tmp

example/CMakeLists.txt

@@ -20,4 +20,4 @@ add_example(ex7 OFF)
 add_example(ex8 OFF)
 add_example(ex9 OFF)
 add_example(ex10 OFF)
-add_example(cfg_ex OFF)
+add_example(cfg_ex ON)

example/cfg_ex.cpp

@@ -1,43 +1,143 @@
 /********************************************************
- *  ██████╗ ███████╗████████╗██╗     
+ *  ██████╗  ██████╗████████╗██╗
  * ██╔════╝ ██╔════╝╚══██╔══╝██║
- * ██║  ███╗███████╗   ██║   ██║     
+ * ██║  ███╗██║        ██║   ██║
- * ██║   ██║╚════██║   ██║   ██║     
+ * ██║   ██║██║        ██║   ██║
- * ╚██████╔╝███████║   ██║   ███████╗
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
- *  ╚═════╝ ╚══════╝   ╚═╝   ╚══════╝                       
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
- * Generic Scientific Template Library
+ * Geophysical Computational Tools & Library (GCTL)
  *
  * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
  *
- * The GSTL is distributed under a dual licensing scheme. You can redistribute 
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
  * it and/or modify it under the terms of the GNU Lesser General Public 
  * License as published by the Free Software Foundation, either version 2 
  * of the License, or (at your option) any later version. You should have 
- * received a copy of the GNU Lesser General Public License (LGPL) along with 
+ * received a copy of the GNU Lesser General Public License along with this 
- * this program. If not, see <http://www.gnu.org/licenses/>.
+ * program. If not, see <http://www.gnu.org/licenses/>.
  * 
  * If the terms and conditions of the LGPL v.2. would prevent you from using 
- * the GSTL, please consider the option to obtain a commercial license for a 
+ * the GCTL, please consider the option to obtain a commercial license for a 
- * fee. These licenses are offered by the GSTL's original author. As a rule, 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
  * licenses are provided "as-is", unlimited in time for a one time fee. Please 
  * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
  * to include some description of your company and the realm of its activities. 
  * Also add information on how to contact you by electronic and paper mail.
  ******************************************************/
 
-#include "../lib/optimization/cmn_grad.h"
+#include "../lib/optimization.h"
 
 using namespace gctl;
 
