      PARAMETER          ( ONE = 1.0, ZERO = 0.0, HALF = 1.0 / 2.0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            I
      REAL               ALPHA, TAUI
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SAXPY, <a name="SLARFG.126"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>, SSYMV, SSYR2, <a name="XERBLA.126"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               SDOT
      EXTERNAL           <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, SDOT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, 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">     Test the input parameters
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = <a name="LSAME.141"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.142"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.150"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SSYTD2.150"></a><a href="ssytd2.f.html#SSYTD2.1">SSYTD2</a>'</span>, -INFO )
         RETURN
      END IF
<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( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Reduce the upper triangle of A
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = N - 1, 1, -1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Generate elementary reflector H(i) = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">           to annihilate A(1:i-1,i+1)
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="SLARFG.168"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI )
            E( I ) = A( I, I+1 )
<span class="comment">*</span><span class="comment">
</span>            IF( TAUI.NE.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Apply H(i) from both sides to A(1:i,1:i)
</span><span class="comment">*</span><span class="comment">
</span>               A( I, I+1 ) = ONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute  x := tau * A * v  storing x in TAU(1:i)
</span><span class="comment">*</span><span class="comment">
</span>               CALL SSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
     $                     TAU, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute  w := x - 1/2 * tau * (x'*v) * v
</span><span class="comment">*</span><span class="comment">
</span>               ALPHA = -HALF*TAUI*SDOT( I, TAU, 1, A( 1, I+1 ), 1 )
               CALL SAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Apply the transformation as a rank-2 update:
</span><span class="comment">*</span><span class="comment">                 A := A - v * w' - w * v'
</span><span class="comment">*</span><span class="comment">
</span>               CALL SSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
     $                     LDA )
<span class="comment">*</span><span class="comment">
</span>               A( I, I+1 ) = E( I )
            END IF
            D( I+1 ) = A( I+1, I+1 )
            TAU( I ) = TAUI
   10    CONTINUE
         D( 1 ) = A( 1, 1 )
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Reduce the lower triangle of A
</span><span class="comment">*</span><span class="comment">
</span>         DO 20 I = 1, N - 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Generate elementary reflector H(i) = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">           to annihilate A(i+2:n,i)
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="SLARFG.208"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,
     $                   TAUI )
            E( I ) = A( I+1, I )
<span class="comment">*</span><span class="comment">
</span>            IF( TAUI.NE.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Apply H(i) from both sides to A(i+1:n,i+1:n)
</span><span class="comment">*</span><span class="comment">
</span>               A( I+1, I ) = ONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute  x := tau * A * v  storing y in TAU(i:n-1)
</span><span class="comment">*</span><span class="comment">
</span>               CALL SSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
     $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute  w := x - 1/2 * tau * (x'*v) * v
</span><span class="comment">*</span><span class="comment">
</span>               ALPHA = -HALF*TAUI*SDOT( N-I, TAU( I ), 1, A( I+1, I ),
     $                 1 )
               CALL SAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Apply the transformation as a rank-2 update:
</span><span class="comment">*</span><span class="comment">                 A := A - v * w' - w * v'
</span><span class="comment">*</span><span class="comment">
</span>               CALL SSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
     $                     A( I+1, I+1 ), LDA )
<span class="comment">*</span><span class="comment">
</span>               A( I+1, I ) = E( I )
            END IF
            D( I ) = A( I, I )
            TAU( I ) = TAUI
   20    CONTINUE
         D( N ) = A( N, N )
      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="SSYTD2.245"></a><a href="ssytd2.f.html#SSYTD2.1">SSYTD2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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