CGERQF man page on IRIX

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CGERQF(3F)							    CGERQF(3F)

NAME
     CGERQF - compute an RQ factorization of a complex M-by-N matrix A

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE
     CGERQF computes an RQ factorization of a complex M-by-N matrix A:	A = R
     * 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, if m <= n, the upper
	     triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
	     triangular matrix R; if m >= n, the elements on and above the
	     (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix
	     R; the remaining elements, with the array TAU, represent the
	     unitary matrix Q as a product of min(m,n) 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(1)' H(2)' . . . H(k)', where k = min(m,n).

									Page 1

CGERQF(3F)							    CGERQF(3F)

     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(n-
     k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
     A(m-k+i,1:n-k+i-1), and tau in TAU(i).

									Page 2

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