diff --git a/paddle/operators/math/.clang-format b/paddle/operators/math/.clang-format
deleted file mode 100644
index 47b8a85206ab457e2b3cb90a68b7a82a0753d327..0000000000000000000000000000000000000000
--- a/paddle/operators/math/.clang-format
+++ /dev/null
@@ -1,5 +0,0 @@
----
-Language:        Cpp
-BasedOnStyle:  Google
-Standard:  Cpp11
-...
diff --git a/paddle/operators/math/CMakeLists.txt b/paddle/operators/math/CMakeLists.txt
index b1d0bc8f8753957a089509ca9176b2791217db0e..84fffe684379a2e4a29006fbe0373292ce9f1362 100644
--- a/paddle/operators/math/CMakeLists.txt
+++ b/paddle/operators/math/CMakeLists.txt
@@ -1,16 +1,13 @@
-if (WITH_GPU)
-    if (WITH_MKLML)
-        nv_library(math_function SRCS math_function.cc math_function.cu DEPS mklml device_context)
-    else()
-        nv_library(math_function SRCS math_function.cc math_function.cu DEPS cblas device_context)
-    endif()
+if(WITH_MKLML)
+    set(BLAS_LIB mklml)
 else()
-    if (WITH_MKLML)
-        cc_library(math_function SRCS math_function.cc DEPS mklml device_context)
-    else()
-        cc_library(math_function SRCS math_function.cc DEPS cblas device_context)
-    endif()
-endif()    
+    set(BLAS_LIB cblas)
+endif()
 
+if(WITH_GPU)
+    nv_library(math_function SRCS math_function.cc math_function.cu DEPS ${BLAS_LIB} device_context)
+else()
+    cc_library(math_function SRCS math_function.cc math_function.cu DEPS ${BLAS_LIB} device_context)
+endif()
 
 nv_test(math_function_test SRCS math_function_test.cc DEPS math_function tensor)
diff --git a/paddle/operators/math/math_function.cc b/paddle/operators/math/math_function.cc
index e5eefedde05d3276a8613570a1b402be996566bf..03a63d063f832f529405f0d080d27a122a1d32da 100644
--- a/paddle/operators/math/math_function.cc
+++ b/paddle/operators/math/math_function.cc
@@ -12,6 +12,44 @@ 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. */
 
+#ifdef PADDLE_USE_MKLML
+#include <mkl_cblas.h>
+#include <mkl_lapacke.h>
+#include <mkl_vml_functions.h>
+#endif
+
+#ifdef PADDLE_USE_MKL
+#include <mkl.h>
+#include <mkl_lapacke.h>
+#endif
+
+#ifdef PADDLE_USE_ATLAS
+extern "C" {
+#include <cblas.h>
+#include <clapack.h>
+}
+#endif
+
+#ifdef PADDLE_USE_OPENBLAS
+#include <cblas.h>
+#include <lapacke.h>
+#endif
+
+#ifndef LAPACK_FOUND
+extern "C" {
+#include <cblas.h>
+int LAPACKE_sgetrf(int matrix_layout, int m, int n, float* a, int lda,
+                   int* ipiv);
+int LAPACKE_dgetrf(int matrix_layout, int m, int n, double* a, int lda,
+                   int* ipiv);
+int LAPACKE_sgetri(int matrix_layout, int n, float* a, int lda,
+                   const int* ipiv);
+int LAPACKE_dgetri(int matrix_layout, int n, double* a, int lda,
+                   const int* ipiv);
+}
+#endif
+
+#include <cmath>
 #include "paddle/operators/math/math_function.h"
 
 namespace paddle {
@@ -48,62 +86,65 @@ void gemm<platform::CPUPlace, double>(const CBLAS_TRANSPOSE transA,
 }
 
