[docs] fix some format issue

python/paddle/distribution/kl.py

@@ -38,11 +38,11 @@ def kl_divergence(p, q):
         KL(p||q) = \int p(x)log\frac{p(x)}{q(x)} \mathrm{d}x
 
     Args:
-        p (Distribution): ``Distribution`` object.
-        q (Distribution): ``Distribution`` object.
+        p (Distribution): ``Distribution`` object. Inherits from the Distribution Base class.
+        q (Distribution): ``Distribution`` object. Inherits from the Distribution Base class.
 
     Returns:
-        Tensor: Batchwise KL-divergence between distribution p and q.
+        Tensor, Batchwise KL-divergence between distribution p and q.
 
     Examples:
 
@@ -71,8 +71,8 @@ def register_kl(cls_p, cls_q):
     implemention funciton by the decorator.
 
     Args:
-        cls_p(Distribution): Subclass derived from ``Distribution``.
-        cls_q(Distribution): Subclass derived from ``Distribution``.
+        cls_p (Distribution): The Distribution type of Instance p. Subclass derived from ``Distribution``.
+        cls_q (Distribution): The Distribution type of Instance q. Subclass derived from ``Distribution``.
 
     Examples:
         .. code-block:: python

python/paddle/distribution/normal.py

@@ -36,7 +36,7 @@ class Normal(distribution.Distribution):
 
     .. math::
 
-        pdf(x; \mu, \sigma) = \\frac{1}{Z}e^{\\frac {-0.5 (x - \mu)^2}  {\sigma^2} }
+        pdf(x; \mu, \sigma) = \frac{1}{Z}e^{\frac {-0.5 (x - \mu)^2}  {\sigma^2} }
 
     .. math::
 
@@ -49,43 +49,43 @@ class Normal(distribution.Distribution):
     * :math:`Z`: is the normalization constant.
 
     Args:
-        loc(int|float|list|tuple|numpy.ndarray|Tensor): The mean of normal distribution.The data type is int, float, list, numpy.ndarray or Tensor.
-        scale(int|float|list|tuple|numpy.ndarray|Tensor): The std of normal distribution.The data type is int, float, list, numpy.ndarray or Tensor.
+        loc(int|float|list|tuple|numpy.ndarray|Tensor): The mean of normal distribution.The data type is float32 and float64.
+        scale(int|float|list|tuple|numpy.ndarray|Tensor): The std of normal distribution.The data type is float32 and float64.
         name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
 
     Examples:
         .. code-block:: python
 
-          import paddle
-          from paddle.distribution import Normal
-
-          # Define a single scalar Normal distribution.
-          dist = Normal(loc=0., scale=3.)
-          # Define a batch of two scalar valued Normals.
-          # The first has mean 1 and standard deviation 11, the second 2 and 22.
-          dist = Normal(loc=[1., 2.], scale=[11., 22.])
-          # Get 3 samples, returning a 3 x 2 tensor.
-          dist.sample([3])
-
-          # Define a batch of two scalar valued Normals.
-          # Both have mean 1, but different standard deviations.
-          dist = Normal(loc=1., scale=[11., 22.])
-
-          # Complete example
-          value_tensor = paddle.to_tensor([0.8], dtype="float32")
-
-          normal_a = Normal([0.], [1.])
-          normal_b = Normal([0.5], [2.])
-          sample = normal_a.sample([2])
-          # a random tensor created by normal distribution with shape: [2, 1]
-          entropy = normal_a.entropy()
-          # [1.4189385] with shape: [1]
-          lp = normal_a.log_prob(value_tensor)
-          # [-1.2389386] with shape: [1]
-          p = normal_a.probs(value_tensor)
-          # [0.28969154] with shape: [1]
-          kl = normal_a.kl_divergence(normal_b)
-          # [0.34939718] with shape: [1]
+            import paddle
+            from paddle.distribution import Normal
+
+            # Define a single scalar Normal distribution.
+            dist = Normal(loc=0., scale=3.)
+            # Define a batch of two scalar valued Normals.
+            # The first has mean 1 and standard deviation 11, the second 2 and 22.
+            dist = Normal(loc=[1., 2.], scale=[11., 22.])
+            # Get 3 samples, returning a 3 x 2 tensor.
+            dist.sample([3])
+
+            # Define a batch of two scalar valued Normals.
+            # Both have mean 1, but different standard deviations.
+            dist = Normal(loc=1., scale=[11., 22.])
+
+            # Complete example
+            value_tensor = paddle.to_tensor([0.8], dtype="float32")
+
+            normal_a = Normal([0.], [1.])
+            normal_b = Normal([0.5], [2.])
+            sample = normal_a.sample([2])
+            # a random tensor created by normal distribution with shape: [2, 1]
+            entropy = normal_a.entropy()
+            # [1.4189385] with shape: [1]
+            lp = normal_a.log_prob(value_tensor)
+            # [-1.2389386] with shape: [1]
+            p = normal_a.probs(value_tensor)
+            # [0.28969154] with shape: [1]
+            kl = normal_a.kl_divergence(normal_b)
+            # [0.34939718] with shape: [1]
     """
 
     def __init__(self, loc, scale, name=None):
@@ -132,11 +132,11 @@ def sample(self, shape, seed=0):
         """Generate samples of the specified shape.
 
