gctl_potential/lib/potential/mkernel_tricone_Ren2017.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 
 * of the License, or (at your option) any later version. You should have 
 * received a copy of the GNU Lesser General Public License along with this 
 * 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 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, 
 * 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 
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 ******************************************************/

#include "mkernel_tricone_Ren2017.h"
#include "cmath"

double mag_tolerance = 1e-16;

void gctl::set_magcone_ren17_tolerance(double tol)
{
	if (tol > 0) mag_tolerance = tol;
	else throw invalid_argument("Invalid tolerance value. From gctl::set_magcone_ren17_tolerance(...)");
	return;
}

void gctl::callink_magnetic_para(array<magcone_ren17> &in_cone, array<magcone_para_ren17> &out_para, const array<point3dc> &mag_B)
{
    point3dc v1, v2, v3, ne, nf;

	out_para.resize(in_cone.size());
	for (int i = 0; i < in_cone.size(); ++i)
	{
		if (in_cone[i].vert[0] == nullptr || in_cone[i].vert[1] == nullptr || 
			in_cone[i].vert[2] == nullptr || in_cone[i].vert[3] == nullptr)
		{
			throw runtime_error("Invalid vertex pointer. From callink_magnetic_para(...)");
		}

		for (int f = 0; f < 4; ++f)
		{
			v1 = *in_cone[i].fget(f, 1) - *in_cone[i].fget(f, 0);
			v2 = *in_cone[i].fget(f, 2) - *in_cone[i].fget(f, 0);
			nf = cross(v1, v2).normal();
			out_para[i].nf[f] = nf;

			for (int e = 0; e < 3; ++e)
			{
				v3 = *in_cone[i].fget(f, (e+1)%3) - *in_cone[i].fget(f, e);
				ne = cross(v3, nf).normal();
				out_para[i].ne[e+f*3] = ne;
				out_para[i].te[e+f*3] = cross(nf, ne).normal();
			}

			out_para[i].mag_amp[f] = dot(mag_B[i], nf);
		}

		in_cone[i].att = out_para.get(i);
	}
    return;
}

void gctl::callink_magnetic_para_earth_sph(array<magcone_ren17> &in_cone, array<magcone_para_ren17> &out_para, 
	double inclina_deg, double declina_deg, array<point3dc> *mag_vec, double field_tense)
{
    if (declina_deg < -180.0 || declina_deg > 180.0 || 
		inclina_deg < -90 || inclina_deg > 90 || field_tense < 0.0)
	{
		throw invalid_argument("Invalid parameters. From gctl::callink_magnetic_para_earth_sph(...)");
	}

	point3dc v1, v2, v3, ne, nf, mag_z, c;
	point3ds s;

	double I = inclina_deg*M_PI/180.0;
	double A = declina_deg*M_PI/180.0;

	if (mag_vec != nullptr) mag_vec->resize(in_cone.size());
	out_para.resize(in_cone.size());
	for (int i = 0; i < in_cone.size(); ++i)
	{
		if (in_cone[i].vert[0] == nullptr || in_cone[i].vert[1] == nullptr || 
			in_cone[i].vert[2] == nullptr || in_cone[i].vert[3] == nullptr)
		{
			throw runtime_error("Invalid vertex pointer. From callink_magnetic_para_earth_sph(...)");
		}

		// magnetization vector at the local coordinates
		// note here the postive direction of the inclination angle is downward
		// note here the postive direction of the declination angle is clockwise
		mag_z.x = cos(I)*sin(A);
		mag_z.y = cos(I)*cos(A);
		mag_z.z = -1.0*sin(I);

        c = 1.0/3.0*(*in_cone[i].vert[0] + *in_cone[i].vert[1] + *in_cone[i].vert[2]);
		s = c.c2s();
		// magnetic susceptibility is taken as one here
		// rotate the local coordinate system to the regular status
		mag_z = field_tense * mag_z.rotate((90.0 - s.lat)*M_PI/180.0, 0.0, (90.0 + s.lon)*M_PI/180.0).normal();
		if (mag_vec != nullptr) mag_vec->at(i) = mag_z;

		for (int f = 0; f < 4; ++f)
		{
			v1 = *in_cone[i].fget(f, 1) - *in_cone[i].fget(f, 0);
			v2 = *in_cone[i].fget(f, 2) - *in_cone[i].fget(f, 0);
			nf = cross(v1, v2).normal();
			out_para[i].nf[f] = nf;