 template <>
-void matmul<platform::CPUPlace, float>(const framework::Tensor& in1, bool in1_T,
-                                       const framework::Tensor& in2, bool in2_T,
-                                       float alpha, framework::Tensor* out,
+void matmul<platform::CPUPlace, float>(const framework::Tensor& matrix_a,
+                                       bool trans_a,
+                                       const framework::Tensor& matrix_b,
+                                       bool trans_b, float alpha,
+                                       framework::Tensor* matrix_out,
                                        float beta,
                                        platform::DeviceContext* context) {
-  auto in1_dim = in1.dims();
-  auto in2_dim = in2.dims();
-  auto out_dim = out->dims();
-  PADDLE_ENFORCE(
-      in1_dim.size() == 2 && in2_dim.size() == 2 && out_dim.size() == 2,
-      "The input and output of matmul be matrix");
-
-  PADDLE_ENFORCE(platform::is_cpu_place(in1.place()) &&
-                     platform::is_cpu_place(in2.place()) &&
-                     platform::is_cpu_place(out->place()),
+  auto dim_a = matrix_a.dims();
+  auto dim_b = matrix_b.dims();
+  auto dim_out = matrix_out->dims();
+  PADDLE_ENFORCE(dim_a.size() == 2 && dim_b.size() == 2 && dim_out.size() == 2,
+                 "The input and output of matmul be matrix");
+
+  PADDLE_ENFORCE(platform::is_cpu_place(matrix_a.place()) &&
+                     platform::is_cpu_place(matrix_b.place()) &&
+                     platform::is_cpu_place(matrix_out->place()),
                  "Matrix must all be in CPUPlace");
 
-  int M = out_dim[0];
-  int N = out_dim[1];
-  int K = (in1_T == false) ? in1_dim[1] : in1_dim[0];
+  int M = dim_out[0];
+  int N = dim_out[1];
+  int K = (trans_a == false) ? dim_a[1] : dim_a[0];
 
-  CBLAS_TRANSPOSE in1_Trans = (in1_T == false) ? CblasNoTrans : CblasTrans;
-  CBLAS_TRANSPOSE in2_Trans = (in2_T == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transA = (trans_a == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transB = (trans_b == false) ? CblasNoTrans : CblasTrans;
 
-  gemm<platform::CPUPlace, float>(in1_Trans, in2_Trans, M, N, K, alpha,
-                                  in1.data<float>(), in2.data<float>(), beta,
-                                  out->data<float>(), context);
+  gemm<platform::CPUPlace, float>(
+      transA, transB, M, N, K, alpha, matrix_a.data<float>(),
+      matrix_b.data<float>(), beta, matrix_out->data<float>(), context);
 }
 
 template <>
-void matmul<platform::CPUPlace, double>(const framework::Tensor& in1,
-                                        bool in1_T,
-                                        const framework::Tensor& in2,
-                                        bool in2_T, float alpha,
-                                        framework::Tensor* out, float beta,
+void matmul<platform::CPUPlace, double>(const framework::Tensor& matrix_a,
+                                        bool trans_a,
+                                        const framework::Tensor& matrix_b,
+                                        bool trans_b, double alpha,
+                                        framework::Tensor* matrix_out,
+                                        double beta,
                                         platform::DeviceContext* context) {
-  auto in1_dim = in1.dims();
-  auto in2_dim = in2.dims();
-  auto out_dim = out->dims();
-  PADDLE_ENFORCE(
-      in1_dim.size() == 2 && in2_dim.size() == 2 && out_dim.size() == 2,
-      "The input and output of matmul be matrix");
-  PADDLE_ENFORCE(platform::is_cpu_place(in1.place()) &&
-                     platform::is_cpu_place(in2.place()) &&
-                     platform::is_cpu_place(out->place()),
+  auto dim_a = matrix_a.dims();
+  auto dim_b = matrix_b.dims();
+  auto dim_out = matrix_out->dims();
+  PADDLE_ENFORCE(dim_a.size() == 2 && dim_b.size() == 2 && dim_out.size() == 2,
+                 "The input and output of matmul be matrix");
+
+  PADDLE_ENFORCE(platform::is_cpu_place(matrix_a.place()) &&
+                     platform::is_cpu_place(matrix_b.place()) &&
+                     platform::is_cpu_place(matrix_out->place()),
                  "Matrix must all be in CPUPlace");
 
