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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 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",
http://en.wikipedia.org/wiki/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')
>>> plt.show()
"""
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)