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function retval = testqr (q, r, a, p)
tol = 10*eps;
retval = 0;
if (nargin == 3)
n1 = norm (q*r-a);
n2 = norm (q'*q-eye(columns(q)));
retval = (n1 < tol && n2 < tol);
else
n1 = norm (q'*q-eye(columns(q)));
retval = (n1 < tol);
if (isvector (p))
n2 = norm (q*r-a(:,p));
retval = (retval && n2 < tol);
else
n2 = norm (q*r - a*p);
retval = (retval && n2 < tol);
endif
endif
endfunction
t = ones (24, 1);
j = 1;
if 0 # eliminate big matrix tests
a = rand(5000,20);
[q,r]=qr(a,0); t(j++) = testqr(q,r,a);
[q,r]=qr(a',0); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a,0); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a',0); t(j++) = testqr(q,r,a',p);
a = a+1i*eps;
[q,r]=qr(a,0); t(j++) = testqr(q,r,a);
[q,r]=qr(a',0); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a,0); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a',0); t(j++) = testqr(q,r,a',p);
endif
a = [ ones(1,15); sqrt(eps)*eye(15) ];
[q,r]=qr(a); t(j++) = testqr(q,r,a);
[q,r]=qr(a'); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a'); t(j++) = testqr(q,r,a',p);
a = a+1i*eps;
[q,r]=qr(a); t(j++) = testqr(q,r,a);
[q,r]=qr(a'); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a'); t(j++) = testqr(q,r,a',p);
a = [ ones(1,15); sqrt(eps)*eye(15) ];
[q,r]=qr(a,0); t(j++) = testqr(q,r,a);
[q,r]=qr(a',0); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a,0); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a',0); t(j++) = testqr(q,r,a',p);
a = a+1i*eps;
[q,r]=qr(a,0); t(j++) = testqr(q,r,a);
[q,r]=qr(a',0); t(j++) = testqr(q,r,a');
[q,r,p]=qr(a,0); t(j++) = testqr(q,r,a,p);
[q,r,p]=qr(a',0); t(j++) = testqr(q,r,a',p);
a = [
611 196 -192 407 -8 -52 -49 29
196 899 113 -192 -71 -43 -8 -44
-192 113 899 196 61 49 8 52
407 -192 196 611 8 44 59 -23
-8 -71 61 8 411 -599 208 208
-52 -43 49 44 -599 411 208 208
-49 -8 8 59 208 208 99 -911
29 -44 52 -23 208 208 -911 99
];
[q,r] = qr(a);
all (t) && norm(q*r-a) < 5000*eps
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