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fix: cargo fmt

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This commit is contained in:
Volodymyr Orlov
2020-06-05 17:52:03 -07:00
parent 685be04488
commit a2784d6345
52 changed files with 3342 additions and 2829 deletions
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src/linalg/evd.rs
+110 -108
View File
@@ -1,75 +1,64 @@
#![allow(non_snake_case)]
use num::complex::Complex;
use crate::linalg::BaseMatrix;
use crate::math::num::FloatExt;
use num::complex::Complex;
use std::fmt::Debug;
#[derive(Debug, Clone)]
pub struct EVD<T: FloatExt, M: BaseMatrix<T>> {
pub struct EVD<T: FloatExt, M: BaseMatrix<T>> {
pub d: Vec<T>,
pub e: Vec<T>,
pub V: M
pub V: M,
}
impl<T: FloatExt, M: BaseMatrix<T>> EVD<T, M> {
pub fn new(V: M, d: Vec<T>, e: Vec<T>) -> EVD<T, M> {
EVD {
d: d,
e: e,
V: V
}
EVD { d: d, e: e, V: V }
}
}
pub trait EVDDecomposableMatrix<T: FloatExt>: BaseMatrix<T> {
fn evd(&self, symmetric: bool) -> EVD<T, Self>{
pub trait EVDDecomposableMatrix<T: FloatExt>: BaseMatrix<T> {
fn evd(&self, symmetric: bool) -> EVD<T, Self> {
self.clone().evd_mut(symmetric)
}
fn evd_mut(mut self, symmetric: bool) -> EVD<T, Self>{
let(nrows, ncols) = self.shape();
fn evd_mut(mut self, symmetric: bool) -> EVD<T, Self> {
let (nrows, ncols) = self.shape();
if ncols != nrows {
panic!("Matrix is not square: {} x {}", nrows, ncols);
}
let n = nrows;
let mut d = vec![T::zero(); n];
let mut e = vec![T::zero(); n];
let mut e = vec![T::zero(); n];
let mut V;
if symmetric {
if symmetric {
V = self;
// Tridiagonalize.
tred2(&mut V, &mut d, &mut e);
// Diagonalize.
tql2(&mut V, &mut d, &mut e);
} else {
let scale = balance(&mut self);
let perm = elmhes(&mut self);
let scale = balance(&mut self);
V = Self::eye(n);
let perm = elmhes(&mut self);
eltran(&self, &mut V, &perm);
V = Self::eye(n);
eltran(&self, &mut V, &perm);
hqr2(&mut self, &mut V, &mut d, &mut e);
balbak(&mut V, &scale);
sort(&mut d, &mut e, &mut V);
}
EVD {
V: V,
d: d,
e: e
}
EVD { V: V, d: d, e: e }
}
}
fn tred2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>) {
let (n, _) = V.shape();
for i in 0..n {
d[i] = V.get(n - 1, i);
@@ -131,7 +120,7 @@ fn tred2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T
for j in 0..i {
f = d[j];
g = e[j];
for k in j..=i-1 {
for k in j..=i - 1 {
V.sub_element_mut(k, j, f * e[k] + g * d[k]);
}
d[j] = V.get(i - 1, j);
@@ -139,10 +128,10 @@ fn tred2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T
}
}
d[i] = h;
}
}
// Accumulate transformations.
for i in 0..n-1 {
for i in 0..n - 1 {
V.set(n - 1, i, V.get(i, i));
V.set(i, i, T::one());
let h = d[i + 1];
@@ -156,7 +145,7 @@ fn tred2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T
g = g + V.get(k, i + 1) * V.get(k, j);
}
for k in 0..=i {
V.sub_element_mut(k, j, g * d[k]);
V.sub_element_mut(k, j, g * d[k]);
}
}
}
@@ -193,7 +182,7 @@ fn tql2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>
break;
}
m += 1;
} else {
} else {
break;
}
}
@@ -219,7 +208,7 @@ fn tql2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>
d[l + 1] = e[l] * (p + r);
let dl1 = d[l + 1];
let mut h = g - d[l];
for i in l+2..n {
for i in l + 2..n {
d[i] = d[i] - h;
}
f = f + h;
@@ -249,7 +238,7 @@ fn tql2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>
for k in 0..n {
h = V.get(k, i + 1);
V.set(k, i + 1, s * V.get(k, i) + c * h);
V.set(k, i, c * V.get(k, i) - s * h);
V.set(k, i, c * V.get(k, i) - s * h);
}
}
p = -s * s2 * c3 * el1 * e[l] / dl1;
@@ -267,7 +256,7 @@ fn tql2<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>
}
// Sort eigenvalues and corresponding vectors.
