conatus.expert.Hermite

class conatus.expert.Hermite(coord, size, center=0.0, scale=1.0, dealias=REQUIRED)

Bases: Basis

Hermite functions on the whole line: f(x) = sum_n c_n psi_n((x - center)/scale), with psi_n(y) = H_n(y) exp(-y^2/2) / sqrt(2^n n! sqrt(pi)) (orthonormal). Every representable function decays like a Gaussian, so no boundary condition exists or is imposed. scale is the declared width of the envelope (a numerical choice like N, printed by explain()).

Operators are banded: d/dx and multiplication by x are tridiagonal, a polynomial coefficient of degree d has half-bandwidth d. Grid: Gauss-Hermite nodes, floor(N * dealias) of them. A product of two Hermite functions is not a finite Hermite series (its envelope is exp(-y^2)), so products projected by quadrature are accurate, not exact (declared).

Parameters:

• coord (Coordinate)

• size (int)

• center (float)

• scale (float)

• dealias (Any)

family = 'Hermite functions (whole line)'

unbounded = True

coeff_space()

Return type:

str