Source code for mars.tensor.random.laplace

#!/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 TensorLaplace(TensorDistribution, TensorRandomOperandMixin):
    _input_fields_ = ["loc", "scale"]
    _op_type_ = OperandDef.RAND_LAPLACE

    _fields_ = "loc", "scale", "size"
    loc = AnyField("loc")
    scale = AnyField("scale")
    _func_name = "laplace"

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

[docs]def laplace( random_state, loc=0.0, scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None ): r""" Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables. Parameters ---------- loc : float or array_like of floats, optional The position, :math:`\mu`, of the distribution peak. Default is 0. scale : float or array_like of floats, optional :math:`\lambda`, the exponential decay. Default is 1. 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 ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. chunks : 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 Laplace distribution. Notes ----- It has the probability density function .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda} \exp\left(-\frac{|x - \mu|}{\lambda}\right). The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] Kotz, Samuel, et. al. "The Laplace Distribution and Generalizations, " Birkhauser, 2001. .. [3] Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. .. [4] Wikipedia, "Laplace distribution", Examples -------- Draw samples from the distribution >>> import mars.tensor as mt >>> loc, scale = 0., 1. >>> s = mt.random.laplace(loc, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s.execute(), 30, normed=True) >>> x = mt.arange(-8., 8., .01) >>> pdf = mt.exp(-abs(x-loc)/scale)/(2.*scale) >>> plt.plot(x.execute(), pdf.execute()) Plot Gaussian for comparison: >>> g = (1/(scale * mt.sqrt(2 * np.pi)) * ... mt.exp(-(x - loc)**2 / (2 * scale**2))) >>> plt.plot(x.execute(),g.execute()) """ if dtype is None: dtype = ( np.random.RandomState() .laplace(handle_array(loc), handle_array(scale), size=(0,)) .dtype ) size = random_state._handle_size(size) seed = gen_random_seeds(1, random_state.to_numpy())[0] op = TensorLaplace(seed=seed, size=size, gpu=gpu, dtype=dtype) return op(loc, scale, chunk_size=chunk_size)