for i in 0..n-1 {
for i in 0..n - 1 {
let mut k = i;
let mut p = d[i];
for j in i + 1..n {
@@ -294,8 +283,8 @@ fn balance<T: FloatExt, M: BaseMatrix<T>>(A: &mut M) -> Vec<T> {
let (n, _) = A.shape();
let mut scale = vec![T::one(); n];
let mut scale = vec![T::one(); n];
let t = T::from(0.95).unwrap();
let mut done = false;
@@ -345,7 +334,7 @@ fn elmhes<T: FloatExt, M: BaseMatrix<T>>(A: &mut M) -> Vec<usize> {
let (n, _) = A.shape();
let mut perm = vec![0; n];
for m in 1..n-1 {
for m in 1..n - 1 {
let mut x = T::zero();
let mut i = m;
for j in m..n {
@@ -353,10 +342,10 @@ fn elmhes<T: FloatExt, M: BaseMatrix<T>>(A: &mut M) -> Vec<usize> {
x = A.get(j, m - 1);
i = j;
}
}
}
perm[m] = i;
if i != m {
for j in (m-1)..n {
for j in (m - 1)..n {
let swap = A.get(i, j);
A.set(i, j, A.get(m, j));
A.set(m, j, swap);
@@ -366,7 +355,7 @@ fn elmhes<T: FloatExt, M: BaseMatrix<T>>(A: &mut M) -> Vec<usize> {
A.set(j, i, A.get(j, m));
A.set(j, m, swap);
}
}
}
if x != T::zero() {
for i in (m + 1)..n {
let mut y = A.get(i, m - 1);
@@ -381,11 +370,11 @@ fn elmhes<T: FloatExt, M: BaseMatrix<T>>(A: &mut M) -> Vec<usize> {
}
}
}
}
}
}
return perm;
}
}
fn eltran<T: FloatExt, M: BaseMatrix<T>>(A: &M, V: &mut M, perm: &Vec<usize>) {
let (n, _) = A.shape();
@@ -405,27 +394,27 @@ fn eltran<T: FloatExt, M: BaseMatrix<T>>(A: &M, V: &mut M, perm: &Vec<usize>) {
}
fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e: &mut Vec<T>) {
let (n, _) = A.shape();
let mut z = T::zero();
let (n, _) = A.shape();
let mut z = T::zero();
let mut s = T::zero();
let mut r = T::zero();
let mut q = T::zero();
let mut p = T::zero();
let mut anorm = T::zero();
for i in 0..n {
for i in 0..n {
for j in i32::max(i as i32 - 1, 0)..n as i32 {
anorm = anorm + A.get(i, j as usize).abs();
anorm = anorm + A.get(i, j as usize).abs();
}
}
}
let mut nn = n - 1;
let mut t = T::zero();
'outer: loop {
'outer: loop {
let mut its = 0;
loop {
let mut l = nn;
while l > 0 {
while l > 0 {
s = A.get(l - 1, l - 1).abs() + A.get(l, l).abs();
if s == T::zero() {
s = anorm;
@@ -433,8 +422,8 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
if A.get(l, l - 1).abs() <= T::epsilon() * s {
A.set(l, l - 1, T::zero());
break;
}
l -= 1;
}
l -= 1;
}
let mut x = A.get(nn, nn);
if l == nn {
@@ -444,7 +433,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
break 'outer;
} else {
nn -= 1;
}
}
} else {
let mut y = A.get(nn - 1, nn - 1);
let mut w = A.get(nn, nn - 1) * A.get(nn - 1, nn);
@@ -453,7 +442,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
q = p * p + w;
z = q.abs().sqrt();
x = x + t;
A.set(nn, nn, x );
A.set(nn, nn, x);
A.set(nn - 1, nn - 1, y + t);
if q >= T::zero() {
z = p + z.copysign(p);
@@ -469,7 +458,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
r = (p * p + q * q).sqrt();
p = p / r;
q = q / r;
for j in nn-1..n {
for j in nn - 1..n {
z = A.get(nn - 1, j);
A.set(nn - 1, j, q * z + p * A.get(nn, j));
A.set(nn, j, q * A.get(nn, j) - p * z);
@@ -490,19 +479,19 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
d[nn - 1] = d[nn];
e[nn - 1] = -e[nn];
}
if nn <= 1 {
break 'outer;
} else {
nn -= 2;
}
}
} else {
if its == 30 {
panic!("Too many iterations in hqr");
}
if its == 10 || its == 20 {
t = t + x;
for i in 0..nn+1 {
for i in 0..nn + 1 {
A.sub_element_mut(i, i, x);
}
s = A.get(nn, nn - 1).abs() + A.get(nn - 1, nn - 2).abs();
