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# Licensed under the Apache License, Version 2.0 (the "License");
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# http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np
from ... import opcodes as OperandDef
from ...serialization.serializables import AnyField
from ..utils import gen_random_seeds
from .core import TensorDistribution, TensorRandomOperandMixin, handle_array
class TensorNoncentralChisquare(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["df", "nonc"]
_op_type_ = OperandDef.RAND_NONCENTRAL_CHISQURE
_fields_ = "df", "nonc", "size"
df = AnyField("df")
nonc = AnyField("nonc")
_func_name = "noncentral_chisquare"
def __call__(self, df, nonc, chunk_size=None):
return self.new_tensor([df, nonc], None, raw_chunk_size=chunk_size)
[docs]def noncentral_chisquare(
random_state, df, nonc, size=None, chunk_size=None, gpu=None, dtype=None
):
r"""
Draw samples from a noncentral chi-square distribution.
The noncentral :math:`\chi^2` distribution is a generalisation of
the :math:`\chi^2` distribution.
Parameters
----------
df : float or array_like of floats
Degrees of freedom, should be > 0.
nonc : float or array_like of floats
Non-centrality, should be non-negative.
size : int or tuple of ints, optional
Output shape. If the given shape is, e.g., ``(m, n, k)``, then
``m * n * k`` samples are drawn. If size is ``None`` (default),
a single value is returned if ``df`` and ``nonc`` are both scalars.
Otherwise, ``mt.broadcast(df, nonc).size`` samples are drawn.
chunk_size : int or tuple of int or tuple of ints, optional
Desired chunk size on each dimension
gpu : bool, optional
Allocate the tensor on GPU if True, False as default
dtype : data-type, optional
Data-type of the returned tensor.
Returns
-------
out : Tensor or scalar
Drawn samples from the parameterized noncentral chi-square distribution.
Notes
-----
The probability density function for the noncentral Chi-square
distribution is
.. math:: P(x;df,nonc) = \sum^{\infty}_{i=0}
\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}
\P_{Y_{df+2i}}(x),
where :math:`Y_{q}` is the Chi-square with q degrees of freedom.
In Delhi (2007), it is noted that the noncentral chi-square is
useful in bombing and coverage problems, the probability of
killing the point target given by the noncentral chi-squared
distribution.
References
----------
.. [1] Delhi, M.S. Holla, "On a noncentral chi-square distribution in
the analysis of weapon systems effectiveness", Metrika,
Volume 15, Number 1 / December, 1970.
.. [2] Wikipedia, "Noncentral chi-square distribution"
http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution
Examples
--------
Draw values from the distribution and plot the histogram
>>> import matplotlib.pyplot as plt
>>> import mars.tensor as mt
>>> values = plt.hist(mt.random.noncentral_chisquare(3, 20, 100000).execute(),
... bins=200, normed=True)
>>> plt.show()
Draw values from a noncentral chisquare with very small noncentrality,
and compare to a chisquare.
>>> plt.figure()
>>> values = plt.hist(mt.random.noncentral_chisquare(3, .0000001, 100000).execute(),
... bins=mt.arange(0., 25, .1).execute(), normed=True)
>>> values2 = plt.hist(mt.random.chisquare(3, 100000).execute(),
... bins=mt.arange(0., 25, .1).execute(), normed=True)
>>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')
>>> plt.show()
Demonstrate how large values of non-centrality lead to a more symmetric
distribution.
>>> plt.figure()
>>> values = plt.hist(mt.random.noncentral_chisquare(3, 20, 100000).execute(),
... bins=200, normed=True)
>>> plt.show()
"""
if dtype is None:
dtype = (
np.random.RandomState()
.noncentral_chisquare(handle_array(df), handle_array(nonc), size=(0,))
.dtype
)
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorNoncentralChisquare(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(df, nonc, chunk_size=chunk_size)