Matrix Expressions

Linear algebra is important. It is a language which both humans and computers understand well which we can use to describe a large class of important problems. Linear Algebra is an alternative approach to communicate with computers – alternative to writing code.

Matrices are used in a number of contexts and, understandably, SymPy represents them in a few ways. You can represent a matrix or linear operator with a Symbol or you can write out a matrix’s components explicitly with a Matrix object. Thanks to recent work by Sherjil over here, Matrix objects are quickly becoming more powerful.

Recently I’ve wanted to build up purely symbolic matrix expressions using Symbol but kept running into problems because I didn’t want to add things to the SymPy core Expr that were specific to matrices.  The standard SymPy Expr wasn’t really designed with Matrices in mind and I found that this was holding me back a bit.

I decided to branch off a MatrixExpr class that, while much less stable, is open to experimentation. It’s been lots of fun so far. I’ve used it for my GSoC project to build up large expressions using block matrices.

I’ll have examples in a future post related to my GSoC project. For now if you’d like to check it out my code resides here:

https://github.com/mrocklin/sympy/tree/matrix_expr/sympy/matrices

There is a MatrixExpr class with associated MatrixSymbol, MatAdd, MatMul, MatPow, Inverse, Transpose, Identity, ZeroMatrix objects. All the things you need for basic expressions. Most of the logic still depends on the subclassed Add, Mul, Pow classes with a little bit added on.

Also, because my GSoC project needed it I built a fun BlockMatrix class that holds MatrixExpr’s and can be freely mixed with normal MatrixExprs in an expression.

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About mrocklin

PhD student studying Computational Mathematics at the University of Chicago.
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One Response to Matrix Expressions

  1. mrocklin says:

    Happy to report that Matrix Expressions have made it into the SymPy trunk! They’re avalaible now if you download the repository or should be available at the next release.

    There is still lots of work to do though. Please help by generating discussion, requesting features/use cases, or even writing and submitting some code on github.

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