Source code for mindspore.nn.probability.distribution.uniform
# Copyright 2020 Huawei Technologies Co., Ltd
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"""Uniform Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_greater, check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic
[docs]class Uniform(Distribution):
r"""
Uniform Distribution.
A Uniform distributio is a continuous distribution with the range :math:`[a, b]`
and the probability density function:
.. math::
f(x, a, b) = 1 / (b - a),
where :math:`a, b` are the lower and upper bound respectively.
Args:
low (int, float, list, numpy.ndarray, Tensor): The lower bound of the distribution. Default: None.
high (int, float, list, numpy.ndarray, Tensor): The upper bound of the distribution. Default: None.
seed (int): The seed uses in sampling. The global seed is used if it is None. Default: None.
dtype (mindspore.dtype): The type of the event samples. Default: mstype.float32.
name (str): The name of the distribution. Default: 'Uniform'.
Note:
`low` must be strictly less than `high`.
`dist_spec_args` are `high` and `low`.
`dtype` must be float type because Uniform distributions are continuous.
Raises:
ValueError: When high <= low.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Uniform distribution of the lower bound 0.0 and the higher bound 1.0.
>>> u1 = msd.Uniform(0.0, 1.0, dtype=mindspore.float32)
>>> # A Uniform distribution can be initialized without arguments.
>>> # In this case, `high` and `low` must be passed in through arguments during function calls.
>>> u2 = msd.Uniform(dtype=mindspore.float32)
>>>
>>> # Here are some tensors used below for testing
>>> value = Tensor([0.5, 0.8], dtype=mindspore.float32)
>>> low_a = Tensor([0., 0.], dtype=mindspore.float32)
>>> high_a = Tensor([2.0, 4.0], dtype=mindspore.float32)
>>> low_b = Tensor([-1.5], dtype=mindspore.float32)
>>> high_b = Tensor([2.5, 5.], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`, have the same arguments.
>>> # Args:
>>> # value (Tensor): the value to be evaluated.
>>> # low (Tensor): the lower bound of the distribution. Default: self.low.
>>> # high (Tensor): the higher bound of the distribution. Default: self.high.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function.
>>> ans = u1.prob(value)
>>> print(ans.shape)
(2,)
>>> # Evaluate with respect to distribution b.
>>> ans = u1.prob(value, low_b, high_b)
>>> print(ans.shape)
(2,)
>>> # `high` and `low` must be passed in during function calls.
>>> ans = u2.prob(value, low_a, high_a)
>>> print(ans.shape)
(2,)
>>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> # low (Tensor): the lower bound of the distribution. Default: self.low.
>>> # high (Tensor): the higher bound of the distribution. Default: self.high.
>>> # Examples of `mean`. `sd`, `var`, and `entropy` are similar.
>>> ans = u1.mean() # return 0.5
>>> print(ans.shape)
()
>>> ans = u1.mean(low_b, high_b) # return (low_b + high_b) / 2
>>> print(ans.shape)
(2,)
>>> # `high` and `low` must be passed in during function calls.
>>> ans = u2.mean(low_a, high_a)
>>> print(ans.shape)
(2,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same.
>>> # Args:
>>> # dist (str): the type of the distributions. Should be "Uniform" in this case.
>>> # low_b (Tensor): the lower bound of distribution b.
>>> # high_b (Tensor): the upper bound of distribution b.
>>> # low_a (Tensor): the lower bound of distribution a. Default: self.low.
>>> # high_a (Tensor): the upper bound of distribution a. Default: self.high.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = u1.kl_loss('Uniform', low_b, high_b)
>>> print(ans.shape)
(2,)
>>> ans = u1.kl_loss('Uniform', low_b, high_b, low_a, high_a)
>>> print(ans.shape)
(2,)
>>> # Additional `high` and `low` must be passed in.
>>> ans = u2.kl_loss('Uniform', low_b, high_b, low_a, high_a)
>>> print(ans.shape)
(2,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # low (Tensor): the lower bound of the distribution. Default: self.low.
>>> # high (Tensor): the upper bound of the distribution. Default: self.high.
>>> ans = u1.sample()
>>> print(ans.shape)
()
>>> ans = u1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = u1.sample((2,3), low_b, high_b)
>>> print(ans.shape)
(2, 3, 2)
>>> ans = u2.sample((2,3), low_a, high_a)
>>> print(ans.shape)
(2, 3, 2)
"""
def __init__(self,
low=None,
high=None,
seed=None,
dtype=mstype.float32,
name="Uniform"):
"""
Constructor of Uniform distribution.
"""
param = dict(locals())
param['param_dict'] = {'low': low, 'high': high}
valid_dtype = mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
super(Uniform, self).__init__(seed, dtype, name, param)
self._low = self._add_parameter(low, 'low')
self._high = self._add_parameter(high, 'high')
if self.low is not None and self.high is not None:
check_greater(self.low, self.high, 'low', 'high')
# ops needed for the class
self.exp = exp_generic
self.log = log_generic
self.squeeze = P.Squeeze(0)
self.cast = P.Cast()
self.const = P.ScalarToTensor()
self.dtypeop = P.DType()
self.fill = P.Fill()
self.less = P.Less()
self.lessequal = P.LessEqual()
self.logicaland = P.LogicalAnd()
self.select = P.Select()
self.shape = P.Shape()
self.sq = P.Square()
self.zeroslike = P.ZerosLike()
self.uniform = C.uniform
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'low = {}, high = {}'.format(self.low, self.high)
else:
s = 'batch_shape = {}'.format(self._broadcast_shape)
return s
@property
def low(self):
"""
Return the lower bound of the distribution after casting to dtype.