-  int M = out_dim[0];
-  int N = out_dim[1];
-  int K = (in1_T == false) ? in1_dim[1] : in1_dim[0];
-  CBLAS_TRANSPOSE in1_Trans = (in1_T == false) ? CblasNoTrans : CblasTrans;
-  CBLAS_TRANSPOSE in2_Trans = (in2_T == false) ? CblasNoTrans : CblasTrans;
+  int M = dim_out[0];
+  int N = dim_out[1];
+  int K = (trans_a == false) ? dim_a[1] : dim_a[0];
+
+  CBLAS_TRANSPOSE transA = (trans_a == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transB = (trans_b == false) ? CblasNoTrans : CblasTrans;
 
-  gemm<platform::CPUPlace, double>(in1_Trans, in2_Trans, M, N, K, alpha,
-                                   in1.data<double>(), in2.data<double>(), beta,
-                                   out->data<double>(), context);
+  gemm<platform::CPUPlace, double>(
+      transA, transB, M, N, K, alpha, matrix_a.data<double>(),
+      matrix_b.data<double>(), beta, matrix_out->data<double>(), context);
 }
 
 }  // namespace math
diff --git a/paddle/operators/math/math_function.cu b/paddle/operators/math/math_function.cu
index ff02c6ad7e0101d10111b2009c44ed587645358e..c1ec2d93eda3d736d334bd55940d8f963a299618 100644
--- a/paddle/operators/math/math_function.cu
+++ b/paddle/operators/math/math_function.cu
@@ -12,7 +12,46 @@ 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. */
 
+#ifdef PADDLE_USE_MKLML
+#include <mkl_cblas.h>
+#include <mkl_lapacke.h>
+#include <mkl_vml_functions.h>
+#endif
+
+#ifdef PADDLE_USE_MKL
+#include <mkl.h>
+#include <mkl_lapacke.h>
+#endif
+
+#ifdef PADDLE_USE_ATLAS
+extern "C" {
+#include <cblas.h>
+#include <clapack.h>
+}
+#endif
+
+#ifdef PADDLE_USE_OPENBLAS
+#include <cblas.h>
+#include <lapacke.h>
+#endif
+
+#ifndef LAPACK_FOUND
+extern "C" {
+#include <cblas.h>
+int LAPACKE_sgetrf(int matrix_layout, int m, int n, float* a, int lda,
+                   int* ipiv);
+int LAPACKE_dgetrf(int matrix_layout, int m, int n, double* a, int lda,
+                   int* ipiv);
+int LAPACKE_sgetri(int matrix_layout, int n, float* a, int lda,
+                   const int* ipiv);
+int LAPACKE_dgetri(int matrix_layout, int n, double* a, int lda,
+                   const int* ipiv);
+}
+#endif
+
+#include <cmath>
 #include "paddle/operators/math/math_function.h"
+
 namespace paddle {
 namespace operators {
 namespace math {
@@ -60,63 +99,67 @@ void gemm<platform::GPUPlace, double>(const CBLAS_TRANSPOSE transA,
 }
 
