refine doc. test=develop

paddle/fluid/operators/spectral_norm_op.cc

@@ -105,11 +105,11 @@ class SpectralNormOpMaker : public framework::OpProtoAndCheckerMaker {
                  "it should be set as 0 if Input(Weight) is the "
                  "weight of fc layer, and should be set as 1 if "
                  "Input(Weight) is the weight of conv layer, "
-                 "default is 0.")
+                 "default 0.")
         .SetDefault(0);
     AddAttr<int>("power_iters",
                  "number of power iterations to calculate "
-                 "spectral norm, default is 1.")
+                 "spectral norm, default 1.")
         .SetDefault(1);
     AddAttr<float>("eps",
                    "epsilob for numerical stability in "
@@ -126,20 +126,28 @@ class SpectralNormOpMaker : public framework::OpProtoAndCheckerMaker {
           with spectral normalize value.
 
           For spectral normalization calculations, we rescaling weight
-          tensor with \sigma, while \sigma{\mathbf{W}} is
+          tensor with :math:`\sigma`, while :math:`\sigma{\mathbf{W}}` is
 
-            \sigma(\mathbf{W}) = \max_{\mathbf{h}: \mathbf{h} \ne 0} \dfrac{\|\mathbf{W} \mathbf{h}\|_2}{\|\mathbf{h}\|_2}
+            $$\sigma(\mathbf{W}) = \max_{\mathbf{h}: \mathbf{h} \ne 0} \\frac{\|\mathbf{W} \mathbf{h}\|_2}{\|\mathbf{h}\|_2}$$
 
-          We calculate \sigma{\mathbf{W}} through power iterations as
+          We calculate :math:`\sigma{\mathbf{W}}` through power iterations as
 
+            $$
             \mathbf{v} = \mathbf{W}^{T} \mathbf{u}
-            \mathbf{v} = \frac{\mathbf{v}}{\|\mathbf{v}\|_2}
+            $$
+            $$
+            \mathbf{v} = \\frac{\mathbf{v}}{\|\mathbf{v}\|_2}
+            $$
+            $$
             \mathbf{u} = \mathbf{W}^{T} \mathbf{v}
-            \mathbf{u} = \frac{\mathbf{u}}{\|\mathbf{u}\|_2}
+            $$
+            $$
+            \mathbf{u} = \\frac{\mathbf{u}}{\|\mathbf{u}\|_2}
+            $$
 
-          And \sigma should be
+          And :math:`\sigma` should be
 
-            \sigma{\mathbf{W}} = \mathbf{u}^{T} \mathbf{W} \mathbf{v}
+            $$\sigma{\mathbf{W}} = \mathbf{u}^{T} \mathbf{W} \mathbf{v}$$
 
           For details of spectral normalization, please refer to paper: 
           `Spectral Normalization <https://arxiv.org/abs/1802.05957>`_ .

python/paddle/fluid/layers/nn.py

@@ -3356,34 +3356,38 @@ def spectral_norm(weight, dim=0, power_iters=1, eps=1e-12, name=None):
     fc, conv1d, conv2d, conv3d layers which should be 2-D, 3-D, 4-D, 5-D
     Parameters. Calculations are showed as followings.
 
-    .. code-block:: text
-
     Step 1:
-        Generate vector u in shape of [h], and v in shape of [w].
-        While h is the attr:`dim`th dimension of the input weights,
-        and w is the product result of remain dimensions.
+    Generate vector U in shape of [H], and V in shape of [W].
+    While H is the :attr:`dim` th dimension of the input weights,
+    and W is the product result of remain dimensions.
 
     Step 2:
-        While attr:`power_iters` is a positive interger, do following
-        iteration calculations with u and v for attr:`power_iters`
-        round.
-            \mathbf{v} = \mathbf{W}^{T} \mathbf{u}
-            \mathbf{v} = \frac{\mathbf{v}}{\|\mathbf{v}\|_2}
-            \mathbf{u} = \mathbf{W}^{T} \mathbf{v}
-            \mathbf{u} = \frac{\mathbf{u}}{\|\mathbf{u}\|_2}
+    :attr:`power_iters` shoule be a positive interger, do following
+    calculations with U and V for :attr:`power_iters` rounds.
+
+    .. math:: 
+
+        \mathbf{v} := \\frac{\mathbf{W}^{T} \mathbf{u}}{\|\mathbf{W}^{T} \mathbf{u}\|_2}
+
+        \mathbf{u} := \\frac{\mathbf{W}^{T} \mathbf{v}}{\|\mathbf{W}^{T} \mathbf{v}\|_2}
 
     Step 3:
-        Calculate \sigma{W} and scale weight values.
-            \sigma{\mathbf{W}} = \mathbf{u}^{T} \mathbf{W} \mathbf{v}
-            \mathbf{W} := \frac{\mathbf{W}}{\sigma{\mathbf{W}}}
+    Calculate :math:`\sigma(\mathbf{W})` and scale weight values.
+
+    .. math::
+
+        \sigma(\mathbf{W}) = \mathbf{u}^{T} \mathbf{W} \mathbf{v}
+
+        \mathbf{W} = \\frac{\mathbf{W}}{\sigma(\mathbf{W})}
                 
 
     Refer to `Spectral Normalization <https://arxiv.org/abs/1802.05957>`_ .
 
     Args:
         weight(${weight_type}): ${weight_comment}
-        dim(${dim_type}): ${dim_comment}
-        eps(${eps_type}): ${eps_comment}
+        dim(int): ${dim_comment}
+        power_iters(int): ${power_iters_comment}
+        eps(float): ${eps_comment}
         name (str): The name of this layer. It is optional.
 
     Returns: