# 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):

Read about this script in Russian here.

## License

Mpseudo is free software licensed under the MIT License.