dedalus.tools.clenshaw

Module Contents

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]

kronecker_clenshaw(val_c, norm_c, A, B, f0, cutoff, coeffs_left=True)

Clenshaw algorithm on matrix coefficients, matrix argument:

S(X) = sum_n kron(f_n(X), c_n)

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

Clenshaw algorithm on scalar coefficients, matrix argument:

S(X) = sum_n c_n f_n(X)

scalar_clenshaw(c, A, B, f0)

Clenshaw algorithm on scalar coefficients, array argument:

S(x) = sum_n c_n f_n(x)