cargo fmt + tests
This commit is contained in:
Sébastien Crozet
parent
9c8b5f0f38
commit
e32f4ee16f
@ -1,31 +0,0 @@
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extern crate nalgebra as na;
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extern crate nalgebra_lapack;
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#[macro_use]
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extern crate approx; // for assert_relative_eq
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use na::Matrix3;
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use nalgebra_lapack::Eigen;
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use num_complex::Complex;
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//Matrix taken from https://textbooks.math.gatech.edu/ila/1553/complex-eigenvalues.html
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fn main() {
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let m = Matrix3::<f64>::new(4.0/5.0, -3.0/5.0, 0.0, 3.0/5.0, 4.0/5.0, 0.0, 1.0, 2.0, 2.0);
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let eigen = Eigen::new(m,true,true).expect("Eigen Creation Failed!");
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let (some_eigenvalues, some_left_vec, some_right_vec) = eigen.get_complex_elements();
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let eigenvalues = some_eigenvalues.expect("Eigenvalues Failed");
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let _left_eigenvectors = some_left_vec.expect("Left Eigenvectors Failed");
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let eigenvectors = some_right_vec.expect("Right Eigenvectors Failed");
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assert_relative_eq!(eigenvalues[0].re, Complex::<f64>::new(4.0/5.0,3.0/5.0).re);
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assert_relative_eq!(eigenvalues[0].im, Complex::<f64>::new(4.0/5.0,3.0/5.0).im);
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assert_relative_eq!(eigenvalues[1].re, Complex::<f64>::new(4.0/5.0,-3.0/5.0).re);
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assert_relative_eq!(eigenvalues[1].im, Complex::<f64>::new(4.0/5.0,-3.0/5.0).im);
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assert_relative_eq!(eigenvectors[0][0].re, -12.0/32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][0].im, -9.0/32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][1].re, -9.0/32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][1].im, 12.0/32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][2].re, 25.0/32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][2].im, 0.0);
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}
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@ -8,7 +8,7 @@ use simba::scalar::RealField;
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use crate::ComplexHelper;
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use na::dimension::{Const, Dim};
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use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar, allocator::Allocator};
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use na::{allocator::Allocator, DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
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use lapack;
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@ -147,7 +147,7 @@ where
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eigenvalues_re: wr,
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eigenvalues_im: wi,
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left_eigenvectors: vl,
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eigenvectors: vr
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eigenvectors: vr,
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})
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}
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@ -168,103 +168,169 @@ where
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det
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}
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/// Returns a tuple of vectors. The elements of the tuple are the real parts of the eigenvalues, left eigenvectors and right eigenvectors respectively.
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pub fn get_real_elements(&self) -> (Vec<T>, Option<Vec<OVector<T, D>>>, Option<Vec<OVector<T, D>>>) where DefaultAllocator: Allocator<T, D> {
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/// Returns a tuple of vectors. The elements of the tuple are the real parts of the eigenvalues, left eigenvectors and right eigenvectors respectively.
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pub fn get_real_elements(
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&self,
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) -> (
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Vec<T>,
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Option<Vec<OVector<T, D>>>,
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Option<Vec<OVector<T, D>>>,
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)
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where
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DefaultAllocator: Allocator<T, D>,
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{
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let (number_of_elements, _) = self.eigenvalues_re.shape_generic();
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let number_of_elements_value = number_of_elements.value();
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let mut eigenvalues = Vec::<T>::with_capacity(number_of_elements_value);
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let mut eigenvectors = match self.eigenvectors.is_some() {
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true => Some(Vec::<OVector<T, D>>::with_capacity(number_of_elements_value)),
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false => None
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true => Some(Vec::<OVector<T, D>>::with_capacity(
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number_of_elements_value,
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)),
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false => None,
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};
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let mut left_eigenvectors = match self.left_eigenvectors.is_some() {
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true => Some(Vec::<OVector<T, D>>::with_capacity(number_of_elements_value)),
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false => None
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true => Some(Vec::<OVector<T, D>>::with_capacity(
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number_of_elements_value,
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)),
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false => None,
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};
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let mut c = 0;
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while c < number_of_elements_value {
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eigenvalues.push(self.eigenvalues_re[c].clone());
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if eigenvectors.is_some() {
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eigenvectors.as_mut().unwrap().push((&self.eigenvectors.as_ref()).unwrap().column(c).into_owned());
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eigenvectors.as_mut().unwrap().push(
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(&self.eigenvectors.as_ref())
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.unwrap()
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.column(c)
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.into_owned(),
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);
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}
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if left_eigenvectors.is_some() {
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left_eigenvectors.as_mut().unwrap().push((&self.left_eigenvectors.as_ref()).unwrap().column(c).into_owned());
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left_eigenvectors.as_mut().unwrap().push(
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(&self.left_eigenvectors.as_ref())
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.unwrap()
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.column(c)
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.into_owned(),
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);
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}
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if self.eigenvalues_im[c] != T::zero() {
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//skip next entry
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c += 1;
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}
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c+=1;
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c += 1;
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}
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(eigenvalues, left_eigenvectors, eigenvectors)
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}
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/// Returns a tuple of vectors. The elements of the tuple are the complex eigenvalues, complex left eigenvectors and complex right eigenvectors respectively.
