sparse_complex

An abstraction layer for sparse21 that adds support for complex sparse matrices.

Complex Number representation

In this implementation, a complex number is represented as a tuple of f64. Where the first element is the real part and the second is the imaginary part, as shown bellow:

rust let complex_number: (f64, f64) = (1.0 , 1.0) // 1 + j1 The use of f64 is a limitation of sparse21.

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:

```rust use sparse_complex::ComplexMatrix;

let mut a = ComplexMatrix::new(); a.addelement(0, 0, (1., 1.)); a.addelement(1, 1, (1., 1.));

let b = [(1., 0.), (0., 1.)];

let solution = a.solve(&b); assert_eq!(solution.unwrap(), vec![(0.5, -0.5), (0.5, 0.5)]); ```

The solution of this system is:

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

Vesion Compatible

The sparse_complex crate is tested for rustc 1.50 and greater.

License

MIT License. See LICENSE.