cgelq2.f.html

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      SUBROUTINE <a name="CGELQ2.1"></a><a href="cgelq2.f.html#CGELQ2.1">CGELQ2</a>( M, N, 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, 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="CGELQ2.17"></a><a href="cgelq2.f.html#CGELQ2.1">CGELQ2</a> computes an LQ factorization of a complex m by n matrix A:
</span><span class="comment">*</span><span class="comment">  A = L * Q.
</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 A.  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 A.  N &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 m by n matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, the elements on and below the diagonal of the array
</span><span class="comment">*</span><span class="comment">          contain the m by min(m,n) lower trapezoidal matrix L (L is
</span><span class="comment">*</span><span class="comment">          lower triangular if m &lt;= n); the elements above the diagonal,
</span><span class="comment">*</span><span class="comment">          with the array TAU, represent the unitary matrix Q as a
</span><span class="comment">*</span><span class="comment">          product of elementary reflectors (see Further Details).
</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 leading 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     (output) COMPLEX array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment">          The scalar factors of the elementary reflectors (see Further
</span><span class="comment">*</span><span class="comment">          Details).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (M)
</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 had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The matrix Q is represented as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Each H(i) has the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H(i) = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where tau is a complex scalar, and v is a complex vector with
</span><span class="comment">*</span><span class="comment">  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
</span><span class="comment">*</span><span class="comment">  A(i,i+1:n), and tau in TAU(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            ONE
      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, K
      COMPLEX            ALPHA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CLACGV.76"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>, <a name="CLARF.76"></a><a href="clarf.f.html#CLARF.1">CLARF</a>, <a name="CLARFG.76"></a><a href="clarfg.f.html#CLARFG.1">CLARFG</a>, <a name="XERBLA.76"></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, 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 arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.94"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGELQ2.94"></a><a href="cgelq2.f.html#CGELQ2.1">CGELQ2</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      K = MIN( M, N )
<span class="comment">*</span><span class="comment">
</span>      DO 10 I = 1, K
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Generate elementary reflector H(i) to annihilate A(i,i+1:n)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="CLACGV.104"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>( N-I+1, A( I, I ), LDA )
         ALPHA = A( I, I )
         CALL <a name="CLARFG.106"></a><a href="clarfg.f.html#CLARFG.1">CLARFG</a>( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA,
     $                TAU( I ) )
         IF( I.LT.M ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Apply H(i) to A(i+1:m,i:n) from the right
</span><span class="comment">*</span><span class="comment">
</span>            A( I, I ) = ONE
            CALL <a name="CLARF.113"></a><a href="clarf.f.html#CLARF.1">CLARF</a>( <span class="string">'Right'</span>, M-I, N-I+1, A( I, I ), LDA, TAU( I ),
     $                  A( I+1, I ), LDA, WORK )
         END IF
         A( I, I ) = ALPHA
         CALL <a name="CLACGV.117"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>( N-I+1, A( I, I ), LDA )
   10 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGELQ2.121"></a><a href="cgelq2.f.html#CGELQ2.1">CGELQ2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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