prysm.jacobi¶
High performance / recursive jacobi polynomial calculation.
-
prysm.jacobi.
weight
(alpha, beta, x)¶ The weight function of the jacobi polynomials for a given alpha, beta value.
-
prysm.jacobi.
a
(n, alpha, beta, x)¶ The leading term of the recurrence relation from Wikipedia, * P_n^(a,b).
-
prysm.jacobi.
b
(n, alpha, beta, x)¶ The second term of the recurrence relation from Wikipedia, * P_n-1^(a,b).
-
prysm.jacobi.
c
(n, alpha, beta, x)¶ The third term of the recurrence relation from Wikipedia, * P_n-2^(a,b).
-
prysm.jacobi.
jacobi
(n, alpha, beta, x, Pnm1=None, Pnm2=None)¶ Jacobi polynomial of order n with weight parameters alpha and beta.
Notes
This function is faster than scipy.special.jacobi when Pnm1 and Pnm2 are supplied and is stable to high order. Performance benefit ranges from 2-5x.
- Parameters
n (int) – polynomial order
alpha (float) – first weight parameter
beta (float) – second weight parameter
x (numpy.ndarray) – x coordinates to evaluate at
Pnm1 (numpy.ndarray, optional) – The n-1th order jacobi polynomial, evaluated at the given points
Pnm2 (numpy.ndarray, optional) – The n-2th order jacobi polynomial, evaluated at the given points
- Returns
jacobi polynomial evaluated at the given points
- Return type
numpy.ndarray
-
prysm.jacobi.
jacobi_sequence
(n_max, alpha, beta, x)¶ Jacobi polynomials of order 0..n_max with weight parameters alpha and beta.
- Parameters
n_max (int) – maximum polynomial order
alpha (float) – first weight parameter
beta (float) – second weight parameter
x (numpy.ndarray) – x coordinates to evaluate at
- Returns
array of shape (n_max+1, len(x))
- Return type
numpy.ndarray