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# derived from 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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#
# 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 TensorTriangular(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["left", "mode", "right"]
_op_type_ = OperandDef.RAND_TRIANGULAR
_fields_ = "left", "mode", "right", "size"
left = AnyField("left")
mode = AnyField("mode")
right = AnyField("right")
_func_name = "triangular"
def __call__(self, left, mode, right, chunk_size=None):
return self.new_tensor([left, mode, right], None, raw_chunk_size=chunk_size)
[docs]def triangular(
random_state, left, mode, right, size=None, chunk_size=None, gpu=None, dtype=None
):
r"""
Draw samples from the triangular distribution over the
interval ``[left, right]``.
The triangular distribution is a continuous probability
distribution with lower limit left, peak at mode, and upper
limit right. Unlike the other distributions, these parameters
directly define the shape of the pdf.
Parameters
----------
left : float or array_like of floats
Lower limit.
mode : float or array_like of floats
The value where the peak of the distribution occurs.
The value should fulfill the condition ``left <= mode <= right``.
right : float or array_like of floats
Upper limit, should be larger than `left`.
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 ``left``, ``mode``, and ``right``
are all scalars. Otherwise, ``mt.broadcast(left, mode, right).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 triangular distribution.
Notes
-----
The probability density function for the triangular distribution is
.. math:: P(x;l, m, r) = \begin{cases}
\frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\
\frac{2(r-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\
0& \text{otherwise}.
\end{cases}
The triangular distribution is often used in ill-defined
problems where the underlying distribution is not known, but
some knowledge of the limits and mode exists. Often it is used
in simulations.
References
----------
.. [1] Wikipedia, "Triangular distribution"
http://en.wikipedia.org/wiki/Triangular_distribution
Examples
--------
Draw values from the distribution and plot the histogram:
>>> import matplotlib.pyplot as plt
>>> import mars.tensor as mt
>>> h = plt.hist(mt.random.triangular(-3, 0, 8, 100000).execute(), bins=200,
... normed=True)
>>> plt.show()
"""
if dtype is None:
dtype = (
np.random.RandomState()
.triangular(
handle_array(left), handle_array(mode), handle_array(right), size=(0,)
)
.dtype
)
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorTriangular(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(left, mode, right, chunk_size=chunk_size)