First half translation of operator definition.

doc/howto/dev/new_op_en.md

+# How to write a new operator
+
+ - [Background](#Background)
+ - [Implementing C++ Types](#Implementing_C++_Types)
+   - [Defining ProtoMaker](#Defining_ProtoMaker)
+   - [Defining Operator](#Defining_Operator)
+
+
+## Background
+
+Here are the base types needed. For details, please refer to the design docs.
+
+- `framework::OperatorBase`: Operator (Op)base class.
+- `framework::OpKernel`: Base class for Op computation.
+- `framework::OperatorWithKernel`: Inherited from OperatorBase, describing an operator with computation.
+- `class OpProtoAndCheckerMaker`: Describes an Operator's input, output, attributes and description, mainly used to interface with Python API.
+
+An operator can be differentiated by whether in has kernel methods. An operator with kernel inherits from `OperatorWithKernel` while the ones without inherit from `OperatorBase`. This tutorial focuses on implementing operators with kernels. In short, an operator includes the following information:
+
+
+ Information           | Where is it defined
+--------------  | :----------------------
+OpProtoMake definition  | `.cc`files, Backward Op does not need an OpProtoMake interface.
+Op definition           | `.cc` files
+Kernel implementation       | The kernel methods shared between CPU and GPU are defined in `.h` files. CPU-specific kernels live in `.cc` files, while GPU-specific kernels are implemented in `.cu`files.
+Registering the Op           | Ops are registered in `.cc` files; For Kernel registration, `.cc` files contain the CPU implementation, while `.cu` files contain the GPU implementation.
+
+
+New Operator implementations are added to the list [paddle/operators](https://github.com/PaddlePaddle/Paddle/tree/develop/paddle/operators), with file names in the format `*_op.h` (if applicable), `*_op.cc`, `*_op.cu` (if applicable).** The system will use the naming scheme to automatically build operators and their corresponding Python extensions. **
+
+
+Let's take matrix multiplication operator, [MulOp](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/operators/mul_op.cc), as an example to introduce the writing of an Operator with Kernel.
+
+
+## Implementing C++ Types
+
+
+### 1. Defining Class ProtoMaker
+
+Matrix Multiplication can be written as $Out = X * Y$, meaning that the operation consists of two inputs and pne output.
+
+First, define `ProtoMaker` to describe the Operator's input, output, and additional comments:
+
+```cpp
+class MulOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  MulOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
+      : OpProtoAndCheckerMaker(proto, op_checker) {
+    AddInput("X", "(Tensor), 2D tensor of size (M x K)");
+    AddInput("Y", "(Tensor), 2D tensor of size (K x N)");
+    AddOutput("Out", "(Tensor), 2D tensor of size (M x N)");
+    AddComment(R"DOC(
+Two Element Mul Operator.
+The equation is: Out = X * Y
+)DOC");
+  }
+};
+```
+
+[`MulOpMaker`](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/operators/mul_op.cc#L43)is inherited from`framework::OpProtoAndCheckerMaker`, consisting of 2 variables in the constructor：
+
+   - `framework::OpProto` stores Operator input and variable attribute, used for generating Python API interfaces.
+   - `framework::OpAttrChecker` is used to validate variable attributes.
+
+The constructor utilizes `AddInput`, `AddOutput`, and `AddComment`, so that the corresponding information will be added to `OpProto`.
+
+The code above adds two inputs `X` and `Y` to `MulOp`, an output `Out`, and their corresponding descriptions, in accordance to Paddle's [naming convention](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/operators/name_convention.md).
+
+
+An additional example [`ScaleOp`](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/operators/scale_op.cc#L37) is implemented as follows:
+
+```cpp
+template <typename AttrType>
+class ScaleOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  ScaleOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
+      : OpProtoAndCheckerMaker(proto, op_checker) {
+    AddInput("X", "The input tensor of scale operator.").NotInGradient();
+    AddOutput("Out", "The output tensor of scale operator.").NotInGradient();
+    AddComment(R"DOC(Scale operator
+The equation is: Out = scale*X
+)DOC");
+    AddAttr<AttrType>("scale", "scale of scale operator.").SetDefault(1.0);
+  }
+};
+```
+
+There are two changes in this example:
+
+- `AddInput("X","...").NotInGradient()` expresses that input `X` is not involved in `ScaleOp`'s corresponding computation. If an input to an operator is not participating in back-propagation, please explicitly set `.NotInGradient()`.
+
+- `AddAttr<AttrType>("scale", "...").SetDefault(1.0);`  adds `scale`constant as an attribute, and sets the default value to 1.0.
+
+
+### 2. Defining Operator
+
+The following code defines the interface for MulOp:
+
+```cpp
+class MulOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+ protected:
+  void InferShape(const framework::InferShapeContext &ctx) const override {
+    auto dim0 = ctx.Input<Tensor>("X")->dims();
+    auto dim1 = ctx.Input<Tensor>("Y")->dims();
+    PADDLE_ENFORCE_EQ(dim0.size(), 2,
+                      "input X(%s) should be a tensor with 2 dims, a matrix",
+                      ctx.op_.Input("X"));
+    PADDLE_ENFORCE_EQ(dim1.size(), 2,
+                      "input Y(%s) should be a tensor with 2 dims, a matrix",
+                      ctx.op_.Input("Y"));
+    PADDLE_ENFORCE_EQ(
+        dim0[1], dim1[0],
+        "First matrix's width must be equal with second matrix's height.");
+    ctx.Output<Tensor>("Out")->Resize({dim0[0], dim1[1]});
+  }
+};
+```
+
+[`MulOp`](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/operators/mul_op.cc#L22) is inherited from `OperatorWithKernel`. Its `public` member
+
+```cpp
+using framework::OperatorWithKernel::OperatorWithKernel;
+```
+
+expresses an operator constructor using base class `OperatorWithKernel`, alternatively written as
+
+```cpp
+MulOp(const std::string &type, const framework::VariableNameMap &inputs,
+      const framework::VariableNameMap &outputs,
+      const framework::AttributeMap &attrs)
+  : OperatorWithKernel(type, inputs, outputs, attrs) {}
+```
+
+`InferShape` interface needs to be re-written.`InferShape` is a constant method and cannot modify Op's member variables, its constant member `const framework::InferShapeContext &ctx` can be used to extract input, output, and attributes. It functions to
+
+  - 1). validate and error out early: it checks input data dimensions and types.
+  - 2). configures the tensor shape in the output.
+
+Usually `OpProtoMaker` and `Op`'s type definitions are written in `.cc` files, which also include the registration methods introduced later.