Future plans for matrices

[josdejong]

Math.js currently supports three types of matrics: nested Arrays, DenseMatrix, and SparseMatrix. DenseMatrix and SparseMatrix both have the same super class Matrix.

DenseMatrix supports 1 to n dimensions and stores data in nested arrays. SparseMatrix is 2 dimensional. Both matrices can hold any type of value, also mixed types. @rjbaucells has spend a lot of effort in working out SparseMatrix support and optimizing for matrices containing values of a single data type.

One longstanding wish has been to rework DenseMatrix to a format where data is stored in a flat Array. That way we could utilize JavaScript typed arrays which will speed up things and make many algorithms easier. Also, this should make many matrix algorithms easier. We could look into into integrating libraries like ndarray for this.

math.js is also moving into becoming an integrator for different data types, powered by external libraries. Currently it builds upon three external libraries (decimal.js, fraction.js, complex.js). I think we should aim for the same construction for matrices and units. Having such a structure, it will become easy to strip out for example bignumber support or matrix support from code bundled for the browser if you don't need it, which becomes more and more relevant since the library is large.

Related discussions:

• Proposal: design API with performance in mind #59 Proposal: design API with performance in mind
• Refactor mathjs to a plugin-based library #71 Refactor mathjs to a plugin-based library
• Change build system to browserify #41 Support for typed arrays

What are your thoughts?

[mofosyne]

Oh btw, I was wondering a bit why this uses python style matrix format, rather than the matlab matrix format when defining matricies?

PYTHON: a = np.array([[1, 2, 3], [3, 4, 6.7], [5, 9.0, 5]])
MATLAB: a = [1, 2, 3 ; 3, 4, 6.7 ; 5, 9.0, 5]

[josdejong]

The expression parser of math.js supports both these styles, but when defining a matrix in plain JavaScript you will have to use nested arrays.

[josdejong]

😂 so many plans so little time.

How would closing this issue and opening it again in a new issue help?

[josdejong]

hm yeah. Anyway I prefer keeping the current issue open, and keep the discussion in a single thread.

[gwhitney]

Relevant to this discussion is whether it's worth continuing to (re-)implement matrix/linear algebra algorithms directly in mathjs anyway. This question came up for me in the fix to #2879 which surfaced the new issue #3036. Seems to me that all this has done before, and mathjs would be better off leveraging existing solutions than rolling its own. One specific possibility seems to be https://github.com/mateogianolio/vectorious, which seems to also afford the possibility of using BLAS/LAPACK under the hood.

[josdejong]

Good point. The ndarray library mentioned on top is not actively developed as far as I can see.

We can also look into using ndarray from https://github.com/stdlib-js/stdlib

[kgryte]

👋 Happy to help out with coordinating to help make building atop stdlib happen. A first step would be to do a bit of requirements gathering, as ndarray integration can be tailored based on how much integration is desired. Most (if not all) of the necessary JavaScript plumbing is present in stdlib to support Math.js out-of-the-box. Namely, lower-level utilities for element-wise iteration, casting, broadcasting, and slicing. stdlib does have its own multi-dispatch layer, but this can be skipped, given that Math.js already has a dispatch layer supporting dtypes which stdlib does not currently support and won't be likely to support in the near future (e.g., fractions and BigInt).

[josdejong]

Thanks Athan! We're currently focusing on a refactor of the core of mathjs, but after that I definitely want to look into this.

[kgryte]

Sounds like a plan!

[dvd101x]

Another area of improvement would be related to matrix broadcasting. It currently grows the size of the involved matrices but maybe by modifying index it could do the broadcasting operations without growing the matrices.
Something like https://numpy.org/doc/stable/reference/generated/numpy.nditer.html

[kgryte]

We've written several lower-level utilities for working with nested arrays in stdlib which can handle this exact use case. Namely, broadcasting without growing matrices. I've done some POCs locally and am fairly confident that this can be used in a relatively straightforward manner in Math.js. Some care needs to be taken with regard to sparse array iteration, but I believe that this can largely be handled via standardized protocols for lazy/deferred element access.

[dvd101x]

Nice, at some point I did look into stdlib and tensorflow js that have this capability for broadcasting matrices in javascript. The current implementation is something that fits with other mathjs functions but I think it's very promising to also benefit from stdlib.

[gwhitney]

See also the thoughts/remarks in #1788.

[gwhitney]

And those in #1709.

[gwhitney]

And #1134 is also a good read ;-)