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/// Returns a tuple of vectors. The elements of the tuple are the complex eigenvalues, complex left eigenvectors and complex right eigenvectors respectively.
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/// The elements appear as conjugate pairs within each vector, with the positive of the pair always being first.
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pub fn get_complex_elements(&self) -> (Option<Vec<Complex<T>>>, Option<Vec<OVector<Complex<T>, D>>>, Option<Vec<OVector<Complex<T>, D>>>) where DefaultAllocator: Allocator<Complex<T>, D> {
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pub fn get_complex_elements(
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&self,
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) -> (
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Option<Vec<Complex<T>>>,
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Option<Vec<OVector<Complex<T>, D>>>,
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Option<Vec<OVector<Complex<T>, D>>>,
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)
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where
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DefaultAllocator: Allocator<Complex<T>, D>,
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{
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match self.eigenvalues_are_real() {
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true => (None, None, None),
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false => {
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let (number_of_elements, _) = self.eigenvalues_re.shape_generic();
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let number_of_elements_value = number_of_elements.value();
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let number_of_complex_entries = self.eigenvalues_im.iter().fold(0, |acc, e| if !e.is_zero() {acc + 1} else {acc});
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let number_of_complex_entries =
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self.eigenvalues_im
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.iter()
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.fold(0, |acc, e| if !e.is_zero() { acc + 1 } else { acc });
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let mut eigenvalues = Vec::<Complex<T>>::with_capacity(number_of_complex_entries);
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let mut eigenvectors = match self.eigenvectors.is_some() {
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true => Some(Vec::<OVector<Complex<T>, D>>::with_capacity(number_of_complex_entries)),
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false => None
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true => Some(Vec::<OVector<Complex<T>, D>>::with_capacity(
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number_of_complex_entries,
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)),
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false => None,
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};
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let mut left_eigenvectors = match self.left_eigenvectors.is_some() {
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true => Some(Vec::<OVector<Complex<T>, D>>::with_capacity(number_of_complex_entries)),
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false => None
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true => Some(Vec::<OVector<Complex<T>, D>>::with_capacity(
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number_of_complex_entries,
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)),
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false => None,
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};
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let mut c = 0;
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while c < number_of_elements_value {
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if self.eigenvalues_im[c] != T::zero() {
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//Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
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eigenvalues.push(Complex::<T>::new(self.eigenvalues_re[c].clone(), self.eigenvalues_im[c].clone()));
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eigenvalues.push(Complex::<T>::new(self.eigenvalues_re[c+1].clone(), self.eigenvalues_im[c+1].clone()));
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eigenvalues.push(Complex::<T>::new(
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self.eigenvalues_re[c].clone(),
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self.eigenvalues_im[c].clone(),
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));
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eigenvalues.push(Complex::<T>::new(
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self.eigenvalues_re[c + 1].clone(),
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self.eigenvalues_im[c + 1].clone(),
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));
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if eigenvectors.is_some() {
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let mut vec = OVector::<Complex<T>, D>::zeros_generic(number_of_elements, Const::<1>);
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let mut vec_conj = OVector::<Complex<T>, D>::zeros_generic(number_of_elements, Const::<1>);
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let mut vec = OVector::<Complex<T>, D>::zeros_generic(
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number_of_elements,
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Const::<1>,
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);
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let mut vec_conj = OVector::<Complex<T>, D>::zeros_generic(
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number_of_elements,
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Const::<1>,
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);
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for r in 0..number_of_elements_value {
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vec[r] = Complex::<T>::new((&self.eigenvectors.as_ref()).unwrap()[(r,c)].clone(),(&self.eigenvectors.as_ref()).unwrap()[(r,c+1)].clone());
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vec_conj[r] = Complex::<T>::new((&self.eigenvectors.as_ref()).unwrap()[(r,c)].clone(),(&self.eigenvectors.as_ref()).unwrap()[(r,c+1)].clone());
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vec[r] = Complex::<T>::new(
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(&self.eigenvectors.as_ref()).unwrap()[(r, c)].clone(),
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(&self.eigenvectors.as_ref()).unwrap()[(r, c + 1)].clone(),
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);
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vec_conj[r] = Complex::<T>::new(
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(&self.eigenvectors.as_ref()).unwrap()[(r, c)].clone(),
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(&self.eigenvectors.as_ref()).unwrap()[(r, c + 1)].clone(),
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);
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}
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eigenvectors.as_mut().unwrap().push(vec);
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eigenvectors.as_mut().unwrap().push(vec_conj);
