!8477 Add Cauchy distribution

From: @shallydeng
Reviewed-by: @zichun_ye
Signed-off-by:

mindspore/nn/probability/bijector/bijector.py

@@ -175,6 +175,8 @@ class Bijector(Cell):
         """
         Calculate batch_shape based on parameters.
         """
+        if 'param_dict' not in self.parameters.keys():
+            return None
         param_dict = self.parameters['param_dict']
         broadcast_shape_tensor = None
         for value in param_dict.values():
@@ -191,6 +193,8 @@ class Bijector(Cell):
         """
         Check if the parameters used during initialization are scalars.
         """
+        if 'param_dict' not in self.parameters.keys():
+            return False
         param_dict = self.parameters['param_dict']
         for value in param_dict.values():
             if value is None:

mindspore/nn/probability/distribution/__init__.py

@@ -27,6 +27,7 @@ from .categorical import Categorical
 from .log_normal import LogNormal
 from .logistic import Logistic
 from .gumbel import Gumbel
+from .cauchy import Cauchy
 
 __all__ = ['Distribution',
            'TransformedDistribution',
@@ -39,4 +40,5 @@ __all__ = ['Distribution',
            'LogNormal',
            'Logistic',
            'Gumbel',
+           'Cauchy',
            ]

mindspore/nn/probability/distribution/_utils/utils.py

@@ -234,6 +234,11 @@ def raise_type_error(name, cur_type, required_type):
     raise TypeError(
         f"For {name} , the type should be or be subclass of {required_type}, but got {cur_type}")
 
+@constexpr
+def raise_not_defined(func_name, obj, *args, **kwargs):
+    raise ValueError(
+        f"{func_name} is undefined for {obj} distribution.")
+
 
 @constexpr
 def check_distribution_name(name, expected_name):

mindspore/nn/probability/distribution/cauchy.py

@@ -0,0 +1,345 @@
+# 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.
+# ============================================================================
+"""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
+
+
+class Cauchy(Distribution):
+    """
+    Cauchy distribution.
+
+    Args:
+        loc (int, float, list, numpy.ndarray, Tensor, Parameter): The location of the Cauchy distribution.
+        scale (int, float, list, numpy.ndarray, Tensor, Parameter): The scale of the Cauchy distribution.
+        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.
+
+    Examples:
+        >>> # To initialize a Cauchy distribution of loc 3.0 and scale 4.0.
+        >>> import mindspore.nn.probability.distribution as msd
+        >>> cauchy = msd.Cauchy(3.0, 4.0, dtype=mstype.float32)
+        >>>
+        >>> # The following creates two independent Cauchy distributions.
+        >>> cauchy = msd.Cauchy([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
+        >>>
+        >>> # A Cauchy distribution can be initilize without arguments.
+        >>> # In this case, 'loc' and `scale` must be passed in through arguments.
+        >>> cauchy = msd.Cauchy(dtype=mstype.float32)
+        >>>
+        >>> # To use a Cauchy distribution in a network.
+        >>> class net(Cell):
+        >>>     def __init__(self):
+        >>>         super(net, self).__init__():
+        >>>         self.cau1 = msd.Cauchy(0.0, 1.0, dtype=mstype.float32)
+        >>>         self.cau2 = msd.Cauchy(dtype=mstype.float32)
+        >>>
+        >>>     # The following calls are valid in construct.
+        >>>     def construct(self, value, loc_b, scale_b, loc_a, scale_a):
+        >>>
+        >>>         # 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 = self.cau1.prob(value)
+        >>>         # Evaluate with respect to distribution b.
+        >>>         ans = self.cau1.prob(value, loc_b, scale_b)
+        >>>         # `loc` and `scale` must be passed in during function calls
+        >>>         ans = self.cau2.prob(value, loc_a, scale_a)
+        >>>
+        >>>         # 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 = self.cau1.mode() # return 0.0
+        >>>         ans = self.cau1.mode(loc_b, scale_b) # return loc_b
+        >>>         # `loc` and `scale` must be passed in during function calls.
+        >>>         ans = self.cau2.mode(loc_a, scale_a)
+        >>>
+        >>>         # 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 = self.cau1.kl_loss('Cauchy', loc_b, scale_b)
+        >>>         ans = self.cau1.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a)
+        >>>         # Additional `loc` and `scale` must be passed in.
+        >>>         ans = self.cau2.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a)
+        >>>
+        >>>         # 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 = self.cau1.sample()
+        >>>         ans = self.cau1.sample((2,3))
+        >>>         ans = self.cau1.sample((2,3), loc_b, s_b)
+        >>>         ans = self.cau2.sample((2,3), loc_a, s_a)
+    """
+
+    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.ScalarToArray()
+        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
+
+
+    def extend_repr(self):
+        if self.is_scalar_batch:
+            str_info = f'location = {self._loc}, scale = {self._scale}'
+        else:
+            str_info = f'batch_shape = {self._broadcast_shape}'
+        return str_info
+
+    @property
+    def loc(self):
+        """
+        Return the location of the distribution.
+        """
+        return self._loc
+
+    @property
+    def scale(self):
+        """
+        Return the scale of the distribution.
+        """
+        return self._scale
+
+    def _get_dist_type(self):
+        return "Cauchy"
+
+    def _get_dist_args(self, loc=None, scale=None):
+        if loc is not None:
+            self.checktensor(loc, 'loc')
+        else:
+            loc = self.loc
+        if scale is not None:
+            self.checktensor(scale, 'scale')
+        else:
+            scale = self.scale
+        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(4 * np.pi * scale)
+
+    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 = - 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.))
+
+    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=None, scale=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, scale = self._check_param_type(loc, scale)
+        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 + scale_b)
+        square_diff = self.sq(loc - loc_b)
+        return self.log(sum_square + square_diff) - \
+                self.log(self.const(4.0)) - self.log(scale) - self.log(scale_b)
+
+    def _cross_entropy(self, dist, loc_b, scale_b, loc=None, scale=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, scale) + self._kl_loss(dist, loc_b, scale_b, loc, scale)
+
+    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)
+        h_one = self.const(1.0)
+        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

