Source code for mars.tensor.random.standard_cauchy

#!/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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import numpy as np

from ... import opcodes as OperandDef
from ..utils import gen_random_seeds
from .core import TensorRandomOperandMixin, TensorDistribution

class TensorStandardCauchy(TensorDistribution, TensorRandomOperandMixin):
    _op_type_ = OperandDef.RAND_STANDARD_CAUCHY
    _func_name = "standard_cauchy"
    _fields_ = ("size",)

    def __call__(self, chunk_size=None):
        return self.new_tensor(None, None, raw_chunk_size=chunk_size)

[docs]def standard_cauchy(random_state, size=None, chunk_size=None, gpu=None, dtype=None): r""" Draw samples from a standard Cauchy distribution with mode = 0. Also known as the Lorentz distribution. Parameters ---------- 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. Default is None, in which case a single value is returned. 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 ------- samples : Tensor or scalar The drawn samples. Notes ----- The probability density function for the full Cauchy distribution is .. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] } and the Standard Cauchy distribution just sets :math:`x_0=0` and :math:`\gamma=1` The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis. When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails. References ---------- .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy Distribution", .. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. .. [3] Wikipedia, "Cauchy distribution" Examples -------- Draw samples and plot the distribution: >>> import mars.tensor as mt >>> import matplotlib.pyplot as plt >>> s = mt.random.standard_cauchy(1000000) >>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well >>> plt.hist(s.execute(), bins=100) >>> """ if dtype is None: dtype = np.random.RandomState().standard_cauchy(size=(0,)).dtype size = random_state._handle_size(size) seed = gen_random_seeds(1, random_state.to_numpy())[0] op = TensorStandardCauchy(size=size, seed=seed, gpu=gpu, dtype=dtype) return op(chunk_size=chunk_size)