cgerq2 man page on Scientific

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CGERQ2(1)		 LAPACK routine (version 3.2)		     CGERQ2(1)

NAME
       CGERQ2 - computes an RQ factorization of a complex m by n matrix A

SYNOPSIS
       SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE
       CGERQ2 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 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) 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(1)' H(2)' . . . H(k)', 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(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).

 LAPACK routine (version 3.2)	 November 2008			     CGERQ2(1)
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