Separate LU decomposition into its own file where other solving stuff will live
parent
8fcb032b1a
commit
543769f691
@ -0,0 +1,153 @@
|
||||
use crate::util::checked_inv;
|
||||
use crate::Matrix;
|
||||
use crate::Vector;
|
||||
use num_traits::real::Real;
|
||||
use num_traits::{One, Zero};
|
||||
use std::iter::{Product, Sum};
|
||||
use std::ops::Index;
|
||||
|
||||
#[derive(Copy, Clone, Debug, PartialEq)]
|
||||
pub struct LUDecomp<T: Copy, const N: usize> {
|
||||
pub lu: Matrix<T, N, N>,
|
||||
pub idx: Vector<usize, N>,
|
||||
pub parity: T,
|
||||
}
|
||||
|
||||
impl<T: Copy + Default, const N: usize> LUDecomp<T, N>
|
||||
where
|
||||
T: Real + Default + Sum + Product,
|
||||
{
|
||||
#[must_use]
|
||||
pub fn decompose(m: &Matrix<T, N, N>) -> Option<Self> {
|
||||
// Implementation from Numerical Recipes §2.3
|
||||
let mut lu = m.clone();
|
||||
let mut idx: Vector<usize, N> = (0..N).collect();
|
||||
let mut parity = T::one();
|
||||
|
||||
let mut vv: Vector<T, N> = m
|
||||
.rows()
|
||||
.map(|row| {
|
||||
let m = row.elements().cloned().reduce(|acc, x| acc.max(x.abs()))?;
|
||||
match m < T::epsilon() {
|
||||
true => None,
|
||||
false => Some(T::one() / m),
|
||||
}
|
||||
})
|
||||
.collect::<Option<_>>()?; // get the inverse maxabs value in each row
|
||||
|
||||
for k in 0..N {
|
||||
// search for the pivot element and its index
|
||||
let (ipivot, _) = (lu.col(k) * vv)
|
||||
.abs()
|
||||
.elements()
|
||||
.enumerate()
|
||||
.skip(k) // below the diagonal
|
||||
.reduce(|(imax, xmax), (i, x)| match x > xmax {
|
||||
// Is the figure of merit for the pivot better than the best so far?
|
||||
true => (i, x),
|
||||
false => (imax, xmax),
|
||||
})?;
|
||||
|
||||
// do we need to interchange rows?
|
||||
if k != ipivot {
|
||||
lu.pivot_row(ipivot, k); // yes, we do
|
||||
idx.pivot_row(ipivot, k);
|
||||
parity = -parity; // change parity of d
|
||||
vv[ipivot] = vv[k] //interchange scale factor
|
||||
}
|
||||
|
||||
let pivot = lu[(k, k)];
|
||||
if pivot.abs() < T::epsilon() {
|
||||
// if the pivot is zero, the matrix is singular
|
||||
return None;
|
||||
};
|
||||
|
||||
for i in (k + 1)..N {
|
||||
// divide by the pivot element
|
||||
let dpivot = lu[(i, k)] / pivot;
|
||||
lu[(i, k)] = dpivot;
|
||||
for j in (k + 1)..N {
|
||||
// reduce remaining submatrix
|
||||
lu[(i, j)] = lu[(i, j)] - (dpivot * lu[(k, j)]);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return Some(Self { lu, idx, parity });
|
||||
}
|
||||
|
||||
#[must_use]
|
||||
pub fn solve<const M: usize>(&self, b: &Matrix<T, N, M>) -> Matrix<T, N, M> {
|
||||
let b_permuted = b.permute_rows(&self.idx);
|
||||
|
||||
Matrix::from_cols(b_permuted.cols().map(|mut x| {
|
||||
// Implementation from Numerical Recipes §2.3
|
||||
// When ii is set to a positive value,
|
||||
// it will become the index of the first nonvanishing element of b
|
||||
let mut ii = 0usize;
|
||||
for i in 0..N {
|
||||
// forward substitution using L
|
||||
let mut sum = x[i];
|
||||
if ii != 0 {
|
||||
for j in (ii - 1)..i {
|
||||
sum = sum - (self.lu[(i, j)] * x[j]);
|
||||
}
|
||||
} else if sum.abs() > T::epsilon() {
|
||||
ii = i + 1;
|
||||
}
|
||||
x[i] = sum;
|
||||
}
|
||||
for i in (0..N).rev() {
|
||||
// back substitution using U
|
||||
let mut sum = x[i];
|
||||
for j in (i + 1)..N {
|
||||
sum = sum - (self.lu[(i, j)] * x[j]);
|
||||
}
|
||||
x[i] = sum / self.lu[(i, i)]
|
||||
}
|
||||
x
|
||||
}))
|
||||
}
|
||||
|
||||
pub fn det(&self) -> T {
|
||||
self.parity * self.lu.diagonals().product()
|
||||
}
|
||||
|
||||
pub fn inverse(&self) -> Matrix<T, N, N> {
|
||||
return self.solve(&Matrix::<T, N, N>::identity());
|
||||
}
|
||||
|
||||
pub fn separate(&self) -> (Matrix<T, N, N>, Matrix<T, N, N>) {
|
||||
let mut l = Matrix::<T, N, N>::identity();
|
||||
let mut u = self.lu; // lu
|
||||
|
||||
for m in 1..N {
|
||||
for n in 0..m {
|
||||
// iterate over lower diagonal
|
||||
l[(m, n)] = u[(m, n)];
|
||||
u[(m, n)] = T::zero();
|
||||
}
|
||||
}
|
||||
|
||||
(l, u)
|
||||
}
|
||||
}
|
||||
|
||||
pub trait LUSolve<T, const N: usize>
|
||||
where
|
||||
T: Copy + Default + Real + Product + Sum,
|
||||
{
|
||||
#[must_use]
|
||||
fn lu(&self) -> Option<LUDecomp<T, N>>;
|
||||
|
||||
#[must_use]
|
||||
fn inverse(&self) -> Option<Matrix<T, N, N>>;
|
||||
|
||||
#[must_use]
|
||||
fn det(&self) -> T;
|
||||
|
||||
#[must_use]
|
||||
fn solve<const M: usize>(&self, b: &Matrix<T, N, M>) -> Option<Matrix<T, N, M>> {
|
||||
Some(self.lu()?.solve(b))
|
||||
}
|
||||
}
|
Loading…
Reference in New Issue