gctl_toolkits/lki/lki.h

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 * Geophysical Computational Tools & Library (GCTL)
 *
 * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
 *
 * 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 
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 * received a copy of the GNU Lesser General Public License along with this 
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 * If the terms and conditions of the LGPL v.2. would prevent you from using 
 * the GCTL, please consider the option to obtain a commercial license for a 
 * fee. These licenses are offered by the GCTL's original author. As a rule, 
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 * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
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// linear conjugate gradient solver library
//#include "lcg/solver.h"
// GCTL library
#include "gctl/core.h"
#include "gctl/algorithms.h"
#include "gctl/geometry.h"
#include "gctl/io.h"
#include "gctl/utility.h"
#include "gctl/optimization.h"

#if defined _WINDOWS || __WIN32__
#include "io.h"
// Test for file existence
#define F_OK 0
#endif

class LKI : public gctl::lcg_solver
{
public:
	LKI(){}
	virtual ~LKI(){}
	void LCG_Ax(const gctl::array<double> &a, gctl::array<double> &b);
	void LCG_Mx(const gctl::array<double> &a, gctl::array<double> &b){}

	void Routine(std::string inname, std::string tarname, std::string outname, std::string col_str, 
		gctl::text_descriptor &desc, int kernel_size, int box_size, double epsilon, 
		std::string variogram_type, std::string variogram_para);
	void ReadConstrainNodes(std::string filename, gctl::text_descriptor &desc);
	void WriteTargetNodes(std::string filename, gctl::text_descriptor &desc);
	void InitTargetNodes(std::string para, gctl::text_descriptor &desc);
	void CalKernel();
	void CalKernel(const gctl::point3dc &tar_node);
	void set_kernel_size(unsigned int k){MatSize = k+1;}

public:
	gctl::array<gctl::point3dc> ConsNodes;
	gctl::array<gctl::point3dc> TargNodes;
	std::vector<gctl::point3dc*> LocalNodes;
	gctl::boxes2d<gctl::point3dc> PntBoxes;

	int ConsSize, MatSize;
	gctl::matrix<double> Kernel;
	gctl::array<double> Wgts;
	gctl::array<double> MidPdt;
	gctl::array<double> B;

	//gctl::array<double> GK;
	//gctl::array<double> DK;
	//gctl::array<double> ADK;

	gctl::variogram_model VarModel;
	gctl::variogram_type_e VarType;

	gctl::getoption gopt;

	gctl::_1i_vector col_index;
};

void LKI::Routine(std::string inname, std::string tarname, std::string outname, std::string col_str, gctl::text_descriptor &desc, 
	int kernel_size, int box_size, double epsilon, std::string variogram_type, std::string variogram_para)
{
	if (variogram_type == "spherical") VarType = gctl::SPHERICAL;
	else if (variogram_type == "exponential") VarType = gctl::EXPONENTIAL;
	else if (variogram_type == "gaussian") VarType = gctl::GAUSSIAN;
	else if (variogram_type == "wave") VarType = gctl::WAVE;
	else if (variogram_type == "rational") VarType = gctl::RATIONAL_Q;
	else if (variogram_type == "circular") VarType = gctl::CIRCULAR;
	else if (variogram_type == "linear") VarType = gctl::LINEAR;
	else throw gctl::runtime_error("Invalid variogram function type. From LKI::Routine(...)");

	gctl::parse_string_to_value(variogram_para, '/', true, VarModel.nugget, VarModel.sill, VarModel.range);
	if (!VarModel.valid()) throw gctl::runtime_error("Invalid variogram parameters. From LKI::Routine(...)");

	gctl::parse_string_to_vector(col_str, ',', col_index);
	if (col_index.size() < 3)
	{
		throw gctl::runtime_error("Invalid column index. From LKI::Routine(...)");
	}

	ReadConstrainNodes(inname, desc);
	InitTargetNodes(tarname, desc);

	unsigned int k_size = kernel_size;
	if (k_size <= 1)
	{
		throw gctl::runtime_error("Invalid local size. From LBSI::Routine(...)");
	}

	if (k_size >= ConsNodes.size())
	{
		GCTL_ShowWhatError("The local size is equal to or bigger than the input node's size. Reduced to the global algorithm.", GCTL_WARNING_ERROR, 0, 0, 0);