         Args:
-          shape (list): 1D `int32`. Shape of the generated samples.
-          seed (int): Python integer number.
+            shape (list): 1D `int32`. Shape of the generated samples.
+            seed (int): Python integer number.
 
         Returns:
-          Tensor: A tensor with prepended dimensions shape.The data type is float32.
+            Tensor, A tensor with prepended dimensions shape.The data type is float32.
 
         """
         if not _non_static_mode():
@@ -177,14 +177,14 @@ def entropy(self):
 
         .. math::
 
-            entropy(\sigma) = 0.5 \\log (2 \pi e \sigma^2)
+            entropy(\sigma) = 0.5 \log (2 \pi e \sigma^2)
 
         In the above equation:
 
         * :math:`scale = \sigma`: is the std.
 
         Returns:
-          Tensor: Shannon entropy of normal distribution.The data type is float32.
+            Tensor, Shannon entropy of normal distribution.The data type is float32.
 
         """
         name = self.name + '_entropy'
@@ -221,10 +221,10 @@ def probs(self, value):
         """Probability density/mass function.
 
         Args:
-          value (Tensor): The input tensor.
+            value (Tensor): The input tensor.
 
         Returns:
-          Tensor: probability.The data type is same with value.
+            Tensor, probability. The data type is same with value.
 
         """
         name = self.name + '_probs'
@@ -243,11 +243,11 @@ def kl_divergence(self, other):
 
         .. math::
 
-            KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\\frac{diff}{\sigma_1})^2 - 1 - 2 \\ln {ratio})
+            KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\frac{diff}{\sigma_1})^2 - 1 - 2 \ln {ratio})
 
         .. math::
 
-            ratio = \\frac{\sigma_0}{\sigma_1}
+            ratio = \frac{\sigma_0}{\sigma_1}
 
         .. math::
 
@@ -266,7 +266,7 @@ def kl_divergence(self, other):
             other (Normal): instance of Normal.
 
         Returns:
-            Tensor: kl-divergence between two normal distributions.The data type is float32.
+            Tensor, kl-divergence between two normal distributions.The data type is float32.
 
         """
         if not _non_static_mode():

python/paddle/distribution/transform.py

@@ -58,7 +58,7 @@ class Transform(object):
     Suppose :math:`X` is a K-dimensional random variable with probability
     density function :math:`p_X(x)`. A new random variable :math:`Y = f(X)` may
     be defined by transforming :math:`X` with a suitably well-behaved funciton
-    :math:`f`. It suffices for what follows to note that if f is one-to-one and
+    :math:`f`. It suffices for what follows to note that if `f` is one-to-one and
     its inverse :math:`f^{-1}` have a well-defined Jacobian, then the density of
     :math:`Y` is
 
@@ -1001,16 +1001,16 @@ class StackTransform(Transform):
     specific axis.
 
     Args:
-        transforms(Sequence[Transform]): The sequence of transformations.
-        axis(int): The axis along which will be transformed.
+        transforms (Sequence[Transform]): The sequence of transformations.
+        axis (int, optional): The axis along which will be transformed. default
+            value is 0.
 
     Examples:
 
         .. code-block:: python
 
             import paddle
 
-
             x = paddle.stack(
                 (paddle.to_tensor([1., 2., 3.]), paddle.to_tensor([1, 2., 3.])), 1)
             t = paddle.distribution.StackTransform(
@@ -1023,11 +1023,13 @@ class StackTransform(Transform):
             #        [[2.71828175 , 1.         ],
             #         [7.38905621 , 4.         ],
             #         [20.08553696, 9.         ]])
+
             print(t.inverse(t.forward(x)))
             # Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
             #        [[1., 1.],
             #         [2., 2.],
             #         [3., 3.]])
+
             print(t.forward_log_det_jacobian(x))
             # Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
             #        [[1.        , 0.69314718],

python/paddle/distribution/uniform.py

@@ -37,7 +37,7 @@ class Uniform(distribution.Distribution):
 
     .. math::
 
-        pdf(x; a, b) = \\frac{1}{Z}, \ a <=x <b
+        pdf(x; a, b) = \frac{1}{Z}, \ a <=x <b
 
     .. math::
 
@@ -50,43 +50,45 @@ class Uniform(distribution.Distribution):
     * :math:`Z`: is the normalizing constant.
 
     The parameters `low` and `high` must be shaped in a way that supports
-    [broadcasting](https://www.paddlepaddle.org.cn/documentation/docs/en/develop/beginners_guide/basic_concept/broadcasting_en.html) (e.g., `high - low` is a valid operation).
+    :ref:`user_guide_broadcasting` (e.g., `high - low` is a valid operation).
 
