chaospy.expansion.hermite

chaospy.expansion.hermite(order, mu=0.0, sigma=1.0, physicist=False, normed=False, retall=False)

Hermite orthogonal polynomial expansion.

Args:

order (int):

The quadrature order.

mu (float):

Non-centrality parameter.

sigma (float):

Scale parameter.

physicist (bool):

Use physicist weights instead of probabilist variant.

normed (bool):

If True orthonormal polynomials will be used.

retall (bool):

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

Returns:

(numpoly.ndpoly, numpy.ndarray):

Hermite polynomial expansion. Norms of the orthogonal expansion on the form E(orth**2, dist).

Examples:

>>> polynomials, norms = chaospy.expansion.hermite(4, retall=True)
>>> polynomials
polynomial([1.0, q0, q0**2-1.0, q0**3-3.0*q0, q0**4-6.0*q0**2+3.0])
>>> norms
array([ 1.,  1.,  2.,  6., 24.])
>>> chaospy.expansion.hermite(3, physicist=True)
polynomial([1.0, 2.0*q0, 4.0*q0**2-2.0, 8.0*q0**3-12.0*q0])
>>> chaospy.expansion.hermite(3, sigma=2.5, normed=True).round(3)
polynomial([1.0, 0.4*q0, 0.113*q0**2-0.707, 0.026*q0**3-0.49*q0])