dedalus.tools.clenshaw
======================

.. py:module:: dedalus.tools.clenshaw




Module Contents
---------------

.. py:function:: jacobi_recursion(N, a, b, X)

   Build Clenshaw recurrence coefficients for Jacobi polynomials.

   .. rubric:: 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]


.. py:function:: 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)


.. py:function:: matrix_clenshaw(c, A, B, f0, cutoff)

   Clenshaw algorithm on scalar coefficients, matrix argument:
       S(X) = sum_n c_n f_n(X)


.. py:function:: scalar_clenshaw(c, A, B, f0)

   Clenshaw algorithm on scalar coefficients, array argument:
       S(x) = sum_n c_n f_n(x)