interpax_fft.PiecewiseChebyshevSeries

class interpax_fft.PiecewiseChebyshevSeries(cheb, domain=(-1, 1))Source

Chebyshev series.

{ fₓ | fₓ : y ↦ ∑ₙ₌₀ᴺ⁻¹ aₙ(x) Tₙ(y) } and Tₙ are Chebyshev polynomials on [−yₘᵢₙ, yₘₐₓ]

Parameters:

• cheb (jnp.ndarray) – Shape (…, X, Y). Chebyshev coefficients aₙ(x) for f(x, y) = ∑ₙ₌₀ᴺ⁻¹ aₙ(x) Tₙ(y).

• domain (tuple[float]) – Domain for y coordinates. Default is [-1, 1].

__init__(cheb, domain=(-1, 1))Source

Make piecewise series from given Chebyshev coefficients.

Methods

__init__(cheb[, domain])	Make piecewise series from given Chebyshev coefficients.
check_intersect1d(z1, z2, k, *[, plot])	Check that intersects are computed correctly.
eval1d(z[, cheb, loop])	Evaluate piecewise Chebyshev series at coordinates z.
evaluate(Y)	Evaluate Chebyshev series at Y Chebyshev points.
extrema1d([sign, num_extrema, fill_value, eps])	Coordinates and function value where derivative vanishes.
intersect1d([k, num_intersect, fill_value, eps])	Coordinates z(x, yᵢ) such that fₓ(yᵢ) = k for every x.
plot1d(cheb[, num, z1, z2, k, ...])	Plot the piecewise Chebyshev series cheb.
stitch(cheb)	Enforce continuity of the piecewise series.

Attributes

X	Number of distinct series that compose the piecewise function.
Y	Chebyshev spectral resolution of each series.
cheb	Chebyshev coefficients.
domain	Domain for y coordinates.