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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 TensorWeibull(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["a"]
_op_type_ = OperandDef.RAND_WEIBULL
_fields_ = "a", "size"
a = AnyField("a")
_func_name = "weibull"
def __call__(self, a, chunk_size=None):
return self.new_tensor([a], None, raw_chunk_size=chunk_size)
[docs]def weibull(random_state, a, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a Weibull distribution.
Draw samples from a 1-parameter Weibull distribution with the given
shape parameter `a`.
.. math:: X = (-ln(U))^{1/a}
Here, U is drawn from the uniform distribution over (0,1].
The more common 2-parameter Weibull, including a scale parameter
:math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`.
Parameters
----------
a : float or array_like of floats
Shape 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 Weibull distribution.
See Also
--------
scipy.stats.weibull_max
scipy.stats.weibull_min
scipy.stats.genextreme
gumbel
Notes
-----
The Weibull (or Type III asymptotic extreme value distribution
for smallest values, SEV Type III, or Rosin-Rammler
distribution) is one of a class of Generalized Extreme Value
(GEV) distributions used in modeling extreme value problems.
This class includes the Gumbel and Frechet distributions.
The probability density for the Weibull distribution is
.. math:: p(x) = \frac{a}
{\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a},
where :math:`a` is the shape and :math:`\lambda` the scale.
The function has its peak (the mode) at
:math:`\lambda(\frac{a-1}{a})^{1/a}`.
When ``a = 1``, the Weibull distribution reduces to the exponential
distribution.
References
----------
.. [1] Waloddi Weibull, Royal Technical University, Stockholm,
1939 "A Statistical Theory Of The Strength Of Materials",
Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939,
Generalstabens Litografiska Anstalts Forlag, Stockholm.
.. [2] Waloddi Weibull, "A Statistical Distribution Function of
Wide Applicability", Journal Of Applied Mechanics ASME Paper
1951.
.. [3] Wikipedia, "Weibull distribution",
http://en.wikipedia.org/wiki/Weibull_distribution
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> a = 5. # shape
>>> s = mt.random.weibull(a, 1000)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> x = mt.arange(1,100.)/50.
>>> def weib(x,n,a):
... return (a / n) * (x / n)**(a - 1) * mt.exp(-(x / n)**a)
>>> count, bins, ignored = plt.hist(mt.random.weibull(5.,1000).execute())
>>> x = mt.arange(1,100.)/50.
>>> scale = count.max()/weib(x, 1., 5.).max()
>>> plt.plot(x.execute(), (weib(x, 1., 5.)*scale).execute())
>>> plt.show()
"""
if dtype is None:
dtype = np.random.RandomState().weibull(handle_array(a), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorWeibull(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(a, chunk_size=chunk_size)