cgelqf man page on IRIX

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CGELQF(3F)							    CGELQF(3F)

NAME
     CGELQF - compute an LQ factorization of a complex M-by-N matrix A

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE
     CGELQF 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 dimension
	     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/output) COMPLEX array, dimension (LWORK)
	     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
	     The dimension of the array WORK.  LWORK >= max(1,M).  For optimum
	     performance LWORK >= M*NB, where NB is the optimal blocksize.

     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

									Page 1

CGELQF(3F)							    CGELQF(3F)

	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).

									Page 2

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