SNAiL

Simple linear algebra library in nim

Example

Solving a linear system with gauss' method with partial pivoting looks like this:

import snail

var A = matrix([[2.0,0],[0.0,3]])
var b = colVec([1.0,1])

proc `\`[N:static[int]](m:Matrix[N,N],v:Vector[N]):Vector[N] = ppge(m,v) # Cosmetic, just to match matlab syntax

let x = A\b
echo x

#> [+0.50|
#> |+0.33]

Compile with nim c -r -d:release test.nim or nim c -r -d:openblas test.nim ( be sure to have openblas installed ). Bonus: nim js -d:release test.nim should work too!

Documentation

Nim-generated docs here

Nimble tasks

If you have nimble and nim installed, run nimble <taskname> in the dir with snail.nimble to exec the corresponding task.

• nimble tests: runs the tests from /tests.
• nimble jstests: builds the tests from /tests. It also generates a index.htmlfile that runs all tests.
• nimble docs: generates the docs in /docs using nim docs2.

Future structure

as in, plans

• for matrix and vector, have a single file (each) implementing basic operations ( sum, multiplication, norms, etc )
• a file for linear systems ( GE, PPGE, hopefully LU/LUP, QR,etc in the future )
• a file for eigenvalues/eigenvectors ( Jacobi, Gauss-Siedel...)
• a file for interpolations ( lagrange polynomial, Chebychev points, Lobatto points, linear interpolation, least squares)
• a file for beziér curves, b-splines, splines ( cubic? ), De Casteljau, control polygon
• a file for numeric integration ( simpson ( and composite ) , trapezoidal... )
• a file for estimating derivatives?

Other?? Linear regressions, finite differences...?

On Perfomance of a naive algebra library

No particular optimization has been done yet, and it is my intention to increase the performance of the nim implementation. As a rough estimate, with -d:openblas multiplying two 100x100 matrices 100 times takes ~0.05s, while the nim implementation
with -d:release takes ~0.3s , so around a 7x difference.

If you need something more complete and are fine with configuring external libraries etc. ( and don't need js support ) consider using linalg.

Misc notes

• Needs to be compiled with "--threads:on", TODO: fallback for when not threaded ( plus a warning? )
• Needs more tests
• Flesh out arrayutils
• ~~Check arrayutils.zip and improve different size array handling ( eg zip(N,M) where M<N or generally M!=N ) ~~
• change name to SNAil? Simple Nim Algebra..i.. lib
• rework the structure to remove includes
• test everything
• try a more functional approach for concatenation of operations?
• use blas when avaliable/useful