chaospy.approximate_inverse

chaospy.approximate_inverse(distribution, idx, qloc, bounds=None, cache=None, parameters=None, xloc0=None, iterations=300, tolerance=1e-12)

Calculate the approximation of the inverse Rosenblatt transformation.

Uses a hybrid Newton-Raphson and binary search method to converge to the inverse values. Includes forward Rosenblatt transformations, probability density function (its derivative), and if not provided, boundary function.

Args:

distribution (Distribution):

Distribution to estimate inverse Rosenblatt on.

idx (int):

The dimension to take approximation along.

qloc (numpy.ndarray):

Input values. All values must be on unit interval (0, 1) and qloc.shape == (dim,size) where dim is the number of dimensions in distribution and size is the number of values to calculate simultaneously.

bounds (Optional[Tuple[numpy.ndarray, numpy.ndarray]]):

Assuming lower and upper bounds is not available, this provides outer bounds for lower and upper to use instead.

cache (Optional[Dict[Distribution, numpy.ndarray]]):

Memory cache for the location in the evaluation so far.

parameters (Optional[Dict[str, Any]]):

The parameters to use. If omitted, get the parameters from distribution.

iterations (int):

The maximum number of iterations allowed.

tolerance (float):

Tolerance criterion determining convergence.

Returns:

(numpy.ndarray):

Approximation of inverse Rosenblatt transformation.

Example:

>>> distribution = chaospy.Normal(1000, 10)
>>> qloc = numpy.array([0.1, 0.2, 0.9])
>>> inverse = distribution.inv(qloc)
>>> inverse.round(4)
array([ 987.1845,  991.5838, 1012.8155])
>>> distribution._ppf = None
>>> numpy.allclose(
...     approximate_inverse(distribution, 0, qloc), inverse)
True