cgelq2 man page on YellowDog

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CGELQ2(l)			       )			     CGELQ2(l)

NAME
       CGELQ2 - compute an LQ factorization of a complex m by n matrix A

SYNOPSIS
       SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

	   COMPLEX	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       CGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L
       * Q.

ARGUMENTS
       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On entry, the m by n matrix A.  On exit, the  elements  on  and
	       below the diagonal of the array contain the m by min(m,n) lower
	       trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
	       elements	 above the diagonal, with the array TAU, represent the
	       unitary matrix Q as a product  of  elementary  reflectors  (see
	       Further	Details).   LDA	    (input) INTEGER The leading dimenā€
	       sion of the array A.  LDA >= max(1,M).

       TAU     (output) COMPLEX array, dimension (min(M,N))
	       The scalar factors of the elementary  reflectors	 (see  Further
	       Details).

       WORK    (workspace) COMPLEX array, dimension (M)

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       The matrix Q is represented as a product of elementary reflectors

	  Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).

       Each H(i) has the form

	  H(i) = I - tau * v * v'

       where  tau is a complex scalar, and v is a complex vector with v(1:i-1)
       = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n),  and
       tau in TAU(i).

LAPACK version 3.0		 15 June 2000			     CGELQ2(l)
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