Do someone know a good way for matrix inversion be...

# mathematics

[altavir]

Do someone know a good way for matrix inversion benchmarking? The problem is that obviously inversion will have different complexity for different matrices, and I can't use random ones because not every matrix could be inverted. To generate them as LUD?

[breandan]

LAPACK has a test suite for generating random matrices with certain properties http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=5F619BE77BBCCBBAD00491FB7D81E4E7?doi=10.1.1.50.1138&rep=rep1&type=pdf http://www.netlib.org/lapack/testing/matgen/

[breandan]

Are you rolling your own implementation or wrapping an existing BLAS?

[altavir]

Thanks, I will look into it, but, I probably won't be able to use lapack for it because it requires binding native code. For now I have only LUD-decomposition ported from commons math. I want to see how bad is it.

[altavir]

It is not my intention to rival BLAS, I just want to have a single pure kotlin linear solver implementation.

[altavir]

For the rest we will have @kyonifer's collection of implementations

[breandan]

JavaCPP has some presets for BLAS binding, for most platforms you only need the Maven artifact https://github.com/bytedeco/javacpp-presets/tree/master/openblas#sample-usage

[breandan]

It's what ND4j/DL4j uses https://github.com/deeplearning4j/nd4j/blob/8f005bcecb240d1fbb83b9d390ad801d1d3b6933/nd4j-backends/nd4j-backend-impls/nd4j-native/src/main/java/org/nd4j/linalg/cpu/nativecpu/blas/CpuBlas.java

[thomasnield]

I never attempted to inverse a matrix from scratch. Isn't it some kind of stochastic local search? Or is that a very naive way to do Gaussian elimination?

[altavir]

Usually it is some variant of elimination. Stochastic is used in special cases. My question is what is a typical use case

[altavir]

https://en.m.wikipedia.org/wiki/LU_decomposition

[elizarov]

Note that for degenerate matrices you’d usually want to get pseudo-inverse, not a failure https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse

[altavir]

Thanks, I've introduced a new thing called matrix feature to list matrix features like degenerate and diagonal as optional tags. I will see how it will play out. The reason behind it is that not all linear algebra contexts will support all features.

[altavir]

I will try to wrap current commons-math implementation for jvm-only and see how it looks like