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

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"""Cauchy 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_zero, check_distribution_name, raise_not_defined
from ._utils.custom_ops import exp_generic, log_generic, log1p_generic


[docs]class Cauchy(Distribution): r""" Cauchy distribution. A Cauchy distributio is a continuous distribution with the range :math:`[0, 1]` and the probability density function: .. math:: f(x, a, b) = 1 / \pi b(1 - ((x - a)/b)^2), where a and b are loc and scale parameter respectively. Args: loc (int, float, list, numpy.ndarray, Tensor): The location of the Cauchy distribution. Default: None. scale (int, float, list, numpy.ndarray, Tensor): The scale of the Cauchy distribution. Default: None. seed (int): The seed used 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: 'Cauchy'. Note: `scale` must be greater than zero. `dist_spec_args` are `loc` and `scale`. `dtype` must be a float type because Cauchy distributions are continuous. Cauchy distribution is not supported on GPU backend. Raises: ValueError: When scale <= 0. TypeError: When the input `dtype` is not a subclass of float. Supported Platforms: ``Ascend`` Examples: >>> import mindspore >>> import mindspore.nn as nn >>> import mindspore.nn.probability.distribution as msd >>> from mindspore import Tensor >>> # To initialize a Cauchy distribution of loc 3.0 and scale 4.0. >>> cauchy1 = msd.Cauchy(3.0, 4.0, dtype=mindspore.float32) >>> # A Cauchy distribution can be initialized without arguments. >>> # In this case, 'loc' and `scale` must be passed in through arguments. >>> cauchy2 = msd.Cauchy(dtype=mindspore.float32) >>> # Here are some tensors used below for testing >>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32) >>> loc_a = Tensor([2.0], dtype=mindspore.float32) >>> scale_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32) >>> loc_b = Tensor([1.0], dtype=mindspore.float32) >>> scale_b = Tensor([1.0, 1.5, 2.0], 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 as follows. >>> # Args: >>> # value (Tensor): the value to be evaluated. >>> # loc (Tensor): the location of the distribution. Default: self.loc. >>> # scale (Tensor): the scale of the distribution. Default: self.scale. >>> # Examples of `prob`. >>> # Similar calls can be made to other probability functions >>> # by replacing 'prob' by the name of the function >>> ans = cauchy1.prob(value) >>> print(ans.shape) (3,) >>> # Evaluate with respect to distribution b. >>> ans = cauchy1.prob(value, loc_b, scale_b) >>> print(ans.shape) (3,) >>> # `loc` and `scale` must be passed in during function calls >>> ans = cauchy2.prob(value, loc_a, scale_a) >>> print(ans.shape) (3,) >>> # Functions `mode` and `entropy` have the same arguments. >>> # Args: >>> # loc (Tensor): the location of the distribution. Default: self.loc. >>> # scale (Tensor): the scale of the distribution. Default: self.scale. >>> # Example of `mode`. >>> ans = cauchy1.mode() # return 3.0 >>> print(ans.shape) () >>> ans = cauchy1.mode(loc_b, scale_b) # return loc_b >>> print(ans.shape) (3,) >>> # `loc` and `scale` must be passed in during function calls. >>> ans = cauchy2.mode(loc_a, scale_a) >>> print(ans.shape) (3,) >>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same: >>> # Args: >>> # dist (str): the type of the distributions. Only "Cauchy" is supported. >>> # loc_b (Tensor): the loc of distribution b. >>> # scale_b (Tensor): the scale distribution b. >>> # loc (Tensor): the loc of distribution a. Default: self.loc. >>> # scale (Tensor): the scale distribution a. Default: self.scale. >>> # Examples of `kl_loss`. `cross_entropy` is similar. >>> ans = cauchy1.kl_loss('Cauchy', loc_b, scale_b) >>> print(ans.shape) (3,) >>> ans = cauchy1.