Matrix Decomposition Methods and performance comparison

[sonideft]

I have been running some performance tests against the use of different matrix decomposition methods available. I am using java20 and the ojalgo source downloaded on Oct 7, 2025.

My matrix is over 600x600 in size and is always positive definite and symmetric. Not tested, but is supposed to be.

I'm wondering if there any tips on usage to improve performance. I expected Cholesky method to be better than LU, but I didn't get those results. Any suggestions welcome.
SolverOptions.java

[apete]

All those decompositions, except LDL, exist in 2 version – dense and raw. If you modify the factory methods you can control which one you get. Maybe you want to make sure you're getting the best one. (If you don't, let me know.)

In text books the stated relative performance of different decomposition algorithms are mostly based on counting the number of mathematical operations (or possibly array read/write operations). In actual (Java) implementations performance is greatly affected by things like cache locality and if auto-vectorisation happens or not.

I believe in RawLU, the implementation details worked out particularly well, and that's what you see in your numbers.

[sonideft]

I'd like to try the dense variation. I used the RawStore.wrap(double[][]) method as that was the only one I could find to create a Store from my double[][] array. Could you suggest an alternative factory method? I did look through the javadoc and can't see another way.

If possible, a second related question; Could we wrap an existing 2D array to a reduced size? The reason is that I need to create a large array for several purposes, but only use a partition of this matrix for solving equations. The rest of the matrix is used in my process later. Currently I copy the first 'x' rows and columns into a new matrix in order to use your library. It would be nice to find a more memory efficient way.

[apete]

RawStore.wrap(double[][]) is good. Then you can do things like: RawStore.wrap(double[][]).limits(500, 500).offsets(3, 5).rows(3, 105, 567).columns(56, 3, 97);

You can feed that directly to the decompositions. No need to explicitly copy anything.

[apete]

https://www.ojalgo.org/2021/08/common-mistake/

[sonideft]

The limits function is what I was missing. Works great. Thanks

[apete]

No need to close discussions