function [Q, R] = piro_band_qr(A)
% Mex function for QR factorization of a matrix. Uses the left looking
% band QR.
%
% Usage:
%  [Q, R] = piro_band_qr(A) ;
%  if A is m x n (sparse/full) matrix and m <= n
%      Q is m x m dense matrix.
%      R is m x n sparse/dense matrix.
%  if A is m x n (sparse/full) matrix and m > n
%      Q is m x n dense matrix.
%      R is n x n sparse/dense matrix.
%  This is the same as [Q, R] = qr(A, 0) ; in MATLAB.
%
% A - band matrix in sparse/full format. The sparse data structure is used to 
% find the bandwidth in sparse format. When A is full, the bandwidth is 
% computed by looking for numerical zeroes.
%
%  QR = piro_band_qr(A) ;
%  where QR is a struct with V, Beta, R, bl and bu.
%  V - householder vectors stored in band format.
%  beta - beta for the householder transformations. 
%  R - upper triangular matrix in band format. 
%  bl - computed lower bandwidth. 
%  bu - computed upper bandwidth.

%   Copyright 2009, Sivasankaran Rajamanickam, Timothy A. Davis
%   http://www.cise.ufl.edu/research/sparse

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