def _mom(self, k, left, right, cache):
"""
Statistical moments.
Example:
>>> numpy.around(chaospy.Uniform().mom([0, 1, 2, 3]), 4)
array([1. , 0.5 , 0.3333, 0.25 ])
>>> numpy.around(chaospy.Power(chaospy.Uniform(), 2).mom([0, 1, 2, 3]), 4)
array([1. , 0.3333, 0.2 , 0.1429])
>>> numpy.around(chaospy.Power(chaospy.Uniform(1, 2), -1).mom([0, 1, 2, 3]), 4)
array([1. , 0.6931, 0.5 , 0.375 ])
>>> numpy.around(chaospy.Power(2, chaospy.Uniform()).mom([0, 1, 2, 3]), 4)
array([1. , 1.4427, 2.164 , 3.3663])
>>> numpy.around(chaospy.Power(2, chaospy.Uniform(-1, 0)).mom([0, 1, 2, 3]), 4)
array([1. , 0.7213, 0.541 , 0.4208])
"""
del cache
if isinstance(right, Distribution):
raise chaospy.UnsupportedFeature(
"distribution as exponent not supported.")
if numpy.any(right < 0):
raise chaospy.UnsupportedFeature(
"distribution to negative power not supported.")
if not numpy.allclose(right, numpy.array(right, dtype=int)):
raise chaospy.UnsupportedFeature(
"distribution to fractional power not supported.")
return left._get_mom(k * right)
def __init__(self, left, right, exclusion=None, repr_args=None):
if not isinstance(left, Distribution):
left = numpy.atleast_1d(left)
if left.ndim > 1:
raise chaospy.UnsupportedFeature(
"distribution operators limited to at-most 1D arrays.")
if not isinstance(right, Distribution):
right = numpy.atleast_1d(right)
if right.ndim > 1:
raise chaospy.UnsupportedFeature(
"distribution operators limited to at-most 1D arrays.")
dependencies, parameters, rotation = chaospy.declare_dependencies(
distribution=self,
parameters=dict(left=left, right=right),
is_operator=True,
)
super(OperatorDistribution, self).__init__(
parameters=parameters,
dependencies=dependencies,
exclusion=exclusion,
repr_args=repr_args,
)
self._cache_copy = {}
self._lower_cache = {}
self._upper_cache = {}
def get_mom_parameters(self):
parameters = self.get_parameters(
idx=None, cache={}, assert_numerical=False)
if any([isinstance(value, Distribution) for value in parameters.values()]):
raise chaospy.UnsupportedFeature(
"operation not supported for %s with dependencies" % self)
return parameters
def _mom(self, kloc, index):
"""
Example:
>>> d0 = chaospy.Uniform()
>>> dist = chaospy.J(d0, d0+chaospy.Uniform())
>>> dist.mom([1, 1]).round(4)
0.5834
>>> dist = chaospy.J(chaospy.Uniform(), chaospy.Normal())
>>> dist.mom([[0, 0, 1], [0, 1, 1]]).round(4)
array([1., 0., 0.])
"""
output = 1.
for idx1 in range(len(self._owners)):
_, dist1 = self._owners[idx1]
for idx2 in range(idx1 + 1, len(self._owners)):
_, dist2 = self._owners[idx2]
if chaospy.shares_dependencies(dist1, dist2):
raise chaospy.UnsupportedFeature(
"Shared dependencies across joint")
kloc = kloc[self._rotation]
for unique_idx in numpy.unique(index[self._rotation]):
output *= self._owners[unique_idx][1]._get_mom(
kloc[index == unique_idx])
return output
def get_parameters(self, idx, cache, assert_numerical=True):
"""
Get distribution parameters.
Uses the cache to replace parameters that are distribution with cached
values.
Args:
cache (Dict[Distribution, numpy.ndarray]):
Collection of already calculated values.
Returns:
(Dict[str, numpy.ndarray]):
Collection of parameters. Probability distributions are
replaced with cached values.
Raise:
UnsupportedFeature:
If a parameter is a probability distribution without cache, it
means the dependency is unresolved.
"""
parameters = super(SimpleDistribution, self).get_parameters(
idx, cache, assert_numerical=assert_numerical)
del parameters["cache"]
del parameters["idx"]
for key, value in parameters.items():
if isinstance(value, Distribution):
value = value._get_cache(idx, cache, get=0)
if isinstance(value, Distribution) and assert_numerical:
raise chaospy.UnsupportedFeature(
"operation not supported for %s with dependencies" %
self)
parameters[key] = value
return parameters
def _mom(self, k, mean, sigma, cache):
if isinstance(mean, chaospy.Distribution):
mean = mean._get_cache(None, cache=cache, get=0)
if isinstance(mean, chaospy.Distribution):
raise chaospy.UnsupportedFeature(
"Analytical moment of a conditional not supported")
out = 0.
