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)