gctl_optimization/example/ex1.cpp

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 * Generic Scientific Template Library
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 * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
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#include "../lib/optimization.h"

#define M 1000
#define N 800

double max_diff(const gctl::array<double> &a, const gctl::array<double> &b)
{
	double max = -1.0;
	for (size_t i = 0; i < a.size(); i++)
	{
		max = std::max(sqrt((a[i] - b[i])*(a[i] - b[i])), max);
	}
	return max;
}

class ex1 : public gctl::lcg_solver
{
public:
	ex1();
	virtual ~ex1();

	// 计算共轭梯度的B项
	void cal_partb(const gctl::array<double> &x, gctl::array<double> &B);

	//定义共轭梯度中Ax的算法
	virtual void LCG_Ax(const gctl::array<double> &x, gctl::array<double> &ax);
	virtual void LCG_Mx(const gctl::array<double> &x, gctl::array<double> &mx);

private:
	gctl::matrix<double> kernel; // 普通二维数组做核矩阵
	gctl::array<double> tmp_arr; // 中间结果数组
	gctl::array<double> p; // 预优矩阵
};

ex1::ex1()
{
	kernel.resize(M, N);
	kernel.random_float(-1.0, 1.0, gctl::RdUniform);

	tmp_arr.resize(M);
	p.resize(N);
	for (size_t i = 0; i < N; i++)
	{
		p[i] = 1.0;
	}

	double diag;
	for (size_t i = 0; i < N; i++)
	{
		diag = 0.0;
		for (size_t j = 0; j < M; j++)
		{
			diag += kernel[j][i]*kernel[j][i];
		}
		p[i] = 1.0/diag;
	}
}

ex1::~ex1(){}

void ex1::cal_partb(const gctl::array<double> &x, gctl::array<double> &B)
{
	LCG_Ax(x, B);
	return;
}

void ex1::LCG_Ax(const gctl::array<double> &x, gctl::array<double> &ax)
{
	matvec(tmp_arr, kernel, x);
	matvec(ax, kernel, tmp_arr, gctl::Trans);
	return;
}

void ex1::LCG_Mx(const gctl::array<double> &x, gctl::array<double> &mx)
{
	vecmul(mx, p, x);
	return;
}

int main(int argc, char const *argv[])
{
	// 生成一组正演解
	gctl::array<double> fm(N);
	fm.random_float(1.0, 2.0, gctl::RdUniform);

	ex1 test;

	// 计算共轭梯度B项
	gctl::array<double> B(N);
	test.cal_partb(fm, B);

	// 声明一组解
	gctl::array<double> m(N, 0.0);

	test.set_lcg_message(gctl::LCG_SOLUTION);

	std::ofstream ofile("log.txt");
	test.LCG_Minimize(m, B, gctl::LCG_CG, ofile);
	ofile << "maximal difference: " << max_diff(fm, m) << std::endl;

	m.assign_all(0.0);
	
	test.LCG_Minimize(m, B, gctl::LCG_PCG, ofile);
	ofile << "maximal difference: " << max_diff(fm, m) << std::endl;

	m.assign_all(0.0);

	test.LCG_Minimize(m, B, gctl::LCG_CGS, ofile);
	ofile << "maximal difference: " << max_diff(fm, m) << std::endl;
	ofile.close();

	test.set_lcg_message(gctl::LCG_SOLUTION);

	m.assign_all(0.0);

	test.LCG_Minimize(m, B, gctl::LCG_BICGSTAB);
	std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;

	m.assign_all(0.0);

	test.LCG_Minimize(m, B, gctl::LCG_BICGSTAB2);
	std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;

	gctl::array<double> low(N, 1.0);
	gctl::array<double> hig(N, 2.0);

	m.assign_all(0.0);

	test.LCG_MinimizeConstrained(m, B, low, hig, gctl::LCG_PG);
	std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;

	m.assign_all(0.0);

	test.LCG_MinimizeConstrained(m, B, low, hig, gctl::LCG_SPG);
	std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
	return 0;
}