diff --git a/paddle/math/BaseMatrix.cu b/paddle/math/BaseMatrix.cu
index 5435808fb7f70fdf1ac98815f7fe8890fb85527c..ba2b47d6cc6961a380b7db2781b4d214dea829db 100644
--- a/paddle/math/BaseMatrix.cu
+++ b/paddle/math/BaseMatrix.cu
@@ -12,21 +12,21 @@ 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. */
 
-#include <paddle/utils/Logging.h>
-#include <string.h>
 #include <cmath>
+#include <string.h>
+#include <paddle/utils/Logging.h>
 #include "BaseMatrix.h"
-#include "MathFunctions.h"
-#include "SIMDFunctions.h"
-#include "hl_matrix_apply.cuh"
-#include "hl_matrix_base.cuh"
 #include "hl_matrix_ops.cuh"
+#include "hl_matrix_base.cuh"
+#include "hl_matrix_apply.cuh"
+#include "SIMDFunctions.h"
+#include "MathFunctions.h"
 
 namespace paddle {
 
 const char* SPARSE_SUPPORT_ERROR = "Sparse Matrix/Vector is not supported.";
 
-template <class T>
+template<class T>
 template <class Op>
 int BaseMatrixT<T>::applyUnary(Op op) {
   MatrixOffset offset(0, 0);
@@ -34,11 +34,9 @@ int BaseMatrixT<T>::applyUnary(Op op) {
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
-int BaseMatrixT<T>::applyUnary(Op op,
-                               int numRows,
-                               int numCols,
+int BaseMatrixT<T>::applyUnary(Op op, int numRows, int numCols,
                                MatrixOffset& offset) {
   CHECK(!this->isSparse()) << SPARSE_SUPPORT_ERROR;
   int dimM = numRows;
@@ -58,7 +56,7 @@ int BaseMatrixT<T>::applyUnary(Op op,
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
 int BaseMatrixT<T>::applyBinary(Op op, BaseMatrixT& b) {
   CHECK(height_ == b.height_ && width_ == b.width_)
@@ -69,23 +67,18 @@ int BaseMatrixT<T>::applyBinary(Op op, BaseMatrixT& b) {
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
-int BaseMatrixT<T>::applyBinary(
-    Op op, BaseMatrixT& b, int numRows, int numCols, MatrixOffset& offset) {
+int BaseMatrixT<T>::applyBinary(Op op, BaseMatrixT& b, int numRows, int numCols,
+                                MatrixOffset& offset) {
   applyBinary(op, b, numRows, numCols, offset, false_type(), false_type());
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op, class bAsRowVector, class bAsColVector>
-int BaseMatrixT<T>::applyBinary(Op op,
-                                BaseMatrixT& b,
-                                int numRows,
-                                int numCols,
-                                MatrixOffset& offset,
-                                bAsRowVector,
-                                bAsColVector) {
+int BaseMatrixT<T>::applyBinary(Op op, BaseMatrixT& b, int numRows, int numCols,
+                            MatrixOffset& offset, bAsRowVector, bAsColVector) {
   CHECK(!this->isSparse()) << SPARSE_SUPPORT_ERROR;
   CHECK(!b.isSparse()) << SPARSE_SUPPORT_ERROR;
   CHECK(useGpu_ == b.useGpu_) << "Matrix type mismatch";
@@ -98,8 +91,8 @@ int BaseMatrixT<T>::applyBinary(Op op,
   T* A = data_;
   T* B = b.data_;
   CAL_MATRIX_START_ADDRESS(A, height_, width_, lda, offset.aCol_, offset.aRow_);
-  CAL_MATRIX_START_ADDRESS(
-      B, b.height_, b.width_, ldb, offset.bCol_, offset.bRow_);
+  CAL_MATRIX_START_ADDRESS(B, b.height_, b.width_, ldb, offset.bCol_,
+                           offset.bRow_);
   CHECK_LE(dimM + offset.aRow_, this->height_);
   CHECK_LE(dimN + offset.aCol_, this->width_);
   if (!bAsRowVector::value && !bAsColVector::value) {
@@ -122,7 +115,7 @@ int BaseMatrixT<T>::applyBinary(Op op,
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
 int BaseMatrixT<T>::applyTernary(Op op, BaseMatrixT& b, BaseMatrixT& c) {
   CHECK_EQ(height_, b.height_);
@@ -136,29 +129,21 @@ int BaseMatrixT<T>::applyTernary(Op op, BaseMatrixT& b, BaseMatrixT& c) {
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
-int BaseMatrixT<T>::applyTernary(Op op,
-                                 BaseMatrixT& b,
-                                 BaseMatrixT& c,
-                                 int numRows,
-                                 int numCols,
+int BaseMatrixT<T>::applyTernary(Op op, BaseMatrixT& b, BaseMatrixT& c,
+                                 int numRows, int numCols,
                                  MatrixOffset& offset) {
   applyTernary(op, b, c, numRows, numCols, offset, false_type(), false_type());
 
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op, class cAsRowVector, class cAsColVector>
-int BaseMatrixT<T>::applyTernary(Op op,
-                                 BaseMatrixT& b,
-                                 BaseMatrixT& c,
-                                 int numRows,
-                                 int numCols,
-                                 MatrixOffset& offset,
-                                 cAsRowVector,
-                                 cAsColVector) {
+int BaseMatrixT<T>::applyTernary(Op op, BaseMatrixT& b, BaseMatrixT& c,
+                                 int numRows, int numCols, MatrixOffset& offset,
+                                 cAsRowVector, cAsColVector) {
   CHECK(!this->isSparse()) << SPARSE_SUPPORT_ERROR;
   CHECK(!b.isSparse()) << SPARSE_SUPPORT_ERROR;
   CHECK(!c.isSparse()) << SPARSE_SUPPORT_ERROR;
@@ -175,10 +160,10 @@ int BaseMatrixT<T>::applyTernary(Op op,
   T* B = b.data_;
   T* C = c.data_;
   CAL_MATRIX_START_ADDRESS(A, height_, width_, lda, offset.aCol_, offset.aRow_);
-  CAL_MATRIX_START_ADDRESS(
-      B, b.height_, b.width_, ldb, offset.bCol_, offset.bRow_);
-  CAL_MATRIX_START_ADDRESS(
-      C, c.height_, c.width_, ldc, offset.cCol_, offset.cRow_);
+  CAL_MATRIX_START_ADDRESS(B, b.height_, b.width_, ldb, offset.bCol_,
+                           offset.bRow_);
+  CAL_MATRIX_START_ADDRESS(C, c.height_, c.width_, ldc, offset.cCol_,
+                           offset.cRow_);
 
   CHECK_LE(dimM + offset.aRow_, this->height_);
   CHECK_LE(dimN + offset.aCol_, this->width_);
@@ -195,21 +180,21 @@ int BaseMatrixT<T>::applyTernary(Op op,
   }
 
   if (true == useGpu_) {
-    hl_gpu_apply_ternary_op<T, Op, cAsRowVector::value, cAsColVector::value>(
+    hl_gpu_apply_ternary_op
+      <T, Op, cAsRowVector::value, cAsColVector::value>(
         op, A, B, C, dimM, dimN, lda, ldb, ldc);
   } else {
-    hl_cpu_apply_ternary_op<T, Op, cAsRowVector::value, cAsColVector::value>(
+    hl_cpu_apply_ternary_op
+      <T, Op, cAsRowVector::value, cAsColVector::value>(
         op, A, B, C, dimM, dimN, lda, ldb, ldc);
   }
 
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
-int BaseMatrixT<T>::applyQuaternary(Op op,
-                                    BaseMatrixT& b,
-                                    BaseMatrixT& c,
+int BaseMatrixT<T>::applyQuaternary(Op op, BaseMatrixT& b, BaseMatrixT& c,
                                     BaseMatrixT& d) {
   CHECK_EQ(height_, b.height_);
   CHECK_EQ(width_, b.width_);
@@ -224,14 +209,10 @@ int BaseMatrixT<T>::applyQuaternary(Op op,
   return 0;
 }
 
