Source code for mindspore.nn.probability.distribution.uniform

# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""Uniform Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from mindspore._checkparam import 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 \exp(\exp(-(x - a) / b) - x), where a and 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'. Inputs and Outputs of APIs: The accessible APIs of the Uniform distribution are defined in the base class, including: - `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival` - `mean`, `sd`, `var`, and `entropy` - `kl_loss` and `cross_entropy` - `sample` For more details of all APIs, including the inputs and outputs of all APIs of the Uniform distribution , please refer to :class:`mindspore.nn.probability.distribution.Distribution`, and examples below. Supported Platforms: ``Ascend`` ``GPU`` 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. 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.ScalarToArray() 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
[docs] 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) h_one = self.const(1.0) 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