dgeql2.f.html

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      SUBROUTINE <a name="DGEQL2.1"></a><a href="dgeql2.f.html#DGEQL2.1">DGEQL2</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>      DOUBLE PRECISION   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="DGEQL2.17"></a><a href="dgeql2.f.html#DGEQL2.1">DGEQL2</a> computes a QL factorization of a real m by n matrix A:
</span><span class="comment">*</span><span class="comment">  A = Q * L.
</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) DOUBLE PRECISION 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, if m &gt;= n, the lower triangle of the subarray
</span><span class="comment">*</span><span class="comment">          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
</span><span class="comment">*</span><span class="comment">          if m &lt;= n, the elements on and below the (n-m)-th
</span><span class="comment">*</span><span class="comment">          superdiagonal contain the m by n lower trapezoidal matrix L;
</span><span class="comment">*</span><span class="comment">          the remaining elements, with the array TAU, represent the
</span><span class="comment">*</span><span class="comment">          orthogonal matrix Q as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">          (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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 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 real scalar, and v is a real vector with
</span><span class="comment">*</span><span class="comment">  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
</span><span class="comment">*</span><span class="comment">  A(1:m-k+i-1,n-k+i), 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>      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, K
      DOUBLE PRECISION   AII
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLARF.78"></a><a href="dlarf.f.html#DLARF.1">DLARF</a>, <a name="DLARFG.78"></a><a href="dlarfg.f.html#DLARFG.1">DLARFG</a>, <a name="XERBLA.78"></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.96"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DGEQL2.96"></a><a href="dgeql2.f.html#DGEQL2.1">DGEQL2</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 = K, 1, -1
<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:m-k+i-1,n-k+i)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLARFG.107"></a><a href="dlarfg.f.html#DLARFG.1">DLARFG</a>( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
     $                TAU( I ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
</span><span class="comment">*</span><span class="comment">
</span>         AII = A( M-K+I, N-K+I )
         A( M-K+I, N-K+I ) = ONE
         CALL <a name="DLARF.114"></a><a href="dlarf.f.html#DLARF.1">DLARF</a>( <span class="string">'Left'</span>, M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
     $               A, LDA, WORK )
         A( M-K+I, N-K+I ) = AII
   10 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DGEQL2.120"></a><a href="dgeql2.f.html#DGEQL2.1">DGEQL2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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