mlmc.moments.Legendre

class mlmc.moments.Legendre(size, domain, ref_domain=None, log=False, safe_eval=True)

Legendre polynomial basis functions for generalized moments.

__init__(size, domain, ref_domain=None, log=False, safe_eval=True)

Initialize the moment function set.

Parameters:

• size – int Number of moment functions.

• domain – tuple(float, float) Domain of the input variable (min, max).

• log – bool If True, use logarithmic transformation of the domain.

• safe_eval – bool If True, clip transformed values outside the reference domain and replace them with NaN.

Methods

__init__(size, domain[, ref_domain, log, ...])	Initialize the moment function set.
change_size(size)	Return a new moment object with a different number of basis functions.
clip(value)	Clip values to the reference domain, replacing outliers with NaN.
eval(i, value)	Evaluate the i-th moment function.
eval_all(value[, size])	Evaluate all moments up to the specified size.
eval_all_der(value[, size, degree])	Evaluate derivatives of all moment functions.
eval_diff(value[, size])	Evaluate first derivatives of all moment functions.
eval_diff2(value[, size])	Evaluate second derivatives of all moment functions.
eval_single_moment(i, value)	Evaluate a single moment function (less efficient for large i).
inv_linear(value)	Inverse linear transformation back to the original domain.
linear(value)	Apply linear transformation to reference domain.