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a) >>> print(ans.shape) (3,) >>> # Additional `loc` and `scale` must be passed in. >>> ans = cauchy2.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a) >>> print(ans.shape) (3,) >>> # Examples of `sample`. >>> # Args: >>> # shape (tuple): the shape of the sample. Default: () >>> # loc (Tensor): the location of the distribution. Default: self.loc. >>> # scale (Tensor): the scale of the distribution. Default: self.scale. >>> ans = cauchy1.sample() >>> print(ans.shape) () >>> ans = cauchy1.sample((2,3)) >>> print(ans.shape) (2, 3) >>> ans = cauchy1.sample((2,3), loc_b, scale_b) >>> print(ans.shape) (2, 3, 3) >>> ans = cauchy2.sample((2,3), loc_a, scale_a) >>> print(ans.shape) (2, 3, 3) """ def __init__(self, loc=None, scale=None, seed=None, dtype=mstype.float32, name="Cauchy"): """ Constructor of Cauchy. """ param = dict(locals()) param['param_dict'] = {'loc': loc, 'scale': scale} valid_dtype = mstype.float_type Validator.check_type_name( "dtype", dtype, valid_dtype, type(self).__name__) super(Cauchy, self).__init__(seed, dtype, name, param) self._loc = self._add_parameter(loc, 'loc') self._scale = self._add_parameter(scale, 'scale') if self._scale is not None: check_greater_zero(self._scale, "scale") # ops needed for the class self.atan = P.Atan() self.cast = P.Cast() self.const = P.ScalarToTensor() self.dtypeop = P.DType() self.exp = exp_generic self.fill = P.Fill() self.less = P.Less() self.log = log_generic self.log1p = log1p_generic self.squeeze = P.Squeeze(0) self.shape = P.Shape() self.sq = P.Square() self.sqrt = P.Sqrt() self.tan = P.Tan() self.uniform = C.uniform self.entropy_const = np.log(4 * np.pi) def extend_repr(self): """Display instance object as string.""" if self.is_scalar_batch: str_info = 'location = {}, scale = {}'.format( self._loc, self._scale) else: str_info = 'batch_shape = {}'.format(self._broadcast_shape) return str_info @property def loc(self): """ Return the location of the distribution after casting to dtype. Output: Tensor, the loc parameter of the distribution. """ return self._loc @property def scale(self): """ Return the scale of the distribution after casting to dtype. Output: Tensor, the scale parameter of the distribution. """ return self._scale def _get_dist_type(self): return "Cauchy" def _get_dist_args(self, loc=None, scale=None): if scale is not None: self.checktensor(scale, 'scale') else: scale = self.scale if loc is not None: self.checktensor(loc, 'loc') else: loc = self.loc return loc, scale def _mode(self, loc=None, scale=None): """ The mode of the distribution. """ loc, scale = self._check_param_type(loc, scale) return loc def _mean(self, *args, **kwargs): return raise_not_defined('mean', 'Cauchy', *args, **kwargs) def _sd(self, *args, **kwargs): return raise_not_defined('standard deviation', 'Cauchy', *args, **kwargs) def _var(self, *args, **kwargs): return raise_not_defined('variance', 'Cauchy', *args, **kwargs) def _entropy(self, loc=None, scale=None): r""" Evaluate entropy. .. math:: H(X) = \log(4 * \Pi * scale) """ loc, scale = self._check_param_type(loc, scale) return self.log(scale) + self.entropy_const def _log_prob(self, value, loc=None, scale=None): r""" Evaluate log probability. Args: value (Tensor): The value to be evaluated. loc (Tensor): The location of the distribution. Default: self.loc. scale (Tensor): The scale of the distribution. Default: self.scale. .. math:: L(x) = \log(\frac{1}{\pi * scale} * \frac{scale^{2}}{(x - loc)^{2} + scale^{2}}) """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) loc, scale = self._check_param_type(loc, scale) z = (value - loc) / scale log_unnormalized_prob = (-1) * self.log1p(self.sq(z)) log_normalization = self.log(np.pi * scale) return log_unnormalized_prob - log_normalization def _cdf(self, value, loc=None, scale=None): r""" Evaluate the cumulative distribution function on the given value. Args: value (Tensor): The value to be evaluated. loc (Tensor): The location of the distribution. Default: self.loc. scale (Tensor): The scale the distribution. Default: self.scale. .. math:: cdf(x) = \frac{\arctan{(x - loc) / scale}}{\pi} + 0.5 """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) loc, scale = self._check_param_type(loc, scale) z = (value - loc) / scale return self.atan(z) / np.pi + 0.5 def _log_cdf(self, value, loc=None, scale=None): r""" Evaluate the log cumulative distribution function on the given value. Args: value (Tensor): The value to be evaluated. loc (Tensor): The location of the distribution. Default: self.loc. scale (Tensor): The scale the distribution. Default: self.scale. .. math:: log_cdf(x) = \log(\frac{\arctan(\frac{x-loc}{scale})}{\pi} + 0.5) = \log {\arctan(\frac{x-loc}{scale}) + 0.5pi}{pi} = \log1p \frac{2 * arctan(\frac{x-loc}{scale})}{pi} - \log2 """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) loc, scale = self._check_param_type(loc, scale) z = (value - loc) / scale return self.log1p(2. * self.atan(z) / np.pi) - self.log(self.const(2., mstype.float32)) def _quantile(self, p, loc=None, scale=None): loc, scale = self._check_param_type(loc, scale) return loc + scale * self.tan(np.pi * (p - 0.5)) def _kl_loss(self, dist, loc_b, scale_b, loc_a=None, scale_a=None): r""" Evaluate Cauchy-Cauchy kl divergence, i.e. KL(a||b). Args: dist (str): The type of the distributions. Should be "Cauchy" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. loc (Tensor): The loc of distribution a. Default: self.loc. scale (Tensor): The scale of distribution a. Default: self.scale. .. math:: KL(a||b) = \log(\frac{(scale_a + scale_b)^{2} + (loc_a - loc_b)^{2}} {4 * scale_a * scale_b}) """ check_distribution_name(dist, 'Cauchy') loc_a, scale_a = self._check_param_type(loc_a, scale_a) loc_b = self._check_value(loc_b, 'loc_b') loc_b = self.cast(loc_b, self.parameter_type) scale_b = self._check_value(scale_b, 'scale_b') scale_b = self.cast(scale_b, self.parameter_type) sum_square = self.sq(scale_a + scale_b) square_diff = self.sq(loc_a - loc_b) return self.log(sum_square + square_diff) - \ self.log(self.const(4.0, mstype.float32)) - self.log(scale_a) - self.log(scale_b) def _cross_entropy(self, dist, loc_b, scale_b, loc_a=None, scale_a=None): r""" Evaluate cross entropy between Cauchy distributions. Args: dist (str): The type of the distributions. Should be "Cauchy" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. loc (Tensor): The loc of distribution a. Default: self.loc. scale (Tensor): The scale of distribution a. Default: self.scale. """ check_distribution_name(dist, 'Cauchy') return self._entropy(loc_a, scale_a) + self._kl_loss(dist, loc_b, scale_b, loc_a, scale_a) def _sample(self, shape=(), loc=None, scale=None): """ Sampling. Args: shape (tuple): The shape of the sample. Default: (). loc (Tensor): The location of the samples. Default: self.loc. scale (Tensor): The scale of the samples. Default: self.scale. Returns: Tensor, with the shape being shape + batch_shape. """ shape = self.checktuple(shape, 'shape') loc, scale = self._check_param_type(loc, scale) batch_shape = self.shape(loc + scale) origin_shape = shape + batch_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 = self._quantile(sample_uniform, loc, scale) value = self.cast(sample, self.dtype) if origin_shape == (): value = self.squeeze(value) return value