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#
# 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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#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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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 TensorStandardGamma(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["shape"]
_op_type_ = OperandDef.RAND_STANDARD_GAMMMA
_fields_ = "shape", "size"
shape = AnyField("shape")
_func_name = "standard_gamma"
def __call__(self, shape, chunk_size=None):
return self.new_tensor([shape], None, raw_chunk_size=chunk_size)
[docs]def standard_gamma(
random_state, shape, size=None, chunk_size=None, gpu=None, dtype=None
):
r"""
Draw samples from a standard Gamma distribution.
Samples are drawn from a Gamma distribution with specified parameters,
shape (sometimes designated "k") and scale=1.
Parameters
----------
shape : float or array_like of floats
Parameter, should be > 0.
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 ``shape`` is a scalar. Otherwise,
``mt.array(shape).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 standard gamma distribution.
See Also
--------
scipy.stats.gamma : probability density function, distribution or
cumulative density function, etc.
Notes
-----
The probability density for the Gamma distribution is
.. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},
where :math:`k` is the shape and :math:`\theta` the scale,
and :math:`\Gamma` is the Gamma function.
The Gamma distribution is often used to model the times to failure of
electronic components, and arises naturally in processes for which the
waiting times between Poisson distributed events are relevant.
References
----------
.. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A
Wolfram Web Resource.
http://mathworld.wolfram.com/GammaDistribution.html
.. [2] Wikipedia, "Gamma distribution",
http://en.wikipedia.org/wiki/Gamma_distribution
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> shape, scale = 2., 1. # mean and width
>>> s = mt.random.standard_gamma(shape, 1000000)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
>>> count, bins, ignored = plt.hist(s.execute(), 50, normed=True)
>>> y = bins**(shape-1) * ((mt.exp(-bins/scale))/ \
... (sps.gamma(shape) * scale**shape))
>>> plt.plot(bins, y.execute(), linewidth=2, color='r')
>>> plt.show()
"""
if dtype is None:
dtype = (
np.random.RandomState().standard_gamma(handle_array(shape), size=(0,)).dtype
)
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorStandardGamma(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(shape, chunk_size=chunk_size)