			for (int e = 0; e < 3; ++e)
			{
				v3 = *in_cone[i].fget(f, (e+1)%3) - *in_cone[i].fget(f, e);
				ne = cross(v3, nf).normal();
				out_para[i].ne[e+f*3] = ne;
				out_para[i].te[e+f*3] = cross(nf, ne).normal();
			}

			out_para[i].mag_amp[f] = dot(mag_z, nf);
		}

		in_cone[i].att = out_para.get(i);
	}
    return;
}

gctl::point3dc gctl::magkernel_single(const magcone_ren17 &a_ele, const point3ds &a_op, tensor *R_ptr)
{
    double Rij_minus, Rij_plus, Sij_plus, Sij_minus, Rij0, mij0, wi0;
	double beta, Aij, sig, absw;
	gctl::point3dc oi, k1, part1, part2;

	// get attribute pointer
	if (a_ele.att == nullptr) throw gctl::runtime_error("[gctl_potential::magcone_ren17] Magnetization parameter not set.");
	gctl::magcone_para_ren17 *mpara = a_ele.att;

    gctl::tensor R;
    if (R_ptr != nullptr) R = *R_ptr;
	else R = transform_matrix(a_op);

	// get the observation site in the local coordinates
	gctl::point3dc site = a_op.s2c();
	gctl::point3dc out_grad(0.0, 0.0, 0.0);
	for (int f = 0; f < 4; ++f)
	{
		k1.set(0.0, 0.0, 0.0);
		for (int j = 0; j < 3; ++j)
		{
			Rij_minus = (site - *a_ele.fget(f, j)).module();
			Rij_plus  = (site - *a_ele.fget(f, (j+1)%3)).module();

			if (j == 0)
			{
				wi0 = gctl::dot(site - *a_ele.fget(f, j), mpara->nf[f]);
				sig = gctl::sign(wi0);
				absw = std::abs(wi0);
			}

			oi = site - wi0*mpara->nf[f];
			Sij_minus = gctl::dot(*a_ele.fget(f, j) - oi, mpara->te[3*f+j]);
			Sij_plus  = gctl::dot(*a_ele.fget(f, (j+1)%3) - oi, mpara->te[3*f+j]);
			mij0 = gctl::dot(*a_ele.fget(f, j) - oi, mpara->ne[3*f+j]);
			Rij0 = std::sqrt(wi0*wi0 + mij0*mij0);

			part2.set(0.0, 0.0, 0.0);
			if (absw > mag_tolerance)
			{
				beta = atan((mij0*Sij_plus)/(Rij0*Rij0 + absw*Rij_plus))
					- atan((mij0*Sij_minus)/(Rij0*Rij0 + absw*Rij_minus));

				part2 = sig*beta*mpara->nf[f];
			}

			if (std::abs(Rij0) > mag_tolerance)
			{
				Aij = std::log((long double)(Rij_plus+Sij_plus)) - std::log((long double)(Rij_minus+Sij_minus));
			}
			else if (Sij_plus > 0.0 && Sij_minus > 0.0)
			{
				Aij = std::log(Sij_plus) - std::log(Sij_minus);
			}
			else if (Sij_plus < 0.0 && Sij_minus < 0.0)
			{
				Aij = std::log(-1.0*Sij_minus) - std::log(-1.0*Sij_plus);
			}
			else
			{
				throw gctl::runtime_error("[gctl_potential::magcone_ren17] Observation site on edge.");
			}

			part1 = Aij * mpara->ne[3*f+j];
			k1 = k1 - (part1 + part2);
		}

		// nT -> T 1e-9 / 4*pi*e-7 = 1/(400*pi)*100 = 1/(4*pi) -> A/m
		out_grad = out_grad - 1.0/(4.0*GCTL_Pi)*k1*mpara->mag_amp[f];
	}

    out_grad = R*out_grad;
    out_grad.x *= -1.0;
	out_grad.y *= -1.0;
	return out_grad;
}

gctl::tensor gctl::magkernel_single_tensor(const magcone_ren17 &a_ele, const point3ds &a_op, tensor *R_ptr)
{
    double Rij_minus, Rij_plus, Sij_plus, Sij_minus, Rij0, mij0, wi0;
	double beta, sig, absw;
	double factor_n_mij, factor_tij;
	gctl::point3dc oi, grad_Aij;
	gctl::point3dc grad_Rij_plus, grad_Rij_minus, grad_Sij_plus, grad_Sij_minus;
	gctl::point3dc grad_mij0, grad_Rij0, grad_abs_wi0;
	gctl::point3dc grad_a_plus, grad_b_plus, grad_a_minus, grad_b_minus;
	gctl::point3dc grad_betaij_plus, grad_betaij_minus, grad_betaij;
	double a_plus, b_plus, a_minus, b_minus;
	double k3;
	gctl::tensor tmp_k, k2;

