interpax_fft.DoubleChebyshevSeries

class interpax_fft.DoubleChebyshevSeries(f, domain_x=(-1, 1), domain_y=(-1, 1), lobatto=False, truncate_x=0, truncate_y=0)Source 

Real-valued 2D Chebyshev series.

f(x, y) = ∑ₘₙ aₘₙ Tₘ(x) Tₙ(y) where Tₘ are Chebyshev polynomials on [xₘᵢₙ, xₘₐₓ] and Tₙ are Chebyshev polynomials on [yₘᵢₙ, yₘₐₓ].

Notes

Performance may improve if X and Y are powers of two.

Parameters:

f (jnp.ndarray) – Shape (…, X, Y). Samples of real function on the ChebyshevSeries.nodes grid.
domain_x (tuple[float]) – Domain for x coordinates. Default is [-1, 1].
domain_y (tuple[float]) – Domain for y coordinates. Default is [-1, 1].
lobatto (bool) – Whether f was sampled on the Gauss-Lobatto (extrema-plus-endpoint) instead of the interior roots grid for Chebyshev points.
truncate_x (int) – Index at which to truncate the Chebyshev series in x coordinate. This will remove aliasing error at the shortest wavelengths where the signal to noise ratio is lowest. The default value is zero which is interpreted as no truncation.
truncate_y (int) – Index at which to truncate the Chebyshev series in y coordinate. This will remove aliasing error at the shortest wavelengths where the signal to noise ratio is lowest. The default value is zero which is interpreted as no truncation.

Chebyshev spectral resolution in x coordinate.

Chebyshev spectral resolution in y coordinate.

__init__(f, domain_x=(-1, 1), domain_y=(-1, 1), lobatto=False, truncate_x=0, truncate_y=0)Source : Interpolate Chebyshev-Chebyshev series to f.

Methods

`__init__`(f[, domain_x, domain_y, lobatto, ...])	Interpolate Chebyshev-Chebyshev series to `f`.
`compute_cheb`(x)	Evaluate at coordinate `x` to get set of 1D Chebyshev series in `y`.
`evaluate`(X, Y)	Evaluate Chebyshev series on tensor-product grid.
`nodes`(X, Y[, L, domain_x, domain_y, lobatto])	Tensor product grid of optimal collocation nodes for this basis.

Attributes