mindspore/nn/probability/distribution/gumbel.py

@@ -21,7 +21,7 @@ import mindspore.nn as nn
 import mindspore.nn.probability.bijector as msb
 import mindspore.nn.probability.distribution as msd
 from .transformed_distribution import TransformedDistribution
-from ._utils.utils import check_distribution_name, raise_not_implemented_util
+from ._utils.utils import check_distribution_name
 from ._utils.custom_ops import exp_generic, expm1_generic, log_generic
 
 class Gumbel(TransformedDistribution):
@@ -39,6 +39,7 @@ class Gumbel(TransformedDistribution):
         `scale` must be greater than zero.
         `dist_spec_args` are `loc` and `scale`.
         `dtype` must be a float type because Gumbel distributions are continuous.
+        `kl_loss` and `cross_entropy` are not supported on GPU backend.
 
     Examples:
         >>> # To initialize a Gumbel distribution of `loc` 3.0 and `scale` 4.0.
@@ -219,8 +220,6 @@ class Gumbel(TransformedDistribution):
             loc_b (Tensor): The loc of distribution b.
             scale_b (Tensor): The scale of distribution b.
         """
-        if self.device_target == 'GPU':
-            raise_not_implemented_util('On GPU backend, cross_entropy', self.name)
         check_distribution_name(dist, 'Gumbel')
         return self._entropy() + self._kl_loss(dist, loc_b, scale_b)
 
@@ -237,8 +236,6 @@ class Gumbel(TransformedDistribution):
             KL(a||b) = \log(scale_b / scale_a) + Euler-Mascheroni_constant * (scale_a / scale_b - 1.) +
                        \exp(\frac{(loc_b - loc_a)}{scale_b}) * \Gamma(scale_a / scale_b + 1.) - 1.
         """
-        if self.device_target == 'GPU':
-            raise_not_implemented_util('On GPU backend, kl_loss', self.name)
         check_distribution_name(dist, 'Gumbel')
         loc_b = self._check_value(loc_b, 'loc_b')
         scale_b = self._check_value(scale_b, 'scale_b')

