Source code for mars.tensor.random.noncentral_chisquare

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2021 Alibaba Group Holding Ltd.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# distributed under the License is distributed on an "AS IS" BASIS,
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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 TensorRandomOperandMixin, handle_array, TensorDistribution

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" 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) >>> 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') >>> 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) >>> """ 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)