
CGEQR2(l) ) CGEQR2(l)
NAME
CGEQR2  compute a QR factorization of a complex m by n matrix A
SYNOPSIS
SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
CGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.
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 above the diagonal of
the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper trian
gular if m >= n); the elements below 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) COMPLEX array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith 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(1:i1) = 0 and v(i) = 1;
v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
LAPACK version 3.0 15 June 2000 CGEQR2(l) 
