dkenefake / optimalpoly

Generates MinMax polynomial approximations of functions. Stable implementation of the Remez Algorithm using multi-precision arithmetic. Also does C/C++ code generation!

Hi there 👋

I am Dustin Kenefake, a 5th year phd student in the Pistikopoulos Group, where I focus mainly on algorithms and software for optimization. Code that my group has made can be found here. Find out more about my research and myself on my website. My hobby projects center around generating random numbers, optimization, and ray tracing.

Current Open Source Projects

• PPOPT - A Scalable multiparametric programming solver written in Python
• SmallPRNG - A header only extensible PRNG library/framework written in C++ (Tested with Testu01)
• SmolPrng - A high performance extendable PRNG crate written in Rust
• SimpleDenseGurobi - A helper package for using the Gurobi Solver, written in Python
• Durandal - A convex NLP solver via successive LP technique, written in Python
• FasterFVA - A FVA tool based on a novel algorithm, written in Python
• Etymrs - A Etymological analysis tool for text passages, written in Rust

Not So Current Projects

• OptimalPoly - A numerically stable optimal approximation of functions, written in Python

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optimalpoly's Issues

Bug in the Code

By setting the first and last points in the extremum array to the start and end of the bound, the minimax polynomial will only be produced in cases where the maximum error in this region is the start and end of the bound:

In cases like the one below, the minimax polynomial will not be generated.

ZeroDivisionError for mp.sign funtion

[/usr/local/lib/python3.7/dist-packages/mpmath/matrices/linalg.py](https://localhost:8080/#) in lu_solve(ctx, A, b, **kwargs)
    224             else:
    225                 # LU factorization
--> 226                 A, p = ctx.LU_decomp(A)
    227                 b = ctx.L_solve(A, b, p)
    228                 x = ctx.U_solve(A, b)

[/usr/local/lib/python3.7/dist-packages/mpmath/matrices/linalg.py](https://localhost:8080/#) in LU_decomp(ctx, A, overwrite, use_cache)
    142             ctx.swap_row(A, j, p[j])
    143             if ctx.absmin(A[j,j]) <= tol:
--> 144                 raise ZeroDivisionError('matrix is numerically singular')
    145             # calculate elimination factors and add rows
    146             for i in xrange(j + 1, n):

ZeroDivisionError: matrix is numerically singular

Rational approximations

Thanks for this, was about to start writing my own remez implementation but yours is very clean!

Have you thought about extending it to rational approximations?