Source code for mars.tensor.random.normal

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

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

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

[docs]def normal( random_state, loc=0.0, scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None ): r""" Draw random samples from a normal (Gaussian) distribution. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [2]_, is often called the bell curve because of its characteristic shape (see the example below). The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [2]_. Parameters ---------- loc : float or array_like of floats Mean ("centre") of the distribution. scale : float or array_like of floats Standard deviation (spread or "width") of the distribution. 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, ``mt.broadcast(loc, scale).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 normal distribution. See Also -------- scipy.stats.norm : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gaussian distribution is .. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, where :math:`\mu` is the mean and :math:`\sigma` the standard deviation. The square of the standard deviation, :math:`\sigma^2`, is called the variance. The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at :math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that `numpy.random.normal` is more likely to return samples lying close to the mean, rather than those far away. References ---------- .. [1] Wikipedia, "Normal distribution", .. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random Variables and Random Signal Principles", 4th ed., 2001, pp. 51, 51, 125. Examples -------- Draw samples from the distribution: >>> import mars.tensor as mt >>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = mt.random.normal(mu, sigma, 1000) Verify the mean and the variance: >>> (abs(mu - mt.mean(s)) < 0.01).execute() True >>> (abs(sigma - mt.std(s, ddof=1)) < 0.01).execute() True 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) >>> plt.plot(bins, (1/(sigma * mt.sqrt(2 * mt.pi)) * ... mt.exp( - (bins - mu)**2 / (2 * sigma**2) )).execute(), ... linewidth=2, color='r') >>> """ if dtype is None: dtype = ( np.random.RandomState() .normal(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 = TensorNormal(size=size, seed=seed, gpu=gpu, dtype=dtype) return op(loc, scale, chunk_size=chunk_size)