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eigen.rs
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eigen.rs
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//! To find Eigenvalue & Eigenvector
//!
//! * Reference : Press, William H., and William T. Vetterling. *Numerical Recipes.* Cambridge: Cambridge Univ. Press, 2007.
pub use self::EigenMethod::*;
use crate::structure::matrix::Matrix;
use crate::traits::matrix::MatrixTrait;
use crate::util::non_macro::eye_shape;
#[derive(Debug, Copy, Clone)]
pub enum EigenMethod {
Jacobi,
}
#[derive(Debug, Clone)]
pub struct Eigen {
pub eigenvalue: Vec<f64>,
pub eigenvector: Matrix,
}
impl Eigen {
pub fn extract(self) -> (Vec<f64>, Matrix) {
(self.eigenvalue, self.eigenvector)
}
}
pub fn eigen(m: &Matrix, em: EigenMethod) -> Eigen {
match em {
Jacobi => {
let mat = m.clone();
let mut j = jacobi(mat);
j.iter();
j.extract()
}
}
}
// =============================================================================
// Jacobi Method
// =============================================================================
/// To do Jacobi method
///
/// * Reference : Press, William H., and William T. Vetterling. *Numerical Recipes.* Cambridge: Cambridge Univ. Press, 2007.
#[derive(Debug)]
pub struct JacobiTemp {
pub n: usize,
pub a: Matrix,
pub v: Matrix,
pub d: Vec<f64>,
pub n_rot: usize,
}
pub fn jacobi(m: Matrix) -> JacobiTemp {
let n = m.row;
let v = eye_shape(n, m.shape);
let d = m.diag();
let a = m;
JacobiTemp {
n,
a,
v,
d,
n_rot: 0,
}
}
impl JacobiTemp {
pub fn new(m: Matrix) -> Self {
jacobi(m)
}
pub fn extract(self) -> Eigen {
let v = self.v;
let d = self.d;
Eigen {
eigenvalue: d,
eigenvector: v,
}
}
/// Main Jacobi traits
///
/// * Reference : Press, William H., and William T. Vetterling. *Numerical Recipes.* Cambridge: Cambridge Univ. Press, 2007.
pub fn iter(&mut self) {
let a = &mut self.a;
let n = self.n;
let v = &mut self.v;
let mut b = a.diag();
let d = &mut self.d;
let mut z = vec![0f64; n];
let mut h: f64;
let mut _n_rot = self.n_rot;
for i in 1..51 {
let mut sm = 0f64;
for ip in 0..n - 1 {
for iq in ip + 1..n {
sm += a[(ip, iq)].abs();
}
}
if sm == 0f64 {
eigsrt(d, v);
return ();
}
let tresh = if i < 4 {
0.2 * sm / (n.pow(2) as f64)
} else {
0f64
};
for ip in 0..n - 1 {
for iq in ip + 1..n {
let g = 100f64 * a[(ip, iq)].abs();
if i > 4 && g <= f64::EPSILON * d[ip].abs() && g <= f64::EPSILON * d[iq].abs() {
a[(ip, iq)] = 0f64;
} else if a[(ip, iq)].abs() > tresh {
h = d[iq] - d[ip];
let t = if g <= f64::EPSILON * h.abs() {
a[(ip, iq)] / h
} else {
let theta = 0.5 * h / a[(ip, iq)];
let mut temp = 1f64 / (theta.abs() + (1f64 + theta.powi(2)).sqrt());
if theta < 0f64 {
temp = -temp;
}
temp
};
let c = 1f64 / (1f64 + t.powi(2)).sqrt();
let s = t * c;
let tau = s / (1f64 + c);
h = t * a[(ip, iq)];
z[ip] -= h;
z[iq] += h;
d[ip] -= h;
d[iq] += h;
a[(ip, iq)] = 0f64;
for j in 0..ip {
rot(a, s, tau, j, ip, j, iq);
}
for j in ip + 1..iq {
rot(a, s, tau, ip, j, j, iq);
}
for j in iq + 1..n {
rot(a, s, tau, ip, j, iq, j);
}
for j in 0..n {
rot(v, s, tau, j, ip, j, iq);
}
_n_rot += 1;
}
}
}
for ip in 0..n {
b[ip] += z[ip];
d[ip] = b[ip];
z[ip] = 0f64;
}
}
assert!(false, "Too many iterations in routine jacobi");
}
}
fn rot(a: &mut Matrix, s: f64, tau: f64, i: usize, j: usize, k: usize, l: usize) {
let g = a[(i, j)];
let h = a[(k, l)];
a[(i, j)] = g - s * (h + g * tau);
a[(k, l)] = h + s * (g - h * tau);
}
/// Given eigenvalue & eigenvector, sorts thod eigenvalues into descending order
///
/// * Reference : Press, William H., and William T. Vetterling. *Numerical Recipes.* Cambridge: Cambridge Univ. Press, 2007.
fn eigsrt(d: &mut Vec<f64>, v: &mut Matrix) {
let mut k: usize;
let n = d.len();
for i in 0..n - 1 {
k = i;
let mut p = d[k];
for j in i..n {
if d[j] >= p {
k = j;
p = d[k];
}
}
if k != i {
d[k] = d[i];
d[i] = p;
for j in 0..n {
p = v[(j, i)];
v[(j, i)] = v[(j, k)];
v[(j, k)] = p;
}
}
}
}