Source code for mars.tensor.random.power

#!/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.
# You may obtain a copy of the License at
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# See the License for the specific language governing permissions and
# limitations under the License.

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 TensorRandomPower(TensorDistribution, TensorRandomOperandMixin):
    _input_fields_ = ["a"]
    _op_type_ = OperandDef.RAND_POWER

    _fields_ = "a", "size"
    a = AnyField("a")
    _func_name = "power"

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

[docs]def power(random_state, a, size=None, chunk_size=None, gpu=None, dtype=None): r""" Draws samples in [0, 1] from a power distribution with positive exponent a - 1. Also known as the power function distribution. Parameters ---------- a : float or array_like of floats Parameter of the distribution. Should be greater than zero. 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 ``a`` is a scalar. Otherwise, ``mt.array(a).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 power distribution. Raises ------ ValueError If a < 1. Notes ----- The probability density function is .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0. The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution. It is used, for example, in modeling the over-reporting of insurance claims. References ---------- .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions in economics and actuarial sciences", Wiley, 2003. .. [2] Heckert, N. A. and Filliben, James J. "NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions", National Institute of Standards and Technology Handbook Series, June 2003. Examples -------- Draw samples from the distribution: >>> import mars.tensor as mt >>> a = 5. # shape >>> samples = 1000 >>> s = mt.random.power(a, samples) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s.execute(), bins=30) >>> x = mt.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*mt.diff(bins)[0]*y >>> plt.plot(x.execute(), normed_y.execute()) >>> Compare the power function distribution to the inverse of the Pareto. >>> from scipy import stats >>> rvs = mt.random.power(5, 1000000) >>> rvsp = mt.random.pareto(5, 1000000) >>> xx = mt.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx.execute(),5) >>> plt.figure() >>> plt.hist(rvs.execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('np.random.power(5)') >>> plt.figure() >>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('inverse of 1 + np.random.pareto(5)') >>> plt.figure() >>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('inverse of stats.pareto(5)') """ if dtype is None: dtype = np.random.RandomState().power(handle_array(a), size=(0,)).dtype size = random_state._handle_size(size) seed = gen_random_seeds(1, random_state.to_numpy())[0] op = TensorRandomPower(size=size, seed=seed, gpu=gpu, dtype=dtype) return op(a, chunk_size=chunk_size)