 template <>
-void matmul<platform::GPUPlace, float>(const framework::Tensor& in1, bool in1_T,
-                                       const framework::Tensor& in2, bool in2_T,
-                                       float alpha, framework::Tensor* out,
+void matmul<platform::GPUPlace, float>(const framework::Tensor& matrix_a,
+                                       bool trans_a,
+                                       const framework::Tensor& matrix_b,
+                                       bool trans_b, float alpha,
+                                       framework::Tensor* matrix_out,
                                        float beta,
                                        platform::DeviceContext* context) {
-  auto in1_dim = in1.dims();
-  auto in2_dim = in2.dims();
-  auto out_dim = out->dims();
-  PADDLE_ENFORCE(
-      in1_dim.size() == 2 && in2_dim.size() == 2 && out_dim.size() == 2,
-      "The input and output of matmul be matrix");
-
-  PADDLE_ENFORCE(platform::is_gpu_place(in1.place()) &&
-                     platform::is_gpu_place(in2.place()) &&
-                     platform::is_gpu_place(out->place()),
+  auto dim_a = matrix_a.dims();
+  auto dim_b = matrix_b.dims();
+  auto dim_out = matrix_out->dims();
+  PADDLE_ENFORCE(dim_a.size() == 2 && dim_b.size() == 2 && dim_out.size() == 2,
+                 "The input and output of matmul be matrix");
+
+  PADDLE_ENFORCE(platform::is_gpu_place(matrix_a.place()) &&
+                     platform::is_gpu_place(matrix_b.place()) &&
+                     platform::is_gpu_place(matrix_out->place()),
                  "Matrix must all be in GPUPlace");
 
-  int M = out_dim[0];
-  int N = out_dim[1];
-  int K = (in1_T == false) ? in1_dim[1] : in1_dim[0];
+  int M = dim_out[0];
+  int N = dim_out[1];
+  int K = (trans_a == false) ? dim_a[1] : dim_a[0];
 
-  CBLAS_TRANSPOSE in1_Trans = (in1_T == false) ? CblasNoTrans : CblasTrans;
-  CBLAS_TRANSPOSE in2_Trans = (in2_T == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transA = (trans_a == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transB = (trans_b == false) ? CblasNoTrans : CblasTrans;
 
-  gemm<platform::GPUPlace, float>(in1_Trans, in2_Trans, M, N, K, alpha,
-                                  in1.data<float>(), in2.data<float>(), beta,
-                                  out->data<float>(), context);
+  gemm<platform::GPUPlace, float>(
+      transA, transB, M, N, K, alpha, matrix_a.data<float>(),
+      matrix_b.data<float>(), beta, matrix_out->data<float>(), context);
 }
 
 template <>
-void matmul<platform::GPUPlace, double>(const framework::Tensor& in1,
-                                        bool in1_T,
-                                        const framework::Tensor& in2,
-                                        bool in2_T, float alpha,
-                                        framework::Tensor* out, float beta,
+void matmul<platform::GPUPlace, double>(const framework::Tensor& matrix_a,
+                                        bool trans_a,
+                                        const framework::Tensor& matrix_b,
+                                        bool trans_b, double alpha,
+                                        framework::Tensor* matrix_out,
+                                        double beta,
                                         platform::DeviceContext* context) {
-  auto in1_dim = in1.dims();
-  auto in2_dim = in2.dims();
-  auto out_dim = out->dims();
-  PADDLE_ENFORCE(
-      in1_dim.size() == 2 && in2_dim.size() == 2 && out_dim.size() == 2,
-      "The input and output of matmul be matrix");
-  PADDLE_ENFORCE(platform::is_gpu_place(in1.place()) &&
-                     platform::is_gpu_place(in2.place()) &&
-                     platform::is_gpu_place(out->place()),
+  auto dim_a = matrix_a.dims();
+  auto dim_b = matrix_b.dims();
+  auto dim_out = matrix_out->dims();
+  PADDLE_ENFORCE(dim_a.size() == 2 && dim_b.size() == 2 && dim_out.size() == 2,
+                 "The input and output of matmul be matrix");
+
+  PADDLE_ENFORCE(platform::is_gpu_place(matrix_a.place()) &&
+                     platform::is_gpu_place(matrix_b.place()) &&
+                     platform::is_gpu_place(matrix_out->place()),
                  "Matrix must all be in GPUPlace");
 
