Package: empirical
empirical README==================Getting Started---------------Check out the examples directory; initial development will focus on gettingthese working first.Getting the latest version--------------------------If the pypi releases are not up-to-date enough for your tastes, or if you'dlike to see how the development is moving along, visithttps://bitbucket.org/dhild/empiricalEmpirical Interpolation-----------------------The empirical interpolation module included has the capability to handlemultiple dimensions in both variables and parameters.Why does this project exist?----------------------------The focus of this project is to create a reduced basis solver for collocationproblems. Initially, the collocation problems will be formulated using themethod of fundamental solutions, but ideally the framework will allow for easyextension to other collocation formulations as well.There is an existing solver for a variety of methods using MATLAB codes, calledmpspack. (See the 'Thanks' section for details). The mfs code base is basicallya port of this code to Python.Since mpspack is available under the GPLv3, there should be no legal issueswith creating a Python version. It should be a benefit to the mathematicalworld to make code like this more widely available. Unfortunately, sincethis project has no official affiliation with mpspack, or its creators AlexBarnett and Timo Betcke, it will make it harder to keep up with any updatesor additions to their library. At the time of inception for this library, Iused the 1.31 version of mpspack.The biggest reason to port mpspack to Python is the fact that Python isfree, and MATLAB is expensive. For my Master's thesis, I need to use theircode, but I also need to run it a huge number of times. While my school doeshave MATLAB, I did not find it simple to get MATLAB to run in parallel. Thisproblem seems to stem from the fact that each running process must have it'sown license; my school does not have an unlimited number of such licenses,and even if they did, I have had lots of trouble getting it to work.The speed impacts are not anticipated to be significant; numpy benchmarks donot typically have much difference from similar MATLAB code.Thanks======mpspack-------Special thanks to Alex Barnett and Timo Betcke, for their MPSPACK software.Originally, much of the code base is based upon their project, which they havedistributed MATLAB codes for under the GPLv3. They have a fantastic design anda well documented, maintained, and complete package, athttps://code.google.com/p/mpspack/legendre-gauss-lobatto algorithm--------------------------------Credit for the LGL algorithm goes to Greg von Winckel. Originally implemented inMATLAB, I found the algorithm athttp://www.mathworks.com/matlabcentral/fileexchange/4775-legende-gauss-lobatto-nodes-and-weightsChangelog=========0.2---------* Improved the empirical interpolation interface.- It no longer tries to perform interpolations, but leaves that to thecalling function.- More and improved examples are added, copying a reference text, seeAanonsen, "Empirical Interpolation with Application to Reduced BasisApproximations", Chapter 3. 2009, Norwegian University of Science andTechnology.* Quadrature points:- Added a linear quadrature function.- Added a function for genericly transforming quadrature from [-1, 1] to someother range [a, b].- Added a common selection method for quadratures.* Added a couple of mesh classes for convenience. Currently only 1- and 2-dimensional classes are implemented, but if they prove useful then a genericversion may be called for.* Removed some of the interpolation code. It has been deemed relativelyunnecessary.* Various asthetics:- Added pylint configuration file, and improved from some of the suggestions.- Made various improvements to the testing functions.0.1--------What works:* Basic support for empirical interpolation method is implemented. The API maychange significantly in future releases.* Method of fundamental solutions, along with basic domain/segment codes.* Quadrature generators all pass some basic tests (code is thanks to mpspackand lglnodes.m):- Periodic trapezoid- Trapezoid- Gaussian- Clenshaw-Curtis- Legendre-Gauss-Lobatto* Interpolation codes have been written, using the following algorithms:- Newton interpolating polynomial (nested form)- Lagrange interpolating polynomial (uses slow method for cardinalpolynomials, probably numerically unstable for large number of nodes)- Lagrange bivariate (also uses a slow method for cardinal polynomials, doesnot yet interface well with the EI class)* Example scripts for empirical interpolation and, method of fundamentalsolutions.* A variety of unit tests have been implemented.* A few of the different classes (Domain, Segment, Scattering) can plot some oftheir features using matplotlib.* Restructured package layout (and changed name from emfs to empirical).0.0--------*  Initial versionWhat works:* The examples/tut_scatt.py script is a port of the mpspack script of the samename. While it is slightly different in some ways, it does successfullycalculate a plane wave scattering problem, and display the resultant fields.* All of the unit tests written so far run successfully. However, there is only60% coverage with these, and even that is not a thorough coverage of all themethods called.