-template <class T>
+template<class T>
 template <class Op>
-int BaseMatrixT<T>::applyQuaternary(Op op,
-                                    BaseMatrixT& b,
-                                    BaseMatrixT& c,
-                                    BaseMatrixT& d,
-                                    int numRows,
-                                    int numCols,
+int BaseMatrixT<T>::applyQuaternary(Op op, BaseMatrixT& b, BaseMatrixT& c,
+                                    BaseMatrixT& d, int numRows, int numCols,
                                     MatrixOffset& offset) {
   CHECK(!this->isSparse()) << SPARSE_SUPPORT_ERROR;
   CHECK(!b.isSparse()) << SPARSE_SUPPORT_ERROR;
@@ -253,12 +234,12 @@ int BaseMatrixT<T>::applyQuaternary(Op op,
   T* C = c.data_;
   T* D = d.data_;
   CAL_MATRIX_START_ADDRESS(A, height_, width_, lda, offset.aCol_, offset.aRow_);
-  CAL_MATRIX_START_ADDRESS(
-      B, b.height_, b.width_, ldb, offset.bCol_, offset.bRow_);
-  CAL_MATRIX_START_ADDRESS(
-      C, c.height_, c.width_, ldc, offset.cCol_, offset.cRow_);
-  CAL_MATRIX_START_ADDRESS(
-      D, d.height_, d.width_, ldd, offset.dCol_, offset.dRow_);
+  CAL_MATRIX_START_ADDRESS(B, b.height_, b.width_, ldb, offset.bCol_,
+                           offset.bRow_);
+  CAL_MATRIX_START_ADDRESS(C, c.height_, c.width_, ldc, offset.cCol_,
+                           offset.cRow_);
+  CAL_MATRIX_START_ADDRESS(D, d.height_, d.width_, ldd, offset.dCol_,
+                           offset.dRow_);
 
   CHECK_LE(dimM + offset.aRow_, this->height_);
   CHECK_LE(dimN + offset.aCol_, this->width_);
@@ -269,29 +250,22 @@ int BaseMatrixT<T>::applyQuaternary(Op op,
   CHECK_LE(dimM + offset.dRow_, d.height_);
   CHECK_LE(dimN + offset.dCol_, d.width_);
   if (true == useGpu_) {
-    hl_gpu_apply_quaternary_op(op, A, B, C, D, dimM, dimN, lda, ldb, ldc, ldd);
+    hl_gpu_apply_quaternary_op(op, A, B, C, D, dimM, dimN, lda, ldb,
+                               ldc, ldd);
   } else {
-    hl_cpu_apply_quaternary_op(op, A, B, C, D, dimM, dimN, lda, ldb, ldc, ldd);
+    hl_cpu_apply_quaternary_op(op, A, B, C, D, dimM, dimN, lda, ldb,
+                               ldc, ldd);
   }
 
   return 0;
 }
 
-template <class T>
-template <class Agg,
-          class Op,
-          class Saver,
-          class aAsRowVector,
+template<class T>
+template <class Agg, class Op, class Saver, class aAsRowVector,
           class aAsColVector>
-int BaseMatrixT<T>::aggregate(Agg agg,
-                              Op op,
-                              Saver sv,
-                              BaseMatrixT& b,
-                              int numRows,
-                              int numCols,
-                              MatrixOffset& offset,
-                              aAsRowVector,
-                              aAsColVector) {
+int BaseMatrixT<T>::aggregate(Agg agg, Op op, Saver sv, BaseMatrixT& b,
+                              int numRows, int numCols, MatrixOffset& offset,
+                              aAsRowVector, aAsColVector) {
   CHECK_EQ(useGpu_, b.useGpu_);
 
   int ld = stride_;
@@ -299,10 +273,10 @@ int BaseMatrixT<T>::aggregate(Agg agg,
 
   T* dst = data_;
   T* B = b.data_;
-  CAL_MATRIX_START_ADDRESS(
-      dst, height_, width_, ld, offset.aCol_, offset.aRow_);
-  CAL_MATRIX_START_ADDRESS(
-      B, b.height_, b.width_, ldb, offset.bCol_, offset.bRow_);
+  CAL_MATRIX_START_ADDRESS(dst, height_, width_, ld, offset.aCol_,
+                           offset.aRow_);
+  CAL_MATRIX_START_ADDRESS(B, b.height_, b.width_, ldb, offset.bCol_,
+                           offset.bRow_);
 
   if (aAsRowVector::value && !aAsColVector::value) {
     if (useGpu_) {
@@ -323,21 +297,12 @@ int BaseMatrixT<T>::aggregate(Agg agg,
   return 0;
 }
 
-template <class T>
-template <class Agg,
-          class Op,
-          class Saver,
-          class aAsRowVector,
+template<class T>
+template <class Agg, class Op, class Saver, class aAsRowVector,
           class aAsColVector>
-int BaseMatrixT<T>::aggregate(Agg agg,
-                              Op op,
-                              Saver sv,
-                              BaseMatrixT& b,
-                              BaseMatrixT& c,
-                              int numRows,
-                              int numCols,
-                              MatrixOffset& offset,
-                              aAsRowVector,
+int BaseMatrixT<T>::aggregate(Agg agg, Op op, Saver sv, BaseMatrixT& b,
+                              BaseMatrixT& c, int numRows, int numCols,
+                              MatrixOffset& offset, aAsRowVector,
                               aAsColVector) {
   CHECK_EQ(useGpu_, b.useGpu_);
   CHECK_EQ(useGpu_, c.useGpu_);
@@ -349,28 +314,28 @@ int BaseMatrixT<T>::aggregate(Agg agg,
   T* dst = data_;
   T* B = b.data_;
   T* C = c.data_;
-  CAL_MATRIX_START_ADDRESS(
-      dst, height_, width_, ld, offset.aCol_, offset.aRow_);
-  CAL_MATRIX_START_ADDRESS(
-      B, b.height_, b.width_, ldb, offset.bCol_, offset.bRow_);
-  CAL_MATRIX_START_ADDRESS(
-      C, c.height_, c.width_, ldc, offset.cCol_, offset.cRow_);
+  CAL_MATRIX_START_ADDRESS(dst, height_, width_, ld, offset.aCol_,
+                           offset.aRow_);
+  CAL_MATRIX_START_ADDRESS(B, b.height_, b.width_, ldb, offset.bCol_,
+                           offset.bRow_);
+  CAL_MATRIX_START_ADDRESS(C, c.height_, c.width_, ldc, offset.cCol_,
+                           offset.cRow_);
 
   if (aAsRowVector::value && !aAsColVector::value) {
     if (useGpu_) {
-      hl_gpu_matrix_column_op(
-          agg, op, sv, numRows, numCols, dst, B, ldb, C, ldc);
+      hl_gpu_matrix_column_op(agg, op, sv, numRows, numCols, dst, B,
+                              ldb, C, ldc);
     } else {
-      hl_cpu_matrix_column_op(
-          agg, op, sv, numRows, numCols, dst, B, ldb, C, ldc);
+      hl_cpu_matrix_column_op(agg, op, sv, numRows, numCols, dst, B,
+                              ldb, C, ldc);
     }
   } else if (!aAsRowVector::value && aAsColVector::value) {
     if (useGpu_) {
-      hl_gpu_matrix_row_op(
-          agg, op, sv, numRows, numCols, dst, ld, B, ldb, C, ldc);
+      hl_gpu_matrix_row_op(agg, op, sv, numRows, numCols, dst, ld, B,
+                           ldb, C, ldc);
     } else {
-      hl_cpu_matrix_row_op(
-          agg, op, sv, numRows, numCols, dst, ld, B, ldb, C, ldc);
+      hl_cpu_matrix_row_op(agg, op, sv, numRows, numCols, dst, ld, B,
+                           ldb, C, ldc);
     }
   } else {
     LOG(FATAL) << "not supported";
@@ -385,19 +350,15 @@ int BaseMatrixT<T>::aggregate(Agg agg,
  */
 
 DEFINE_MATRIX_UNARY_OP(Neg, a = -a);
-template <class T>
-void BaseMatrixT<T>::neg() {
-  applyUnary(unary::Neg<T>());
-}
+template<class T>
+void BaseMatrixT<T>::neg() { applyUnary(unary::Neg<T>()); }
 
 DEFINE_MATRIX_UNARY_OP(Exp, a = exp(a));
-template <>
-void BaseMatrixT<real>::exp2() {
-  applyUnary(unary::Exp<real>());
-}
+template<>
+void BaseMatrixT<real>::exp2() { applyUnary(unary::Exp<real>()); }
 
 DEFINE_MATRIX_UNARY_OP(Log, a = log(a));
-template <>
+template<>
 void BaseMatrixT<real>::log2() {
   if (useGpu_) {
     applyUnary(unary::Log<real>());
@@ -407,42 +368,30 @@ void BaseMatrixT<real>::log2() {
 }
 
 DEFINE_MATRIX_UNARY_OP(Sqrt, a = sqrt(a));
-template <>
-void BaseMatrixT<real>::sqrt2() {
-  applyUnary(unary::Sqrt<real>());
-}
+template<>
+void BaseMatrixT<real>::sqrt2() { applyUnary(unary::Sqrt<real>()); }
 
 DEFINE_MATRIX_UNARY_OP(Square, a = a * a);
-template <class T>
-void BaseMatrixT<T>::square2() {
-  applyUnary(unary::Square<T>());
-}
+template<class T>
+void BaseMatrixT<T>::square2() { applyUnary(unary::Square<T>()); }
 