tests/st/probability/distribution/test_cauchy.py

@@ -0,0 +1,282 @@
+# Copyright 2019 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.
+# ============================================================================
+"""test cases for Cauchy distribution"""
+import numpy as np
+from scipy import stats
+import mindspore.context as context
+import mindspore.nn as nn
+import mindspore.nn.probability.distribution as msd
+from mindspore import Tensor
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Prob(nn.Cell):
+    """
+    Test class: probability of Cauchy distribution.
+    """
+    def __init__(self):
+        super(Prob, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.prob(x_)
+
+def test_pdf():
+    """
+    Test pdf.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_pdf = cauchy_benchmark.pdf([1.0, 2.0]).astype(np.float32)
+    pdf = Prob()
+    output = pdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_pdf) < tol).all()
+
+class LogProb(nn.Cell):
+    """
+    Test class: log probability of Cauchy distribution.
+    """
+    def __init__(self):
+        super(LogProb, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.log_prob(x_)
+
+def test_log_likelihood():
+    """
+    Test log_pdf.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_logpdf = cauchy_benchmark.logpdf([1.0, 2.0]).astype(np.float32)
+    logprob = LogProb()
+    output = logprob(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_logpdf) < tol).all()
+
+class KL(nn.Cell):
+    """
+    Test class: kl_loss of Cauchy distribution.
+    """
+    def __init__(self):
+        super(KL, self).__init__()
+        self.c = msd.Cauchy(np.array([3.]), np.array([4.]), dtype=dtype.float32)
+
+    def construct(self, mu, s):
+        return self.c.kl_loss('Cauchy', mu, s)
+
+def test_kl_loss():
+    """
+    Test kl_loss.
+    """
+    loc_b = np.array([0.]).astype(np.float32)
+    scale_b = np.array([1.]).astype(np.float32)
+
+    loc_a = np.array([3.0]).astype(np.float32)
+    scale_a = np.array([4.0]).astype(np.float32)
+
+    sum_square = np.square(scale_a + scale_b)
+    square_diff = np.square(loc_a - loc_b)
+    expect_kl_loss = np.log(sum_square + square_diff) - \
+                np.log(4.0 * scale_a  * scale_b)
+
+    kl_loss = KL()
+    loc = Tensor(loc_b, dtype=dtype.float32)
+    scale = Tensor(scale_b, dtype=dtype.float32)
+    output = kl_loss(loc, scale)
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_kl_loss) < tol).all()
+
+class Basics(nn.Cell):
+    """
+    Test class: mode of Cauchy distribution.
+    """
+    def __init__(self):
+        super(Basics, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([2.0, 4.0]), dtype=dtype.float32)
+
+    def construct(self):
+        return self.c.mode()
+
+def test_basics():
+    """
+    Test mode.
+    """
+    basics = Basics()
+    mode = basics()
+    expect_mode = np.array([3.0, 3.0])
+    tol = 1e-6
+    assert (np.abs(mode.asnumpy() - expect_mode) < tol).all()
+
+class Sampling(nn.Cell):
+    """
+    Test class: sample of Cauchy distribution.
+    """
+    def __init__(self, shape, seed=0):
+        super(Sampling, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), seed=seed, dtype=dtype.float32)
+        self.shape = shape
+
+    def construct(self, mean=None, sd=None):
+        return self.c.sample(self.shape, mean, sd)
+
+def test_sample():
+    """
+    Test sample.
+    """
+    shape = (2, 3)
+    seed = 10
+    mean = Tensor([2.0], dtype=dtype.float32)
+    sd = Tensor([2.0, 2.0, 2.0], dtype=dtype.float32)
+    sample = Sampling(shape, seed=seed)
+    output = sample(mean, sd)
+    assert output.shape == (2, 3, 3)
