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About ChebPy and Chebfun

ChebPy is a Python adaptation of Chebfun, the open-source numerical computing system for functions originally developed in Oxford's Numerical Analysis Group at the Mathematical Institute, University of Oxford. ChebPy reimplements a portion of the Chebfun design in Python; the mathematics, algorithms, and overall architecture are Chebfun's. The notes below give a brief account of where those ideas come from, and which members of the Chebfun community to credit. They are deliberately a summary — for a full account, see Chebfun's own History and People pages.

Timeline

Origins (2002–2005)

The project began as an idea of Nick Trefethen in late 2001: that one could overload MATLAB vectors so they behave like the continuous functions they sample. Zachary Battles worked out the consequences as his DPhil thesis at Oxford under Trefethen, producing Chebfun Version 1 for smooth functions on \([-1, 1]\) (Battles & Trefethen, SIAM J. Sci. Comp., 2004).

Version 2 (2006–2008)

Version 2 grew out of EPSRC-funded work from 2006 onwards. Ricardo Pachón extended the representation to piecewise-continuous functions on arbitrary intervals; Rodrigo Platte added automatic subdivision and edge detection; and Toby Driscoll, joining from the University of Delaware in 2008, led the introduction of linear operators, ODEs, integral operators, eigenvalue problems, and operator exponentials, in collaboration with Folkmar Bornemann. Version 2 shipped in June 2008.

Key references for this era:

  • Pachón, Platte & Trefethen, Piecewise smooth chebfuns, IMA J. Numer. Anal. (2010).
  • Driscoll, Bornemann & Trefethen, The chebop system for automatic solution of differential equations, BIT Numer. Math. (2008).

Version 3 (2008–2009)

Nick Hale joined as Trefethen's DPhil student and then postdoc, and contributed Gauss-quadrature machinery for very large node counts and the pde15s time-stepper for nonlinear PDEs. Ásgeir Birkisson introduced automatic differentiation and nonlinear BVPs. Mark Richardson added support for poles and endpoint singularities — the part of Chebfun whose direct descendant is ChebPy's Singfun. Further contributions came from Pedro Gonnet, Sheehan Olver, Joris Van Deun, and Alex Townsend. Version 3 was released in December 2009, coordinated by Platte and Hale.

Open source and the v5 rewrite (2010–2014)

Chebfun was relicensed under a BSD licence in 2010 and moved to GitHub. The next four years saw the differential-equation infrastructure of Driscoll and Hale, the Chebgui graphical interface (Birkisson and Hale), and a curated Examples collection led by Trefethen. A 2012 ERC Advanced Grant brought in a new generation of DPhil students and postdocs — Anthony Austin, Mohsin Javed, Hadrien Montanelli, Hrothgar, Kuan Xu, Behnam Hashemi, Jared Aurentz, Olivier Sète, and others. The September 2012 Chebfun and Beyond workshop set the direction for a ground-up rewrite, and the modular, GitHub-hosted Chebfun Version 5 was released in June 2014, led by Hale.

In parallel, Trefethen's textbook Approximation Theory and Approximation Practice was published by SIAM in 2013 (extended edition 2019) and remains the mathematical foundation of the project.

2D, 3D and periodic extensions (2013–2016)

Alex Townsend built Chebfun2 for two-dimensional functions on rectangles using low-rank representations; Behnam Hashemi later followed with Chebfun3 (2016).

During a 2014 sabbatical at Oxford, Grady Wright (Boise State) introduced a 'trig' option for trigonometric Fourier-based chebfuns — the "trigfun" capability that is the direct ancestor of ChebPy's Trigtech module. Wright, Townsend, and Heather Wilber then built Spherefun (May 2016); Wilber went on to lead Diskfun.

References:

  • Townsend & Trefethen, An extension of Chebfun to two dimensions, SIAM J. Sci. Comp. (2013).
  • Hashemi & Trefethen, Chebfun in three dimensions, SIAM J. Sci. Comp. (2017).
  • Wright, Javed, Montanelli & Trefethen, Extension of Chebfun to periodic functions, SIAM J. Sci. Comp. (2015).
  • Townsend, Wilber & Wright, Computing with functions in spherical and polar geometries I & II, SIAM J. Sci. Comp. (2016).

Later work (2014–)

Subsequent additions to Chebfun include unification of IVPs and BVPs under u = N\f (Birkisson), the spin/spin2/spin3/spinsphere exponential-integrator solvers for stiff PDEs (Montanelli), and the AAA algorithm and minimax for rational approximation (Yuji Nakatsukasa, Olivier Sète, Trefethen, and Silviu Filip). Birkisson's IVP/BVP work informs the book Exploring ODEs by Trefethen, Birkisson, and Driscoll.

