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// The Great Computer Language Shootout
//
// contributed by Ian Osgood
function A(i,j) {
return 1/((i+j)*(i+j+1)/2+i+1);
}
function Au(u,v) {
for (var i=0; i<u.length; ++i) {
var t = 0;
for (var j=0; j<u.length; ++j)
t += A(i,j) * u[j];
v[i] = t;
}
}
function Atu(u,v) {
for (var i=0; i<u.length; ++i) {
var t = 0;
for (var j=0; j<u.length; ++j)
t += A(j,i) * u[j];
v[i] = t;
}
}
function AtAu(u,v,w) {
Au(u,w);
Atu(w,v);
}
function spectralnorm(n) {
var i, u=[], v=[], w=[], vv=0, vBv=0;
for (i=0; i<n; ++i) {
u[i] = 1; v[i] = w[i] = 0;
}
for (i=0; i<10; ++i) {
AtAu(u,v,w);
AtAu(v,u,w);
}
for (i=0; i<n; ++i) {
vBv += u[i]*v[i];
vv += v[i]*v[i];
}
return Math.sqrt(vBv/vv);
}
var actual = '';
for (var i = 6; i <= 48; i *= 2) {
actual += spectralnorm(i) + ',';
}
assertEq(actual, "1.2657786149754053,1.2727355112619148,1.273989979775574,1.274190125290389,");