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}
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if left_eigenvectors.is_some() {
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let mut vec = OVector::<Complex<T>, D>::zeros_generic(number_of_elements, Const::<1>);
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let mut vec_conj = OVector::<Complex<T>, D>::zeros_generic(number_of_elements, Const::<1>);
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let mut vec = OVector::<Complex<T>, D>::zeros_generic(
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number_of_elements,
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Const::<1>,
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);
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let mut vec_conj = OVector::<Complex<T>, D>::zeros_generic(
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number_of_elements,
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Const::<1>,
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);
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for r in 0..number_of_elements_value {
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vec[r] = Complex::<T>::new((&self.left_eigenvectors.as_ref()).unwrap()[(r,c)].clone(),(&self.left_eigenvectors.as_ref()).unwrap()[(r,c+1)].clone());
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vec_conj[r] = Complex::<T>::new((&self.left_eigenvectors.as_ref()).unwrap()[(r,c)].clone(),(&self.left_eigenvectors.as_ref()).unwrap()[(r,c+1)].clone());
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vec[r] = Complex::<T>::new(
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(&self.left_eigenvectors.as_ref()).unwrap()[(r, c)].clone(),
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(&self.left_eigenvectors.as_ref()).unwrap()[(r, c + 1)].clone(),
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);
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vec_conj[r] = Complex::<T>::new(
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(&self.left_eigenvectors.as_ref()).unwrap()[(r, c)].clone(),
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(&self.left_eigenvectors.as_ref()).unwrap()[(r, c + 1)].clone(),
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);
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}
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left_eigenvectors.as_mut().unwrap().push(vec);
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left_eigenvectors.as_mut().unwrap().push(vec_conj);
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}
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//skip next entry
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c += 1;
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}
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c+=1;
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c += 1;
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}
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(Some(eigenvalues), left_eigenvectors, eigenvectors)
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}
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}
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}
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}
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/*
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@ -58,8 +58,8 @@ proptest! {
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let sol1 = chol.solve(&b1).unwrap();
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let sol2 = chol.solve(&b2).unwrap();
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prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-4));
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prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-4));
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}
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}
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@ -84,7 +84,7 @@ proptest! {
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let id1 = &m * &m1;
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let id2 = &m1 * &m;
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prop_assert!(id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5))
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prop_assert!(id1.is_identity(1.0e-4) && id2.is_identity(1.0e-4))
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}
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}
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}
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@ -1,19 +1,47 @@
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use std::cmp;
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use na::{Matrix3};
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use na::Matrix3;
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use nalgebra_lapack::Eigen;
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use num_complex::Complex;
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use crate::proptest::*;
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use proptest::{prop_assert, proptest};
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#[test]
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fn complex_eigen() {
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let m = Matrix3::<f64>::new(
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4.0 / 5.0,
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-3.0 / 5.0,
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0.0,
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3.0 / 5.0,
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4.0 / 5.0,
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0.0,
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1.0,
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2.0,
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2.0,
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);
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let eigen = Eigen::new(m, true, true).expect("Eigen Creation Failed!");
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let (some_eigenvalues, some_left_vec, some_right_vec) = eigen.get_complex_elements();
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let eigenvalues = some_eigenvalues.expect("Eigenvalues Failed");
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let _left_eigenvectors = some_left_vec.expect("Left Eigenvectors Failed");
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let eigenvectors = some_right_vec.expect("Right Eigenvectors Failed");
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proptest! {
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//#[test]
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// fn complex_eigen() {
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// let n = cmp::max(1, cmp::min(n, 10));
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// let m = DMatrix::<f64>::new_random(n, n);
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// let eig = SymmetricEigen::new(m.clone());
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// let recomp = eig.recompose();
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// prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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// }
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assert_relative_eq!(
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eigenvalues[0].re,
