https://github.com/andrenarchy/pseudopy

PseudoPy computes and visualizes the pseudospectrum of a matrix
https://github.com/andrenarchy/pseudopy

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PseudoPy computes and visualizes the pseudospectrum of a matrix

• Host: GitHub
• URL: https://github.com/andrenarchy/pseudopy
• Owner: andrenarchy
• License: mit
• Created: 2014-01-31T15:54:17.000Z (almost 11 years ago)
• Default Branch: master
• Last Pushed: 2018-11-29T10:16:57.000Z (about 6 years ago)
• Last Synced: 2024-08-08T22:37:38.438Z (6 months ago)
• Language: Python
• Size: 122 KB
• Stars: 24
• Watchers: 6
• Forks: 5
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# PseudoPy [![Build Status](https://travis-ci.org/andrenarchy/pseudopy.png?branch=master)](https://travis-ci.org/andrenarchy/pseudopy)

PseudoPy computes and visualizes the pseudospectrum of a matrix. It is a Python version of the original [eigtool](http://www.cs.ox.ac.uk/pseudospectra/eigtool/) by Thomas G. Wright. The algorithms used in this package can be found in the book [Spectra and pseudospectra](http://press.princeton.edu/titles/8113.html) by [Nick Trefethen](http://www.maths.ox.ac.uk/people/profiles/nick.trefethen) and [Mark Embree](http://www.caam.rice.edu/~embree/).

## Example

The pseudospectrum of the Grcar matrix looks like this:

![Pseudospectrum of Grcar matrix](grcar.png)

If no knowledge about the location of the pseudospectrum of the given matrix is available, the following lines of code can be used to obtain an approximation:

```python

from pseudopy import NonnormalAuto, demo

from matplotlib import pyplot

from scipy.linalg import eigvals

# get Grcar matrix

A = demo.grcar(32).todense()

# compute pseudospectrum for the levels of interest between [1e-5, 1]

pseudo = NonnormalAuto(A, 1e-5, 1)

# plot

pseudo.plot([10**k for k in range(-4, 0)], spectrum=eigvals(A))

pyplot.show()

```

## Installation

### Dependencies

PseudoPy depends on numpy, scipy, matplotlib and shapely. If you are on Debian/Ubuntu, you can install these dependencies with

```

sudo apt-get install python-numpy python-scipy python-matplotlib python-shapely

```

### pip

```pip install pseudopy```

Note that you may need to add `sudo` if you want to install it system-wide.

## License

PseudoPy is free software licensed under the [MIT License](http://opensource.org/licenses/mit-license.php).