+
+class CDF(nn.Cell):
+    """
+    Test class: cdf of Cauchy distribution.
+    """
+    def __init__(self):
+        super(CDF, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.cdf(x_)
+
+
+def test_cdf():
+    """
+    Test cdf.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_cdf = cauchy_benchmark.cdf([1.0, 2.0]).astype(np.float32)
+    cdf = CDF()
+    output = cdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 2e-5
+    assert (np.abs(output.asnumpy() - expect_cdf) < tol).all()
+
+class LogCDF(nn.Cell):
+    """
+    Test class: log_cdf of Cauchy distribution.
+    """
+    def __init__(self):
+        super(LogCDF, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.log_cdf(x_)
+
+def test_log_cdf():
+    """
+    Test log cdf.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_logcdf = cauchy_benchmark.logcdf([1.0, 2.0]).astype(np.float32)
+    logcdf = LogCDF()
+    output = logcdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 5e-5
+    assert (np.abs(output.asnumpy() - expect_logcdf) < tol).all()
+
+class SF(nn.Cell):
+    """
+    Test class: survival function of Cauchy distribution.
+    """
+    def __init__(self):
+        super(SF, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.survival_function(x_)
+
+def test_survival():
+    """
+    Test log_survival.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_survival = cauchy_benchmark.sf([1.0, 2.0]).astype(np.float32)
+    survival_function = SF()
+    output = survival_function(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 2e-5
+    assert (np.abs(output.asnumpy() - expect_survival) < tol).all()
+
+class LogSF(nn.Cell):
+    """
+    Test class: log survival function of Cauchy distribution.
+    """
+    def __init__(self):
+        super(LogSF, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.c.log_survival(x_)
+
+def test_log_survival():
+    """
+    Test log_survival.
+    """
+    cauchy_benchmark = stats.cauchy(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_log_survival = cauchy_benchmark.logsf([1.0, 2.0]).astype(np.float32)
+    log_survival = LogSF()
+    output = log_survival(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 2e-5
+    assert (np.abs(output.asnumpy() - expect_log_survival) < tol).all()
+
+class EntropyH(nn.Cell):
+    """
+    Test class: entropy of Cauchy distribution.
+    """
+    def __init__(self):
+        super(EntropyH, self).__init__()
+        self.c = msd.Cauchy(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self):
+        return self.c.entropy()
+
+def test_entropy():
+    """
+    Test entropy.
+    """
+    expect_entropy = np.log(4 * np.pi * np.array([[2.0], [4.0]]))
+    entropy = EntropyH()
+    output = entropy()
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_entropy) < tol).all()
+
+class CrossEntropy(nn.Cell):
+    """
+    Test class: cross entropy between Cauchy distributions.
+    """
+    def __init__(self):
+        super(CrossEntropy, self).__init__()
+        self.c = msd.Cauchy(np.array([3.]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    def construct(self, mu, s):
+        entropy = self.c.entropy()
+        kl_loss = self.c.kl_loss('Cauchy', mu, s)
+        h_sum_kl = entropy + kl_loss
+        cross_entropy = self.c.cross_entropy('Cauchy', mu, s)
+        return h_sum_kl - cross_entropy
+
+def test_cross_entropy():
+    """
+    Test cross_entropy.
+    """
+    cross_entropy = CrossEntropy()
+    mean = Tensor([1.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    diff = cross_entropy(mean, sd)
+    tol = 1e-6
+    assert (np.abs(diff.asnumpy() - np.zeros(diff.shape)) < tol).all()