+class cfg : public lgd_solver
+{
+private:
+    std::vector<gaussian_para2d> gs1_, gs2_;
+    array<double> g1_, g2_;
+
+    common_gradient cmg_;
+
+    array<double> x_;
+    array<double> xm_;
+    array<double> xs_;
+
+public:
+    cfg(/* args */){}
+    ~cfg(){}
+
+    virtual double LGD_Evaluate(const array<double> &x, array<double> &g);
+    void read_gaussians(std::string file, std::vector<gaussian_para2d> &gs);
+    void routine(int argc, char *argv[]);
+};
+
+double cfg::LGD_Evaluate(const array<double> &x, array<double> &g)
+{
+    double f, fx = 0.0;
+	g1_.assign(0.0);
+	g2_.assign(0.0);
+
+    f = 0.0;
+	for (int i = 0; i < gs1_.size(); i++)
+	{
+		f += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs1_[i]);
+		g1_[0] += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs1_[i], gctl::Dx);
+		g1_[1] += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs1_[i], gctl::Dy);
+	}
+
+    cmg_.fill_model_gradient(0, f, g1_);
+    fx += f;
+
+    f = 0.0;
+    for (int i = 0; i < gs2_.size(); i++)
+	{
+		f += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs2_[i]);
+		g2_[0] += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs2_[i], gctl::Dx);
+		g2_[1] += -1e+3*gctl::gaussian_dist2d(x[0], x[1], gs2_[i], gctl::Dy);
+	}
+
+    cmg_.fill_model_gradient(1, f, g2_);
+    fx += f;
+	fx += 0.666027; // 目标值
+
+    g = cmg_.get_common_gradient();
+    return fx;
+}
+
+void cfg::read_gaussians(std::string file, std::vector<gaussian_para2d> &gs)
+{
+    gaussian_para2d tmp_p;
+	std::string tmp_str;
+	std::stringstream tmp_ss;
+
+    std::ifstream infile;
+	gctl::open_infile(infile, file, ".txt");
+
+	while(getline(infile, tmp_str))
+	{
+		if (tmp_str[0] == '#') continue;
+		else
+		{
+			gctl::str2ss(tmp_str, tmp_ss);
+			tmp_ss >> tmp_p.mu_x >> tmp_p.mu_y >> tmp_p.sigma_x >> tmp_p.sigma_y >> tmp_p.rho;
+			gs.push_back(tmp_p);
+		}
+	}
+	infile.close();
+    return;
+}
+
+void cfg::routine(int argc, char *argv[])
+{
+    cmg_.init(2, 2);
+    g1_.resize(2);
+    g2_.resize(2);
+
+    read_gaussians("example/data/gauss_model", gs1_);
+    read_gaussians("example/data/gauss_model2", gs2_);
+
+    x_.resize(2, 20.0);
+    xm_.resize(2, 0.0);
+    xs_.resize(2, 0.0);
+    array<double> low(2, 0.0);
+    array<double> high(2, 100.0);
+
+    lgd_para para = default_lgd_para();
+    para.alpha = 0.01;
+    para.flight_times = 1000;
+    set_lgd_para(para);
+
+    set_lgd_record_trace();
+    LGD_Minimize(x_, xm_, xs_, low, high);
+
+    save_lgd_trace("trace.txt");
+    std::cout << "x = (" << x_[0] << ", " << x_[1] << ")\n";
+    return;
+}
+
 int main(int argc, char *argv[]) try
 {
-    common_gradient cmg;
+    cfg c;
-    cmg.init(2, 2);
+    c.routine(argc, argv);
-    cmg.fill_model_gradient(0, _1d_array({1.0, 0.5}));
-    cmg.fill_model_gradient(1, _1d_array({-0.6, 1.0}));
-
-    _1d_array x = cmg.get_common_gradient(false);
-    std::cout << "x = (" << x[0] << ", " << x[1] << ")\n";
     return 0;
 }
 catch (const std::exception& e)

example/data/forward.sh

@@ -0,0 +1,7 @@
+#!/bin/bash
+
+# 系统里有一个隐藏的错误设置 不然不需要在这里手动设置动态库的地址
+export DYLD_LIBRARY_PATH=/usr/local/lib:$DYLD_LIBRARY_PATH
+
+#g++ gaussian2d.cpp -o gaussian2d -lgctl -lnetcdfcxx_legacy -std=c++17 -I/opt/homebrew/include
+./gaussian2d gauss_model.txt

example/data/gauss_model.txt

@@ -0,0 +1,2 @@
+32.0 66.0 24.0 22.0 -0.1
+32.0 10.0 26.0 24.0 0.6

example/data/gauss_model2.txt

@@ -0,0 +1,2 @@
+75.0 25.0 22.0 28.0 0.5
+32.0 66.0 24.0 22.0 -0.1

example/data/gaussian2d.cpp

@@ -0,0 +1,70 @@
+/**
+ * @defgroup   MAIN main
+ *
+ * @brief      测试非线形最优化中的局部极小值问题
+ *
+ * @author     Zhangyi
+ * @date       2020
+ */
+
+#include "gctl/core.h"
+#include "gctl/io.h"
+
+// 声明我们所使用的二维高斯分布的参数
+static std::vector<gctl::gaussian_para2d> p;
+
+int main(int argc, char *argv[])
+{
+	std::ifstream infile;
+	gctl::open_infile(infile, argv[1], "");
+
+	gctl::gaussian_para2d tmp_p;
+	std::string tmp_str;
+	std::stringstream tmp_ss;
+	while(getline(infile, tmp_str))
+	{
+		if (tmp_str[0] == '#') continue;
+		else
+		{
+			gctl::str2ss(tmp_str, tmp_ss);
+			tmp_ss >> tmp_p.mu_x >> tmp_p.mu_y >> tmp_p.sigma_x 
+				>> tmp_p.sigma_y >> tmp_p.rho;
+			p.push_back(tmp_p);
+		}
+	}
+
+	infile.close();
+
+	// 我们先来确认高斯分布的参数 生成解空间
+	int m = 101, n = 101;
+	gctl::array<double> gauss_dist(m*n, 0.0);
+	for (int t = 0; t < p.size(); t++)
+	{
+		for (int i = 0; i < n; i++)
+		{
+			for (int j = 0; j < m; j++)
+			{
+				gauss_dist[j + i*m] += -1e+3*gctl::gaussian_dist2d(1.0*j, 1.0*i, p[t]);
+			}
+		}
+	}
+
+	// 输出最小值及对应的解
+	double f_min = 1e+30, x_min, y_min;
+	for (int i = 0; i < n; i++)
+	{
+		for (int j = 0; j < m; j++)
+		{
+			if (gauss_dist[j + i*m] < f_min)
+			{
+				f_min = gauss_dist[j + i*m];
+				x_min = j; y_min = i;
+			}
+		}
+	}
+	std::cout << "f_min(" << x_min << ", " << y_min << ") = " << std::setprecision(10) << f_min << std::endl;
+
+	// 保存计算结果
+	gctl::save_netcdf_grid("gauss_dist", gauss_dist, m, n, 0, 1, 0, 1);
+	return 0;
+}

example/data/plot_movie.sh

@@ -0,0 +1,27 @@
+#!/usr/bin/env bash
+
+# 1. Create files needed in the loop
+cat << 'EOF' > pre.sh
+gmt begin pre
+	gmt set FONT_ANNOT_PRIMARY=15p,Times-Roman,black
+	gmt set FONT_LABEL=15p,Times-Roman,black
+	gmt set MAP_GRID_CROSS_SIZE_PRIMARY=5p
+	gmt set MAP_FRAME_PEN=thinnest,black
+	gmt set MAP_TICK_LENGTH_PRIMARY=4p/2p
+	gmt grd2cpt gauss_dist.nc -Clapaz -R0/100/0/100 -Z -D
+	gmt grdimage gauss_dist.nc -R0/100/0/100 -Bxag+l"x (m)" -Byag+l"y (m)" -JX15c/15c -X4.5c -Y1.5c
+gmt end
+EOF
+
+# 2. Set up the main frame script
+cat << 'EOF' > main.sh
+gmt begin
+	# Plot smooth blue curve and dark red dots at all steps so far
+	gmt convert trace.txt -qi0:${MOVIE_FRAME} > data.txt
+	gmt plot data.txt -W0.05p,white -R0/100/0/100 -JX15c/15c -X4.5c -Y1.5c
+	gmt plot data.txt -Sc0.05i -Gred
+gmt end
+EOF
+
+# 3. Run the movie
+gmt movie main.sh -Sbpre.sh -Cxga -Ttrace.txt -Vi -D24 -Zs -Nlgd_anim -Fmp4

example/ex1.cpp

@@ -1,24 +1,24 @@
 /********************************************************
- *  ██████╗ ███████╗████████╗██╗     
+ *  ██████╗  ██████╗████████╗██╗
  * ██╔════╝ ██╔════╝╚══██╔══╝██║
- * ██║  ███╗███████╗   ██║   ██║     
+ * ██║  ███╗██║        ██║   ██║
- * ██║   ██║╚════██║   ██║   ██║     
+ * ██║   ██║██║        ██║   ██║
- * ╚██████╔╝███████║   ██║   ███████╗
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
- *  ╚═════╝ ╚══════╝   ╚═╝   ╚══════╝                       
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
- * Generic Scientific Template Library
+ * Geophysical Computational Tools & Library (GCTL)
  *
  * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
  *
- * The GSTL is distributed under a dual licensing scheme. You can redistribute 
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
  * it and/or modify it under the terms of the GNU Lesser General Public 
  * License as published by the Free Software Foundation, either version 2 
  * of the License, or (at your option) any later version. You should have 
- * received a copy of the GNU Lesser General Public License (LGPL) along with 
+ * received a copy of the GNU Lesser General Public License along with this 
- * this program. If not, see <http://www.gnu.org/licenses/>.
+ * program. If not, see <http://www.gnu.org/licenses/>.
  * 
  * If the terms and conditions of the LGPL v.2. would prevent you from using 
- * the GSTL, please consider the option to obtain a commercial license for a 
+ * the GCTL, please consider the option to obtain a commercial license for a 
- * fee. These licenses are offered by the GSTL's original author. As a rule, 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
  * licenses are provided "as-is", unlimited in time for a one time fee. Please 
  * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
  * to include some description of your company and the realm of its activities. 

