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Feature Matrix: Chebfun ↔ ChebPy¶

This page is a side-by-side reference of MATLAB Chebfun features and their status in ChebPy. ChebPy adapts a focused subset of Chebfun's univariate machinery to Python; many of Chebfun's larger subsystems (2D/3D, ODEs, chebops, GUI, etc.) are out of scope.

Legend: ✅ supported · 🟡 partial / different shape · ❌ not implemented.

Core representation¶

Capability	Chebfun (MATLAB)	ChebPy	Notes
Smooth functions on \([-1, 1]\) via Chebyshev-T expansion	`chebtech2`	`Chebtech`	Chebyshev points of the second kind.
Functions on bounded \([a, b]\)	`bndfun`	`Bndfun`	Affine wrap of `Chebtech`.
Piecewise (multi-domain) functions	`chebfun`	`Chebfun`	Multi-piece domains supported.
Periodic (trigonometric) functions	`chebfun(..., 'trig')` / `trigtech`	`trigfun` / `Trigtech`	Fourier-based, equispaced grid.
Infinite / semi-infinite intervals	`chebfun(..., [-Inf, Inf])`	`CompactFun`	🟡 ChebPy uses an explicit `CompactFun` wrapper rather than `unbndfun`; same compactification idea.
Endpoint singularities	`chebfun(..., 'blowup', 'on')` / `singfun`	`Singfun`	🟡 ChebPy uses the Adcock–Richardson slit-strip map (no exponent prescription needed).
Quasimatrices	`chebfun` array (column quasimatrix)	`Quasimatrix`	Continuous columns; QR / SVD / `\`.
User preferences	`chebfunpref`	`UserPreferences`	Tolerance, max length, splitting.

Construction¶

Capability	Chebfun	ChebPy	Notes
Adaptive construction from a callable	`chebfun(@f)`	`chebfun(f)`
Fixed-length construction	`chebfun(@f, n)`	`chebfun(f, n=n)`
Construction from coefficients	`chebfun(coeffs, 'coeffs')`	`Chebtech.initcoeffs`	Lower-level entry point.
Construction on a domain	`chebfun(@f, [a, b])`	`chebfun(f, [a, b])`
Splitting (automatic breakpoints)	`'splitting', 'on'`	breakpoints passed explicitly	🟡 ChebPy currently expects breakpoints to be supplied by the user.
Identity / linear function	`chebfun('x')`	`Chebfun.initidentity`
Constant function	`chebfun(c)`	`Chebfun.initconst` / `pwc`	`pwc` for piecewise constants.
Equispaced data input	`chebfun(values, 'equi')`	❌	Use `polyfit` from samples instead.

Arithmetic and elementary operations¶

Capability	Chebfun	ChebPy	Notes
`+`, `-`, ``, `/`, `*`	✅	✅	Operator overloads on `Chebfun`.
Unary `-`, `abs`, `sign`	✅	✅
`floor`, `ceil`	✅	✅
`min(f, g)`, `max(f, g)`	✅	✅	`f.minimum(g)`, `f.maximum(g)`.
Composition `f(g)`	✅	✅	`__call__` accepts a `Chebfun`.
NumPy ufuncs (`sin`, `exp`, `log`, …)	n/a	✅	Via `np.<ufunc>(f)`.
Complex-valued functions	✅	✅	`f.real`, `f.imag`, `f.iscomplex`.
`restrict` to a sub-interval	✅	✅
Translate (shift domain)	✅	✅	`f.translate(d)`.
Vector-valued (array-valued) chebfuns	✅	🟡	Use `Quasimatrix` for column collections.

Calculus¶

Capability	Chebfun	ChebPy	Notes
Definite integral	`sum(f)`	`f.sum()`
Indefinite integral	`cumsum(f)`	`f.cumsum()`
Derivative	`diff(f)`	`f.diff()`	Higher-order via repeated calls.
Norms (\(L^2\), \(L^1\), \(L^\infty\))	`norm(f, p)`	`f.norm(p)`
Inner product	`f' * g`	`f.dot(g)`
Convolution	`conv(f, g)`	`f.conv(g)`	Hale–Townsend Legendre convolution.
Cross-correlation	`xcorr`	❌
Antiderivative with constant	`cumsum(f) + c`	same

Rootfinding and extrema¶

Capability	Chebfun	ChebPy	Notes
Real roots in domain	`roots(f)`	`f.roots()`	Colleague-matrix recursion.
Complex roots	`roots(f, 'complex')`	❌
Maximum / minimum value & location	`max(f)`, `min(f)`	`f.maximum()`, `f.minimum()`
`argmax` / `argmin`	✅	🟡	Returned together with the extreme value.

Plotting¶

Capability	Chebfun	ChebPy	Notes
Plot the function	`plot(f)`	`f.plot()`	matplotlib backend.
Plot Chebyshev coefficients	`plotcoeffs(f)`	`f.plotcoeffs()`
Domain / breakpoint markers	✅	✅
3D / surface plots	`plot3`, `surf`	❌	(No 2D representation in ChebPy.)

Linear algebra (quasimatrices)¶

Capability	Chebfun	ChebPy	Notes
Quasimatrix construction	column array of chebfuns	`Quasimatrix([f1, f2, …])`
QR factorisation	`qr(A)`	`Q, R = A.qr()`	Householder triangularisation.
SVD	`svd(A)`	`U, S, V = A.svd()`
Polynomial least-squares fit	`polyfit`	`polyfit`	Top-level helper.
Backslash `A \ b`	✅	🟡	Use SVD/QR-based solve for now.

Gaussian process regression¶

Capability	Chebfun	ChebPy	Notes
GP posterior as a function object	n/a	`gpr(...)` returns a `Chebfun`	ChebPy-only; no Chebfun analogue.

Out of scope (Chebfun features not in ChebPy)¶

Chebfun feature	Status in ChebPy
Linear operators / `chebop`	❌
ODE BVP / IVP solvers (`solvebvp`, `bvp4c` glue)	❌
Time-dependent PDEs (`pde15s`, `spin`, `spin2`, `spin3`, `spinsphere`)	❌
Automatic differentiation	❌
`Chebgui` graphical interface	❌
2D functions on rectangles (`Chebfun2`)	❌
3D functions (`Chebfun3`)	❌
Spherical / polar geometries (`Spherefun`, `Diskfun`)	❌
Rational approximation (`aaa`, `minimax`, `remez`, `cf`, `chebpade`, `padeapprox`, `ratinterp`)	❌
Equispaced-data construction (`'equi'` flag)	❌
Carathéodory–Féjer (`cf`)	❌
`dirac` / distributional features	❌
Lebesgue functions / constants (`lebesgue`)	❌
Examples gallery (`cheb.gallery`)	❌

See also¶

The User Guide for narrative documentation of the features that are implemented.
The About page for the history of Chebfun and the contributors whose work ChebPy adapts.
The API Reference for the full Python API.
chebfun.org for the canonical MATLAB Chebfun project.