 DEFINE_MATRIX_UNARY_OP(Reciprocal, a = 1.0f / a);
-template <class T>
-void BaseMatrixT<T>::reciprocal2() {
-  applyUnary(unary::Reciprocal<T>());
-}
+template<class T>
+void BaseMatrixT<T>::reciprocal2() { applyUnary(unary::Reciprocal<T>()); }
 
 DEFINE_MATRIX_UNARY_OP(Abs, a = a > 0 ? a : -a);
-template <class T>
-void BaseMatrixT<T>::abs2() {
-  applyUnary(unary::Abs<T>());
-}
+template<class T>
+void BaseMatrixT<T>::abs2() { applyUnary(unary::Abs<T>()); }
 
 DEFINE_MATRIX_UNARY_OP(Sign, a = (a > 0) - (a < 0));
-template <class T>
-void BaseMatrixT<T>::sign2() {
-  applyUnary(unary::Sign<T>());
-}
+template<class T>
+void BaseMatrixT<T>::sign2() { applyUnary(unary::Sign<T>()); }
 
 DEFINE_MATRIX_UNARY_OP(Zero, a = 0);
-template <class T>
-void BaseMatrixT<T>::zero() {
-  applyUnary(unary::Zero<T>());
-}
+template<class T>
+void BaseMatrixT<T>::zero() { applyUnary(unary::Zero<T>()); }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::zeroAtOffset(int64_t columnOffset, int64_t numColumns) {
   int numRows = height_;
   int numCols = numColumns;
@@ -451,13 +400,11 @@ void BaseMatrixT<T>::zeroAtOffset(int64_t columnOffset, int64_t numColumns) {
 }
 
 DEFINE_MATRIX_UNARY_OP(One, a = 1);
-template <class T>
-void BaseMatrixT<T>::one() {
-  applyUnary(unary::One<T>());
-}
+template<class T>
+void BaseMatrixT<T>::one() { applyUnary(unary::One<T>()); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(Pow, ONE_PARAMETER, a = pow(a, p));
-template <>
+template<>
 void BaseMatrixT<real>::pow2(real p) {
   if (useGpu_) {
     applyUnary(unary::Pow<real>(p));
@@ -467,67 +414,51 @@ void BaseMatrixT<real>::pow2(real p) {
 }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(SubScalar, ONE_PARAMETER, a -= p);
-template <class T>
-void BaseMatrixT<T>::subScalar(T p) {
-  applyUnary(unary::SubScalar<T>(p));
-}
+template<class T>
+void BaseMatrixT<T>::subScalar(T p) { applyUnary(unary::SubScalar<T>(p)); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(MulScalar, ONE_PARAMETER, a *= p);
-template <class T>
-void BaseMatrixT<T>::mulScalar(T p) {
-  applyUnary(unary::MulScalar<T>(p));
-}
+template<class T>
+void BaseMatrixT<T>::mulScalar(T p) { applyUnary(unary::MulScalar<T>(p)); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(DivScalar, ONE_PARAMETER, a /= p);
-template <class T>
-void BaseMatrixT<T>::divScalar(T p) {
-  applyUnary(unary::DivScalar<T>(p));
-}
+template<class T>
+void BaseMatrixT<T>::divScalar(T p) { applyUnary(unary::DivScalar<T>(p)); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(Assign, ONE_PARAMETER, a = p);
-template <class T>
-void BaseMatrixT<T>::assign(T p) {
-  applyUnary(unary::Assign<T>(p));
-}
+template<class T>
+void BaseMatrixT<T>::assign(T p) { applyUnary(unary::Assign<T>(p)); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(Add, ONE_PARAMETER, a += p);
-template <class T>
-void BaseMatrixT<T>::add(T p) {
-  applyUnary(unary::Add<T>(p));
-}
+template<class T>
+void BaseMatrixT<T>::add(T p) { applyUnary(unary::Add<T>(p)); }
 
 DEFINE_MATRIX_UNARY_PARAMETER_OP(Add2, TWO_PARAMETER, a = a * p1 + p2);
-template <class T>
-void BaseMatrixT<T>::add(T p1, T p2) {
-  applyUnary(unary::Add2<T>(p1, p2));
-}
+template<class T>
+void BaseMatrixT<T>::add(T p1, T p2) { applyUnary(unary::Add2<T>(p1, p2)); }
 
-DEFINE_MATRIX_UNARY_PARAMETER_OP(Clip,
-                                 TWO_PARAMETER,
+DEFINE_MATRIX_UNARY_PARAMETER_OP(Clip, TWO_PARAMETER,
                                  a = a < p1 ? p1 : (a > p2 ? p2 : a));
-template <class T>
-void BaseMatrixT<T>::clip(T p1, T p2) {
-  applyUnary(unary::Clip<T>(p1, p2));
-}
+template<class T>
+void BaseMatrixT<T>::clip(T p1, T p2) { applyUnary(unary::Clip<T>(p1, p2)); }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(ClipDerivative,
-                                  TWO_PARAMETER,
-                                  a = b < p1 ? 0 : (b > p2 ? 0 : 1));
-template <class T>
+DEFINE_MATRIX_BINARY_PARAMETER_OP(ClipDerivative, TWO_PARAMETER,
+    a = b < p1 ? 0 : (b > p2 ? 0 : 1));
+template<class T>
 void BaseMatrixT<T>::clipDerivative(BaseMatrixT& b, T p1, T p2) {
   applyBinary(binary::ClipDerivative<T>(p1, p2), b);
 }
 
-DEFINE_MATRIX_UNARY_PARAMETER_OP(BiggerThanScalar,
-                                 ONE_PARAMETER,
+DEFINE_MATRIX_UNARY_PARAMETER_OP(BiggerThanScalar, ONE_PARAMETER,
                                  a = a > p ? 1.0f : 0.0f);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::biggerThanScalar(T p) {
   applyUnary(unary::BiggerThanScalar<T>(p));
 }
 
-DEFINE_MATRIX_UNARY_PARAMETER_OP(DownClip, ONE_PARAMETER, a = a > p ? a : p);
-template <class T>
+DEFINE_MATRIX_UNARY_PARAMETER_OP(DownClip, ONE_PARAMETER,
+                                 a = a > p ? a : p);
+template<class T>
 void BaseMatrixT<T>::downClip(T p) {
   applyUnary(unary::DownClip<T>(p));
 }
@@ -538,12 +469,12 @@ void BaseMatrixT<T>::downClip(T p) {
  */
 
 DEFINE_MATRIX_BINARY_OP(Add, a += b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add(BaseMatrixT& b) {
   applyBinary(binary::Add<T>(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::add(BaseMatrixT& b) {
   if (useGpu_) {
     applyBinary(binary::Add<real>(), b);
@@ -554,7 +485,7 @@ void BaseMatrixT<real>::add(BaseMatrixT& b) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addAtOffset(BaseMatrixT& b, int64_t columnOffset) {
   if (columnOffset + b.width_ <= width_) {
     int numRows = height_;
@@ -573,53 +504,43 @@ void BaseMatrixT<T>::addAtOffset(BaseMatrixT& b, int64_t columnOffset) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addP2P(BaseMatrixT& b) {
   T* A = data_;
   T* B = b.data_;
   int dimM = height_;
   int dimN = width_;
 
-  hl_gpu_apply_binary_op<T, binary::Add<T>, 0, 0>(
-      binary::Add<T>(), A, B, dimM, dimN, dimN, dimN);
+  hl_gpu_apply_binary_op<T, binary::Add<T>, 0, 0>
+    (binary::Add<T>(), A, B, dimM, dimN, dimN, dimN);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addColVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::Add<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              false_type(),
+  applyBinary(binary::Add<T>(), b, numRows, numCols, offset, false_type(),
               true_type() /* bAsColVector */);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addRowVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::Add<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              true_type() /* bAsRowVector */,
-              false_type());
+  applyBinary(binary::Add<T>(), b, numRows, numCols, offset,
+              true_type() /* bAsRowVector */, false_type());
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(Add1, ONE_PARAMETER, a += b * p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add(BaseMatrixT& b, T p) {
   applyBinary(binary::Add1<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(Pow, ONE_PARAMETER, a = pow(b, p));
-template <>
+template<>
 void BaseMatrixT<real>::pow2(BaseMatrixT& b, real p) {
   if (useGpu_) {
     applyBinary(binary::Pow<real>(p), b);
@@ -629,45 +550,36 @@ void BaseMatrixT<real>::pow2(BaseMatrixT& b, real p) {
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(Add2, TWO_PARAMETER, a = p1 * a + p2 * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add(BaseMatrixT& b, T p1, T p2) {
   applyBinary(binary::Add2<T>(p1, p2), b);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addBias(BaseMatrixT& b, T scale) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::Add1<T>(scale),
-              b,
-              numRows,
-              numCols,
-              offset,
-              true_type() /* bAsRowVector */,
-              false_type());
+  applyBinary(binary::Add1<T>(scale), b, numRows, numCols, offset,
+              true_type() /* bAsRowVector */, false_type());
 }
 
 DEFINE_MATRIX_BINARY_OP(Sub, a -= b);
-template <class T>
-void BaseMatrixT<T>::sub(BaseMatrixT& b) {
-  applyBinary(binary::Sub<T>(), b);
-}
+template<class T>
+void BaseMatrixT<T>::sub(BaseMatrixT& b) { applyBinary(binary::Sub<T>(), b); }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(Sub1, ONE_PARAMETER, a -= b * p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sub(BaseMatrixT& b, T p) {
   applyBinary(binary::Sub1<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Relu, b = a > 0.0f ? a : 0.0f);
-template <class T>
-void BaseMatrixT<T>::relu(BaseMatrixT& b) {
-  applyBinary(binary::Relu<T>(), b);
-}
+template<class T>
+void BaseMatrixT<T>::relu(BaseMatrixT& b) { applyBinary(binary::Relu<T>(), b); }
 
 DEFINE_MATRIX_BINARY_OP(ReluDerivative, a *= (b > 0.0f ? 1.0f : 0.0f));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::reluDerivative(BaseMatrixT& b) {
   applyBinary(binary::ReluDerivative<T>(), b);
 }
@@ -677,7 +589,7 @@ DEFINE_MATRIX_BINARY_OP(Softrelu, const T THRESHOLD = 40.0;
                                               ? THRESHOLD
                                               : ((a < -THRESHOLD) ? (-THRESHOLD)
                                                                   : a))));
-template <>
+template<>
 void BaseMatrixT<real>::softrelu(BaseMatrixT& b) {
   applyBinary(binary::Softrelu<real>(), b);
 }
@@ -687,100 +599,97 @@ DEFINE_MATRIX_BINARY_OP(
     a *= (1.0 - exp(-1.0 * ((b > THRESHOLD)
                                 ? THRESHOLD
                                 : ((b < -THRESHOLD) ? (-THRESHOLD) : b)))));
-template <>
+template<>
 void BaseMatrixT<real>::softreluDerivative(BaseMatrixT& b) {
   applyBinary(binary::SoftreluDerivative<real>(), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(Brelu, TWO_PARAMETER, b = a > p1 ? a : p1;
                                   b = b < p2 ? b : p2);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::brelu(BaseMatrixT& b) {
-  int p1 = 0, p2 = 24;  //! TODO(yuyang18): Make p1,p2 configuable.
+  int p1 = 0, p2 = 24;    //! TODO(yuyang18): Make p1,p2 configuable.
   applyBinary(binary::Brelu<T>(p1, p2), b);
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(BreluDerivative,
-                                  TWO_PARAMETER,
+DEFINE_MATRIX_BINARY_PARAMETER_OP(BreluDerivative, TWO_PARAMETER,
                                   a *= (b > p1 && b < p2) ? 1.0 : 0.0);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::breluDerivative(BaseMatrixT& b) {
   int p1 = 0, p2 = 24;
   applyBinary(binary::BreluDerivative<T>(p1, p2), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Square, b = a * a);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::square2(BaseMatrixT& b) {
   applyBinary(binary::Square<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(SquareDerivative, a *= 2.0 * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::squareDerivative(BaseMatrixT& b) {
   applyBinary(binary::SquareDerivative<T>(), b);
 }
 
-DEFINE_MATRIX_BINARY_OP(Tanh, T tmp = -2.0 * a;
-                        tmp = (tmp > EXP_MAX_INPUT) ? EXP_MAX_INPUT : tmp;
-                        b = 2.0 / (1.0 + std::exp(tmp)) - 1.0);
-template <>
+DEFINE_MATRIX_BINARY_OP(Tanh,
+    T tmp = -2.0 * a;
+    tmp = (tmp > EXP_MAX_INPUT) ? EXP_MAX_INPUT : tmp;
+    b = 2.0 / (1.0 + std::exp(tmp)) - 1.0);
+template<>
 void BaseMatrixT<real>::tanh(BaseMatrixT& b) {
   applyBinary(binary::Tanh<real>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(TanhDerivative, a *= 1 - b * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::tanhDerivative(BaseMatrixT& b) {
   applyBinary(binary::TanhDerivative<T>(), b);
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(
-    ScaledTanh, TWO_PARAMETER, b = p1 * (2.0 / (1.0 + exp(-2 * p2 * a)) - 1.0));
-template <>
+DEFINE_MATRIX_BINARY_PARAMETER_OP(ScaledTanh, TWO_PARAMETER,
+                                  b = p1 *
+                                      (2.0 / (1.0 + exp(-2 * p2 * a)) - 1.0));
+template<>
 void BaseMatrixT<real>::scaledTanh(BaseMatrixT& b, real p1, real p2) {
   applyBinary(binary::ScaledTanh<real>(p1, p2), b);
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(ScaledTanhDerivative,
-                                  TWO_PARAMETER,
+DEFINE_MATRIX_BINARY_PARAMETER_OP(ScaledTanhDerivative, TWO_PARAMETER,
                                   a *= p2 * (p1 - b * b));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::scaledTanhDerivative(BaseMatrixT& b, T p1, T p2) {
   applyBinary(binary::ScaledTanhDerivative<T>(p1 * p1, p2 / p1), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Reciprocal, b = 1.0f / a);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::reciprocal2(BaseMatrixT& b) {
   applyBinary(binary::Reciprocal<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(ReciprocalDerivative, a *= -b * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::reciprocalDerivative(BaseMatrixT& b) {
   applyBinary(binary::ReciprocalDerivative<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Abs, b = a > 0.0f ? a : -a);
-template <class T>
-void BaseMatrixT<T>::abs2(BaseMatrixT& b) {
-  applyBinary(binary::Abs<T>(), b);
-}
+template<class T>
+void BaseMatrixT<T>::abs2(BaseMatrixT& b) { applyBinary(binary::Abs<T>(), b); }
 
 DEFINE_MATRIX_BINARY_OP(AbsDerivative, a = (b > 0) ? a : (b < 0) ? -a : 0);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::absDerivative(BaseMatrixT& b) {
   applyBinary(binary::AbsDerivative<T>(), b);
 }
 
-DEFINE_MATRIX_BINARY_OP(Sigmoid, const T THRESHOLD_MIN = -40.0;
-                        const T THRESHOLD_MAX = 13.0;
-                        T tmp = (a < THRESHOLD_MIN)
-                                    ? THRESHOLD_MIN
-                                    : ((a > THRESHOLD_MAX) ? THRESHOLD_MAX : a);
-                        b = 1.0f / (1.0f + exp(-tmp)));
-template <>
+DEFINE_MATRIX_BINARY_OP(
+    Sigmoid, const T THRESHOLD_MIN = -40.0; const T THRESHOLD_MAX = 13.0;
+    T tmp = (a < THRESHOLD_MIN) ? THRESHOLD_MIN
+                                   : ((a > THRESHOLD_MAX) ? THRESHOLD_MAX : a);
+    b = 1.0f / (1.0f + exp(-tmp)));
+template<>
 void BaseMatrixT<real>::sigmoid(BaseMatrixT& b) {
   if (useGpu_) {
     applyBinary(binary::Sigmoid<real>(), b);
@@ -814,31 +723,31 @@ void BaseMatrixT<real>::sigmoid(BaseMatrixT& b) {
 }
 
 DEFINE_MATRIX_BINARY_OP(SigmoidDerivative, a *= b * (1 - b));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sigmoidDerivative(BaseMatrixT& b) {
   applyBinary(binary::SigmoidDerivative<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(ExpDerivative, a *= b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::expDerivative(BaseMatrixT& b) {
   applyBinary(binary::ExpDerivative<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Sign, b = a > 0.0f ? 1.0f : -1.0f);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sign2(BaseMatrixT& b) {
   applyBinary(binary::Sign<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Exp, a = exp(b));
-template <>
+template<>
 void BaseMatrixT<real>::exp2(BaseMatrixT& b) {
   applyBinary(binary::Exp<real>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(Log, a = log(b));
-template <>
+template<>
 void BaseMatrixT<real>::log2(BaseMatrixT& b) {
   if (useGpu_) {
     applyBinary(binary::Log<real>(), b);
@@ -848,13 +757,13 @@ void BaseMatrixT<real>::log2(BaseMatrixT& b) {
 }
 
 DEFINE_MATRIX_BINARY_OP(Sqrt, a = sqrt(b));
-template <>
+template<>
 void BaseMatrixT<real>::sqrt2(BaseMatrixT& b) {
   applyBinary(binary::Sqrt<real>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(InvSqrt, a = 1.0f / sqrt(b));
-template <>
+template<>
 void BaseMatrixT<real>::invSqrt(BaseMatrixT& b) {
   if (useGpu_) {
     applyBinary(binary::InvSqrt<real>(), b);
@@ -866,37 +775,37 @@ void BaseMatrixT<real>::invSqrt(BaseMatrixT& b) {
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(IsEqual, ONE_PARAMETER, a = (b == p));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::isEqualTo(BaseMatrixT& b, T value) {
   applyBinary(binary::IsEqual<T>(value), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(AddScalar, ONE_PARAMETER, a = b + p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addScalar(BaseMatrixT& b, T p) {
   applyBinary(binary::AddScalar<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(SubScalar, ONE_PARAMETER, a = b - p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::subScalar(BaseMatrixT& b, T p) {
   applyBinary(binary::SubScalar<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(MulScalar, ONE_PARAMETER, a = b * p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::mulScalar(BaseMatrixT& b, T p) {
   applyBinary(binary::MulScalar<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(DivScalar, ONE_PARAMETER, a = b / p);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::divScalar(BaseMatrixT& b, T p) {
   applyBinary(binary::DivScalar<T>(p), b);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(ScalarDiv, ONE_PARAMETER, a = p / b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::scalarDiv(BaseMatrixT& b, T p) {
   applyBinary(binary::ScalarDiv<T>(p), b);
 }
@@ -908,20 +817,20 @@ void BaseMatrixT<T>::scalarDiv(BaseMatrixT& b, T p) {
 
 DEFINE_MATRIX_TERNARY_OP(SoftCrossEntropy,
                          a = -c * log(b) - (1 - c) * log(1 - b));
-template <>
+template<>
 void BaseMatrixT<real>::softCrossEntropy(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::SoftCrossEntropy<real>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(SoftCrossEntropyBp, a += (b - c) / (b * (1 - b)));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::softCrossEntropyBp(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::SoftCrossEntropyBp<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(BinaryCrossEntropy,
                          a = c > 0.5 ? -log(b) : -log(1.0 - b));
-template <>
+template<>
 void BaseMatrixT<real>::binaryLabelCrossEntropy(BaseMatrixT& b,
                                                 BaseMatrixT& c) {
   if (useGpu_) {
@@ -949,73 +858,70 @@ void BaseMatrixT<real>::binaryLabelCrossEntropy(BaseMatrixT& b,
 
 DEFINE_MATRIX_TERNARY_OP(BinaryCrossEntropyBp,
                          a += c > 0.5 ? -1.0 / b : 1.0 / (1.0 - b));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::binaryLabelCrossEntropyBp(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::BinaryCrossEntropyBp<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(Add, a = b + c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::Add<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_PARAMETER_OP(Add1, TWO_PARAMETER, a = p1 * b + p2 * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add(BaseMatrixT& b, T p1, BaseMatrixT& c, T p2) {
   applyTernary(ternary::Add1<T>(p1, p2), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(Sub, a = b - c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sub(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::Sub<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_PARAMETER_OP(Sub1, TWO_PARAMETER, a = p1 * b - p2 * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sub(BaseMatrixT& b, T p1, BaseMatrixT& c, T p2) {
   applyTernary(ternary::Sub1<T>(p1, p2), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(Add2, a = a + b + c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add2(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::Add2<T>(), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(Add3,
-                                   THREE_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(Add3, THREE_PARAMETER,
                                    a = p1 * a + p2 * b + p3 * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::add2(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2, T p3) {
   applyTernary(ternary::Add3<T>(p1, p2, p3), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(SgdUpdate,
-                                   THREE_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(SgdUpdate, THREE_PARAMETER,
                                    c = p2 * c - p1 * (b + p3 * a);
                                    a = a + c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sgdUpdate(BaseMatrixT& b,  // grad
                                BaseMatrixT& c,  // mom
-                               T p1,            // learningRate,
-                               T p2,            // momentum,
-                               T p3) {          // decayRate
+                               T p1,        // learningRate,
+                               T p2,        // momentum,
+                               T p3) {      // decayRate
   applyTernary(ternary::SgdUpdate<T>(p1, p2, p3), b, c);
 }
 
-DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(SgdUpdate,
-                                      THREE_PARAMETER,
+DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(SgdUpdate, THREE_PARAMETER,
                                       c = p2 * c - p1 * d * (b + p3 * a);
                                       a += c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::sgdUpdate(BaseMatrixT& b,  // grad,
                                BaseMatrixT& c,  // mom,
                                BaseMatrixT& d,  // lr,
-                               T p1,            // learningRate,
-                               T p2,            // momentum,
-                               T p3) {          // decayRate
+                               T p1,        // learningRate,
+                               T p2,        // momentum,
+                               T p3) {      // decayRate
   applyQuaternary(quaternary::SgdUpdate<T>(p1, p2, p3), b, c, d);
 }
 
@@ -1023,22 +929,19 @@ DEFINE_MATRIX_BINARY_PARAMETER_OP(ApplyL1, ONE_PARAMETER, T lambda = p * b;
                                   a = (a > lambda)
                                           ? (a - lambda)
                                           : (a < -lambda) ? (a + lambda) : 0);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::applyL1(BaseMatrixT& lr, T learningRate, T decayRate) {
   applyBinary(binary::ApplyL1<T>(learningRate * decayRate), lr);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::applyL1(BaseMatrixT& lr,
                                 real learningRate,
                                 real decayRate) {
   if (useGpu_) {
     applyBinary(binary::ApplyL1<real>(learningRate * decayRate), lr);
   } else {
-    simd::decayL1(this->data_,
-                  this->data_,
-                  lr.data_,
-                  learningRate * decayRate,
+    simd::decayL1(this->data_, this->data_, lr.data_, learningRate * decayRate,
                   height_ * width_);
   }
 }
@@ -1047,25 +950,24 @@ DEFINE_MATRIX_UNARY_PARAMETER_OP(ApplyL1, ONE_PARAMETER, T lambda = p;
                                  a = (a > lambda)
                                          ? (a - lambda)
                                          : (a < -lambda) ? (a + lambda) : 0);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::applyL1(T learningRate, T decayRate) {
   applyUnary(unary::ApplyL1<T>(learningRate * decayRate));
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::applyL1(real learningRate, real decayRate) {
   if (useGpu_) {
     applyUnary(unary::ApplyL1<real>(learningRate * decayRate));
   } else {
-    simd::decayL1(
-        this->data_, this->data_, learningRate * decayRate, height_ * width_);
+    simd::decayL1(this->data_, this->data_, learningRate * decayRate,
+                  height_ * width_);
   }
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(ApplyL2,
-                                  ONE_PARAMETER,
+DEFINE_MATRIX_BINARY_PARAMETER_OP(ApplyL2, ONE_PARAMETER,
                                   a *= (1.0f / (1.0f + p * b)));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::applyL2(BaseMatrixT& lr, T learningRate, T decayRate) {
   if (useGpu_) {
     applyBinary(binary::ApplyL2<T>(learningRate * decayRate), lr);
@@ -1078,33 +980,32 @@ void BaseMatrixT<T>::applyL2(BaseMatrixT& lr, T learningRate, T decayRate) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::applyL2(T learningRate, T decayRate) {
   BaseMatrixT<T>::mulScalar(1.0f / (1.0f + learningRate * decayRate));
 }
 
 DEFINE_MATRIX_BINARY_OP(DotMul, a *= b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotMul(BaseMatrixT& b) {
   applyBinary(binary::DotMul<T>(), b);
 }
 
 DEFINE_MATRIX_TERNARY_OP(DotMul, a = b * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotMul(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::DotMul<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(DotDiv, a = (b == 0.0) ? 0.0 : b / c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotDiv(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::DotDiv<T>(), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotDiv2P,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotDiv2P, TWO_PARAMETER,
                                    a = (b + p1) / (c + p2));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotDiv(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2) {
   applyTernary(ternary::DotDiv2P<T>(p1, p2), b, c);
 }
@@ -1114,7 +1015,7 @@ DEFINE_MATRIX_QUATERNARY_OP(RankLoss, const T THRESHOLD = 40.0; a = b - c;
                                     ? THRESHOLD
                                     : ((a < -THRESHOLD) ? (-THRESHOLD) : a);
                             a = log(1 + exp(a)) - a * d);
-template <>
+template<>
 void BaseMatrixT<real>::rankLoss(BaseMatrixT& b,
                                  BaseMatrixT& c,
                                  BaseMatrixT& d) {
@@ -1125,9 +1026,8 @@ DEFINE_MATRIX_QUATERNARY_OP(RankLossBp, const T THRESHOLD = 40.0; a = b - c;
                             a = (a > THRESHOLD)
                                     ? THRESHOLD
                                     : ((a < -THRESHOLD) ? (-THRESHOLD) : a);
-                            a = exp(a);
-                            a = (a / (1 + a) - d));
-template <>
+                            a = exp(a); a = (a / (1 + a) - d));
+template<>
 void BaseMatrixT<real>::rankLossBp(BaseMatrixT& b,
                                    BaseMatrixT& c,
                                    BaseMatrixT& d) {
@@ -1140,7 +1040,7 @@ DEFINE_MATRIX_TERNARY_OP(LogisticRegressionLoss, const T THRESHOLD = 40.0;
                                                                  ? -THRESHOLD
                                                                  : b;
                          a = log(1 + exp(x)) - c * x);
-template <>
+template<>
 void BaseMatrixT<real>::logisticRegressionLoss(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::LogisticRegressionLoss<real>(), b, c);
 }
@@ -1150,23 +1050,22 @@ DEFINE_MATRIX_TERNARY_OP(LogisticRegressionLossBp, const T THRESHOLD = 40.0;
                          T x = (b > THRESHOLD) ? THRESHOLD : (b < -THRESHOLD)
                                                                  ? -THRESHOLD
                                                                  : b;
-                         x = exp(x);
-                         a = x / (1 + x) - c);
-template <>
+                         x = exp(x); a = x / (1 + x) - c);
+template<>
 void BaseMatrixT<real>::logisticRegressionLossBp(BaseMatrixT& b,
                                                  BaseMatrixT& c) {
   applyTernary(ternary::LogisticRegressionLossBp<real>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(BiggerThan, a = (b > c) ? 1.0f : 0.0f);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::biggerThan(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::BiggerThan<T>(), b, c);
 }
 
 DEFINE_MATRIX_QUATERNARY_OP(
     BiggerThan, a = ((b > c && d > 0.5f) || (b < c && d < 0.5f)) ? 1.0f : 0.0f);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::biggerThan(BaseMatrixT& b,
                                 BaseMatrixT& c,
                                 BaseMatrixT& d) {
@@ -1174,34 +1073,25 @@ void BaseMatrixT<T>::biggerThan(BaseMatrixT& b,
 }
 
 DEFINE_MATRIX_TERNARY_OP(Max, a = (b > c) ? b : c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::max2(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::Max<T>(), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(BinaryClassificationError,
-                                   ONE_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(BinaryClassificationError, ONE_PARAMETER,
                                    c += ((a > p) == (b > p)) ? 0.0f : 1.0f);
-template <class T>
-void BaseMatrixT<T>::binaryClassificationError2(size_t destCol,
-                                                BaseMatrixT& b,
-                                                BaseMatrixT& c,
-                                                T p) {
+template<class T>
+void BaseMatrixT<T>::binaryClassificationError2(size_t destCol, BaseMatrixT& b,
+                                                BaseMatrixT& c, T p) {
   CHECK(!useGpu_) << "do not support gpu";
   MatrixOffset offset(0, 0, 0, 0, destCol, 0);
   int numRows = b.height_;
   int numCols = b.width_;
-  b.applyTernary(ternary::BinaryClassificationError<T>(p),
-                 c,
-                 *this,
-                 numRows,
-                 numCols,
-                 offset,
-                 false_type(),
-                 true_type() /*cAsColVector*/);
+  b.applyTernary(ternary::BinaryClassificationError<T>(p), c, *this, numRows,
+                 numCols, offset, false_type(), true_type() /*cAsColVector*/);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::binaryClassificationError(size_t destCol,
                                                   BaseMatrixT& b,
                                                   BaseMatrixT& c,
@@ -1209,148 +1099,127 @@ void BaseMatrixT<real>::binaryClassificationError(size_t destCol,
   MatrixOffset offset(destCol, 0, 0, 0, 0, 0);
   int numRows = b.height_;
   int numCols = b.width_;
-  aggregate(aggregate::sum(),
-            base::binary::classificationError(p),
-            base::binary::add(),
-            b,
-            c,
-            numRows,
-            numCols,
-            offset,
-            false_type(),
+  aggregate(aggregate::sum(), base::binary::classificationError(p),
+            base::binary::add(), b, c, numRows, numCols, offset, false_type(),
             true_type() /*aAsColVector*/);
 }
 
-DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(Add3,
-                                      THREE_PARAMETER,
+DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(Add3, THREE_PARAMETER,
                                       a = p1 * b + p2 * c + p3 * d);
-template <class T>
-void BaseMatrixT<T>::add3(
-    BaseMatrixT& b, BaseMatrixT& c, BaseMatrixT& d, T p1, T p2, T p3) {
+template<class T>
+void BaseMatrixT<T>::add3(BaseMatrixT& b, BaseMatrixT& c, BaseMatrixT& d, T p1,
+                          T p2, T p3) {
   applyQuaternary(quaternary::Add3<T>(p1, p2, p3), b, c, d);
 }
 
 DEFINE_MATRIX_TERNARY_OP(DotMulSquare, a = b * c * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotMulSquare(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::DotMulSquare<T>(), b, c);
 }
 
 DEFINE_MATRIX_TERNARY_OP(DotSquareSquare, a = b * b * c * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotSquareSquare(BaseMatrixT& b, BaseMatrixT& c) {
   applyTernary(ternary::DotSquareSquare<T>(), b, c);
 }
 
 DEFINE_MATRIX_BINARY_OP(DotMulSquare, a *= b * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotMulSquare(BaseMatrixT& b) {
   applyBinary(binary::DotMulSquare<T>(), b);
 }
 
 DEFINE_MATRIX_BINARY_OP(DotSquareMul, a = a * a * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotSquareMul(BaseMatrixT& b) {
   applyBinary(binary::DotSquareMul<T>(), b);
 }
 
-DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(AddSquareSum,
-                                      THREE_PARAMETER,
+DEFINE_MATRIX_QUATERNARY_PARAMETER_OP(AddSquareSum, THREE_PARAMETER,
                                       T tmp = p1 * b + p2 * c + p3 * d;
                                       a += tmp * tmp);
-template <class T>
-void BaseMatrixT<T>::addSquareSum(
-    BaseMatrixT& b, BaseMatrixT& c, BaseMatrixT d, T p1, T p2, T p3) {
+template<class T>
+void BaseMatrixT<T>::addSquareSum(BaseMatrixT& b, BaseMatrixT& c, BaseMatrixT d,
+                                  T p1, T p2, T p3) {
   applyQuaternary(quaternary::AddSquareSum<T>(p1, p2, p3), b, c, d);
 }
 
 DEFINE_MATRIX_BINARY_PARAMETER_OP(AddSquare, ONE_PARAMETER, a += p * b * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addSquare(BaseMatrixT& b, T p) {
   applyBinary(binary::AddSquare<T>(p), b);
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(DecayAddSquare,
-                                  TWO_PARAMETER,
+DEFINE_MATRIX_BINARY_PARAMETER_OP(DecayAddSquare, TWO_PARAMETER,
                                   a = p1 * a + p2 * b * b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::decayAddSquare(BaseMatrixT& b, T p1, T p2) {
   applyBinary(binary::DecayAddSquare<T>(p1, p2), b);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(DecayAddSquareMul,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(DecayAddSquareMul, TWO_PARAMETER,
                                    a = p1 * a + p2 * b * b * c * c);
-template <class T>
-void BaseMatrixT<T>::decayAddSquareMul(BaseMatrixT& b,
-                                       BaseMatrixT& c,
-                                       T p1,
+template<class T>
+void BaseMatrixT<T>::decayAddSquareMul(BaseMatrixT& b, BaseMatrixT& c, T p1,
                                        T p2) {
   applyTernary(ternary::DecayAddSquareMul<T>(p1, p2), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(ReciprocalSum,
-                                   THREE_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(ReciprocalSum, THREE_PARAMETER,
                                    a = 1 / (p1 * b + p2 * c + p3));
-template <class T>
-void BaseMatrixT<T>::reciprocalSum(
-    BaseMatrixT& b, BaseMatrixT& c, T p1, T p2, T p3) {
+template<class T>
+void BaseMatrixT<T>::reciprocalSum(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2,
+                                   T p3) {
   applyTernary(ternary::ReciprocalSum<T>(p1, p2, p3), b, c);
 }
 
-DEFINE_MATRIX_BINARY_PARAMETER_OP(Reciprocal2,
-                                  TWO_PARAMETER,
+DEFINE_MATRIX_BINARY_PARAMETER_OP(Reciprocal2, TWO_PARAMETER,
                                   a = 1 / (p1 * b + p2));
-template <class T>
+template<class T>
 void BaseMatrixT<T>::reciprocal2(BaseMatrixT& b, T p1, T p2) {
   applyBinary(binary::Reciprocal2<T>(p1, p2), b);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotMulSquareSum,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotMulSquareSum, TWO_PARAMETER,
                                    T tmp = p1 * b + p2 * c;
                                    a *= tmp * tmp);
-template <class T>
-void BaseMatrixT<T>::dotMulSquareSum(BaseMatrixT& b,
-                                     BaseMatrixT& c,
-                                     T p1,
+template<class T>
+void BaseMatrixT<T>::dotMulSquareSum(BaseMatrixT& b, BaseMatrixT& c, T p1,
                                      T p2) {
   applyTernary(ternary::DotMulSquareSum<T>(p1, p2), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotSquareSum,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotSquareSum, TWO_PARAMETER,
                                    T tmp = p1 * b + p2 * c;
                                    a = tmp * tmp);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotSquareSum(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2) {
   applyTernary(ternary::DotSquareSum<T>(p1, p2), b, c);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotMulSum,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(DotMulSum, TWO_PARAMETER,
                                    a *= p1 * b + p2 * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::dotMulSum(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2) {
   applyTernary(ternary::DotMulSum<T>(p1, p2), b, c);
 }
 
 DEFINE_MATRIX_BINARY_OP(CopyAndClear, b = a; a = 0);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::copyAndClear(BaseMatrixT& b) {
   applyBinary(binary::CopyAndClear<T>(), b);
 }
 
-DEFINE_MATRIX_TERNARY_PARAMETER_OP(AddDotMul,
-                                   TWO_PARAMETER,
+DEFINE_MATRIX_TERNARY_PARAMETER_OP(AddDotMul, TWO_PARAMETER,
                                    a = p1 * a + p2 * b * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addDotMul(BaseMatrixT& b, BaseMatrixT& c, T p1, T p2) {
   applyTernary(ternary::AddDotMul<T>(p1, p2), b, c);
 }
 
 DEFINE_MATRIX_BINARY_OP(Assign, a = b;);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::assign(BaseMatrixT& b) {
   if (useGpu_) {
     applyBinary(binary::Assign<T>(), b);
@@ -1361,7 +1230,7 @@ void BaseMatrixT<T>::assign(BaseMatrixT& b) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::assignAtOffset(BaseMatrixT& b, int64_t columnOffset) {
   if (columnOffset + b.width_ <= width_) {
     int numRows = height_;
@@ -1381,31 +1250,24 @@ void BaseMatrixT<T>::assignAtOffset(BaseMatrixT& b, int64_t columnOffset) {
 }
 
 DEFINE_MATRIX_BINARY_OP(DeepSwap, T tmp = a; a = b; b = tmp);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::deepSwap(BaseMatrixT& b) {
-  applyBinary(binary::DeepSwap<T>(), b);
+    applyBinary(binary::DeepSwap<T>(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::rowDotMul(size_t destCol,
                                   BaseMatrixT& b,
                                   BaseMatrixT& c) {
   int numRows = b.height_;
   int numCols = b.width_;
   MatrixOffset offset(destCol, 0, 0, 0, 0, 0);
-  aggregate(aggregate::sum(),
-            base::binary::mul(),
-            base::binary::add(),
-            b,
-            c,
-            numRows,
-            numCols,
-            offset,
-            false_type(),
+  aggregate(aggregate::sum(), base::binary::mul(), base::binary::add(), b, c,
+            numRows, numCols, offset, false_type(),
             true_type() /*aAsColVector*/);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::rowDotMul2(size_t destCol,
                                 BaseMatrixT& b,
                                 BaseMatrixT& c) {
@@ -1428,24 +1290,17 @@ void BaseMatrixT<T>::rowDotMul2(size_t destCol,
   }
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::addDotMulVMM(BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
   int numRows = b.height_;
   int numCols = b.width_;
-  aggregate(aggregate::sum(),
-            base::binary::mul(),
-            base::binary::add(),
-            b,
-            c,
-            numRows,
-            numCols,
-            offset,
-            true_type() /*aAsRowVector*/,
+  aggregate(aggregate::sum(), base::binary::mul(), base::binary::add(), b, c,
+            numRows, numCols, offset, true_type() /*aAsRowVector*/,
             false_type());
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addDotMulVMM2(BaseMatrixT& b, BaseMatrixT& c) {
   CHECK(!useGpu_) << "do not support gpu";
 
@@ -1466,22 +1321,16 @@ void BaseMatrixT<T>::addDotMulVMM2(BaseMatrixT& b, BaseMatrixT& c) {
 }
 
 DEFINE_MATRIX_TERNARY_OP(addDotMulMMV, a += b * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addDotMulMMV(BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::addDotMulMMV<T>(),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               true_type() /*cAsRowVector*/,
-               false_type());
+  applyTernary(ternary::addDotMulMMV<T>(), b, c, numRows, numCols, offset,
+               true_type() /*cAsRowVector*/, false_type());
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addDotMulMMV2(BaseMatrixT& b, BaseMatrixT& c) {
   CHECK(!useGpu_) << "do not support gpu";
 
@@ -1501,22 +1350,16 @@ void BaseMatrixT<T>::addDotMulMMV2(BaseMatrixT& b, BaseMatrixT& c) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::rowScale(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, cCol, 0);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::DotMul<T>(),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               false_type(),
-               true_type() /*cAsColVector*/);
+  applyTernary(ternary::DotMul<T>(), b, c, numRows, numCols, offset,
+    false_type(), true_type() /*cAsColVector*/);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::rowScale2(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   CHECK(!useGpu_) << "do not support gpu";
 
@@ -1536,82 +1379,52 @@ void BaseMatrixT<T>::rowScale2(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::colScale(size_t cRow, BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, 0, cRow);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::DotMul<T>(),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               true_type() /* cAsRowVector */,
-               false_type() /* cAsColVector */);
+  applyTernary(ternary::DotMul<T>(), b, c, numRows, numCols, offset,
+               true_type() /* cAsRowVector */, false_type() /* cAsColVector */);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addColScale(size_t cRow, BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, 0, cRow);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::addDotMulMMV<T>(),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               true_type() /* cAsRowVector */,
-               false_type() /* cAsColVector */);
+  applyTernary(ternary::addDotMulMMV<T>(), b, c, numRows, numCols, offset,
+               true_type() /* cAsRowVector */, false_type() /* cAsColVector */);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::addRowScale(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, cCol, 0);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::addDotMulMMV<T>(),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               false_type(),
-               true_type() /*cAsColVector*/);
+  applyTernary(ternary::addDotMulMMV<T>(), b, c, numRows, numCols, offset,
+               false_type(), true_type() /*cAsColVector*/);
 }
 
 DEFINE_MATRIX_TERNARY_PARAMETER_OP(RowAdd, ONE_PARAMETER, a = b + p * c);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::rowAdd(size_t cCol, BaseMatrixT& b, BaseMatrixT& c, T p) {
   MatrixOffset offset(0, 0, 0, 0, cCol, 0);
   int numRows = height_;
   int numCols = width_;
-  applyTernary(ternary::RowAdd<T>(p),
-               b,
-               c,
-               numRows,
-               numCols,
-               offset,
-               false_type(),
-               true_type() /*cAsColVector*/);
+  applyTernary(ternary::RowAdd<T>(p), b, c, numRows, numCols, offset,
+    false_type(), true_type() /*cAsColVector*/);
 }
 
 DEFINE_MATRIX_TERNARY_OP(RowPow, a = pow(b, c));
-template <>
+template<>
 void BaseMatrixT<real>::rowPow(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   if (useGpu_) {
     MatrixOffset offset(0, 0, 0, 0, cCol, 0);
     int numRows = height_;
     int numCols = width_;
-    applyTernary(ternary::RowPow<real>(),
-                 b,
-                 c,
-                 numRows,
-                 numCols,
-                 offset,
-                 false_type(),
-                 true_type() /*cAsColVector*/);
+    applyTernary(ternary::RowPow<real>(), b, c, numRows, numCols, offset,
+                 false_type(), true_type() /*cAsColVector*/);
   } else {
     size_t height = this->height_;
     size_t width = this->width_;
@@ -1628,64 +1441,44 @@ void BaseMatrixT<real>::rowPow(size_t cCol, BaseMatrixT& b, BaseMatrixT& c) {
   }
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::mulRowVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::DotMul<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              true_type() /* bAsRowVector */,
-              false_type());
+  applyBinary(binary::DotMul<T>(), b, numRows, numCols, offset,
+              true_type() /* bAsRowVector */, false_type());
 }
 
 DEFINE_MATRIX_BINARY_OP(DotDiv, a /= b);
-template <class T>
+template<class T>
 void BaseMatrixT<T>::divRowVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::DotDiv<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              true_type() /* bAsRowVector */,
-              false_type());
+  applyBinary(binary::DotDiv<T>(), b, numRows, numCols, offset,
+              true_type() /* bAsRowVector */, false_type());
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::mulColVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::DotMul<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              false_type(),
-              true_type() /* bAsColVector */);
+  applyBinary(binary::DotMul<T>(), b, numRows, numCols, offset,
+              false_type(), true_type() /* bAsColVector */);
 }
 
-template <class T>
+template<class T>
 void BaseMatrixT<T>::divColVector(BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0);
   int numRows = height_;
   int numCols = width_;
-  applyBinary(binary::DotDiv<T>(),
-              b,
-              numRows,
-              numCols,
-              offset,
-              false_type(),
-              true_type() /* bAsColVector */);
+  applyBinary(binary::DotDiv<T>(), b, numRows, numCols, offset,
+              false_type(), true_type() /* bAsColVector */);
 }
 
-template <>
+template<>
 template <class Agg>
 int BaseMatrixT<real>::applyRow(Agg agg, BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
@@ -1693,20 +1486,13 @@ int BaseMatrixT<real>::applyRow(Agg agg, BaseMatrixT& b) {
   size_t numCols = b.width_;
   CHECK_EQ(height_, numRows);
   CHECK_EQ(width_, 1UL);
-  aggregate(agg,
-            base::unary::identity(),
-            base::binary::second(),
-            b,
-            numRows,
-            numCols,
-            offset,
-            false_type(),
-            true_type() /*aAsColVector*/);
+  aggregate(agg, base::unary::identity(), base::binary::second(), b, numRows,
+            numCols, offset, false_type(), true_type() /*aAsColVector*/);
 
   return 0;
 }
 
-template <>
+template<>
 template <class Agg, class Saver>
 int BaseMatrixT<real>::applyRow(Agg agg, Saver sv, BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
@@ -1714,25 +1500,16 @@ int BaseMatrixT<real>::applyRow(Agg agg, Saver sv, BaseMatrixT& b) {
   size_t numCols = b.width_;
   CHECK_EQ(height_, numRows);
   CHECK_EQ(width_, 1UL);
-  aggregate(agg,
-            base::unary::identity(),
-            sv,
-            b,
-            numRows,
-            numCols,
-            offset,
-            false_type(),
-            true_type() /*aAsColVector*/);
+  aggregate(agg, base::unary::identity(), sv, b, numRows, numCols, offset,
+            false_type(), true_type() /*aAsColVector*/);
 
   return 0;
 }
 
-template <>
+template<>
 template <class Agg>
-int BaseMatrixT<real>::applyRow(Agg agg,
-                                real scaleDest,
-                                real scaleAgg,
-                                BaseMatrixT& b) {
+int BaseMatrixT<real>::applyRow(
+     Agg agg, real scaleDest, real scaleAgg, BaseMatrixT& b) {
   if (scaleDest != 0) {
     applyRow(agg, base::binary::add2(scaleDest, scaleAgg), b);
   } else {
@@ -1744,10 +1521,10 @@ int BaseMatrixT<real>::applyRow(Agg agg,
   return 0;
 }
 
-template <>
+template<>
 template <class Agg, class Op, class Saver>
-int BaseMatrixT<real>::applyRow(
-    Agg agg, Op op, Saver sv, BaseMatrixT& b, BaseMatrixT& c) {
+int BaseMatrixT<real>::applyRow(Agg agg, Op op, Saver sv,
+                                BaseMatrixT& b, BaseMatrixT& c) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
   size_t numRows = b.height_;
   size_t numCols = b.width_;
@@ -1755,27 +1532,16 @@ int BaseMatrixT<real>::applyRow(
   CHECK_EQ(width_, 1UL);
   CHECK_EQ(c.height_, numRows);
   CHECK_EQ(c.width_, numCols);
-  aggregate(agg,
-            op,
-            sv,
-            b,
-            c,
-            numRows,
-            numCols,
-            offset,
-            false_type(),
-            true_type() /*aAsColVector*/);
+  aggregate(agg, op, sv,
+            b, c, numRows, numCols, offset,
+            false_type(), true_type() /*aAsColVector*/);
   return 0;
 }
 
-template <>
+template<>
 template <class Agg, class Op>
-int BaseMatrixT<real>::applyRow(Agg agg,
-                                Op op,
-                                real scaleDest,
-                                real scaleAgg,
-                                BaseMatrixT& b,
-                                BaseMatrixT& c) {
+int BaseMatrixT<real>::applyRow(Agg agg, Op op, real scaleDest, real scaleAgg,
+                                BaseMatrixT& b, BaseMatrixT& c) {
   if (scaleDest != 0) {
     applyRow(agg, op, base::binary::add2(scaleDest, scaleAgg), b, c);
   } else {
@@ -1787,7 +1553,7 @@ int BaseMatrixT<real>::applyRow(Agg agg,
   return 0;
 }
 
-template <>
+template<>
 template <class Agg>
 int BaseMatrixT<real>::applyCol(Agg agg, BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
@@ -1795,20 +1561,13 @@ int BaseMatrixT<real>::applyCol(Agg agg, BaseMatrixT& b) {
   size_t numCols = b.width_;
   CHECK_EQ(width_, numCols);
   CHECK_EQ(height_, 1UL);
-  aggregate(agg,
-            base::unary::identity(),
-            base::binary::second(),
-            b,
-            numRows,
-            numCols,
-            offset,
-            true_type() /*aAsRowVector*/,
-            false_type());
+  aggregate(agg, base::unary::identity(), base::binary::second(), b, numRows,
+            numCols, offset, true_type() /*aAsRowVector*/, false_type());
 
   return 0;
 }
 
-template <>
+template<>
 template <class Agg, class Saver>
 int BaseMatrixT<real>::applyCol(Agg agg, Saver sv, BaseMatrixT& b) {
   MatrixOffset offset(0, 0, 0, 0, 0, 0);
@@ -1816,25 +1575,16 @@ int BaseMatrixT<real>::applyCol(Agg agg, Saver sv, BaseMatrixT& b) {
   size_t numCols = b.width_;
   CHECK_EQ(width_, numCols);
   CHECK_EQ(height_, 1UL);
-  aggregate(agg,
-            base::unary::identity(),
-            sv,
-            b,
-            numRows,
-            numCols,
-            offset,
-            true_type() /*aAsRowVector*/,
-            false_type());
+  aggregate(agg, base::unary::identity(), sv, b, numRows, numCols, offset,
+            true_type() /*aAsRowVector*/, false_type());
 
   return 0;
 }
 
-template <>
+template<>
 template <class Agg>
-int BaseMatrixT<real>::applyCol(Agg agg,
-                                real scaleDest,
-                                real scaleAgg,
-                                BaseMatrixT& b) {
+int BaseMatrixT<real>::applyCol(
+     Agg agg, real scaleDest, real scaleAgg, BaseMatrixT& b) {
   if (scaleDest != 0) {
     applyCol(agg, base::binary::add2(scaleDest, scaleAgg), b);
   } else {
@@ -1846,51 +1596,48 @@ int BaseMatrixT<real>::applyCol(Agg agg,
   return 0;
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::sumRows(BaseMatrixT& b, real scaleSum, real scaleDest) {
   applyRow(aggregate::sum(), scaleDest, scaleSum, b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::maxRows(BaseMatrixT& b) {
   applyRow(aggregate::max(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::minRows(BaseMatrixT& b) {
   applyRow(aggregate::min(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::maxCols(BaseMatrixT& b) {
   applyCol(aggregate::max(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::minCols(BaseMatrixT& b) {
   applyCol(aggregate::min(), b);
 }
 
-template <>
+template<>
 void BaseMatrixT<real>::sumCols(BaseMatrixT& b, real scaleSum, real scaleDest) {
   applyCol(aggregate::sum(), scaleDest, scaleSum, b);
 }
 
-template <>
-void BaseMatrixT<real>::sumOfSquaredDiffs(BaseMatrixT& b,
-                                          BaseMatrixT& c,
-                                          real scaleSum,
-                                          real scaleDest) {
-  applyRow(
-      aggregate::sum(), base::binary::squaredDiff(), scaleDest, scaleSum, b, c);
+template<>
+void BaseMatrixT<real>::sumOfSquaredDiffs(
+    BaseMatrixT& b, BaseMatrixT& c, real scaleSum, real scaleDest) {
+  applyRow(aggregate::sum(), base::binary::squaredDiff(),
+           scaleDest, scaleSum, b, c);
 }
 
-template <>
-void BaseMatrixT<real>::sumOfProducts(BaseMatrixT& b,
-                                      BaseMatrixT& c,
-                                      real scaleSum,
-                                      real scaleDest) {
-  applyRow(aggregate::sum(), base::binary::mul(), scaleDest, scaleSum, b, c);
+template<>
+void BaseMatrixT<real>::sumOfProducts(
+    BaseMatrixT& b, BaseMatrixT& c, real scaleSum, real scaleDest) {
+  applyRow(aggregate::sum(), base::binary::mul(),
+           scaleDest, scaleSum, b, c);
 }
 
 template class BaseMatrixT<real>;