dedalus.libraries.dedalus_sphere.clenshaw

Module Contents

ncc_matrix(N, a_ncc, b_ncc, a_arg, b_arg, coeffs, cutoff=1e-06)

Build NCC matrix via Clenshaw algorithm.

jacobi_recursion(N, a, b, X)

Build Clenshaw recurrence coefficients for Jacobi polynomials.

Notes

Jacobi matrix recursion:

J[n,n-1]*f[n-1] + J[n,n]*f[n] + J[n,n+1]*f[n+1] = X*f[n] f[n+1] = (X - J[n,n])/J[n,n+1]*f[n] - J[n,n-1]/J[n,n+1]*f[n-1]

Clenshaw coefficients:

A[n] = (X - J[n,n])/J[n,n+1] B[n] = - J[n,n-1]/J[n,n+1]

matrix_clenshaw(c, A, B, f0, cutoff)

Clenshaw algorithm on scalar coefficients, matrix argument:

S(X) = sum_n c_n f_n(X)

jacobi_matrix(N, a, b)

class DeferredTuple(entry_function, size)