andrenarchy / pseudopy

PseudoPy computes and visualizes the pseudospectrum of a matrix

PseudoPy

PseudoPy computes and visualizes the pseudospectrum of a matrix. It is a Python version of the original eigtool by Thomas G. Wright. The algorithms used in this package can be found in the book Spectra and pseudospectra by Nick Trefethen and Mark Embree.

Example

The pseudospectrum of the Grcar matrix looks like this:

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:

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.

pseudopy's Issues

PseudoPsectrum of Random Matrix.

why my kernel dies when I put :

n  = 2000
mu = 0  
sigma = 1
A  = np.random.normal(mu, sigma, (n,n))

pseudo = NonnormalAuto(A, 1e-5, 1)
pseudo.plot([10**k for k in range(-4, 3)], spectrum=eigvals(A))
pyplot.show()

Add determination of bounding box for pseudospectrum

Non-square matrix

Hi,
I would like to know if your code is capable of computing the pseudospectrum of a rectangular matrix.
Thank you,
Georgios

Non Square matrix

I want to find the pseudospectrum of a rectangular matrix but your code wants square error.
I have read here by Trefethen that there is an algorithm.

import numpy as np
import matplotlib.pyplot as plt
from pseudopy import *
from scipy.linalg import eigvals

A = np.array([[1, 3, 2],
              [5, 3, 1],
              [3, 4, 5],
              [3, 4, 5]])
pseudo = NonnormalAuto(A, 1e-5, 1)
pseudo.plot([10**k for k in range(-1, 1)], spectrum=eigvals(A))
pyplot.show()

Support singular matrices?

It seems like the code for non-normal matrices requires the matrix to be non-singular. Am I missing something? If not, is there any plans to support non-singular matrices in the near future?

problems with importing pseudopy

I just installed pseudopy on my ubuntu machine and that seemed to go smoothly.

However, when I try importing it I get the following error.

I am sorry to bug you with this but if you have any advice on how to fix this I would be very keen to start playing with this library. It looks great!

import pseudopy
Traceback (most recent call last):
File "", line 1, in
File "/usr/local/lib/python2.7/dist-packages/pseudopy/init.py", line 5, in
from .normal import Normal, NormalEvals
File "/usr/local/lib/python2.7/dist-packages/pseudopy/normal.py", line 3, in
import shapely.geometry as geom
ImportError: No module named shapely.geometry

AttributeError: 'NoneType' object has no attribute 'get_view_interval'

When I run demo.grcar_demo(), I got this error, even it is able to calculate and plot.
Could anyone help with this? Thanks!