Output:
Tensor, the lower bound of the distribution.
"""
return self._low
@property
def high(self):
"""
Return the upper bound of the distribution after casting to dtype.
Output:
Tensor, the upper bound of the distribution.
"""
return self._high
def _get_dist_type(self):
return "Uniform"
def _get_dist_args(self, low=None, high=None):
if low is not None:
self.checktensor(low, 'low')
else:
low = self.low
if high is not None:
self.checktensor(high, 'high')
else:
high = self.high
return low, high
def _range(self, low=None, high=None):
r"""
Return the range of the distribution.
.. math::
range(U) = high -low
"""
low, high = self._check_param_type(low, high)
return high - low
def _mean(self, low=None, high=None):
r"""
.. math::
MEAN(U) = \frac{low + high}{2}.
"""
low, high = self._check_param_type(low, high)
return (low + high) / 2.
def _var(self, low=None, high=None):
r"""
.. math::
VAR(U) = \frac{(high -low) ^ 2}{12}.
"""
low, high = self._check_param_type(low, high)
return self.sq(high - low) / 12.0
def _entropy(self, low=None, high=None):
r"""
.. math::
H(U) = \log(high - low).
"""
low, high = self._check_param_type(low, high)
return self.log(high - low)
def _cross_entropy(self, dist, low_b, high_b, low=None, high=None):
"""
Evaluate cross entropy between Uniform distributions.
Args:
dist (str): The type of the distributions. Should be "Uniform" in this case.
low_b (Tensor): The lower bound of distribution b.
high_b (Tensor): The upper bound of distribution b.
low_a (Tensor): The lower bound of distribution a. Default: self.low.
high_a (Tensor): The upper bound of distribution a. Default: self.high.
"""
check_distribution_name(dist, 'Uniform')
return self._entropy(low, high) + self._kl_loss(dist, low_b, high_b, low, high)
def _prob(self, value, low=None, high=None):
r"""
pdf of Uniform distribution.
Args:
value (Tensor): The value to be evaluated.
low (Tensor): The lower bound of the distribution. Default: self.low.
high (Tensor): The upper bound of the distribution. Default: self.high.
.. math::
pdf(x) = 0 if x < low;
pdf(x) = \frac{1.0}{high -low} if low <= x <= high;
pdf(x) = 0 if x > high;
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
low, high = self._check_param_type(low, high)
neg_ones = self.fill(self.dtype, self.shape(value), -1.0)
prob = self.exp(neg_ones * self.log(high - low))
broadcast_shape = self.shape(prob)
zeros = self.fill(self.dtypeop(prob), broadcast_shape, 0.0)
comp_lo = self.less(value, low)
comp_hi = self.lessequal(value, high)
less_than_low = self.select(comp_lo, zeros, prob)
return self.select(comp_hi, less_than_low, zeros)
def _kl_loss(self, dist, low_b, high_b, low=None, high=None):
"""
Evaluate uniform-uniform KL divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "Uniform" in this case.
low_b (Tensor): The lower bound of distribution b.
high_b (Tensor): The upper bound of distribution b.
low_a (Tensor): The lower bound of distribution a. Default: self.low.
high_a (Tensor): The upper bound of distribution a. Default: self.high.
"""
check_distribution_name(dist, 'Uniform')
low_b = self._check_value(low_b, 'low_b')
low_b = self.cast(low_b, self.parameter_type)
high_b = self._check_value(high_b, 'high_b')
high_b = self.cast(high_b, self.parameter_type)
low_a, high_a = self._check_param_type(low, high)
kl = self.log(high_b - low_b) - self.log(high_a - low_a)
comp = self.logicaland(self.lessequal(
low_b, low_a), self.lessequal(high_a, high_b))
inf = self.fill(self.dtypeop(kl), self.shape(kl), np.inf)
return self.select(comp, kl, inf)
def _cdf(self, value, low=None, high=None):
r"""
The cumulative distribution function of Uniform distribution.
Args:
value (Tensor): The value to be evaluated.
low (Tensor): The lower bound of the distribution. Default: self.low.
high (Tensor): The upper bound of the distribution. Default: self.high.
.. math::
cdf(x) = 0 if x < low;
cdf(x) = \frac{x - low}{high -low} if low <= x <= high;
cdf(x) = 1 if x > high;
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
low, high = self._check_param_type(low, high)
prob = (value - low) / (high - low)
broadcast_shape = self.shape(prob)
zeros = self.fill(self.dtypeop(prob), broadcast_shape, 0.0)
ones = self.fill(self.dtypeop(prob), broadcast_shape, 1.0)
comp_lo = self.less(value, low)
comp_hi = self.less(value, high)
less_than_low = self.select(comp_lo, zeros, prob)
return self.select(comp_hi, less_than_low, ones)
def _sample(self, shape=(), low=None, high=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
low (Tensor): The lower bound of the distribution. Default: self.low.
high (Tensor): The upper bound of the distribution. Default: self.high.
Returns:
Tensor, with the shape being shape + batch_shape.
"""
shape = self.checktuple(shape, 'shape')
low, high = self._check_param_type(low, high)
broadcast_shape = self.shape(low + high)
origin_shape = shape + broadcast_shape
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
l_zero = self.const(0.0, mstype.float32)
h_one = self.const(1.0, mstype.float32)
sample_uniform = self.uniform(sample_shape, l_zero, h_one, self.seed)
sample = (high - low) * sample_uniform + low
value = self.cast(sample, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value