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#![allow(non_snake_case)]
//use num_traits::Float;
use ndarray::prelude::*;
use ndarray_inverse::*;
use ndarray::Zip;
fn main() {
/*
println!("Example 1:");
let A: Array2<f64> = arr2(&[
[1.0, 3.0, 5.0],
[2.0, 4.0, 7.0],
[1.0, 1.0, 0.0],
]);
println!("A \n {}", A);
let (L, U, P) = lu_decomp(&A);
println!("L \n {}", L);
println!("U \n {}", U);
println!("P \n {}", P);
*/
println!("\nExample 2:");
/*
let A: Array2<f64> = arr2(&[
[11.0, 9.0, 24.0, 2.0],
[1.0, 5.0, 2.0, 6.0],
[3.0, 17.0, 18.0, 1.0],
[2.0, 5.0, 7.0, 1.0],
]);
let A: Array2<f64> = array![
[4.3552 , 6.25851, 4.12662, 1.93708, 0.21272, 3.25683, 6.53326],
[4.24746, 1.84137, 6.71904, 0.59754, 3.5806 , 3.63597, 5.347 ],
[2.30479, 1.70591, 3.05354, 1.82188, 5.27839, 7.9166 , 2.04607],
[2.40158, 6.38524, 7.90296, 4.69683, 6.63801, 7.32958, 1.45936],
[0.42456, 6.47456, 1.55398, 8.28979, 4.20987, 0.90401, 4.94587],
[5.78903, 1.92032, 6.20261, 5.78543, 1.94331, 8.25178, 7.47273],
[1.44797, 7.41157, 7.69495, 8.90113, 3.05983, 0.41582, 6.42932]];
let A: Array2<f64> = array![
[-68.0, 68.0, -16.0, 4.0],
[-36.0, 35.0, -9.0, 3.0],
[48.0, -47.0, 11.0, -3.0],
[64.0, -64.0, 16.0, -4.0]];
*/
let A: Array2<f64> = array![
[1.0, 1.0, 3.0, 4.0, 9.0, 3.0],
[10.0, 10.0, 1.0, 2.0, 2.0, 5.0],
[2.0, 9.0, 6.0, 10.0, 10.0, 9.0],
[10.0, 9.0, 9.0, 7.0, 3.0, 6.0],
[7.0, 6.0, 6.0, 2.0, 9.0, 5.0],
[3.0, 8.0, 1.0, 4.0, 1.0, 5.0]
];
//let A: Array2<f64> = array![[7.0, 3.0, -1.0, 2.0], [3.0, 8.0, 1.0, -4.0], [-1.0, 1.0, 4.0, -1.0], [2.0, -4.0, -1.0, 6.0]];
if let Some((L, U, P)) = lu_decomp(&A) {
/*
//println!("A \n {}", A);
*/
println!("L \n {}", L);
println!("U \n {}", U);
println!("P \n {}", P);
//println!("Linv \n {:?}", linv(&L, 4));
//println!("linv {:?}", L.inv());
//println!("Uinv \n {:?}", uinv(&U, 4));
println!("inverse \n{:?}", inverse(&A));
println!("inv \n{:?}", A.inv());
/*
//println!("uinv {:?}", U.inv());
println!("inv {:?}", inverse(&A));
let inv2 = inverse(&inverse(&A).unwrap()).unwrap();
println!("inv inv {:?}", inv2);
//let inv4 = inverse(&inverse(&inv2).unwrap()).unwrap();
//println!("inv inv inv inv {:?}", inv4);
//println!("linv {:?}", linv(&L, 7));
//println!("uinv {:?}", uinv(&U, 7));
//assert!(inverse(&A) == A.inv());
let mut _q = inverse(&A);
for i in 0 .. 1000000 {
_q = inverse(&A);
}
*/
}
}
fn lu_decomp<T: NdFloat>(A: &Array2<T>) -> Option<(Array2<T>, Array2<T>, Array2<T>)> {
fn pivot<T: NdFloat>(A: &Array2<T>) -> Array2<T> {
fn swap<T: NdFloat>(A: &mut Array2<T>, ir1: usize, ir2: usize) {
/*
let (.., mut rest) = A.view_mut().split_at(Axis(0), ir1);
let (r0, mut rest) = rest.view_mut().split_at(Axis(0), 1);
let (.., mut rest) = rest.view_mut().split_at(Axis(0), ir2 - ir1 - 1);
let (r1, ..) = rest.view_mut().split_at(Axis(0), 1);
*/
let (r0, r1) = A.multi_slice_mut((s![ir1, ..], s![ir2, ..]));
Zip::from(r0).and(r1).for_each(std::mem::swap);
}
let n = A.raw_dim()[0];
let mut P: Array2<T> = Array::eye(n);
for (idx, col) in A.axis_iter(Axis(1)).enumerate() {
// find index of maximum value in column i
let mut mp = idx;
for i in idx .. n {
if col[mp].abs() < col[i].abs() {
mp = i;
}
}
// swap rows when different
if mp != idx {
//println!("{idx}, {mp}");
//println!("< {:?}", P);
swap(&mut P, idx, mp);
//println!("> {:?}", P);
}
}
P
}
let d = A.raw_dim();
let n = d[0];
assert_eq!(n, d[1], "LU decomposition must take a square matrix.");
let P = pivot(A);
let pA = P.dot(A);
let mut L: Array2<T> = Array::eye(n);
let mut U: Array2<T> = Array::zeros((n, n));
for c in 0 .. n {
for r in 0 .. n {
let pAs = pA[[r, c]] - U.slice(s![0..r, c]).dot(&L.slice(s![r, 0..r]));
if pAs.is_nan() || pAs.is_infinite() {
return None;
}
if r < c + 1 { // U
U[[r, c]] = pAs;
} else { // L
L[[r, c]] = (pAs) / U[[c, c]];
}
}
}
Some((L, U, P))
}
fn inverse(s: &Array2<f64>) -> Option<Array2<f64>> {
fn linv(l: &Array2<f64>, n: usize) -> Array2<f64> {
let mut m: Array2<f64> = Array2::zeros((n, n));
for i in 0 .. n {
m[(i, i)] = 1.0 / l[(i, i)];
for j in 0 .. i {
for k in j .. i {
m[(i, j)] += l[(i, k)] * m[(k, j)];
}
m[(i, j)] = -m[(i, j)] / l[(i, i)];
}
}
m
}
fn uinv(u: &Array2<f64>, n: usize) -> Array2<f64> {
linv(&u.t().to_owned(), n).t().to_owned()
}
let d = s.raw_dim();
let n = d[0];
assert!(d[0] == d[1]);
if let Some((l, u, p)) = lu_decomp(s) {
let lt = linv(&l, n);
let ut = uinv(&u, n);
Some(ut.dot(<).dot(&p))
} else {
None
}
}