## sparse_complex

A simple solver for complex sparse matrices

### 3 releases

 0.1.4 Jun 9, 2022 May 24, 2022 Apr 8, 2021 Mar 11, 2021 Mar 11, 2021

#479 in Math

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# sparse_complex

An simple solver for sparse complex linear systems based on Eigen::SparseLU.

## Complex Number representation

We use num::Complex to represent complex numbers. See num crate for more information.

## Example

Lets consider the complex linear system bellow:

$$\begin{bmatrix} 1 - j1 & 0\ 0 & -1 + j1 \end{bmatrix} \begin{bmatrix} x_1 \ x_2 \end{bmatrix}= \begin{bmatrix} 1 \ j1 \end{bmatrix}$$

We can solve this system as follows:

use num::Complex;
use sparse_complex::ComplexMatrix;

let mut m = ComplexMatrix::<f64>::new();
m.add_element(0, 0, Complex { re: 1., im: -1. });
m.add_element(1, 1, Complex { re: -1., im: 1. });
let mut b = vec![Complex::new(1., 0.), Complex::new(0., 1.)];
m.solve(&mut b).unwrap();

let expected = vec![Complex::new(0.5, 0.5), Complex::new(0.5, -0.5)];
assert_eq!(b, expected);


The solution of this system is:

$$\frac{1}{2} \begin{bmatrix} 1 + j1 \ 1 - j1 \end{bmatrix}$$

## Version Compatible

The sparse_complex crate is tested for rustc 1.61 and greater.

sparse_complex also depends on Eigen v3.4.0 which is licensed under MPL v2.0. The source code of Eigen can be found on Eigen's Home Page.