@@ -527,14 +516,15 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
break;
}
let u = A.get(m, m - 1).abs() * (q.abs() + r.abs());
let v = p.abs() * (A.get(m - 1, m - 1).abs() + z.abs() + A.get(m + 1, m + 1).abs());
let v = p.abs()
* (A.get(m - 1, m - 1).abs() + z.abs() + A.get(m + 1, m + 1).abs());
if u <= T::epsilon() * v {
break;
}
m -= 1;
}
for i in m..nn-1 {
A.set(i + 2, i , T::zero());
for i in m..nn - 1 {
A.set(i + 2, i, T::zero());
if i != m {
A.set(i + 2, i - 1, T::zero());
}
@@ -547,7 +537,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
if k + 1 != nn {
r = A.get(k + 2, k - 1);
}
x = p.abs() + q.abs() +r.abs();
x = p.abs() + q.abs() + r.abs();
if x != T::zero() {
p = p / x;
q = q / x;
@@ -583,8 +573,8 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
mmin = nn;
} else {
mmin = k + 3;
}
for i in 0..mmin+1 {
}
for i in 0..mmin + 1 {
p = x * A.get(i, k) + y * A.get(i, k + 1);
if k + 1 != nn {
p = p + z * A.get(i, k + 2);
@@ -609,7 +599,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
if l + 1 >= nn {
break;
}
};
}
}
if anorm != T::zero() {
@@ -659,7 +649,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
}
}
}
if i == 0{
if i == 0 {
break;
} else {
i -= 1;
@@ -672,13 +662,14 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
A.set(na, na, q / A.get(nn, na));
A.set(na, nn, -(A.get(nn, nn) - p) / A.get(nn, na));
} else {
let temp = Complex::new(T::zero(), -A.get(na, nn)) / Complex::new(A.get(na, na) - p, q);
let temp = Complex::new(T::zero(), -A.get(na, nn))
/ Complex::new(A.get(na, na) - p, q);
A.set(na, na, temp.re);
A.set(na, nn, temp.im);
}
A.set(nn, na, T::zero());
A.set(nn, nn, T::one());
if nn >= 2 {
if nn >= 2 {
for i in (0..nn - 1).rev() {
let w = A.get(i, i) - p;
let mut ra = T::zero();
@@ -694,25 +685,40 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
} else {
m = i;
if e[i] == T::zero() {
let temp = Complex::new(-ra, -sa) / Complex::new(w, q);
let temp = Complex::new(-ra, -sa) / Complex::new(w, q);
A.set(i, na, temp.re);
A.set(i, nn, temp.im);
} else {
let x = A.get(i, i + 1);
let y = A.get(i + 1, i);
let mut vr = (d[i] - p).powf(T::two()) + (e[i]).powf(T::two()) - q * q;
let mut vr =
(d[i] - p).powf(T::two()) + (e[i]).powf(T::two()) - q * q;
let vi = T::two() * q * (d[i] - p);
if vr == T::zero() && vi == T::zero() {
vr = T::epsilon() * anorm * (w.abs() + q.abs() + x.abs() + y.abs() + z.abs());
vr = T::epsilon()
* anorm
* (w.abs() + q.abs() + x.abs() + y.abs() + z.abs());
}
let temp = Complex::new(x * r - z * ra + q * sa, x * s - z * sa - q * ra) / Complex::new(vr, vi);
let temp =
Complex::new(x * r - z * ra + q * sa, x * s - z * sa - q * ra)
/ Complex::new(vr, vi);
A.set(i, na, temp.re);
A.set(i, nn, temp.im);
if x.abs() > z.abs() + q.abs() {
A.set(i + 1, na, (-ra - w * A.get(i, na) + q * A.get(i, nn)) / x);
A.set(i + 1, nn, (-sa - w * A.get(i, nn) - q * A.get(i, na)) / x);
A.set(
i + 1,
na,
(-ra - w * A.get(i, na) + q * A.get(i, nn)) / x,
);
A.set(
i + 1,
nn,
(-sa - w * A.get(i, nn) - q * A.get(i, na)) / x,
);
} else {
let temp = Complex::new(-r - y * A.get(i, na), -s - y * A.get(i, nn)) / Complex::new(z, q);
let temp =
Complex::new(-r - y * A.get(i, na), -s - y * A.get(i, nn))
/ Complex::new(z, q);
A.set(i + 1, na, temp.re);
A.set(i + 1, nn, temp.im);
}
@@ -728,7 +734,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
}
}
}
