gctl_potential/lib/potential/gm_regular_grid.cpp

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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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 * If the terms and conditions of the LGPL v.2. would prevent you from using 
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 * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
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 ******************************************************/

#include "gm_regular_grid.h"

#ifdef GCTL_POTENTIAL_FFTW3
// include fftw head files
#include "fftw3.h"
#endif //GCTL_POTENTIAL_FFTW3

gctl::gm_regular_grid::gm_regular_grid(){}

gctl::gm_regular_grid::~gm_regular_grid(){}

gctl::gm_regular_grid::gm_regular_grid(std::string in_name, std::string in_info, int xnum, int ynum, 
	double xmin, double ymin, double dx, double dy) : regular_grid::regular_grid(in_name, in_info, xnum, 
	ynum, xmin, ymin, dx, dy){}

#ifdef GCTL_POTENTIAL_FFTW3

void gctl::gm_regular_grid::gradient(std::string datname, std::string gradname, gravitational_field_type_e c_type, int order)
{
	meshdata &data = get_data(datname);
	mesh_data_value_e value_type = data.valtype_;
	mesh_data_type_e data_type = data.loctype_;

	if(value_type != Scalar)
	{
		throw std::runtime_error("[gctl::gm_regular_grid::gradient] Invalid value type.");
	}

	if (c_type != Tzz && c_type != Tzx && c_type != Tzy)
	{
		throw std::runtime_error("[gctl::gm_regular_grid::gradient] The gradient type must be Tzz, Tzx and Tzy.");
	}

	// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
	meshdata &new_data = add_data(data_type, value_type, gradname, 0.0);
	gctl::array<double> ingrid_ex;

	int M = -1, N = -1;
	int ori_row, ori_col;
	if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
	else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);

	fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
	fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);

	for (int i = 0; i < M*N; i++)
	{
		in[i][0] = ingrid_ex[i];
		in[i][1] = 0.0;
	}

	fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	int half_M = ceil(M/2);
	int half_N = ceil(N/2);
	double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
	double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);

	int idx1, idx2, idx3, idx4;
	double u, v;
	if (c_type == Tzx)
	{
		for (int i = 0; i < M; i++)
		{
			for (int j = 0; j < half_N; j++)
			{
				v = dv*(j+1);

				idx1 = i*N+j;
				idx2 = i*N+N-1-j;

				in[idx1][0] = -1.0*out[idx1][1]*pow(v, order);
				in[idx1][1] = out[idx1][0]*pow(v, order);

				in[idx2][0] = -1.0*out[idx2][1]*pow(-1.0*v, order);
				in[idx2][1] = out[idx2][0]*pow(-1.0*v, order);
			}
		}
		
	}
	else if (c_type == Tzy)
	{
		for (int i = 0; i < half_M; i++)
		{
			u = du*(i+1);
			for (int j = 0; j < N; j++)
			{
				idx1 = i*N+j;
				idx3 = (M-1-i)*N+j;

				in[idx1][0] = -1.0*out[idx1][1]*pow(u, order);
				in[idx1][1] = out[idx1][0]*pow(u, order);

				in[idx3][0] = -1.0*out[idx3][1]*pow(-1.0*u, order);
				in[idx3][1] = out[idx3][0]*pow(-1.0*u, order);
			}
		}
	}
	else
	{
		for (int i = 0; i < half_M; i++)
		{
			u = du*(i+1);
			for (int j = 0; j < half_N; j++)
			{
				v = dv*(j+1);

				idx1 = i*N+j;
				idx2 = i*N+N-1-j;
				idx3 = (M-1-i)*N+j;
				idx4 = (M-1-i)*N+N-1-j;

				in[idx1][0] = out[idx1][0]*pow(sqrt(u*u+v*v), order);
				in[idx1][1] = out[idx1][1]*pow(sqrt(u*u+v*v), order);

				in[idx2][0] = out[idx2][0]*pow(sqrt(u*u+v*v), order);
				in[idx2][1] = out[idx2][1]*pow(sqrt(u*u+v*v), order);

				in[idx3][0] = out[idx3][0]*pow(sqrt(u*u+v*v), order);
				in[idx3][1] = out[idx3][1]*pow(sqrt(u*u+v*v), order);

				in[idx4][0] = out[idx4][0]*pow(sqrt(u*u+v*v), order);
				in[idx4][1] = out[idx4][1]*pow(sqrt(u*u+v*v), order);
			}
		}
	}

	p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	for (int i = 0; i < M; i++)
	{
		for (int j = 0; j < N; j++)
		{
			ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
		}
	}

	if (data_type == NodeData)
	{
		for (int i = 0; i < rg_ynum; i++)
		{
			for (int j = 0; j < rg_xnum; j++)
			{
				new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}
	else
	{
		for (int i = 0; i < rg_ynum-1; i++)
		{
			for (int j = 0; j < rg_xnum-1; j++)
			{
				new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}

	fftw_destroy_plan(p);
	fftw_free(in); 
	fftw_free(out);
	return;
}

void gctl::gm_regular_grid::rtp(std::string datname, std::string rtpname, double inc, double dec)
{
	meshdata &data = get_data(datname);
	mesh_data_value_e value_type = data.valtype_;
	mesh_data_type_e data_type = data.loctype_;

	if(value_type != Scalar)
	{
		std::string err_str = "Invalid value type. From gctl::gm_regular_grid::rtp(...)";
		throw runtime_error(err_str);
	}

	// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
	meshdata &new_data = add_data(data_type, value_type, rtpname, 0.0);
	gctl::array<double> ingrid_ex;

	int M = -1, N = -1;
	int ori_row, ori_col;
	if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
	else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);

	fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
	fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);

	for (int i = 0; i < M*N; i++)
	{
		in[i][0] = ingrid_ex[i];
		in[i][1] = 0.0;
	}

	fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	int half_M = ceil(M/2);
	int half_N = ceil(N/2);
	double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
	double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);

	double cc = cosd(dec)*cosd(inc);
	double sc = sind(dec)*cosd(inc);
	double s  = sind(inc);

	int idx;
	double U, V, Rpart, Ipart;
	double temp, temp1, temp2, temp3, temp4, base;
	for (int i = 0; i < half_M; i++)
	{
		for (int j = 0; j < half_N; j++)
		{
			U = (i+1)*du; V = (j+1)*dv;
			temp = U*U+V*V;

			idx = i*N+j;
			temp1 = cc*U+sc*V;
			temp2 = s*s*temp-temp1*temp1;
			base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
			Rpart = temp*temp2/base;
			Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
			temp3 = out[idx][0];
			temp4 = out[idx][1];
			in[idx][0] = Rpart*temp3-temp4*Ipart;
			in[idx][1] = Rpart*temp4+Ipart*temp3;

			idx = (M-1-i)*N+j;
			temp1 = -cc*U+sc*V;
			temp2 = s*s*temp-temp1*temp1;
			base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
			Rpart = temp*temp2/base;
			Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
			temp3 = out[idx][0];
			temp4 = out[idx][1];
			in[idx][0] = Rpart*temp3-temp4*Ipart;
			in[idx][1] = Rpart*temp4+Ipart*temp3;

			idx = i*N+N-1-j;
			temp1 = cc*U-sc*V;
			temp2 = s*s*temp-temp1*temp1;
			base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
			Rpart = temp*temp2/base;
			Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
			temp3 = out[idx][0];
			temp4 = out[idx][1];
			in[idx][0] = Rpart*temp3-temp4*Ipart;
			in[idx][1] = Rpart*temp4+Ipart*temp3;

			idx = (M-1-i)*N+N-1-j;
			temp1 = -cc*U-sc*V;
			temp2 = s*s*temp-temp1*temp1;
			base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
			Rpart = temp*temp2/base;
			Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
			temp3 = out[idx][0];
			temp4 = out[idx][1];
			in[idx][0] = Rpart*temp3-temp4*Ipart;
			in[idx][1] = Rpart*temp4+Ipart*temp3;
		}
	}

	p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	for (int i = 0; i < M; i++)
	{
		for (int j = 0; j < N; j++)
		{
			ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
		}
	}

	if (data_type == NodeData)
	{
		for (int i = 0; i < rg_ynum; i++)
		{
			for (int j = 0; j < rg_xnum; j++)
			{
				new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}
	else
	{
		for (int i = 0; i < rg_ynum-1; i++)
		{
			for (int j = 0; j < rg_xnum-1; j++)
			{
				new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}

	fftw_destroy_plan(p);
	fftw_free(in); 
	fftw_free(out);
	return;
}

void gctl::gm_regular_grid::drtp(std::string datname, std::string incname, 
	std::string decname, std::string drtpname, int order)
{
	// 首先获取数据并确定所有数据类型和格式都是一致的
	meshdata *md_ptr = get_data_ptr(datname);
	mesh_data_value_e dat_valtype = md_ptr->valtype_;
	mesh_data_type_e dat_datype = md_ptr->loctype_;

	md_ptr = get_data_ptr(incname);
	mesh_data_value_e inc_valtype = md_ptr->valtype_;
	mesh_data_type_e inc_datype = md_ptr->loctype_;

	md_ptr = get_data_ptr(decname);
	mesh_data_value_e dec_valtype = md_ptr->valtype_;
	mesh_data_type_e dec_datype = md_ptr->loctype_;

	std::string err_str;
	if (dat_valtype != Scalar)
	{
		err_str = "Invalid value type. From gctl::gm_regular_grid::drtp(...)";
		throw runtime_error(err_str);
	}

	if (dat_datype != inc_datype || dat_datype != dec_datype)
	{
		err_str = "Incompatible data type. From gctl::gm_regular_grid::drtp(...)";
		throw runtime_error(err_str);
	}