     Args:
-        low(int|float|list|tuple|numpy.ndarray|Tensor): The lower boundary of uniform distribution.The data type is int, float, list, numpy.ndarray or Tensor
-        high(int|float|list|tuple|numpy.ndarray|Tensor): The higher boundary of uniform distribution.The data type is int, float, list, numpy.ndarray or Tensor
-        name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
+        low(int|float|list|tuple|numpy.ndarray|Tensor): The lower boundary of
+            uniform distribution.The data type is float32 and float64.
+        high(int|float|list|tuple|numpy.ndarray|Tensor): The higher boundary
+            of uniform distribution.The data type is float32 and float64.
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Examples:
         .. code-block:: python
 
-          import paddle
-          from paddle.distribution import Uniform
-
-          # Without broadcasting, a single uniform distribution [3, 4]:
-          u1 = Uniform(low=3.0, high=4.0)
-          # 2 distributions [1, 3], [2, 4]
-          u2 = Uniform(low=[1.0, 2.0], high=[3.0, 4.0])
-          # 4 distributions
-          u3 = Uniform(low=[[1.0, 2.0], [3.0, 4.0]],
-                    high=[[1.5, 2.5], [3.5, 4.5]])
-
-          # With broadcasting:
-          u4 = Uniform(low=3.0, high=[5.0, 6.0, 7.0])
-
-          # Complete example
-          value_tensor = paddle.to_tensor([0.8], dtype="float32")
-
-          uniform = Uniform([0.], [2.])
-
-          sample = uniform.sample([2])
-          # a random tensor created by uniform distribution with shape: [2, 1]
-          entropy = uniform.entropy()
-          # [0.6931472] with shape: [1]
-          lp = uniform.log_prob(value_tensor)
-          # [-0.6931472] with shape: [1]
-          p = uniform.probs(value_tensor)
-          # [0.5] with shape: [1]
+            import paddle
+            from paddle.distribution import Uniform
+
+            # Without broadcasting, a single uniform distribution [3, 4]:
+            u1 = Uniform(low=3.0, high=4.0)
+            # 2 distributions [1, 3], [2, 4]
+            u2 = Uniform(low=[1.0, 2.0], high=[3.0, 4.0])
+            # 4 distributions
+            u3 = Uniform(low=[[1.0, 2.0], [3.0, 4.0]],
+                        high=[[1.5, 2.5], [3.5, 4.5]])
+
+            # With broadcasting:
+            u4 = Uniform(low=3.0, high=[5.0, 6.0, 7.0])
+
+            # Complete example
+            value_tensor = paddle.to_tensor([0.8], dtype="float32")
+
+            uniform = Uniform([0.], [2.])
+
+            sample = uniform.sample([2])
+            # a random tensor created by uniform distribution with shape: [2, 1]
+            entropy = uniform.entropy()
+            # [0.6931472] with shape: [1]
+            lp = uniform.log_prob(value_tensor)
+            # [-0.6931472] with shape: [1]
+            p = uniform.probs(value_tensor)
+            # [0.5] with shape: [1]
     """
 
     def __init__(self, low, high, name=None):
@@ -132,11 +134,11 @@ def sample(self, shape, seed=0):
         """Generate samples of the specified shape.
 
         Args:
-          shape (list): 1D `int32`. Shape of the generated samples.
-          seed (int): Python integer number.
+            shape (list): 1D `int32`. Shape of the generated samples.
+            seed (int): Python integer number.
 
         Returns:
-          Tensor: A tensor with prepended dimensions shape.The data type is float32.
+            Tensor, A tensor with prepended dimensions shape. The data type is float32.
 
         """
         if not _non_static_mode():
@@ -179,10 +181,10 @@ def log_prob(self, value):
         """Log probability density/mass function.
 
         Args:
-          value (Tensor): The input tensor.
+            value (Tensor): The input tensor.
 
         Returns:
-          Tensor: log probability.The data type is same with value.
+            Tensor, log probability.The data type is same with value.
 
         """
         value = self._check_values_dtype_in_probs(self.low, value)
@@ -216,10 +218,10 @@ def probs(self, value):
         """Probability density/mass function.
 
         Args:
-          value (Tensor): The input tensor.
+            value (Tensor): The input tensor.
 
         Returns:
-          Tensor: probability.The data type is same with value.
+            Tensor, probability. The data type is same with value.
 
         """
         value = self._check_values_dtype_in_probs(self.low, value)
@@ -256,7 +258,7 @@ def entropy(self):
             entropy(low, high) = \\log (high - low)
 
         Returns:
-          Tensor: Shannon entropy of uniform distribution.The data type is float32.
+            Tensor, Shannon entropy of uniform distribution.The data type is float32.
 
         """
         name = self.name + '_entropy'