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// Based on spectalnorm.gcc by Sebastien Loisel
use std;
fn eval_A(i: uint, j: uint) -> float {
1.0/(((i+j)*(i+j+1u)/2u+i+1u) as float)
}
fn eval_A_times_u(u: [const float], Au: [mut float]) {
let N = vec::len(u);
let mut i = 0u;
while i < N {
Au[i] = 0.0;
let mut j = 0u;
while j < N {
Au[i] += eval_A(i, j) * u[j];
j += 1u;
}
i += 1u;
}
}
fn eval_At_times_u(u: [const float], Au: [mut float]) {
let N = vec::len(u);
let mut i = 0u;
while i < N {
Au[i] = 0.0;
let mut j = 0u;
while j < N {
Au[i] += eval_A(j, i) * u[j];
j += 1u;
}
i += 1u;
}
}
fn eval_AtA_times_u(u: [const float], AtAu: [mut float]) {
let v = vec::to_mut(vec::from_elem(vec::len(u), 0.0));
eval_A_times_u(u, v);
eval_At_times_u(v, AtAu);
}
fn main(args: [str]) {
let N = if vec::len(args) == 2u {
option::get(uint::from_str(args[1]))
} else {
1000u
};
let u = vec::to_mut(vec::from_elem(N, 1.0));
let v = vec::to_mut(vec::from_elem(N, 0.0));
let mut i = 0u;
while i < 10u {
eval_AtA_times_u(u, v);
eval_AtA_times_u(v, u);
i += 1u;
}
let mut vBv = 0.0;
let mut vv = 0.0;
let mut i = 0u;
while i < N {
vBv += u[i] * v[i];
vv += v[i] * v[i];
i += 1u;
}
io::println(#fmt("%0.9f\n", float::sqrt(vBv / vv)));
}
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