tests/ut/python/nn/probability/distribution/test_cauchy.py

@@ -0,0 +1,231 @@
+# 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.
+# ============================================================================
+"""
+Test nn.probability.distribution.cauchy.
+"""
+import pytest
+
+import mindspore.nn as nn
+import mindspore.nn.probability.distribution as msd
+from mindspore import dtype
+from mindspore import Tensor
+
+def test_cauchy_shape_errpr():
+    """
+    Invalid shapes.
+    """
+    with pytest.raises(ValueError):
+        msd.Cauchy([[2.], [1.]], [[2.], [3.], [4.]], dtype=dtype.float32)
+
+def test_type():
+    with pytest.raises(TypeError):
+        msd.Cauchy(0., 1., dtype=dtype.int32)
+
+def test_name():
+    with pytest.raises(TypeError):
+        msd.Cauchy(0., 1., name=1.0)
+
+def test_seed():
+    with pytest.raises(TypeError):
+        msd.Cauchy(0., 1., seed='seed')
+
+def test_scale():
+    with pytest.raises(ValueError):
+        msd.Cauchy(0., 0.)
+    with pytest.raises(ValueError):
+        msd.Cauchy(0., -1.)
+
+def test_arguments():
+    """
+    args passing during initialization.
+    """
+    l = msd.Cauchy()
+    assert isinstance(l, msd.Distribution)
+    l = msd.Cauchy([3.0], [4.0], dtype=dtype.float32)
+    assert isinstance(l, msd.Distribution)
+
+
+class CauchyProb(nn.Cell):
+    """
+    Cauchy distribution: initialize with loc/scale.
+    """
+    def __init__(self):
+        super(CauchyProb, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self, value):
+        prob = self.cauchy.prob(value)
+        log_prob = self.cauchy.log_prob(value)
+        cdf = self.cauchy.cdf(value)
+        log_cdf = self.cauchy.log_cdf(value)
+        sf = self.cauchy.survival_function(value)
+        log_sf = self.cauchy.log_survival(value)
+        return prob + log_prob + cdf + log_cdf + sf + log_sf
+
+def test_cauchy_prob():
+    """
+    Test probability functions: passing value through construct.
+    """
+    net = CauchyProb()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    ans = net(value)
+    assert isinstance(ans, Tensor)
+
+
+class CauchyProb1(nn.Cell):
+    """
+    Cauchy distribution: initialize without loc/scale.
+    """
+    def __init__(self):
+        super(CauchyProb1, self).__init__()
+        self.cauchy = msd.Cauchy()
+
+    def construct(self, value, mu, s):
+        prob = self.cauchy.prob(value, mu, s)
+        log_prob = self.cauchy.log_prob(value, mu, s)
+        cdf = self.cauchy.cdf(value, mu, s)
+        log_cdf = self.cauchy.log_cdf(value, mu, s)
+        sf = self.cauchy.survival_function(value, mu, s)
+        log_sf = self.cauchy.log_survival(value, mu, s)
+        return prob + log_prob + cdf + log_cdf + sf + log_sf
+
+def test_cauchy_prob1():
+    """
+    Test probability functions: passing loc/scale, value through construct.
+    """
+    net = CauchyProb1()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mu = Tensor([0.0], dtype=dtype.float32)
+    s = Tensor([1.0], dtype=dtype.float32)
+    ans = net(value, mu, s)
+    assert isinstance(ans, Tensor)
+
+class KL(nn.Cell):
+    """
+    Test kl_loss and cross entropy.
+    """
+    def __init__(self):
+        super(KL, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0)
+        self.cauchy1 = msd.Cauchy()
+
+    def construct(self, mu, s, mu_a, s_a):
+        kl = self.cauchy.kl_loss('Cauchy', mu, s)
+        kl1 = self.cauchy1.kl_loss('Cauchy', mu, s, mu_a, s_a)
+        cross_entropy = self.cauchy.cross_entropy('Cauchy', mu, s)
+        cross_entropy1 = self.cauchy.cross_entropy('Cauchy', mu, s, mu_a, s_a)
+        return kl + kl1 + cross_entropy + cross_entropy1
+
+def test_kl_cross_entropy():
+    """
+    Test kl_loss and cross_entropy.
+    """
+    net = KL()
+    mu = Tensor([0.0], dtype=dtype.float32)
+    s = Tensor([1.0], dtype=dtype.float32)
+    mu_a = Tensor([0.0], dtype=dtype.float32)
+    s_a = Tensor([1.0], dtype=dtype.float32)
+    ans = net(mu, s, mu_a, s_a)
+    assert isinstance(ans, Tensor)
+
+
+class CauchyBasics(nn.Cell):
+    """
+    Test class: basic loc/scale function.
+    """
+    def __init__(self):
+        super(CauchyBasics, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self):
+        mode = self.cauchy.mode()
+        entropy = self.cauchy.entropy()
+        return mode + entropy
+
+class CauchyMean(nn.Cell):
+    """
+    Test class: basic loc/scale function.
+    """
+    def __init__(self):
+        super(CauchyMean, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self):
+        return self.cauchy.mean()
+
+class CauchyVar(nn.Cell):
+    """
+    Test class: basic loc/scale function.
+    """
+    def __init__(self):
+        super(CauchyVar, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self):
+        return self.cauchy.var()
+
+class CauchySd(nn.Cell):
+    """
+    Test class: basic loc/scale function.
+    """
+    def __init__(self):
+        super(CauchySd, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self):
+        return self.cauchy.sd()
+
+def test_bascis():
+    """
+    Test mean/sd/var/mode/entropy functionality of Cauchy.
+    """
+    net = CauchyBasics()
+    ans = net()
+    assert isinstance(ans, Tensor)
+    with pytest.raises(ValueError):
+        net = CauchyMean()
+        ans = net()
+    with pytest.raises(ValueError):
+        net = CauchyVar()
+        ans = net()
+    with pytest.raises(ValueError):
+        net = CauchySd()
+        ans = net()
+
+class CauchyConstruct(nn.Cell):
+    """
+    Cauchy distribution: going through construct.
+    """
+    def __init__(self):
+        super(CauchyConstruct, self).__init__()
+        self.cauchy = msd.Cauchy(3.0, 4.0)
+        self.cauchy1 = msd.Cauchy()
+
+    def construct(self, value, mu, s):
+        prob = self.cauchy('prob', value)
+        prob1 = self.cauchy('prob', value, mu, s)
+        prob2 = self.cauchy1('prob', value, mu, s)
+        return prob + prob1 + prob2
+
+def test_cauchy_construct():
+    """
+    Test probability function going through construct.
+    """
+    net = CauchyConstruct()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mu = Tensor([0.0], dtype=dtype.float32)
+    s = Tensor([1.0], dtype=dtype.float32)
+    ans = net(value, mu, s)
+    assert isinstance(ans, Tensor)