  • Nakatsukasa, Sète & Trefethen, The AAA algorithm for rational approximation, SIAM J. Sci. Comp. (2018).

Key contributors

The Chebfun project is the work of many people; the names below are those whose contributions most directly shape what ChebPy adapts. The Chebfun team maintains a comprehensive list at chebfun.org/about/people.html; that page is the canonical reference.

The founders and Version 1–2 leads that ChebPy most directly inherits from are:

  • Nick Trefethen — invented Chebfun (2002) and led the project throughout; author of ATAP and co-author of Exploring ODEs.
  • Zachary Battles — Chebfun Version 1; quasimatrix qr, svd, \, roots.
  • Ricardo Pachón — piecewise polynomials; remez, chebpade, lebesgue.
  • Rodrigo Platte — extension to infinite intervals; edge detection and splitting on.
  • Toby Driscoll — ODE/integral side from 2008; solvebvp, eigs, expm, volt, fred; rectangular and block spectral discretisations.
  • Nick Hale — Chebfun project director 2010–2014; led the v5 rewrite; quadrature, pde15s, conv, legpts, cheb2leg.

Other contributors whose work appears in features ChebPy adapts (or intends to adapt) include:

  • Ásgeir Birkisson — automatic differentiation; nonlinear BVPs/IVPs; Chebgui.
  • Alex Townsend — Chebfun2; legpts, sum, conv, cheb2leg, nufft; co-author of Spherefun.
  • Mark Richardson — blowup on; poles and singularities (the basis of ChebPy's Singfun).
  • Folkmar Bornemann — lazy-evaluation idea enabling operators.
  • Pedro Gonnet — ratinterp, padeapprox.
  • Stefan Güttel — rational functions; chebsnake.
  • Anthony Austin — preferences architecture; technical leadership.
  • Mohsin Javed — dirac, trigremez; coding-style guide.
  • Georges Klein — chebfun(...,'equi') for equispaced data.
  • Hrothgar — v5 website; block operators and adjoints.
  • Kuan Xu — rectangular differentiation matrices; v5 unbounded intervals.
  • Hadrien Montanelli — spin, spin2, spin3, spinsphere, cheb.choreo.
  • Behnam Hashemi — Chebfun3.
  • Jared Aurentz — standardChop, adjoint; continuous Krylov methods.
  • Olivier Sète — co-author of aaa.
  • Yuji Nakatsukasa — aaa, minimax; fast linear algebra for spinsphere.
  • Silviu Filip — minimax rational best approximation.
  • Grady Wright — the 'trig' (trigfun) capability that ChebPy's Trigtech is descended from; led Spherefun.
  • Heather Wilber — co-author of Spherefun; led Diskfun.
  • Sheehan Olver — ultraspherical spectral methods (with Townsend).
  • Vanni Noferini — fast rootfinding for Chebfun2.
  • Marcus Webb — barycentric formulas; analytic continuation; improvements to bary.
  • Joris Van Deun — cf for Carathéodory–Féjer approximation.
  • Richard Mikael Slevinsky — quadrature, ultraspherical methods, ApproxFun link.
  • Jean-Paul Berrut — championed the barycentric formulas that were the original spark for Chebfun.
  • Lourenço Peixoto — ultrapts, improvements to jacpts.

Foundational publications

The Chebfun project maintains a comprehensive publications list. The papers below are the most directly relevant to the algorithms and design adapted in ChebPy.

Books

Chebfun fundamentals

Periodic functions (the Trigtech ancestor)

Quadrature and convolution (used by ChebPy's conv)

Quasimatrix algebra (used by ChebPy's quasimatrix module)

Rational approximation

Sponsors of the Chebfun project

Chebfun has been supported over the years by EPSRC (UK Engineering and Physical Sciences Research Council), the European Research Council (Trefethen Advanced Grant, 2012–2017), MathWorks, and the Oxford Centre for Collaborative Applied Mathematics (OCCAM). See the Chebfun sponsors page.

Citing ChebPy and Chebfun

If you use ChebPy in published work, please also cite the original Chebfun project:

T. A. Driscoll, N. Hale, and L. N. Trefethen, editors, Chebfun Guide, Pafnuty Publications, Oxford, 2014.

Where the topic is closer to a specific Chebfun paper above (for instance periodic representations or Hale–Townsend convolution), please cite that paper in addition.

This page summarises material from the Chebfun project's history and people pages, © Copyright the University of Oxford and the Chebfun Developers, used here for attribution.