		ConsSize = ConsNodes.size();
		MatSize = ConsSize + 1;
		Kernel.resize(MatSize, MatSize);
		Wgts.resize(MatSize);
		B.resize(MatSize);

		CalKernel();

		gctl::lu lu_k(Kernel);
		lu_k.decompose();

		double dist, sum;
		for (int i = 0; i < TargNodes.size(); ++i)
		{
			for (int j = 0; j < ConsSize; ++j)
			{
				dist = sqrt((ConsNodes[j].x - TargNodes[i].x)*(ConsNodes[j].x - TargNodes[i].x) 
					+ (ConsNodes[j].y - TargNodes[i].y)*(ConsNodes[j].y - TargNodes[i].y));

				B[j] = variogram(dist, VarModel, VarType);	
			}
			B[ConsSize] = 1.0;

			lu_k.solve(B, Wgts);

			sum = 0.0;
			for (int j = 0; j < ConsSize; ++j)
			{
				sum += ConsNodes[j].z*Wgts[j];	
			}
			TargNodes[i].z = sum;
		}
		
		WriteTargetNodes(outname, desc);
		return;
	}

	set_kernel_size(k_size);
	LocalNodes.resize(MatSize-1);
	Kernel.resize(MatSize, MatSize);
	Wgts.resize(MatSize);
	MidPdt.resize(MatSize);
	B.resize(MatSize);
	//GK.resize(MatSize);
	//DK.resize(MatSize);
	//ADK.resize(MatSize);

	gctl::lcg_para my_para = default_lcg_para();
	//my_para.max_iterations = 1000;
	my_para.epsilon = epsilon;
	set_lcg_para(my_para);

	gctl::array<double> xs(ConsNodes.size());
	gctl::array<double> ys(ConsNodes.size());
	for (int i = 0; i < ConsNodes.size(); ++i)
	{
		xs[i] = ConsNodes[i].x;
		ys[i] = ConsNodes[i].y;
	}

	PntBoxes.init(xs, ys, ConsNodes, box_size, box_size);

	double dist, sum;
	gctl::progress_bar bar(TargNodes.size());
	for (int i = 0; i < TargNodes.size(); ++i)
	{
		bar.progressed(i);

		Kernel.assign_all(0.0);
		Wgts.assign(0.0);

		CalKernel(TargNodes[i]);

		// run the inversion process in factory mode
		//lcg(_AxProduct, nullptr, Wgts.get(), B.get(), MatSize, &my_para, this, GK.get(), DK.get(), ADK.get());
		lcg(Wgts, B);

		sum = 0.0;
		for (int j = 0; j < MatSize-1; ++j)
		{
			sum += LocalNodes[j]->z*Wgts[j];
		}
		TargNodes[i].z = sum;
	}

	WriteTargetNodes(outname, desc);
	return;
}

void LKI::ReadConstrainNodes(std::string filename, gctl::text_descriptor &desc)
{
	//read_text2array(filename, ConsNodes);

	gctl::_2d_vector table_data;
	desc.file_name_ = filename;
	gctl::read_text2vector2d(desc, table_data);

	if (table_data.size() <= 1)
	{
		throw gctl::runtime_error("Not enough constraint points. From LBSI::ReadConstrainNodes(...)");
	}

	ConsNodes.resize(table_data.size());
	for (int i = 0; i < table_data.size(); ++i)
	{
		ConsNodes[i].x = table_data[i][col_index[0]];
		ConsNodes[i].y = table_data[i][col_index[1]];
		ConsNodes[i].z = table_data[i][col_index[2]];
	}

	gctl::destroy_vector(table_data);
	return;
}

void LKI::WriteTargetNodes(std::string filename, gctl::text_descriptor &desc)
{
	desc.file_name_ = filename;
	save_array2text(desc, TargNodes);
	return;
}

void LKI::InitTargetNodes(std::string para, gctl::text_descriptor &desc)
{
	// try to use the para as a file name
	if (access(para.c_str(), F_OK) != -1)
	{
		desc.file_name_ = para;
		std::vector<gctl::point2dc> tmp_vec;
		gctl::read_text2vector(desc, tmp_vec);