	// 获取数据指针
	md_ptr = get_data_ptr(datname);
	array<double> *dat_ptr = &md_ptr->datval_;

	md_ptr = get_data_ptr(incname);
	array<double> *inc_ptr = &md_ptr->datval_;

	md_ptr = get_data_ptr(decname);
	array<double> *dec_ptr = &md_ptr->datval_;

	// 检查是否存在同名的数据 若有则检查是否需要重新建立数据
	add_data(dat_datype, dat_valtype, drtpname, 0.0);
	md_ptr = get_data_ptr(drtpname);
	// 获取数据指针
	array<double> *drtp_ptr = &md_ptr->datval_;

	// 新建临时数据并获取数据指针
	std::string tmp_name = drtpname+"tmp";
	add_data(dat_datype, dat_valtype, tmp_name, 0.0);
	md_ptr = get_data_ptr(tmp_name);
	array<double> *tmp_ptr = &md_ptr->datval_;

	std::string diff1_name = drtpname+"diff1";
	add_data(dat_datype, dat_valtype, diff1_name, 0.0);
	md_ptr = get_data_ptr(diff1_name);
	array<double> *diff1_ptr = &md_ptr->datval_;

	std::string diff2_name = drtpname+"diff2";
	add_data(dat_datype, dat_valtype, diff2_name, 0.0);
	array<double> *diff2_ptr = &md_ptr->datval_;

	// 计算平均磁化参数
	double meaninc = 0.0, meandec = 0.0;
	for (int i = 0; i < inc_ptr->size(); i++)
	{
		meaninc += inc_ptr->at(i);
		meandec += dec_ptr->at(i);
	}
	meaninc /= inc_ptr->size();
	meandec /= dec_ptr->size();

	// 计算平均化极结果
	rtp(datname, tmp_name, meaninc, meandec);
	for (int i = 0; i < drtp_ptr->size(); i++)
	{
		drtp_ptr->at(i) = tmp_ptr->at(i);
	}

	// 使用微小扰动计算RTP相对与倾角与偏角的导数
	double dinc = 0.01, ddec = 0.01;
	// 计算一阶变角度化极结果
	rtp(datname, diff1_name, meaninc+dinc, meandec);
	rtp(datname, diff2_name, meaninc, meandec+ddec);
	for (int i = 0; i < drtp_ptr->size(); i++)
	{
		diff1_ptr->at(i) = (inc_ptr->at(i) - meaninc)
			*(diff1_ptr->at(i) - tmp_ptr->at(i))/dinc;
		drtp_ptr->at(i) += diff1_ptr->at(i);

		diff2_ptr->at(i) = (dec_ptr->at(i) - meandec)
			*(diff2_ptr->at(i) - tmp_ptr->at(i))/ddec;
		drtp_ptr->at(i) += diff2_ptr->at(i);
	}

	double factor;
	for (int o = 2; o <= order; o++)
	{
		factor = 1.0;
		for (int n = o; n > 1; n--)
		{
			factor *= n;
		}
		factor = 1.0/factor;

		rtp(diff1_name, tmp_name, meaninc, meandec);
		rtp(diff1_name, diff1_name, meaninc+dinc, meandec);
		for (int i = 0; i < drtp_ptr->size(); i++)
		{
			diff1_ptr->at(i) = factor*pow(inc_ptr->at(i) - meaninc, o)
				*(diff1_ptr->at(i) - tmp_ptr->at(i))/dinc;
			drtp_ptr->at(i) += diff1_ptr->at(i);
		}

		rtp(diff2_name, tmp_name, meaninc, meandec);
		rtp(diff2_name, diff2_name, meaninc, meandec+ddec);
		for (int i = 0; i < drtp_ptr->size(); i++)
		{
			diff2_ptr->at(i) = factor*pow(dec_ptr->at(i) - meandec, o)
				*(diff2_ptr->at(i) - tmp_ptr->at(i))/ddec;
			drtp_ptr->at(i) += diff2_ptr->at(i);
		}
	}

	// 删除临时数据
	remove_data(tmp_name);
	remove_data(diff1_name);
	remove_data(diff2_name);
	return;
}

void gctl::gm_regular_grid::conti(std::string datname, std::string retname, double height)
{
	meshdata &data = get_data(datname);
	mesh_data_value_e value_type = data.valtype_;
	mesh_data_type_e data_type = data.loctype_;

	if(value_type != Scalar)
	{
		throw std::runtime_error("[gctl::gm_regular_grid::conti] Invalid value type.");
	}

	// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
	meshdata &new_data = add_data(data_type, value_type, retname, 0.0);
	gctl::array<double> ingrid_ex;

	int M = -1, N = -1;
	int ori_row, ori_col;
	if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
	else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);

	fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
	fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);

	for (int i = 0; i < M*N; i++)
	{
		in[i][0] = ingrid_ex[i];
		in[i][1] = 0.0;
	}

	fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	int half_M = ceil(M/2);
	int half_N = ceil(N/2);
	double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
	double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);

	int idx1, idx2, idx3, idx4;
	double u, v;
	for (int i = 0; i < half_M; i++)
	{
		u = du*(i+1);
		for (int j = 0; j < half_N; j++)
		{
			v = dv*(j+1);

			idx1 = i*N+j;
			idx2 = i*N+N-1-j;
			idx3 = (M-1-i)*N+j;
			idx4 = (M-1-i)*N+N-1-j;

			in[idx1][0] = out[idx1][0]*exp(sqrt(u*u+v*v)*height);
			in[idx1][1] = out[idx1][1]*exp(sqrt(u*u+v*v)*height);

			in[idx2][0] = out[idx2][0]*exp(sqrt(u*u+v*v)*height);
			in[idx2][1] = out[idx2][1]*exp(sqrt(u*u+v*v)*height);

			in[idx3][0] = out[idx3][0]*exp(sqrt(u*u+v*v)*height);
			in[idx3][1] = out[idx3][1]*exp(sqrt(u*u+v*v)*height);

			in[idx4][0] = out[idx4][0]*exp(sqrt(u*u+v*v)*height);
			in[idx4][1] = out[idx4][1]*exp(sqrt(u*u+v*v)*height);
		}
	}

	p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
	fftw_execute(p);

	for (int i = 0; i < M; i++)
	{
		for (int j = 0; j < N; j++)
		{
			ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
		}
	}

	if (data_type == NodeData)
	{
		for (int i = 0; i < rg_ynum; i++)
		{
			for (int j = 0; j < rg_xnum; j++)
			{
				new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}
	else
	{
		for (int i = 0; i < rg_ynum-1; i++)
		{
			for (int j = 0; j < rg_xnum-1; j++)
			{
				new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
			}
		}
	}

	fftw_destroy_plan(p);
	fftw_free(in); 
	fftw_free(out);
	return;
}

#endif //GCTL_POTENTIAL_FFTW3

void gctl::gm_regular_grid::trend(std::string datname, std::string regname, std::string resname, int wx_size, int wy_size, int x_order, int y_order)
{
	meshdata &data = get_data(datname);
	mesh_data_value_e value_type = data.valtype_;
	mesh_data_type_e data_type = data.loctype_;

	if(value_type != Scalar)
	{
		throw std::runtime_error("Invalid value type. From gctl::gm_regular_grid::trend(...)");
	}

	// 检查是否存在与趋势场局部场数据同名的数据 若有则检查是否需要重新建立数据
	meshdata &reg_data = add_data(data_type, value_type, regname, 0.0);
	meshdata &res_data = add_data(data_type, value_type, resname, 0.0);

	matrix<double> data_mat;
	if (data_type == NodeData)
	{
		data_mat.resize(rg_ynum, rg_xnum);
		for (size_t i = 0; i < rg_ynum; i++)
		{
			for (size_t j = 0; j < rg_xnum; j++)
			{
				data_mat[i][j] = data.datval_[i*rg_xnum+j];
			}
		}
	}
	else
	{
		data_mat.resize(rg_ynum-1, rg_xnum-1);
		for (size_t i = 0; i < rg_ynum-1; i++)
		{
			for (size_t j = 0; j < rg_xnum-1; j++)
			{
				data_mat[i][j] = data.datval_[i*(rg_xnum-1)+j];
			}
		}
	}

	trend_2d(data_mat, wy_size, wx_size, y_order, x_order);

	if (data_type == NodeData)
	{
		for (size_t i = 0; i < rg_ynum; i++)
		{
			for (size_t j = 0; j < rg_xnum; j++)
			{
				reg_data.datval_[i*rg_xnum+j] = data_mat[i][j];
				res_data.datval_[i*rg_xnum+j] = data.datval_[i*rg_xnum+j] - data_mat[i][j];
			}
		}
	}
	else
	{
		for (size_t i = 0; i < rg_ynum-1; i++)
		{
			for (size_t j = 0; j < rg_xnum-1; j++)
			{
				reg_data.datval_[i*(rg_xnum-1)+j] = data_mat[i][j];
				res_data.datval_[i*(rg_xnum-1)+j] = data.datval_[i*(rg_xnum-1)+j] - data_mat[i][j];
			}
		}
	}
	return;
}