Matrix utilities for Chez Scheme

Implementation of common matrix usages / operations for Chez 9.5 as a way to go through the rite of passage and learn some scheme. For better or worse, I've decided to represent matrices/tensors as expansions of vector operations. E.g., if you were to index into a 2x2 matrix, (matrix-ref A i j), this would expand to (vector-ref (vector-ref A i) j). Therefore matrices are simply nested vectors of uniform size across each axis. Because of this, these may be useful in constructing a data-frame-esque record type with the underlying operations being any-typed 2x2 matrix operations.

Related SRFIs:

• SRFI 63 for array types
• SRFI 164 for multidimensional array utilities)

Disclaimer

1. Currently very barebones! The structure isn't great!
2. I've never used scheme before so this will be potentially not-very-scheme-like.
3. I don't know the quirks on scheme function implementations and their computational complexity. In light of this, I've tried to implement slightly-better-than-naiive solutions rather than highly optimized with the hope of going back later after benchmarking

Lamentations

I think the scheme vector function interface vector-* is clunky for matrices. What I would like to do is implement matrices and tensors as functions acting on, e.g., four numbers: their indices. This is consistent with the mathematical definition of index-based structures as simply being a map f: Natural Number -> Value so that f_i := f(i). This also gives a much more natural syntax for array references, (A i j). Unfortunately, this would result in extensive computation for even very simple operations (such as obtaining the length along each axis of A). This also has the downside of obscuring the structure of a matrix from the user: a lambda could be anything! I'm not adept enough with scheme (alt: don't know enough about existing SRFIs), so things might look primitive.

UPDATE [2021-11-13]: speaking of not knowing the SRFIs, I now know there have been lots of efforts in introducing efficient array types into scheme (SRFI 63 for array types, SRFI 164 for multidimensional array utilities).

Running

If you have akku, life is easy:

akku install
.akku/env
./tests/test-chez-matrices.sps

This repo depends on SRFI 64 for the test suite. A life without a testing library is a sad one after-all.

Outstanding issues

Check out the issues tab to see what isn't here yet. Most of the usual matrix operations are implemented (although probably not very efficiently).

Complete implementations:

• Common matrix operations (make-matrix, matrix-ref, matrix-set!, matrix-rows, matrix-cols, matrix-copy, matrix?, matrix-ref-row, matrix-slice ...)
• Common matrix functions (matrix-min, matrix-max, mul, T (transpose), tr (trace), euclidean-norm ...)
• Functions/macros to iterate over a matrix (do-matrix, matrix-fold, matrix-map, matrix-contract (only 1D contractions)).
• do-matrix is a notable macro to iterate over a matrix. It allows syntax of the form:

  (do-matrix m (i j () l) ...)

  Where m is the matrix to iterate over, i, j, _, l are indices to loop over. Indices can be skipped with an empty list () and the iteration goes over the entire length of an axis.