		TargNodes.resize(tmp_vec.size());
		for (int i = 0; i < tmp_vec.size(); ++i)
		{
			TargNodes[i].x = tmp_vec[i].x;
			TargNodes[i].y = tmp_vec[i].y;
			TargNodes[i].z = 0.0;
		}

		gctl::destroy_vector(tmp_vec);
		return;
	}

	double dx, dy, xmin, xmax, ymin, ymax, ele = 0.0;
	gctl::parse_string_to_value(para, '/', true, xmin, dx, xmax, ymin, dy, ymax);
	gctl::grid_points_2d(TargNodes, xmin, xmax, ymin, ymax, dx, dy, ele);
	return;
}

void LKI::CalKernel()
{
	// 计算出所有成对的协方差函数值 成对的
	double dist;
	for (int i = 0; i < ConsSize; ++i)
	{
		Kernel[i][i] = variogram(0.0, VarModel, VarType);
		for (int j = i+1; j < ConsSize; ++j)
		{
			dist = sqrt((ConsNodes[i].x - ConsNodes[j].x)*(ConsNodes[i].x - ConsNodes[j].x) 
				+ (ConsNodes[i].y - ConsNodes[j].y)*(ConsNodes[i].y - ConsNodes[j].y));

			Kernel[i][j] = Kernel[j][i] = variogram(dist, VarModel, VarType);
		}
	}

	// 最后一行系数全为1
	for (int i = 0; i < ConsSize; ++i)
	{
		Kernel[ConsSize][i] = Kernel[i][ConsSize] = 1.0;
	}

	Kernel[ConsSize][ConsSize] = 0.0;
	return;
}

void LKI::CalKernel(const gctl::point3dc &tar_node)
{
	// 找出距离tar_node最近的一组控制点
	PntBoxes.get_by_number(tar_node.x, tar_node.y, MatSize-1, LocalNodes);
	
	// 计算出所有成对的格林函数值
	double dist;
	for (int j = 0; j < MatSize-1; ++j)
	{
		Kernel[j][j] = variogram(0.0, VarModel, VarType);
		for (int k = j+1; k < MatSize-1; ++k)
		{
			dist = sqrt((LocalNodes[j]->x - LocalNodes[k]->x)*(LocalNodes[j]->x - LocalNodes[k]->x) 
				+ (LocalNodes[j]->y - LocalNodes[k]->y)*(LocalNodes[j]->y - LocalNodes[k]->y));

			Kernel[j][k] = Kernel[k][j] = variogram(dist, VarModel, VarType);
		}
	}

	// 最后一行系数全为1
	for (int i = 0; i < MatSize-1; ++i)
	{
		Kernel[MatSize-1][i] = Kernel[i][MatSize-1] = 1.0;
	}
	Kernel[MatSize-1][MatSize-1] = 0.0;

	for (int j = 0; j < MatSize-1; ++j)
	{
		dist = sqrt((LocalNodes[j]->x - tar_node.x)*(LocalNodes[j]->x - tar_node.x) 
			+ (LocalNodes[j]->y - tar_node.y)*(LocalNodes[j]->y - tar_node.y));

		MidPdt[j] = variogram(dist, VarModel, VarType);	
	}
	MidPdt[MatSize-1] = 1.0;

	for (int i = 0; i < MatSize; ++i)
	{
		B[i] = 0;
		for (int j = 0; j < MatSize; ++j)
		{
			B[i] += Kernel[j][i] * MidPdt[j];
		}
	}
	return;
}

void LKI::LCG_Ax(const gctl::array<double> &a, gctl::array<double> &b)
{
	for (int i = 0; i < MatSize; ++i)
	{
		MidPdt[i] = 0;
		for (int j = 0; j < MatSize; ++j)
		{
			MidPdt[i] += a[j] * Kernel[i][j];
		}
	}

	for (int i = 0; i < MatSize; ++i)
	{
		b[i] = 0;
		for (int j = 0; j < MatSize; ++j)
		{
			b[i] += MidPdt[j] * Kernel[j][i];
		}
	}
	return;
}