}
}
for j in (0..n).rev() {
for i in 0..n {
@@ -739,7 +745,7 @@ fn hqr2<T: FloatExt, M: BaseMatrix<T>>(A: &mut M, V: &mut M, d: &mut Vec<T>, e:
V.set(i, j, z);
}
}
}
}
}
fn balbak<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, scale: &Vec<T>) {
@@ -751,7 +757,7 @@ fn balbak<T: FloatExt, M: BaseMatrix<T>>(V: &mut M, scale: &Vec<T>) {
}
}
fn sort<T: FloatExt, M: BaseMatrix<T>>(d: &mut Vec<T>, e: &mut Vec<T>, V: &mut M) {
fn sort<T: FloatExt, M: BaseMatrix<T>>(d: &mut Vec<T>, e: &mut Vec<T>, V: &mut M) {
let n = d.len();
let mut temp = vec![T::zero(); n];
for j in 1..n {
@@ -781,74 +787,72 @@ fn sort<T: FloatExt, M: BaseMatrix<T>>(d: &mut Vec<T>, e: &mut Vec<T>, V: &mut M
}
#[cfg(test)]
mod tests {
use super::*;
mod tests {
use super::*;
use crate::linalg::naive::dense_matrix::DenseMatrix;
#[test]
fn decompose_symmetric() {
fn decompose_symmetric() {
let A = DenseMatrix::from_array(&[
&[0.9000, 0.4000, 0.7000],
&[0.4000, 0.5000, 0.3000],
&[0.7000, 0.3000, 0.8000]]);
&[0.7000, 0.3000, 0.8000],
]);
let eigen_values: Vec<f64> = vec![1.7498382, 0.3165784, 0.1335834];
let eigen_vectors = DenseMatrix::from_array(&[
&[0.6881997, -0.07121225, 0.7220180],
&[0.3700456, 0.89044952, -0.2648886],
&[0.6240573, -0.44947578, -0.6391588]
&[0.6240573, -0.44947578, -0.6391588],
]);
let evd = A.evd(true);
let evd = A.evd(true);
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
for i in 0..eigen_values.len() {
assert!((eigen_values[i] - evd.d[i]).abs() < 1e-4);
}
for i in 0..eigen_values.len() {
assert!((0f64 - evd.e[i]).abs() < std::f64::EPSILON);
}
}
#[test]
fn decompose_asymmetric() {
fn decompose_asymmetric() {
let A = DenseMatrix::from_array(&[
&[0.9000, 0.4000, 0.7000],
&[0.4000, 0.5000, 0.3000],
&[0.8000, 0.3000, 0.8000]]);
&[0.8000, 0.3000, 0.8000],
]);
let eigen_values: Vec<f64> = vec![1.79171122, 0.31908143, 0.08920735];
let eigen_vectors = DenseMatrix::from_array(&[
&[0.7178958, 0.05322098, 0.6812010],
&[0.7178958, 0.05322098, 0.6812010],
&[0.3837711, -0.84702111, -0.1494582],
&[0.6952105, 0.43984484, -0.7036135]
&[0.6952105, 0.43984484, -0.7036135],
]);
let evd = A.evd(false);
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
let evd = A.evd(false);
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
for i in 0..eigen_values.len() {
assert!((eigen_values[i] - evd.d[i]).abs() < 1e-4);
}
for i in 0..eigen_values.len() {
assert!((0f64 - evd.e[i]).abs() < std::f64::EPSILON);
}
}
#[test]
fn decompose_complex() {
fn decompose_complex() {
let A = DenseMatrix::from_array(&[
&[3.0, -2.0, 1.0, 1.0],
&[4.0, -1.0, 1.0, 1.0],
&[1.0, 1.0, 3.0, -2.0],
&[1.0, 1.0, 4.0, -1.0]]);
&[1.0, 1.0, 4.0, -1.0],
]);
let eigen_values_d: Vec<f64> = vec![0.0, 2.0, 2.0, 0.0];
let eigen_values_e: Vec<f64> = vec![2.2361, 0.9999, -0.9999, -2.2361];
@@ -857,19 +861,17 @@ mod tests {
&[-0.9159, -0.1378, 0.3816, -0.0806],
&[-0.6707, 0.1059, 0.901, 0.6289],
&[0.9159, -0.1378, 0.3816, 0.0806],
&[0.6707, 0.1059, 0.901, -0.6289]
&[0.6707, 0.1059, 0.901, -0.6289],
]);
let evd = A.evd(false);
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
let evd = A.evd(false);
assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));
for i in 0..eigen_values_d.len() {
assert!((eigen_values_d[i] - evd.d[i]).abs() < 1e-4);
}
for i in 0..eigen_values_e.len() {
assert!((eigen_values_e[i] - evd.e[i]).abs() < 1e-4);
}
}
}
}