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# Licensed under the Apache License, Version 2.0 (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 ...serialization.serializables import AnyField
from ..utils import gen_random_seeds
from .core import TensorDistribution, TensorRandomOperandMixin, handle_array
class TensorRayleigh(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["scale"]
_op_type_ = OperandDef.RAND_RAYLEIGH
_fields_ = "scale", "size"
scale = AnyField("scale")
_func_name = "rayleigh"
def __call__(self, scale, chunk_size=None):
return self.new_tensor([scale], None, raw_chunk_size=chunk_size)
[docs]def rayleigh(random_state, scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a Rayleigh distribution.
The :math:`\chi` and Weibull distributions are generalizations of the
Rayleigh.
Parameters
----------
scale : float or array_like of floats, optional
Scale, also equals the mode. Should be >= 0. 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 ``scale`` is a scalar. Otherwise,
``mt.array(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 Rayleigh distribution.
Notes
-----
The probability density function for the Rayleigh distribution is
.. math:: P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}}
The Rayleigh distribution would arise, for example, if the East
and North components of the wind velocity had identical zero-mean
Gaussian distributions. Then the wind speed would have a Rayleigh
distribution.
References
----------
.. [1] Brighton Webs Ltd., "Rayleigh Distribution,"
http://www.brighton-webs.co.uk/distributions/rayleigh.asp
.. [2] Wikipedia, "Rayleigh distribution"
http://en.wikipedia.org/wiki/Rayleigh_distribution
Examples
--------
Draw values from the distribution and plot the histogram
>>> import matplotlib.pyplot as plt
>>> import mars.tensor as mt
>>> values = plt.hist(mt.random.rayleigh(3, 100000).execute(), bins=200, normed=True)
Wave heights tend to follow a Rayleigh distribution. If the mean wave
height is 1 meter, what fraction of waves are likely to be larger than 3
meters?
>>> meanvalue = 1
>>> modevalue = mt.sqrt(2 / mt.pi) * meanvalue
>>> s = mt.random.rayleigh(modevalue, 1000000)
The percentage of waves larger than 3 meters is:
>>> (100.*mt.sum(s>3)/1000000.).execute()
0.087300000000000003
"""
if dtype is None:
dtype = np.random.RandomState().rayleigh(handle_array(scale), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorRayleigh(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(scale, chunk_size=chunk_size)