example/ex2.cpp

@@ -1,24 +1,24 @@
 /********************************************************
- *  ██████╗ ███████╗████████╗██╗     
+ *  ██████╗  ██████╗████████╗██╗
  * ██╔════╝ ██╔════╝╚══██╔══╝██║
- * ██║  ███╗███████╗   ██║   ██║     
+ * ██║  ███╗██║        ██║   ██║
- * ██║   ██║╚════██║   ██║   ██║     
+ * ██║   ██║██║        ██║   ██║
- * ╚██████╔╝███████║   ██║   ███████╗
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
- *  ╚═════╝ ╚══════╝   ╚═╝   ╚══════╝                       
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
- * Generic Scientific Template Library
+ * Geophysical Computational Tools & Library (GCTL)
  *
  * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
  *
- * The GSTL is distributed under a dual licensing scheme. You can redistribute 
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
  * it and/or modify it under the terms of the GNU Lesser General Public 
  * License as published by the Free Software Foundation, either version 2 
  * of the License, or (at your option) any later version. You should have 
- * received a copy of the GNU Lesser General Public License (LGPL) along with 
+ * received a copy of the GNU Lesser General Public License along with this 
- * this program. If not, see <http://www.gnu.org/licenses/>.
+ * program. If not, see <http://www.gnu.org/licenses/>.
  * 
  * If the terms and conditions of the LGPL v.2. would prevent you from using 
- * the GSTL, please consider the option to obtain a commercial license for a 
+ * the GCTL, please consider the option to obtain a commercial license for a 
- * fee. These licenses are offered by the GSTL's original author. As a rule, 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
  * licenses are provided "as-is", unlimited in time for a one time fee. Please 
  * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
  * to include some description of your company and the realm of its activities. 

example/ex9.cpp

@@ -1,24 +1,24 @@
 /********************************************************
- *  ██████╗ ███████╗████████╗██╗     
+ *  ██████╗  ██████╗████████╗██╗
  * ██╔════╝ ██╔════╝╚══██╔══╝██║
- * ██║  ███╗███████╗   ██║   ██║     
+ * ██║  ███╗██║        ██║   ██║
- * ██║   ██║╚════██║   ██║   ██║     
+ * ██║   ██║██║        ██║   ██║
- * ╚██████╔╝███████║   ██║   ███████╗
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
- *  ╚═════╝ ╚══════╝   ╚═╝   ╚══════╝                       
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
- * Generic Scientific Template Library
+ * Geophysical Computational Tools & Library (GCTL)
  *
  * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
  *
- * The GSTL is distributed under a dual licensing scheme. You can redistribute 
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
  * it and/or modify it under the terms of the GNU Lesser General Public 
  * License as published by the Free Software Foundation, either version 2 
  * of the License, or (at your option) any later version. You should have 
- * received a copy of the GNU Lesser General Public License (LGPL) along with 
+ * received a copy of the GNU Lesser General Public License along with this 
- * this program. If not, see <http://www.gnu.org/licenses/>.
+ * program. If not, see <http://www.gnu.org/licenses/>.
  * 
  * If the terms and conditions of the LGPL v.2. would prevent you from using 
- * the GSTL, please consider the option to obtain a commercial license for a 
+ * the GCTL, please consider the option to obtain a commercial license for a 
- * fee. These licenses are offered by the GSTL's original author. As a rule, 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
  * licenses are provided "as-is", unlimited in time for a one time fee. Please 
  * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
  * to include some description of your company and the realm of its activities. 

