refine doc. test=develop

paddle/fluid/operators/spectral_norm_op.cc

@@ -78,7 +78,7 @@ class SpectralNormOpMaker : public framework::OpProtoAndCheckerMaker {
   void Make() override {
     AddInput("Weight",
              "The input weight tensor of spectral_norm operator, "
-             "This can be a 2-D, 3-D, 4-D, 5-D tensor which is the"
+             "This can be a 2-D, 3-D, 4-D, 5-D tensor which is the "
              "weights of fc, conv1d, conv2d, conv3d layer.");
     AddInput("U",
              "The weight_u tensor of spectral_norm operator, "
@@ -90,29 +90,29 @@ class SpectralNormOpMaker : public framework::OpProtoAndCheckerMaker {
              "be in shape [C, 1].");
     AddInput("V",
              "The weight_v tensor of spectral_norm operator, "
-             "This can be a 1-D tensor in shape [W, 1],"
-             "W is the 2nd dimentions of Weight after reshape"
-             "corresponding by Attr(dim). As for Attr(dim) = 1"
-             "in conv2d layer with weight shape [M, C, K1, K2]"
-             "Weight will be reshape to [C, M*K1*K2], V will"
+             "This can be a 1-D tensor in shape [W, 1], "
+             "W is the 2nd dimentions of Weight after reshape "
+             "corresponding by Attr(dim). As for Attr(dim) = 1 "
+             "in conv2d layer with weight shape [M, C, K1, K2] "
+             "Weight will be reshape to [C, M*K1*K2], V will "
              "be in shape [M*K1*K2, 1].");
     AddOutput("Out",
               "The output weight tensor of spectral_norm operator, "
               "This tensor is in same shape with Input(Weight).");
 
     AddAttr<int>("dim",
-                 "dimension corresponding to number of outputs,"
-                 "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.")
+                 "dimension corresponding to number of outputs, "
+                 "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 0.")
         .SetDefault(0);
     AddAttr<int>("power_iters",
-                 "number of power iterations to calculate"
-                 "spectral norm, default is 1.")
+                 "number of power iterations to calculate "
+                 "spectral norm, default 1.")
         .SetDefault(1);
     AddAttr<float>("eps",
-                   "epsilob for numerical stability in"
+                   "epsilob for numerical stability in "
                    "calculating norms")
         .SetDefault(1e-12);
 
@@ -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.
 
-        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.
+    Step 2:
+    :attr:`power_iters` shoule be a positive interger, do following
+    calculations with U and V for :attr:`power_iters` rounds.
 
-        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}
-
-        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}}}
+    .. 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 :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: