diff --git a/paddle/math/tests/TensorCheck.h b/paddle/math/tests/TensorCheck.h
index 796f2fce6428edc55e745e5977df022973237a38..956bcf61a455dea6fdded823cd2fdd4801b0771a 100644
--- a/paddle/math/tests/TensorCheck.h
+++ b/paddle/math/tests/TensorCheck.h
@@ -12,9 +12,18 @@ 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. */
 
+#pragma once
+
+/**
+ * This file provides a TensorCheck template function, which can be used to
+ * compare CpuMatrix and GpuMatrix, CpuVector and GpuVector, and so on.
+ */
+
 #include <cmath>
 #include "paddle/math/Matrix.h"
 
+namespace autotest {
+
 using paddle::Matrix;
 using paddle::CpuMatrix;
 using paddle::GpuMatrix;
@@ -22,8 +31,6 @@ using paddle::VectorT;
 using paddle::CpuVectorT;
 using paddle::GpuVectorT;
 
-namespace autotest {
-
 class AssertEqual {
 public:
   AssertEqual(real err = 0) : err_(err) {}
diff --git a/paddle/math/tests/TestUtils.h b/paddle/math/tests/TestUtils.h
index fe78f7bf09b1949f1491719483e5238d5409903b..85a582258ab02e67d5c9c3c1f1bdc21149f98b1d 100644
--- a/paddle/math/tests/TestUtils.h
+++ b/paddle/math/tests/TestUtils.h
@@ -12,8 +12,13 @@ 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. */
 
+#pragma once
+
 /**
  * TestUtils.h is used to automatically compare CPU and GPU code is consistent.
+ * This file provides a class(AutoCompare) and a template
+ * function(BaseMatrixCompare) to simplify the comparison
+ * of CPU and GPU member functions.
  * Refer test_Matrix.cpp and test_BaseMatrix.cpp for how to use autotest.
 */
 
@@ -22,14 +27,14 @@ limitations under the License. */
 #include "paddle/math/SparseMatrix.h"
 #include "TensorCheck.h"
 
+namespace autotest {
+
 using paddle::BaseMatrix;
 using paddle::CpuIVector;
 using paddle::GpuIVector;
 using paddle::CpuSparseMatrix;
 using paddle::GpuSparseMatrix;
 
-namespace autotest {
-
 template <typename T1, typename T2>
 class ReplaceType {
 public:
@@ -66,7 +71,7 @@ T construct(int height, int width);
 
 template <>
 float construct(int height, int width) {
-  return 0.0;
+  return 0.5;
 }
 
 template <>
@@ -89,15 +94,7 @@ GpuMatrix construct(int height, int width) {
 
 // init a argument
 template <typename T>
-void init(T& v);
-
-template <>
-void init(float& v) {
-  v = 0.5;
-}
-
-template <>
-void init(size_t& v) {
+void init(T& v) {
   return;
 }
 
@@ -125,15 +122,7 @@ template <std::size_t I = 0, typename... Args>
 
 // copy a argument, copy src to dest
 template <typename T1, typename T2>
-void copy(T1& dest, T2& src);
-
-template <>
-void copy(float& dest, float& src) {
-  dest = src;
-}
-
-template <>
-void copy(size_t& dest, size_t& src) {
+void copy(T1& dest, T2& src) {
   dest = src;
 }
 
@@ -155,28 +144,6 @@ template <std::size_t I = 0, typename... Args1, typename... Args2>
   copyTuple<I + 1>(dest, src);
 }
 
-// Compare output
-template <std::size_t I = 0,
-          typename... Args1,
-          typename... Args2,
-          typename AssertEq>
-inline typename std::enable_if<I == sizeof...(Args1), void>::type checkTuple(
-    std::tuple<Args1...>& args1,
-    std::tuple<Args2...>& args2,
-    AssertEq compare) {}
-
-template <std::size_t I = 0,
-          typename... Args1,
-          typename... Args2,
-          typename AssertEq>
-    inline typename std::enable_if <
-    I<sizeof...(Args1), void>::type checkTuple(std::tuple<Args1...>& args1,
-                                               std::tuple<Args2...>& args2,
-                                               AssertEq compare) {
-  TensorCheck(compare, std::get<I>(args1), std::get<I>(args2));
-  checkTuple<I + 1>(args1, args2, compare);
-}
-
 // call member function
 template <typename C,
           typename FC,
@@ -227,6 +194,7 @@ void BaseMatrixCompare(R (C::*f)(Args...), AssertEq compare) {
   }
 }
 
+// AutoCompare
 template <typename T>
 class ReturnType {
 public:
@@ -252,32 +220,31 @@ public:
 };
 
 template <typename T>
-typename ReturnType<T>::type autoArgs(T v) {
+typename ReturnType<T>::type autoArgs(T& v) {
   return v;
 }
 
 template <>
-GpuMatrix autoArgs(CpuMatrix v) {
+GpuMatrix autoArgs(CpuMatrix& v) {
   GpuMatrix a(v.getHeight(), v.getWidth());
   a.copyFrom(v);
   return a;
 }
 
 template <>
-GpuIVector autoArgs(CpuIVector v) {
+GpuIVector autoArgs(CpuIVector& v) {
   GpuIVector a(v.getSize());
   a.copyFrom(v);
   return a;
 }
 
 template <>
-GpuSparseMatrix autoArgs(CpuSparseMatrix v) {
+GpuSparseMatrix autoArgs(CpuSparseMatrix& v) {
   GpuSparseMatrix a(v.getHeight(),
                     v.getWidth(),
                     v.getElementCnt(),
                     v.getValueType(),
                     v.getFormat());
-
   a.copyFrom(v, HPPL_STREAM_DEFAULT);
   hl_stream_synchronize(HPPL_STREAM_DEFAULT);
   return a;
diff --git a/paddle/math/tests/test_Matrix.cpp b/paddle/math/tests/test_Matrix.cpp
index b766e5ebe27f087108b65235999de78aa4539d5a..b2b6aa5b5f2ae393a5c1a03c8d83780edf4fa397 100644
--- a/paddle/math/tests/test_Matrix.cpp
+++ b/paddle/math/tests/test_Matrix.cpp
@@ -14,7 +14,7 @@ limitations under the License. */
 
 #ifndef PADDLE_ONLY_CPU
 /**
- * This test file use AutoCompare to compares the implementation
+ * This test file use autotest::AutoCompare to compares the implementation
  * of CPU and GPU member function in Matrix.cpp.
  *
  * 1. Constructs an AutoCompare object, a AutoCompare object contains
@@ -28,20 +28,21 @@ limitations under the License. */
  *  AutoCompare test(...);
  *  Init Argument arg1,arg2...
  *  test(function, arg1, arg2....)
- *
  */
 
 #include <gtest/gtest.h>
 #include "TestUtils.h"
 
+using paddle::BaseMatrix;
+using paddle::Matrix;
 using paddle::CpuMatrix;
+using paddle::CpuIVector;
+using paddle::CpuSparseMatrix;
 using paddle::SparseValueType;
 using paddle::SparseFormat;
 using paddle::NO_VALUE;
 using paddle::SPARSE_CSR;
 using paddle::initMain;
-using autotest::TensorCheckEqual;
-using autotest::TensorCheckErr;
 using autotest::AutoCompare;
 
 void testBilinearFwdBwd(int numSamples,