diff --git a/example/kde_ex.cpp b/example/kde_ex.cpp
index fd37a20..423732b 100644
--- a/example/kde_ex.cpp
+++ b/example/kde_ex.cpp
@@ -86,7 +86,7 @@ int main(int argc, char const *argv[]) try
 
     a[0] = 0;
     b[0] = 1.5;
-    k.get_gradient_y_at(0, 0, a, b, d);
+    k.get_gradient_y_at(0, a, b, d);
 
     double t, sum = 0;
     for (size_t i = 0; i < y.size(); i++)
diff --git a/lib/algorithm/kde.cpp b/lib/algorithm/kde.cpp
index 655f9d8..349656f 100644
--- a/lib/algorithm/kde.cpp
+++ b/lib/algorithm/kde.cpp
@@ -236,9 +236,8 @@ void gctl::kde2d::get_distribution(const array<double> &mx,
     return;
 }
 
-void gctl::kde2d::get_gradient_x_at(size_t mx_id, size_t my_id,
-    const array<double> &mx, const array<double> &my, 
-    array<double> &dmx, kde_kernel_e k_type)
+void gctl::kde2d::get_gradient_x_at(size_t m_id, const array<double> &mx, 
+    const array<double> &my, array<double> &dmx, kde_kernel_e k_type)
 {
     if (mx.size() != my.size()) throw std::runtime_error("[gctl::kde2d] Invalid evaluating size.");;
     int ms = mx.size();
@@ -251,16 +250,15 @@ void gctl::kde2d::get_gradient_x_at(size_t mx_id, size_t my_id,
         {
             for (size_t j = 0; j < xs_; j++)
             {
-                dmx[i*xs_ + j] = ((x_[j] - mx[mx_id])/hx_)*gaussian_kernel((x_[j] - mx[mx_id])/hx_, (y_[i] - my[my_id])/hy_)/(hx_*hx_*hy_*ms);
+                dmx[i*xs_ + j] = ((x_[j] - mx[m_id])/hx_)*gaussian_kernel((x_[j] - mx[m_id])/hx_, (y_[i] - my[m_id])/hy_)/(hx_*hx_*hy_*ms);
             }
         }
     }
     return;
 }
 
-void gctl::kde2d::get_gradient_y_at(size_t mx_id, size_t my_id,
-    const array<double> &mx, const array<double> &my, 
-    array<double> &dmy, kde_kernel_e k_type)
+void gctl::kde2d::get_gradient_y_at(size_t m_id, const array<double> &mx, 
+    const array<double> &my, array<double> &dmy, kde_kernel_e k_type)
 {
     if (mx.size() != my.size()) throw std::runtime_error("[gctl::kde2d] Invalid evaluating size.");;
     int ms = mx.size();
@@ -273,7 +271,7 @@ void gctl::kde2d::get_gradient_y_at(size_t mx_id, size_t my_id,
         {
             for (size_t j = 0; j < xs_; j++)
             {
-                dmy[i*xs_ + j] = ((y_[i] - my[my_id])/hy_)*gaussian_kernel((x_[j] - mx[mx_id])/hx_, (y_[i] - my[my_id])/hy_)/(hy_*hy_*hx_*ms);
+                dmy[i*xs_ + j] = ((y_[i] - my[m_id])/hy_)*gaussian_kernel((x_[j] - mx[m_id])/hx_, (y_[i] - my[m_id])/hy_)/(hy_*hy_*hx_*ms);
             }
         }
     }
diff --git a/lib/algorithm/kde.h b/lib/algorithm/kde.h
index 929c516..f0c1bf6 100644
--- a/lib/algorithm/kde.h
+++ b/lib/algorithm/kde.h
@@ -143,30 +143,26 @@ namespace gctl
         /**
          * @brief Get the gradient at object
          * 
-         * @param mx_id 
-         * @param my_id 
+         * @param m_id 
          * @param mx 
          * @param my 
          * @param dmx
          * @param k_type 
          */
-        void get_gradient_x_at(size_t mx_id, size_t my_id,
-            const array<double> &mx, const array<double> &my, 
-            array<double> &dmx, kde_kernel_e k_type = KDE_Gaussian);
+        void get_gradient_x_at(size_t m_id, const array<double> &mx, 
+            const array<double> &my, array<double> &dmx, kde_kernel_e k_type = KDE_Gaussian);
 
         /**
          * @brief Get the gradient y at object
          * 
-         * @param mx_id 
-         * @param my_id 
+         * @param m_id 
          * @param mx 
          * @param my 
          * @param dmy 
          * @param k_type 
          */
-        void get_gradient_y_at(size_t mx_id, size_t my_id,
-            const array<double> &mx, const array<double> &my, 
-            array<double> &dmy, kde_kernel_e k_type = KDE_Gaussian);
+        void get_gradient_y_at(size_t m_id, const array<double> &mx, 
+            const array<double> &my, array<double> &dmy, kde_kernel_e k_type = KDE_Gaussian);
     
     private:
         size_t xs_, ys_;