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feat: extends interface of Matrix to support for broad range of types

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This commit is contained in:
Volodymyr Orlov
2020-03-26 15:28:26 -07:00
parent 84ffd331cd
commit 02b85415d9
27 changed files with 1021 additions and 868 deletions
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src/linalg/svd.rs
+72 -70
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@@ -1,19 +1,21 @@
#![allow(non_snake_case)]
use crate::linalg::BaseMatrix;
use crate::math::num::FloatExt;
use std::fmt::Debug;
#[derive(Debug, Clone)]
pub struct SVD<M: SVDDecomposableMatrix> {
pub struct SVD<T: FloatExt + Debug, M: SVDDecomposableMatrix<T>> {
pub U: M,
pub V: M,
pub s: Vec<f64>,
pub s: Vec<T>,
full: bool,
m: usize,
n: usize,
tol: f64
tol: T
}
pub trait SVDDecomposableMatrix: BaseMatrix {
pub trait SVDDecomposableMatrix<T: FloatExt + Debug>: BaseMatrix<T> {
fn svd_solve_mut(self, b: Self) -> Self {
self.svd_mut().solve(b)
@@ -23,50 +25,50 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
self.svd().solve(b)
}
fn svd(&self) -> SVD<Self> {
fn svd(&self) -> SVD<T, Self> {
self.clone().svd_mut()
}
fn svd_mut(self) -> SVD<Self> {
fn svd_mut(self) -> SVD<T, Self> {
let mut U = self;
let (m, n) = U.shape();
let (mut l, mut nm) = (0usize, 0usize);
let (mut anorm, mut g, mut scale) = (0f64, 0f64, 0f64);
let (mut anorm, mut g, mut scale) = (T::zero(), T::zero(), T::zero());
let mut v = Self::zeros(n, n);
let mut w = vec![0f64; n];
let mut rv1 = vec![0f64; n];
let mut w = vec![T::zero(); n];
let mut rv1 = vec![T::zero(); n];
for i in 0..n {
l = i + 2;
rv1[i] = scale * g;
g = 0f64;
let mut s = 0f64;
scale = 0f64;
g = T::zero();
let mut s = T::zero();
scale = T::zero();
if i < m {
for k in i..m {
scale += U.get(k, i).abs();
scale = scale + U.get(k, i).abs();
}
if scale.abs() > std::f64::EPSILON {
if scale.abs() > T::epsilon() {
for k in i..m {
U.div_element_mut(k, i, scale);
s += U.get(k, i) * U.get(k, i);
s = s + U.get(k, i) * U.get(k, i);
}
let mut f = U.get(i, i);
g = -s.sqrt().copysign(f);
g = -s.sqrt().copysign(f);
let h = f * g - s;
U.set(i, i, f - g);
for j in l - 1..n {
s = 0f64;
s = T::zero();
for k in i..m {
s += U.get(k, i) * U.get(k, j);
s = s + U.get(k, i) * U.get(k, j);
}
f = s / h;
for k in i..m {
@@ -80,19 +82,19 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
w[i] = scale * g;
g = 0f64;
let mut s = 0f64;
scale = 0f64;
g = T::zero();
let mut s = T::zero();
scale = T::zero();
if i + 1 <= m && i + 1 != n {
for k in l - 1..n {
scale += U.get(i, k).abs();
scale = scale + U.get(i, k).abs();
}
if scale.abs() > std::f64::EPSILON {
if scale.abs() > T::epsilon() {
for k in l - 1..n {
U.div_element_mut(i, k, scale);
s += U.get(i, k) * U.get(i, k);
s = s + U.get(i, k) * U.get(i, k);
}
let f = U.get(i, l - 1);
@@ -105,9 +107,9 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
for j in l - 1..m {
s = 0f64;
s = T::zero();
for k in l - 1..n {
s += U.get(j, k) * U.get(i, k);
s = s + U.get(j, k) * U.get(i, k);
}
for k in l - 1..n {
@@ -122,19 +124,19 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
anorm = f64::max(anorm, w[i].abs() + rv1[i].abs());
anorm = T::max(anorm, w[i].abs() + rv1[i].abs());
}
for i in (0..n).rev() {
if i < n - 1 {
if g != 0.0 {
if g != T::zero() {
for j in l..n {
v.set(j, i, (U.get(i, j) / U.get(i, l)) / g);
}
for j in l..n {
let mut s = 0f64;
let mut s = T::zero();
for k in l..n {
s += U.get(i, k) * v.get(k, j);
s = s + U.get(i, k) * v.get(k, j);
}
for k in l..n {
v.add_element_mut(k, j, s * v.get(k, i));
@@ -142,11 +144,11 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
}
for j in l..n {
v.set(i, j, 0f64);
v.set(j, i, 0f64);
v.set(i, j, T::zero());
v.set(j, i, T::zero());
}
}
v.set(i, i, 1.0);
v.set(i, i, T::one());
g = rv1[i];
l = i;
}
@@ -155,15 +157,15 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
l = i + 1;
g = w[i];
for j in l..n {
U.set(i, j, 0f64);
U.set(i, j, T::zero());
}
if g.abs() > std::f64::EPSILON {
g = 1f64 / g;
if g.abs() > T::epsilon() {
g = T::one() / g;
for j in l..n {
let mut s = 0f64;
let mut s = T::zero();
for k in l..m {
s += U.get(k, i) * U.get(k, j);
s = s + U.get(k, i) * U.get(k, j);
}
let f = (s / U.get(i, i)) * g;
for k in i..m {
