.TH CGERQ2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
CGERQ2 - an RQ factorization of a complex m by n matrix A
.SH SYNOPSIS
.TP 19
SUBROUTINE CGERQ2(
M, N, A, LDA, TAU, WORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, M, N
.TP 19
.ti +4
COMPLEX
A( LDA, * ), TAU( * ), WORK( * )
.SH PURPOSE
CGERQ2 computes an RQ factorization of a complex m by n matrix A:
A = R * Q.
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.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
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).
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
.TP 8
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
.TP 8
WORK (workspace) COMPLEX array, dimension (M)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(1)\(aq H(2)\(aq . . . H(k)\(aq, where k = min(m,n).
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Each H(i) has the form
.br
H(i) = I - tau * v * v\(aq
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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).
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