-  int M = out_dim[0];
-  int N = out_dim[1];
-  int K = (in1_T == false) ? in1_dim[1] : in1_dim[0];
-  CBLAS_TRANSPOSE in1_Trans = (in1_T == false) ? CblasNoTrans : CblasTrans;
-  CBLAS_TRANSPOSE in2_Trans = (in2_T == false) ? CblasNoTrans : CblasTrans;
+  int M = dim_out[0];
+  int N = dim_out[1];
+  int K = (trans_a == false) ? dim_a[1] : dim_a[0];
+
+  CBLAS_TRANSPOSE transA = (trans_a == false) ? CblasNoTrans : CblasTrans;
+  CBLAS_TRANSPOSE transB = (trans_b == false) ? CblasNoTrans : CblasTrans;
 
-  gemm<platform::GPUPlace, double>(in1_Trans, in2_Trans, M, N, K, alpha,
-                                   in1.data<double>(), in2.data<double>(), beta,
-                                   out->data<double>(), context);
+  gemm<platform::GPUPlace, double>(
+      transA, transB, M, N, K, alpha, matrix_a.data<double>(),
+      matrix_b.data<double>(), beta, matrix_out->data<double>(), context);
 }
+
 }  // namespace math
 }  // namespace operators
 }  // namespace paddle
diff --git a/paddle/operators/math/math_function.h b/paddle/operators/math/math_function.h
index 12d1706afb82d37f0381facb7d448251372497d9..c20e6a3b39fb57aad88d35131e35cf43e3cd38b1 100644
--- a/paddle/operators/math/math_function.h
+++ b/paddle/operators/math/math_function.h
@@ -14,44 +14,6 @@ limitations under the License. */
 
 #pragma once
 
-#ifdef PADDLE_USE_MKLML
-#include <mkl_cblas.h>
-#include <mkl_lapacke.h>
-#include <mkl_vml_functions.h>
-#endif
-
-#ifdef PADDLE_USE_MKL
-#include <mkl.h>
-#include <mkl_lapacke.h>
-#endif
-
-#ifdef PADDLE_USE_ATLAS
-extern "C" {
-#include <cblas.h>
-#include <clapack.h>
-}
-#endif
-
-#ifdef PADDLE_USE_OPENBLAS
-#include <cblas.h>
-#include <lapacke.h>
-#endif
-
-#ifndef LAPACK_FOUND
-extern "C" {
-#include <cblas.h>
-int LAPACKE_sgetrf(int matrix_layout, int m, int n, float* a, int lda,
-                   int* ipiv);
-int LAPACKE_dgetrf(int matrix_layout, int m, int n, double* a, int lda,
-                   int* ipiv);
-int LAPACKE_sgetri(int matrix_layout, int n, float* a, int lda,
-                   const int* ipiv);
-int LAPACKE_dgetri(int matrix_layout, int n, double* a, int lda,
-                   const int* ipiv);
-}
-#endif
-
-#include <cmath>
 #include "paddle/framework/tensor.h"
 #include "paddle/platform/device_context.h"
 #include "paddle/platform/enforce.h"
@@ -60,17 +22,20 @@ namespace paddle {
 namespace operators {
 namespace math {
 
-// support continuous memory now
-template <typename Place, typename T>
+// Support continuous memory now
+// If transA = N, and transB = N
+// Then matrixA: M * K, matrixB: K * N matrixC : M * N
+// For more detailed info, please refer to
+// http://www.netlib.org/lapack/explore-html/d4/de2/sgemm_8f.html
 void gemm(const CBLAS_TRANSPOSE transA, const CBLAS_TRANSPOSE transB,
           const int M, const int N, const int K, const T alpha, const T* A,
           const T* B, const T beta, T* C, platform::DeviceContext* context);
 
 // matrix multiply with continuous memory
 template <typename Place, typename T>
-void matmul(const framework::Tensor& in1, bool in1_T,
-            const framework::Tensor& in2, bool in2_T, float alpha,
-            framework::Tensor* out, float beta,
+void matmul(const framework::Tensor& matrix_a, bool trans_a,
+            const framework::Tensor& matrix_b, bool trans_b, float alpha,
+            framework::Tensor* matrix_out, float beta,
             platform::DeviceContext* context);
 
 }  // namespace math