def orthonormal_polynomials(self, *max_degree):
'''
Return the max_degree-1 first orthonormal polynomials associated with
the LebesgueMeasure on [a,b].
Parameters
----------
max_degree : int, optional
The maximum degree of the returned polynomials. The default is
None, choosing the default maximum degree associated with the
constructor of the polynomials.
Returns
-------
poly : tensap.OrthonormalPolynomials
The generated orthonormal polynomials.
'''
poly = tensap.LegendrePolynomials(*max_degree)
poly._orthogonal_polynomials_norms = poly._orthogonal_polynomials_norms * np.sqrt(
self.mass())
if self != LebesgueMeasure(-1, 1):
poly = tensap.ShiftedOrthonormalPolynomials(
poly, (self.a + self.b) / 2, (self.b - self.a) / 2)
return poly
def orthonormal_polynomials(self, *max_degree):
'''
Return the max_degree-1 first orthonormal polynomials associated with
the UniformRandomVariable.
Parameters
----------
max_degree : int, optional
The maximum degree of the returned polynomials. The default is
None, choosing the default maximum degree associated with the
constructor of the polynomials.
Returns
-------
poly : tensap.OrthonormalPolynomials
The generated orthonormal polynomials.
'''
poly = tensap.LegendrePolynomials(*max_degree)
if self != UniformRandomVariable(-1, 1):
# print('ShiftedOrthonormalPolynomials are created.')
poly = tensap.ShiftedOrthonormalPolynomials(poly,
(self.inf+self.sup)/2,
(self.sup-self.inf)/2)
return poly
def orthonormal_polynomials(self, *args):
p = tensap.EmpiricalPolynomials(self, *args)
m = np.mean(self.sample)
s = np.std(self.sample)
if np.abs(m) > np.finfo(float).eps or \
np.abs(s-1) > np.finfo(float).eps:
p = tensap.ShiftedOrthonormalPolynomials(p, m, s)
return p
def orthonormal_polynomials(self, *max_degree):
'''
Return the max_degree-1 first orthonormal polynomials associated with
the NormalRandomVariable.
Parameters
----------
max_degree : int, optional
The maximum degree of the returned polynomials. The default is
None, choosing the default maximum degree associated with the
constructor of the polynomials.
Returns
-------
poly : tensap.OrthonormalPolynomials
The generated orthonormal polynomials.
'''
poly = tensap.HermitePolynomials(*max_degree)
if self != NormalRandomVariable(0, 1):
# print('ShiftedOrthonormalPolynomials are created.')
poly = tensap.ShiftedOrthonormalPolynomials(poly, self.mu,
self.sigma)
return poly