for idx, kdx in enumerate(numpy.ndindex(*[_+1 for _ in k])):
coef = numpy.prod(special.comb(k.T, kdx).T, 0)
diff = k.T-kdx
pos = diff >= 0
diff = diff*pos
pos = numpy.all(pos)
location_ = numpy.prod(mean**diff, -1)
out = out+pos*coef*location_*isserlis_moment(tuple(kdx), sigma)
return out
def _ttr(self, kloc, idx, dist, cache):
"""
Example:
>>> dist = chaospy.J(chaospy.Uniform(), chaospy.Normal(), chaospy.Exponential())
>>> dist.ttr([[1, 2, 3], [1, 2, 3], [1, 2, 3]]).round(4)
array([[[0.5 , 0.5 , 0.5 ],
[0. , 0. , 0. ],
[3. , 5. , 7. ]],
<BLANKLINE>
[[0.0833, 0.0667, 0.0643],
[1. , 2. , 3. ],
[1. , 4. , 9. ]]])
>>> d0 = chaospy.Uniform()
>>> dist = chaospy.J(d0, d0+chaospy.Uniform())
>>> dist.ttr([1, 1]) # doctest: +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
chaospy.distributions.baseclass.UnsupportedFeature: Joint ...
"""
if self.stochastic_dependent:
raise chaospy.UnsupportedFeature(
"Joint distribution with dependencies not supported.")
return dist._get_ttr(kloc, idx)
def _pdf(self, xloc, idx, df, cache):
raise chaospy.UnsupportedFeature("Copula not supported.")
def _ttr(self, kloc, **kwargs):
"""Default TTR generator, throws error."""
raise chaospy.UnsupportedFeature(
"%s: does not support analytical recurrence coefficients." % self)
def _mom(self, kloc, **kwargs):
"""Default moment generator, throws error."""
raise chaospy.UnsupportedFeature(
"%s: does not support analytical raw moments." % self)
def _ttr(self, kloc, idx, left, right, cache):
raise chaospy.UnsupportedFeature(
"%s: Analytical TTR for logarithm not supported", self)
def _mom(self, kloc, left, right, cache):
raise chaospy.UnsupportedFeature(
"%s: Analytical moments for logarithm not supported", self)
def _ttr(self, kloc, **kwargs):
raise chaospy.UnsupportedFeature(
"three terms recursion not supported for this distribution")
def __init__(self,
cdf,
pdf=None,
lower=None,
upper=None,
ppf=None,
mom=None,
ttr=None,
parameters=None):
"""
Args:
cdf (Callable[[numpy.ndarray, ...], numpy.ndarray]):
Cumulative distribution function.
pdf (Callable[[numpy.ndarray, ...], numpy.ndarray]):
Probability density function.
lower (Callable[[...], numpy.ndarray]):
Lower boundary.
upper (Callable[[...], numpy.ndarray]):
Upper boundary.
ppf (Callable[[numpy.ndarray, ...], numpy.ndarray]):
Point percentile function.
mom (Callable[[numpy.ndarray, ...], numpy.ndarray]):
Raw moment generator.
ttr (Callable[[numpy.ndarray, ...], numpy.ndarray]):
Three terms recurrence coefficient generator.
parameters (Dict[str, numpy.ndarray]):
Parameters to pass to each of the distribution methods.
"""
self._cdf = cdf
repr_args = [str(cdf)]
if ppf is None and (lower is None or upper is None):
raise chaospy.UnsupportedFeature(
"either ppf or lower+upper should be provided.")
if pdf is not None:
repr_args.append("pdf=%s" % pdf)
self._pdf = pdf
if lower is not None:
repr_args.append("lower=%s" % lower)
self._lower = lower
if upper is not None:
repr_args.append("upper=%s" % upper)
self._upper = upper
if ppf is not None:
repr_args.append("ppf=%s" % ppf)
self._ppf = ppf
if mom is not None:
repr_args.append("mom=%s" % mom)
self._mom = mom
if ttr is not None:
repr_args.append("ttr=%s" % ttr)
self._ttr = ttr
parameters = parameters if parameters else {}
if parameters:
params = [("%s=%s" % (key, parameters[key]))
for key in sorted(parameters)]
repr_args.append("parameters=dict(%s)" % ", ".join(params))
super(UserDistribution, self).__init__(repr_args=repr_args,
parameters=parameters)
def _mom(self, kloc, **kwargs):
raise chaospy.UnsupportedFeature(
"moments not supported for this distribution")
def _pdf(self, xloc, **kwargs):
raise chaospy.UnsupportedFeature(
"%s: does not support analytical pdf." % self)
def _upper(self, **kwargs): # pragma: no cover
"""Backend upper bound."""
raise chaospy.UnsupportedFeature("lower not supported")
def _ppf(self, qloc, idx, theta, cache):
raise chaospy.UnsupportedFeature("Copula not supported.")
def _lower(self, **kwargs):
"""Backend lower bound."""
raise chaospy.UnsupportedFeature("lower not supported")
def not_implemented(*args, **kwargs):
raise chaospy.UnsupportedFeature()
def _ttr(self, xloc, idx, dist, trans, cache):
raise chaospy.UnsupportedFeature("Copula not supported.")