lib/optimization/cmn_grad.cpp

@@ -41,6 +41,7 @@ gctl::common_gradient::~common_gradient(){}
 
 void gctl::common_gradient::LCG_Ax(const array<double> &x, array<double> &ax)
 {
+    // Ax product of the linear system
     matvec(t_, G_, x, NoTrans);
     vecmul(t_, t_, w_);
     matvec(ax, G_, t_, Trans);
@@ -64,24 +65,18 @@ void gctl::common_gradient::set_weights(const _1d_array &w)
     return;
 }
 
-void gctl::common_gradient::set_exp_weight(double T)
-{
-    T_ = T;
-    return;
-}
-
 void gctl::common_gradient::init(size_t Ln, size_t Mn)
 {
+    zero_iter_ = true;
     Ln_ = Ln; 
     Mn_ = Mn;
-    T_ = 1.0;
     g_.resize(Mn_);
     B_.resize(Mn_);
     G_.resize(Ln_, Mn_);
     t_.resize(Ln_);
     gm_.resize(Ln_);
-    lx_.resize(Ln_);
+    fx_.resize(Ln_);
-    lt_.resize(Ln_, 1.0);
+    fx0_.resize(Ln_);
     w_.resize(Ln_, 1.0);
     x_.resize(Ln_, 1.0);
     filled_.resize(Ln_, false);
@@ -95,13 +90,16 @@ void gctl::common_gradient::fill_model_gradient(size_t id, double fx, const _1d_
 
     G_.fill_row(id, g);
     gm_[id] = g.module();
-    lx_[id] = fx;
+    fx_[id] = fx;
+    if (zero_iter_) fx0_[id] = fx;
     filled_[id] = true;
     return;
 }
 
 const gctl::_1d_array &gctl::common_gradient::get_common_gradient(bool normalized, bool fixed_w)
 {
+    zero_iter_ = false; // set to false after the first evaluation.
+
     for (size_t i = 0; i < Ln_; i++)
     {
         if (!filled_[i]) throw std::runtime_error("[gctl::common_gradient] Unfilled model gradient.");
@@ -114,13 +112,15 @@ const gctl::_1d_array &gctl::common_gradient::get_common_gradient(bool normalize
         double a;
         for (size_t i = 0; i < Ln_; i++)
         {
-            a = abs(lx_[i] - lt_[i]);
+            // the bigger gradient module is, the bigger weight is
-            w_[i] = 1.0/pow(1.0/(1.0 + exp(-0.05*a) + 0.5), 6);
+            // the faster convergence is, the smaller weight is
+            a = gm_[i]*fx_[i]/fx0_[i];
+            w_[i] = 1.0/a;
         }
     }
 
     rcd_wgts_.push_back(w_);
-    rcd_fxs_.push_back(lx_);
+    rcd_fxs_.push_back(fx_);
 
     G_.normalize(RowMajor);
     matvec(B_, G_, x_, Trans);
@@ -130,19 +130,6 @@ const gctl::_1d_array &gctl::common_gradient::get_common_gradient(bool normalize
     LCG_Minimize(g_, B_, LCG_CG);
 
     if (normalized) g_.normalize();
-    else
-    {
-        g_.normalize();
-        matvec(t_, G_, g_, NoTrans);
-
-        double tmod = t_.module(L1);
-        double gmod = 0.0;
-        for (size_t i = 0; i < Ln_; i++)
-        {
-            gmod += gm_[i]*abs(t_[i])/tmod;
-        }
-        g_.scale(gmod);
-    }
     return g_;
 }
 
@@ -151,7 +138,7 @@ void gctl::common_gradient::save_records(std::string file)
     std::ofstream fout;
     open_outfile(fout, file, ".csv");
 
