# mpseudo Release 0.1.4

Computation of pseudospectra of matrices in parallel

Keywords
matrix, pseudospectra, eigenvalue, problem, computational, algebra, rectangular, matricies
MIT
Install
``` pip install mpseudo==0.1.4 ```

# Mpseudo Mpseudo performs multicore and precise computation of pseudospectra of (square or rectangular) matricies. It uses pseudospectra definition and find epsilon-values on a regular grid of a complex plane. It uses `multiprocessing` module to share computations between cpu-cores, and `mpmath` module to make calculations with high precision.

##Dependencies `Mpmath` module is needed to perform computations with high precision.

`pip install mpmath`

If you don't need ability of high precision pseudospectra computation (more than 15 digits), the `mpseudo` can work without `mpmath`. The only requirement - NumPy. It should be installed on your system or in virtual environment.

## Installation

`git clone https://github.com/scidam/mpseudo.git`

## Example

The pseudospectrum of the gallery(5) MatLab matrix looks like this (up to 100-digits of accuracy used for a matrix resolvent computation): The pseudospectra above is obtained via the following lines of code:

```from matplotlib import pyplot
from mpseudo import pseudo

# Gallery(5) MatLab matrix (exact eigenvalue is 0 (the only!))
A = [[-9, 11, -21, 63, -252],
[70, -69, 141, -421, 1684],
[-575, 575, -1149, 3451, -13801],
[3891, -3891, 7782, -23345, 93365],
[1024, -1024, 2048, -6144, 24572]]

# compute pseudospectrum in the bounding box [-0.05,0.05,-0.05,0.05] with
# resolution 100x100 (ncpu = 2 processes) and 50-digits precision.
psa, X, Y = pseudo(A, ncpu=2, digits=50, ppd=100, bbox=[-0.05,0.05,-0.05,0.05])

# show results
pyplot.conourf(X, Y, psa)
pyplot.show()```

Note, if `mpmath` module is not installed, pseudospectrum of the matrix will be computed with standard (double, 15-digits) precision, which is not sufficient for this case.

Interesting, but Eigtool or PseudoPy tools (along with `scipy eigvals` function) applied to the matrix A in the example above lead to inaccurate results (due to insufficient (double) precision): 