chaospy.expansion.cholesky

chaospy.expansion.cholesky(order, dist, normed=False, graded=True, reverse=True, cross_truncation=1.0, retall=False)

Create orthogonal polynomial expansion from Cholesky decomposition.

Args:

order (int):

Order of polynomial expansion

dist (Distribution):

Distribution space where polynomials are orthogonal

normed (bool):

If True orthonormal polynomials will be used instead of monic.

graded (bool):

Graded sorting, meaning the indices are always sorted by the index sum. E.g. q0**2*q1**2*q2**2 has an exponent sum of 6, and will therefore be consider larger than both q0**2*q1*q2, q0*q1**2*q2 and q0*q1*q2**2, which all have exponent sum of 5.

reverse (bool):

Reverse lexicographical sorting meaning that q0*q1**3 is considered bigger than q0**3*q1, instead of the opposite.

cross_truncation (float):

Use hyperbolic cross truncation scheme to reduce the number of terms in expansion.

retall (bool):

If true return numerical stabilized norms as well. Roughly the same as cp.E(orth**2, dist).

Examples:

>>> distribution = chaospy.Normal()
>>> expansion, norms = chaospy.expansion.cholesky(3, distribution, retall=True)
>>> expansion.round(4)
polynomial([1.0, q0, q0**2-1.0, q0**3-3.0*q0])
>>> norms
array([1., 1., 2., 6.])