function [H,R] = myqr (A)
%MYQR QR factorization using Householder reflections
% uses function [v,beta,xnorm] = hmake1 (x)
% and function hx = happly (v, beta, x)
%
% Example
%   [H,R] = myqr (A)
% See also: testall

% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+

[m n] = size (A) ;

H = zeros (m,n) ;
R = zeros (m,n) ;

for k = 1:n

    % apply prior H's
    % fprintf ('\n-----------------init %d\n', k) ;
    x = A (:,k) ;
    for i = 1:k-1
        v = H(((i+1):m),i) ;
        v = [1 ; v] ;                                                       %#ok
        beta = H (i,i) ;
        % n1 = norm (x (i:m)) ;
        x (i:m) = happly (v, beta, x (i:m)) ;
        % n2 = norm (x (i:m)) ;
        % fprintf ('=============== i %d %g %g\n', i, n1, n2) ;
        % beta
        % v'
        % X = x'
        % pause
        % i
        % x
    end
    % k
    % x

    % make Hk
    % fprintf ('x(k:m) = ') ; x (k:m)
    [v,beta,xnorm] = hmake1 (x (k:m)) ;

    H (k,k) = beta ;
    H (k+1:m, k) = v (2:end) ;

    R (1:(k-1),k) = x (1:(k-1)) ;
    R (k,k) = xnorm ;
    % full (R)
    % pause
end

% s2 = svd (full (R)) ;
% [s1 s2 s1-s2]