Source code for mars.tensor.random.hypergeometric

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2020 Alibaba Group Holding Ltd.
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# 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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#      http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np

from ... import opcodes as OperandDef
from ...serialize import AnyField
from .core import TensorRandomOperandMixin, handle_array, TensorDistribution


class TensorHypergeometric(TensorDistribution, TensorRandomOperandMixin):
    __slots__ = '_ngood', '_nbad', '_nsample', '_size'
    _input_fields_ = ['_ngood', '_nbad', '_nsample']
    _op_type_ = OperandDef.RAND_HYPERGEOMETRIC

    _ngood = AnyField('ngood')
    _nbad = AnyField('nbad')
    _nsample = AnyField('nsample')
    _func_name = 'hypergeometric'

    def __init__(self, state=None, size=None, dtype=None, gpu=None, **kw):
        dtype = np.dtype(dtype) if dtype is not None else dtype
        super().__init__(_state=state, _size=size, _dtype=dtype, _gpu=gpu, **kw)

    @property
    def ngood(self):
        return self._ngood

    @property
    def nbad(self):
        return self._nbad

    @property
    def nsample(self):
        return self._nsample

    def __call__(self, ngood, nbad, nsample, chunk_size=None):
        return self.new_tensor([ngood, nbad, nsample], None, raw_chunk_size=chunk_size)


[docs]def hypergeometric(random_state, ngood, nbad, nsample, size=None, chunk_size=None, gpu=None, dtype=None): r""" Draw samples from a Hypergeometric distribution. Samples are drawn from a hypergeometric distribution with specified parameters, ngood (ways to make a good selection), nbad (ways to make a bad selection), and nsample = number of items sampled, which is less than or equal to the sum ngood + nbad. Parameters ---------- ngood : int or array_like of ints Number of ways to make a good selection. Must be nonnegative. nbad : int or array_like of ints Number of ways to make a bad selection. Must be nonnegative. nsample : int or array_like of ints Number of items sampled. Must be at least 1 and at most ``ngood + nbad``. 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 ``ngood``, ``nbad``, and ``nsample`` are all scalars. Otherwise, ``np.broadcast(ngood, nbad, nsample).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 hypergeometric distribution. See Also -------- scipy.stats.hypergeom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Hypergeometric distribution is .. math:: P(x) = \frac{\binom{m}{n}\binom{N-m}{n-x}}{\binom{N}{n}}, where :math:`0 \le x \le m` and :math:`n+m-N \le x \le n` for P(x) the probability of x successes, n = ngood, m = nbad, and N = number of samples. Consider an urn with black and white marbles in it, ngood of them black and nbad are white. If you draw nsample balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample. Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial. References ---------- .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html .. [3] Wikipedia, "Hypergeometric distribution", http://en.wikipedia.org/wiki/Hypergeometric_distribution Examples -------- Draw samples from the distribution: >>> import mars.tensor as mt >>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = mt.random.hypergeometric(ngood, nbad, nsamp, 1000) >>> hist(s) # note that it is very unlikely to grab both bad items Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color? >>> s = mt.random.hypergeometric(15, 15, 15, 100000) >>> (mt.sum(s>=12)/100000. + mt.sum(s<=3)/100000.).execute() # answer = 0.003 ... pretty unlikely! """ if dtype is None: dtype = np.random.RandomState().hypergeometric( handle_array(ngood), handle_array(nbad), handle_array(nsample), size=(0,)).dtype size = random_state._handle_size(size) op = TensorHypergeometric(state=random_state.to_numpy(), size=size, gpu=gpu, dtype=dtype) return op(ngood, nbad, nsample, chunk_size=chunk_size)