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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 TensorChisquareDist(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["df"]
_op_type_ = OperandDef.RAND_CHISQUARE
_fields_ = "df", "size"
df = AnyField("df")
_func_name = "chisquare"
def __call__(self, df, chunk_size=None):
return self.new_tensor([df], self.size, raw_chunk_size=chunk_size)
[docs]def chisquare(random_state, df, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a chi-square distribution.
When `df` independent random variables, each with standard normal
distributions (mean 0, variance 1), are squared and summed, the
resulting distribution is chi-square (see Notes). This distribution
is often used in hypothesis testing.
Parameters
----------
df : float or array_like of floats
Number of degrees of freedom, should be > 0.
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`` is a scalar. Otherwise,
``mt.array(df).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 chi-square distribution.
Raises
------
ValueError
When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``)
is given.
Notes
-----
The variable obtained by summing the squares of `df` independent,
standard normally distributed random variables:
.. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i
is chi-square distributed, denoted
.. math:: Q \sim \chi^2_k.
The probability density function of the chi-squared distribution is
.. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)}
x^{k/2 - 1} e^{-x/2},
where :math:`\Gamma` is the gamma function,
.. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt.
References
----------
.. [1] NIST "Engineering Statistics Handbook"
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
Examples
--------
>>> import mars.tensor as mt
>>> mt.random.chisquare(2,4).execute()
array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272])
"""
if dtype is None:
dtype = np.random.RandomState().chisquare(handle_array(df), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorChisquareDist(seed=seed, size=size, gpu=gpu, dtype=dtype)
return op(df, chunk_size=chunk_size)