Metadata-Version: 1.1
Name: mpseudo
Version: 0.1.3.post1
Summary: Computation of pseudospectra of matrices in parallel
Home-page: https://github.com/scidam/mpseudo
Author: Dmitry E. Kislov
Author-email: kislov@easydan.com
License: UNKNOWN
Description: # Mpseudo [![Build Status](https://travis-ci.org/scidam/mpseudo.svg?branch=master)](https://travis-ci.org/scidam/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](http://numpy.org). 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):
        
        ![Pseudospectrum of gallery(5) MatLab matrix](gal5pseudo.png)
        
        The pseudospectra above is obtained via the following lines of code:
        ```python
        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](http://www.cs.ox.ac.uk/pseudospectra/eigtool/) or [PseudoPy](https://github.com/andrenarchy/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):
        
        ![Pseudospectrum of gallery(5) MatLab matrix plotted via PseudoPy](inacpseudo.png)
        
        Read about this script in Russian [here](http://easydan.com/arts/arch/high-prec-pseudospectra/).
        
        ## License
        Mpseudo is free software licensed under the [MIT License](http://opensource.org/licenses/mit-license.php).
        
Keywords: matrix pseudospectra,eigenvalue problem,computational algebra,rectangular matricies
Platform: UNKNOWN
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 3
Classifier: Topic :: Scientific/Engineering :: Mathematics
