84 lines
2.7 KiB
Rust
84 lines
2.7 KiB
Rust
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use std::fmt::Display;
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use std::cmp;
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use num_complex::Complex;
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use alga::general::Real;
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use std::ops::MulAssign;
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use core::{DefaultAllocator, SquareMatrix, VectorN, MatrixN, Hessenberg, Unit, Vector2, Vector3};
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use core::dimension::{Dim, DimSub, DimDiff, Dynamic, U1, U2, U3};
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use core::storage::Storage;
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use constraint::{ShapeConstraint, DimEq};
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use allocator::Allocator;
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use linalg::householder;
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use linalg::RealSchur;
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use geometry::{Reflection, UnitComplex};
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/// The eigendecomposition of a matrix with real eigenvalues.
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pub struct RealEigen<N: Real, D: Dim>
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where DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, D> {
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pub eigenvectors: MatrixN<N, D>,
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pub eigenvalues: VectorN<N, D>
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}
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impl<N: Real, D: Dim> RealEigen<N, D>
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where D: DimSub<U1>, // For Hessenberg.
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ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>>, // For Hessenberg.
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DefaultAllocator: Allocator<N, D, DimDiff<D, U1>> + // For Hessenberg.
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Allocator<N, DimDiff<D, U1>> + // For Hessenberg.
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Allocator<N, D, D> +
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Allocator<N, D>,
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// XXX: for debug
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DefaultAllocator: Allocator<usize, D, D>,
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MatrixN<N, D>: Display {
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/// Computes the eigendecomposition of a diagonalizable matrix with real eigenvalues.
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pub fn new(m: MatrixN<N, D>) -> Option<RealEigen<N, D>> {
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assert!(m.is_square(), "Unable to compute the eigendecomposition of a non-square matrix.");
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let dim = m.nrows();
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let (mut eigenvectors, mut eigenvalues) = RealSchur::new(m, 0).unwrap().unpack();
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println!("Schur eigenvalues: {}", eigenvalues);
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// Check that the eigenvalues are all real.
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for i in 0 .. dim - 1 {
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if !eigenvalues[(i + 1, i)].is_zero() {
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return None;
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}
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}
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for j in 1 .. dim {
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for i in 0 .. j {
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let diff = eigenvalues[(i, i)] - eigenvalues[(j, j)];
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if diff.is_zero() && !eigenvalues[(i, j)].is_zero() {
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return None;
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}
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let z = -eigenvalues[(i, j)] / diff;
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for k in j + 1 .. dim {
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eigenvalues[(i, k)] -= z * eigenvalues[(j, k)];
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}
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for k in 0 .. dim {
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eigenvectors[(k, j)] += z * eigenvectors[(k, i)];
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}
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}
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}
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// Normalize the eigenvector basis.
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for i in 0 .. dim {
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let _ = eigenvectors.column_mut(i).normalize_mut();
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}
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Some(RealEigen {
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eigenvectors: eigenvectors,
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eigenvalues: eigenvalues.diagonal()
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})
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}
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}
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