-    fout << "Num";
+    fout << "num";
     for (size_t j = 0; j < Ln_; j++)
     {
         fout << ",l" << j;
@@ -161,11 +148,10 @@ void gctl::common_gradient::save_records(std::string file)
     {
         fout << ",w" << j;
     }
-    fout << std::endl;
 
     for (size_t i = 0; i < rcd_wgts_.size(); i++)
     {
-        fout << i;
+        fout << std::endl << i;
         for (size_t j = 0; j < Ln_; j++)
         {
             fout << "," << rcd_fxs_[i][j];
@@ -175,7 +161,6 @@ void gctl::common_gradient::save_records(std::string file)
         {
             fout << "," << rcd_wgts_[i][j];
         }
-        fout << std::endl;
     }
     fout.close();
     return;

lib/optimization/cmn_grad.h

@@ -57,15 +57,14 @@ namespace gctl
         void set_solver(const lcg_para &para);
 
         /**
-         * @brief Set the weights for the loss functions
+         * @brief Set the weights for the loss functions.
+         * 
+         * The number of weights equal to the number of the loss functions.
+         * The bigger weights is the calculated gradient is more dependent
+         * on the corresponding gradients.
          */
         void set_weights(const _1d_array &w);
 
-        /**
-         * @brief Set the weight for the exponential weighting function
-         */
-        void set_exp_weight(double T);
-
         /**
          * @brief Initialize the common_gradient object
          * 
@@ -100,15 +99,15 @@ namespace gctl
         void save_records(std::string file);
 
     private:
-        double T_;
+        bool zero_iter_;
-        size_t Ln_, Mn_; // lc: loss count, Ln_: loss_func number，Mn_: model number
+        size_t Ln_, Mn_; // Ln_: loss_func number，Mn_: model number
-        _2d_matrix G_;
+        _2d_matrix G_; // kernel martix
-        _1d_array B_, g_, t_, x_;
+        _1d_array B_, g_, t_, x_; // variables of the linear system
-        _1d_array gm_, w_;
+        _1d_array gm_, w_; // gradient module and functions' weight
-        _1d_array lx_, lt_;
+        _1d_array fx_, fx0_; // functions' value, initial functions' value
-        array<bool> filled_;
+        array<bool> filled_; // new gradient filled for the current round of evaluation
-        std::vector<array<double> > rcd_wgts_;
+        std::vector<array<double> > rcd_wgts_; // weights records
-        std::vector<array<double> > rcd_fxs_;
+        std::vector<array<double> > rcd_fxs_; // fx records
     };
 };
 

tool/levy_planner/levy_planner.cpp

@@ -1,24 +1,24 @@
 /********************************************************
- *  ██████╗ ███████╗████████╗██╗     
+ *  ██████╗  ██████╗████████╗██╗
  * ██╔════╝ ██╔════╝╚══██╔══╝██║
- * ██║  ███╗███████╗   ██║   ██║     
+ * ██║  ███╗██║        ██║   ██║
- * ██║   ██║╚════██║   ██║   ██║     
+ * ██║   ██║██║        ██║   ██║
- * ╚██████╔╝███████║   ██║   ███████╗
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
- *  ╚═════╝ ╚══════╝   ╚═╝   ╚══════╝                       
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
- * Generic Scientific Template Library
+ * Geophysical Computational Tools & Library (GCTL)
  *
  * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
  *
- * The GSTL is distributed under a dual licensing scheme. You can redistribute 
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
  * it and/or modify it under the terms of the GNU Lesser General Public 
  * License as published by the Free Software Foundation, either version 2 
  * of the License, or (at your option) any later version. You should have 
- * received a copy of the GNU Lesser General Public License (LGPL) along with 
+ * received a copy of the GNU Lesser General Public License along with this 
- * this program. If not, see <http://www.gnu.org/licenses/>.
+ * program. If not, see <http://www.gnu.org/licenses/>.
  * 
  * If the terms and conditions of the LGPL v.2. would prevent you from using 
- * the GSTL, please consider the option to obtain a commercial license for a 
+ * the GCTL, please consider the option to obtain a commercial license for a 
- * fee. These licenses are offered by the GSTL's original author. As a rule, 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
  * licenses are provided "as-is", unlimited in time for a one time fee. Please 
  * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
  * to include some description of your company and the realm of its activities.