function test_piro_band_qr()
% Usage : test_piro_band_qr()
% Finds the QR using the band reduction algorithm for random input matrices and
% compares the result with MATLAB's QR.
% random input matrices.
%

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

    fprintf('All norms printed should be small\n') ;
    fprintf('n1 is the norm(qr(A) - piro_band_qr(A)) \n') ;
    fprintf('n2 is the norm(A - (Q * R))  \n\n') ;

    A = banded(10, 10, 5, 5) ;
    piro_band_verify_qr(A) ;

    A = banded(10, 20, 5, 5) ;
    piro_band_verify_qr(A) ;

    A = banded(20, 10, 5, 5) ;
    piro_band_verify_qr(A) ;

    A = banded(20, 10, 5, 6) ;
    piro_band_verify_qr(A) ;

    fprintf('\n------------------------ Complex QR ------------ \n\n') 
    A = banded(10, 10, 5, 5) ;
    A1 = banded(10, 10, 5, 5) ;
    A = A + i * A1 ;
    piro_band_verify_qr(A) ;

    A = banded(10, 20, 6, 9) ;
    A1 = banded(10, 20, 6, 9) ;
    A = A + i * A1 ;
    piro_band_verify_qr(A) ;

    A = banded(20, 10, 6, 9) ;
    A1 = banded(20, 10, 6, 9) ;
    A = A + i * A1 ;
    piro_band_verify_qr(A) ;

function piro_band_verify_qr(A) 
%
    [Q, R] = piro_band_qr(A) ;
    A1 = Q * R ;

    [m, n] = size(A) ;
    %Rmat = qr(A) ;
    %n1 = norm(full(Rmat - R)) ;
    %full(A)
    %full(A1)
    %full(R)
    %full(Q)
    n2 = norm(A1 - A) ;

    fprintf('A -- %d x %d, ---------  n2 = %g\n', m, n, n2) ;