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use traits::operations::{Transpose, ApproxEq};
use traits::structure::{ColSlice, Eye, Indexable, Diag, SquareMat, BaseFloat};
use traits::geometry::Norm;
use std::cmp::min;
use std::ops::{Mul, Add, Sub};
pub fn householder_matrix<N, V, M>(dim: usize, start: usize, vec: V) -> M
where N: BaseFloat,
M: Eye + Indexable<(usize, usize), N>,
V: Indexable<usize, N> {
let mut qk : M = Eye::new_identity(dim);
let subdim = vec.shape();
let stop = subdim + start;
assert!(dim >= stop);
for j in (start .. stop) {
for i in (start .. stop) {
unsafe {
let vv = vec.unsafe_at(i - start) * vec.unsafe_at(j - start);
let qkij = qk.unsafe_at((i, j));
qk.unsafe_set((i, j), qkij - vv - vv);
}
}
}
qk
}
pub fn qr<N, V, M>(m: &M) -> (M, M)
where N: BaseFloat,
V: Indexable<usize, N> + Norm<N>,
M: Copy + Eye + ColSlice<V> + Transpose + Indexable<(usize, usize), N> +
Mul<M, Output = M> {
let (rows, cols) = m.shape();
assert!(rows >= cols);
let mut q : M = Eye::new_identity(rows);
let mut r = *m;
for ite in 0..min(rows - 1, cols) {
let mut v = r.col_slice(ite, ite, rows);
let alpha =
if unsafe { v.unsafe_at(ite) } >= ::zero() {
-Norm::norm(&v)
}
else {
Norm::norm(&v)
};
unsafe {
let x = v.unsafe_at(0);
v.unsafe_set(0, x - alpha);
}
if !::is_zero(&v.normalize_mut()) {
let qk: M = householder_matrix(rows, ite, v);
r = qk * r;
q = q * Transpose::transpose(&qk);
}
}
(q, r)
}
pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: usize) -> (M, V)
where N: BaseFloat,
V: Mul<M, Output = V>,
VS: Indexable<usize, N> + Norm<N>,
M: Indexable<(usize, usize), N> + SquareMat<N, V> + Add<M, Output = M> +
Sub<M, Output = M> + ColSlice<VS> +
ApproxEq<N> + Copy {
let mut eigenvectors: M = ::one::<M>();
let mut eigenvalues = *m;
let mut iter = 0;
for _ in 0..niter {
let mut stop = true;
for j in 0..::dim::<M>() {
for i in 0..j {
if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
stop = false;
break;
}
}
for i in j + 1..::dim::<M>() {
if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
stop = false;
break;
}
}
}
if stop {
break;
}
iter = iter + 1;
let (q, r) = qr(&eigenvalues);;
eigenvalues = r * q;
eigenvectors = eigenvectors * q;
}
(eigenvectors, eigenvalues.diag())
}
pub fn cholesky<N, V, VS, M>(m: &M) -> Result<M, &'static str>
where N: BaseFloat,
V: Mul<M, Output = V>,
VS: Indexable<usize, N> + Norm<N>,
M: Indexable<(usize, usize), N> + SquareMat<N, V> + Add<M, Output = M> +
Sub<M, Output = M> + ColSlice<VS> +
ApproxEq<N> + Copy {
let mut out = m.clone().transpose();
if !ApproxEq::approx_eq(&out, &m) {
return Err("Cholesky: Input matrix is not symmetric");
}
for i in 0 .. out.nrows() {
for j in 0 .. (i + 1) {
let mut sum: N = out[(i, j)];
for k in 0 .. j {
sum = sum - out[(i, k)] * out[(j, k)];
}
if i > j {
out[(i, j)] = sum / out[(j, j)];
}
else if sum > N::zero() {
out[(i, i)] = sum.sqrt();
}
else {
return Err("Cholesky: Input matrix is not positive definite to machine precision");
}
}
}
for i in 0 .. out.nrows() {
for j in i + 1 .. out.ncols() {
out[(i, j)] = N::zero();
}
}
return Ok(out);
}