cung2r.f.html

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      SUBROUTINE <a name="CUNG2R.1"></a><a href="cung2r.f.html#CUNG2R.1">CUNG2R</a>( M, N, K, A, LDA, TAU, WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            INFO, K, LDA, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CUNG2R.17"></a><a href="cung2r.f.html#CUNG2R.1">CUNG2R</a> generates an m by n complex matrix Q with orthonormal columns,
</span><span class="comment">*</span><span class="comment">  which is defined as the first n columns of a product of k elementary
</span><span class="comment">*</span><span class="comment">  reflectors of order m
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Q  =  H(1) H(2) . . . H(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  as returned by <a name="CGEQRF.23"></a><a href="cgeqrf.f.html#CGEQRF.1">CGEQRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix Q. M &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix Q. M &gt;= N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  K       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of elementary reflectors whose product defines the
</span><span class="comment">*</span><span class="comment">          matrix Q. N &gt;= K &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the i-th column must contain the vector which
</span><span class="comment">*</span><span class="comment">          defines the elementary reflector H(i), for i = 1,2,...,k, as
</span><span class="comment">*</span><span class="comment">          returned by <a name="CGEQRF.41"></a><a href="cgeqrf.f.html#CGEQRF.1">CGEQRF</a> in the first k columns of its array
</span><span class="comment">*</span><span class="comment">          argument A.
</span><span class="comment">*</span><span class="comment">          On exit, the m by n matrix Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The first dimension of the array A. LDA &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) COMPLEX array, dimension (K)
</span><span class="comment">*</span><span class="comment">          TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment">          reflector H(i), as returned by <a name="CGEQRF.50"></a><a href="cgeqrf.f.html#CGEQRF.1">CGEQRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0: successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0: if INFO = -i, the i-th argument has an illegal value
</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            ONE, ZERO
      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
     $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J, L
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CLARF.69"></a><a href="clarf.f.html#CLARF.1">CLARF</a>, CSCAL, <a name="XERBLA.69"></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">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<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 arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.89"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CUNG2R.89"></a><a href="cung2r.f.html#CUNG2R.1">CUNG2R</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><span class="comment">*</span><span class="comment">     Initialise columns k+1:n to columns of the unit matrix
</span><span class="comment">*</span><span class="comment">
</span>      DO 20 J = K + 1, N
         DO 10 L = 1, M
            A( L, J ) = ZERO
   10    CONTINUE
         A( J, J ) = ONE
   20 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      DO 40 I = K, 1, -1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply H(i) to A(i:m,i:n) from the left
</span><span class="comment">*</span><span class="comment">
</span>         IF( I.LT.N ) THEN
            A( I, I ) = ONE
            CALL <a name="CLARF.113"></a><a href="clarf.f.html#CLARF.1">CLARF</a>( <span class="string">'Left'</span>, M-I+1, N-I, A( I, I ), 1, TAU( I ),
     $                  A( I, I+1 ), LDA, WORK )
         END IF
         IF( I.LT.M )
     $      CALL CSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
         A( I, I ) = ONE - TAU( I )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Set A(1:i-1,i) to zero
</span><span class="comment">*</span><span class="comment">
</span>         DO 30 L = 1, I - 1
            A( L, I ) = ZERO
   30    CONTINUE
   40 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CUNG2R.128"></a><a href="cung2r.f.html#CUNG2R.1">CUNG2R</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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