Announcing my first Julia package, 'HypergeoMat'

Package Announcements
1

Hello,

Just to announce my first Julia package.

Cheers.

22 Likes
2

This is awesome! The math is way over my head but new packages with detailed docs is a beautiful thing to see. Congrats!

3

Thanks for sharing this package. In addition to the references provided, it would be nice if you will, to indicate some applications of these hypergeometric functions of a matrix argument, providing some links in the documentation to use cases where such code is required.

1 Like
4

A small blurb describing the package is generally helpful in the announcement (you can still edit your post).

4 Likes
5

The package is described in the doc :smile:

I don’t know a ton of applications. The only ones I know are related to random matrix theory: these hypergeometric functions appear in the density functions, Laplace transforms or Fourier transforms of several kind of random matrices.

1 Like
6

That’s an excellent enough application in itself!

7

Thanks.

Here is my second Julia package (Jack polynomials), related to the first one.

8

Damn, fast production! :slight_smile:

9

Lol, no, I had this code for a while, and I just packaged it, now that I know how to do a package :slight_smile:

10

Now my R package jack can calculate the Jack polynomials with Julia (thanks to the,JuliaConnectoR package). Observe the difference of speed (Julia 1.6):

## Unit: milliseconds
##   expr          min           lq       mean     median         uq       max
##      R 15767.690900 16131.731601 16546.8662 16381.9088 17123.5399 17329.460
##  Julia     8.395101     9.733001   458.8062    11.0415    90.6334  2174.228

1600x faster than R! Amazing.

11

That’s strange. On my Linux laptop I have Julia 1.7 and it is slower:

Unit: milliseconds
  expr         min          lq       mean      median          uq       max neval cld
     R 21411.06068 21418.31391 21475.3985 21423.03423 21531.32397 21593.260     5   b
 Julia    48.71635    49.13159   312.7035    52.17541    84.16258  1329.331     5  a
12

Hmm looks like the slowness is due to the R version. If I benchmark directly in Julia 1.7, it takes only 3ms.

julia> @benchmark Jack([1/2; 2/3; 1; 2/3; -1; -2; 1], [5;3;2;2;1], 3.0)
BenchmarkTools.Trial: 1575 samples with 1 evaluation.
 Range (min … max):  2.823 ms …   7.333 ms  ┊ GC (min … max): 0.00% … 47.20%
 Time  (median):     2.873 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   3.162 ms ± 945.253 μs  ┊ GC (mean ± σ):  8.44% ± 14.43%
13

Update of JackPolyomials.jl, now it can deal with a symbolic parameter alpha:

julia> jack = JackPolynomial(2, [2 ; 1])
(alpha + 2)*x_1^2*x_2 + (alpha + 2)*x_1*x_2^2

julia> jack(1,2)
6*alpha + 12

Thanks to AbstractAlgebra.

1 Like