@@ -175,11 +177,11 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
} else {
for j in i..m {
U.set(j, i, 0f64);
U.set(j, i, T::zero());
}
}
U.add_element_mut(i, i, 1f64);
U.add_element_mut(i, i, T::one());
}
for k in (0..n).rev() {
@@ -187,30 +189,30 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
let mut flag = true;
l = k;
while l != 0 {
if l == 0 || rv1[l].abs() <= std::f64::EPSILON * anorm {
if l == 0 || rv1[l].abs() <= T::epsilon() * anorm {
flag = false;
break;
}
nm = l - 1;
if w[nm].abs() <= std::f64::EPSILON * anorm {
if w[nm].abs() <= T::epsilon() * anorm {
break;
}
l -= 1;
}
if flag {
let mut c = 0.0;
let mut s = 1.0;
let mut c = T::zero();
let mut s = T::one();
for i in l..k+1 {
let f = s * rv1[i];
rv1[i] = c * rv1[i];
if f.abs() <= std::f64::EPSILON * anorm {
if f.abs() <= T::epsilon() * anorm {
break;
}
g = w[i];
let mut h = f.hypot(g);
w[i] = h;
h = 1.0 / h;
h = T::one() / h;
c = g * h;
s = -f * h;
for j in 0..m {
@@ -224,7 +226,7 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
let z = w[k];
if l == k {
if z < 0f64 {
if z < T::zero() {
w[k] = -z;
for j in 0..n {
v.set(j, k, -v.get(j, k));
@@ -242,11 +244,11 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
let mut y = w[nm];
g = rv1[nm];
let mut h = rv1[k];
let mut f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = f.hypot(1.0);
let mut f = ((y - z) * (y + z) + (g - h) * (g + h)) / (T::two() * h * y);
g = f.hypot(T::one());
f = ((x - z) * (x + z) + h * ((y / (f + g.copysign(f))) - h)) / x;
let mut c = 1f64;
let mut s = 1f64;
let mut c = T::one();
let mut s = T::one();
for j in l..=nm {
let i = j + 1;
@@ -261,7 +263,7 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y *= c;
y = y * c;
for jj in 0..n {
x = v.get(jj, j);
@@ -272,8 +274,8 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
z = f.hypot(h);
w[j] = z;
if z.abs() > std::f64::EPSILON {
z = 1.0 / z;
if z.abs() > T::epsilon() {
z = T::one() / z;
c = f * z;
s = h * z;
}
@@ -288,15 +290,15 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
}
rv1[l] = 0.0;
rv1[l] = T::zero();
rv1[k] = f;
w[k] = x;
}
}
let mut inc = 1usize;
let mut su = vec![0f64; m];
let mut sv = vec![0f64; n];
let mut su = vec![T::zero(); m];
let mut sv = vec![T::zero(); n];
loop {
inc *= 3;
@@ -347,12 +349,12 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
for k in 0..n {
let mut s = 0.;
for i in 0..m {
if U.get(i, k) < 0. {
if U.get(i, k) < T::zero() {
s += 1.;
}
}
for j in 0..n {
if v.get(j, k) < 0. {
if v.get(j, k) < T::zero() {
s += 1.;
}
}
@@ -371,12 +373,12 @@ pub trait SVDDecomposableMatrix: BaseMatrix {
}
}
impl<M: SVDDecomposableMatrix> SVD<M> {
pub fn new(U: M, V: M, s: Vec<f64>) -> SVD<M> {
impl<T: FloatExt + Debug, M: SVDDecomposableMatrix<T>> SVD<T, M> {
pub fn new(U: M, V: M, s: Vec<T>) -> SVD<T, M> {
let m = U.shape().0;
let n = V.shape().0;
let full = s.len() == m.min(n);
let tol = 0.5 * ((m + n) as f64 + 1.).sqrt() * s[0] * std::f64::EPSILON;
let tol = T::half() * (T::from(m + n).unwrap() + T::one()).sqrt() * s[0] * T::epsilon();
SVD {
U: U,
V: V,
@@ -396,22 +398,22 @@ impl<M: SVDDecomposableMatrix> SVD<M> {
}
for k in 0..p {
let mut tmp = vec![0f64; self.n];
let mut tmp = vec![T::zero(); self.n];
for j in 0..self.n {
let mut r = 0f64;
let mut r = T::zero();
if self.s[j] > self.tol {
for i in 0..self.m {
r += self.U.get(i, j) * b.get(i, k);
r = r + self.U.get(i, j) * b.get(i, k);
}
r /= self.s[j];
r = r / self.s[j];
}
tmp[j] = r;
}
for j in 0..self.n {
let mut r = 0.0;
let mut r = T::zero();
for jj in 0..self.n {
r += self.V.get(j, jj) * tmp[jj];
r = r + self.V.get(j, jj) * tmp[jj];
}
b.set(j, k, r);
}
@@ -434,7 +436,7 @@ mod tests {
&[0.4000, 0.5000, 0.3000],
&[0.7000, 0.3000, 0.8000]]);
let s = vec![1.7498382, 0.3165784, 0.1335834];
let s: Vec<f64> = vec![1.7498382, 0.3165784, 0.1335834];
let U = DenseMatrix::from_array(&[
&[0.6881997, -0.07121225, 0.7220180],
@@ -471,7 +473,7 @@ mod tests {
&[0.12641406, -0.8710055, -0.2712301, 0.2296515, 1.1781535, -0.2158704, -0.27529472]
]);
let s = vec![3.8589375, 3.4396766, 2.6487176, 2.2317399, 1.5165054, 0.8109055, 0.2706515];
let s: Vec<f64> = vec![3.8589375, 3.4396766, 2.6487176, 2.2317399, 1.5165054, 0.8109055, 0.2706515];
let U = DenseMatrix::from_array(&[
&[-0.3082776, 0.77676231, 0.01330514, 0.23231424, -0.47682758, 0.13927109, 0.02640713],