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 _mom(self, key, left, right, cache):
"""
Statistical moments.
Example:
>>> chaospy.Uniform().mom([0, 1, 2, 3]).round(4)
array([1. , 0.5 , 0.3333, 0.25 ])
>>> Multiply(chaospy.Uniform(), 2).mom([0, 1, 2, 3]).round(4)
array([1. , 1. , 1.3333, 2. ])
>>> Multiply(2, chaospy.Uniform()).mom([0, 1, 2, 3]).round(4)
array([1. , 1. , 1.3333, 2. ])
>>> Multiply(chaospy.Uniform(), chaospy.Uniform()).mom([0, 1, 2, 3]).round(4)
array([1. , 0.25 , 0.1111, 0.0625])
"""
del cache
if isinstance(left, Distribution):
if chaospy.shares_dependencies(left, right):
raise chaospy.StochasticallyDependentError(
"product of dependent distributions not feasible: "
"{} and {}".format(left, right)
)
left = left._get_mom(key)
else:
left = (numpy.array(left).T ** key).T
if isinstance(right, Distribution):
right = right._get_mom(key)
else:
right = (numpy.array(right).T ** key).T
return numpy.prod(left) * numpy.prod(right)
def _mom(self, keys, left, right, cache):
"""
Statistical moments.
Example:
>>> chaospy.Uniform().mom([0, 1, 2, 3]).round(4)
array([1. , 0.5 , 0.3333, 0.25 ])
>>> chaospy.Add(chaospy.Uniform(), 2).mom([0, 1, 2, 3]).round(4)
array([ 1. , 2.5 , 6.3333, 16.25 ])
>>> chaospy.Add(2, chaospy.Uniform()).mom([0, 1, 2, 3]).round(4)
array([ 1. , 2.5 , 6.3333, 16.25 ])
"""
del cache
keys_ = numpy.mgrid[tuple(slice(0, key + 1, 1) for key in keys)]
keys_ = keys_.reshape(len(self), -1)
if isinstance(left, Distribution):
if chaospy.shares_dependencies(left, right):
raise chaospy.StochasticallyDependentError(
"%s: left and right side of sum stochastically dependent."
% self)
left = [left._get_mom(key) for key in keys_.T]
else:
left = list(reversed(numpy.array(left).T**keys_.T))
if isinstance(right, Distribution):
right = [right._get_mom(key) for key in keys_.T]
else:
right = list(
reversed(numpy.prod(numpy.array(right).T**keys_.T, -1)))
out = 0.0
for idx in range(keys_.shape[1]):
key = keys_.T[idx]
coef = numpy.prod(comb(keys, key))
out += coef * left[idx] * right[idx] * numpy.all(key <= keys)
return out