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Complex::<f64>::new(4.0 / 5.0, 3.0 / 5.0).re
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);
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assert_relative_eq!(
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eigenvalues[0].im,
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Complex::<f64>::new(4.0 / 5.0, 3.0 / 5.0).im
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);
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assert_relative_eq!(
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eigenvalues[1].re,
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Complex::<f64>::new(4.0 / 5.0, -3.0 / 5.0).re
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);
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assert_relative_eq!(
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eigenvalues[1].im,
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Complex::<f64>::new(4.0 / 5.0, -3.0 / 5.0).im
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);
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assert_relative_eq!(eigenvectors[0][0].re, -12.0 / 32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][0].im, -9.0 / 32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][1].re, -9.0 / 32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][1].im, 12.0 / 32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][2].re, 25.0 / 32.7871926215100059134410999);
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assert_relative_eq!(eigenvectors[0][2].im, 0.0);
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}
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@ -51,10 +51,10 @@ proptest! {
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let tr_sol1 = lup.solve_transpose(&b1).unwrap();
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let tr_sol2 = lup.solve_transpose(&b2).unwrap();
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prop_assert!(relative_eq!(&m * sol1, b1, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(&m * sol2, b2, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(&m * sol1, b1, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(&m * sol2, b2, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-5));
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}
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#[test]
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@ -68,10 +68,10 @@ proptest! {
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let tr_sol1 = lup.solve_transpose(&b1).unwrap();
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let tr_sol2 = lup.solve_transpose(&b2).unwrap();
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prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-5));
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prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-5));
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}
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#[test]
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@ -1,4 +1,5 @@
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mod cholesky;
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mod complex_eigen;
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mod generalized_eigenvalues;
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mod lu;
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mod qr;
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@ -7,4 +8,3 @@ mod real_eigensystem;
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mod schur;
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mod svd;
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mod symmetric_eigen;
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mod complex_eigen;
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@ -13,30 +13,36 @@ proptest! {
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let m = DMatrix::<f64>::new_random(n, n);
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if let Some(eig) = Eigen::new(m.clone(), true, true) {
|
||||
let eigvals = DMatrix::from_diagonal(&eig.eigenvalues);
|
||||
let transformed_eigvectors = &m * eig.eigenvectors.as_ref().unwrap();
|
||||
let scaled_eigvectors = eig.eigenvectors.as_ref().unwrap() * &eigvals;
|
||||
// TODO: test the complex case too.
|
||||
if eig.eigenvalues_are_real() {
|
||||
let eigvals = DMatrix::from_diagonal(&eig.eigenvalues_re);
|
||||
let transformed_eigvectors = &m * eig.eigenvectors.as_ref().unwrap();
|
||||
let scaled_eigvectors = eig.eigenvectors.as_ref().unwrap() * &eigvals;
|
||||
|
||||
let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.as_ref().unwrap();
|
||||
let scaled_left_eigvectors = eig.left_eigenvectors.as_ref().unwrap() * &eigvals;
|
||||
let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.as_ref().unwrap();
|
||||
let scaled_left_eigvectors = eig.left_eigenvectors.as_ref().unwrap() * &eigvals;
|
||||
|
||||
prop_assert!(relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-7));
|
||||
prop_assert!(relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-7));
|
||||
prop_assert!(relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-5));
|
||||
prop_assert!(relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-5));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn eigensystem_static(m in matrix4()) {
|
||||
if let Some(eig) = Eigen::new(m, true, true) {
|
||||
let eigvals = Matrix4::from_diagonal(&eig.eigenvalues);
|
||||
let transformed_eigvectors = m * eig.eigenvectors.unwrap();
|
||||
let scaled_eigvectors = eig.eigenvectors.unwrap() * eigvals;
|
||||
// TODO: test the complex case too.
|
||||
if eig.eigenvalues_are_real() {
|
||||
let eigvals = Matrix4::from_diagonal(&eig.eigenvalues_re);
|
||||
let transformed_eigvectors = m * eig.eigenvectors.unwrap();
|
||||
let scaled_eigvectors = eig.eigenvectors.unwrap() * eigvals;
|
||||
|
||||
let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.unwrap();
|
||||
let scaled_left_eigvectors = eig.left_eigenvectors.unwrap() * eigvals;
|
||||
let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.unwrap();
|
||||
let scaled_left_eigvectors = eig.left_eigenvectors.unwrap() * eigvals;
|
||||
|
||||
prop_assert!(relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-7));
|
||||
prop_assert!(relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-7));
|
||||
prop_assert!(relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-5));
|
||||
prop_assert!(relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-5));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
@ -11,14 +11,17 @@ proptest! {
|
||||
let n = cmp::max(1, cmp::min(n, 10));
|
||||
let m = DMatrix::<f64>::new_random(n, n);
|
||||
|
||||
let (vecs, vals) = Schur::new(m.clone()).unpack();
|
||||
|
||||
prop_assert!(relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
|
||||
if let Some(schur) = Schur::try_new(m.clone()) {
|
||||
let (vecs, vals) = schur.unpack();
|
||||
prop_assert!(relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-5))
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn schur_static(m in matrix4()) {
|
||||
let (vecs, vals) = Schur::new(m.clone()).unpack();
|
||||
prop_assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
|
||||
if let Some(schur) = Schur::try_new(m.clone()) {
|
||||
let (vecs, vals) = schur.unpack();
|
||||
prop_assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-5))
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user