Chebyshev Series

cheb_series This base class can be instantiated by its name

import pygsl.chebyshev
s=pygsl.chebyshev.cheb_series()
__init__(n) ... number of coefficients
init(f, a, b)
This function computes the Chebyshev approximation for the
function F over the range (a,b) to the previously specified order. The
computation of the Chebyshev approximation is an O(\ :math:`n^2`)
process, and requires n function evaluations.

f … a gsl_function a … lower limit b … upper limit

evalx This function evaluates the Chebyshev series at a given point X.

eval_errx This function computes the Chebyshev series at a given point X, estimating both the series RESULT and its absolute error ABSERR. The error estimate is made from the first neglected term in the series.

eval_nn, x This function evaluates the Chebyshev series at a given point x, to (at most) the given order n

eval_n_errn, x This function evaluates a Chebyshev series at a given point X, estimating both the series RESULT and its absolute error ABSERR, to (at most) the given order ORDER. The error estimate is made from the first neglected term in the series.

calc_deriv This method computes the derivative of the series CS. It returns a new instance of the cheb_series class.

calc_integ This method computes the integral of the series CS. It returns a new instance of the cheb_series class.

get_a Get the lower boundary of the current representation

get_b Get the upper boundary of the current representation

get_coefficients Get the chebyshev coefficients.

get_f Get the value f (what is it ?) The documentation does not tell anything about it.

get_order_sp Get the value f (what is it ?) The documentation does not tell anything about it.

set_a Set the lower boundary of the current representation

set_b Set the upper boundary of the current

set_coefficients Sets the chebyshev coefficients.

set_ff Set the value f (what is it ?)

set_order_sp… Set the value f (what is it ?)

gsl_functionf, params

This class defines the callbacks known as gsl_function to gsl.

e.g to supply the function f:

def f(x, params): a = params[0] b = parmas[1] c = params[3] return a * x ** 2 + b * x + c

to some solver, use

function = gsl_function(f, params)