    // get attribute pointer
	if (a_ele.att == nullptr) throw gctl::runtime_error("[gctl_potential::magcone_ren17] Magnetization parameter not set.");
	gctl::magcone_para_ren17 *mpara = a_ele.att;

    gctl::tensor R, R_T;
    if (R_ptr != nullptr) R = *R_ptr;
	else R = transform_matrix(a_op);
    R_T = R.transpose();

    // get the observation site in the local coordinates
	gctl::point3dc site = a_op.s2c();
	gctl::tensor out_tensor(0.0);
	for (int f = 0; f < 4; ++f)
	{
		k2.set(0.0);
		k3 = 0.0;
		for (int j = 0; j < 3; ++j)
		{
			Rij_minus = (site - *a_ele.fget(f, j)).module();
			Rij_plus  = (site - *a_ele.fget(f, (j+1)%3)).module();

			if (j == 0)
			{
				wi0 = gctl::dot(site - *a_ele.fget(f, j), mpara->nf[f]);
				sig = gctl::sign(wi0);
				absw = std::abs(wi0);
			}

			oi = site - wi0*mpara->nf[f];
			Sij_minus = gctl::dot(*a_ele.fget(f, j) - oi, mpara->te[3*f+j]);
			Sij_plus  = gctl::dot(*a_ele.fget(f, (j+1)%3) - oi, mpara->te[3*f+j]);
			mij0 = gctl::dot(*a_ele.fget(f, j) - oi, mpara->ne[3*f+j]);
			Rij0 = std::sqrt(wi0*wi0 + mij0*mij0);

			if (std::abs(Rij0) > mag_tolerance)
			{
				factor_n_mij = -1.0*(Sij_plus/(Rij0*Rij0*Rij_plus) - Sij_minus/(Rij0*Rij0*Rij_minus));
				factor_tij   = -1.0/Rij_plus + 1.0/Rij_minus;
				grad_Aij = (wi0*factor_n_mij)*mpara->nf[f] + factor_tij*mpara->te[3*f+j] 
					- (mij0*factor_n_mij)*mpara->ne[3*f+j];
			}
			else
			{
				factor_tij   = -1.0/Rij_plus + 1.0/Rij_minus;
				grad_Aij = factor_tij*mpara->te[3*f+j];
			}

			//tmp_k = gctl::kron(grad_Aij, ne_[e][3*f+j]);
			tmp_k = gctl::kron(mpara->ne[3*f+j], grad_Aij);
			k2 = k2 - tmp_k;

			if (absw > mag_tolerance)
			{
				grad_Rij_plus  = (1.0/Rij_plus)*(site - *a_ele.fget(f, (j+1)%3));
				grad_Rij_minus = (1.0/Rij_minus)*(site - *a_ele.fget(f, j));
				grad_Sij_plus  = -1.0*mpara->te[3*f+j];
				grad_Sij_minus = -1.0*mpara->te[3*f+j];
				grad_mij0    = -1.0*mpara->ne[3*f+j];
				grad_Rij0    = (1.0/Rij0)*(wi0*mpara->nf[f] - mij0*mpara->ne[3*f+j]);
				grad_abs_wi0 = sig*mpara->nf[f];
				a_plus = Rij0*Rij0 + absw*Rij_plus;
				b_plus = mij0*Sij_plus;
				grad_a_plus = (2.0*Rij0)*grad_Rij0 + Rij_plus*grad_abs_wi0 + absw*grad_Rij_plus;
				grad_b_plus = Sij_plus*grad_mij0 + mij0*grad_Sij_plus;
				a_minus = Rij0*Rij0 + absw*Rij_minus;
				b_minus = mij0*Sij_minus;
				grad_a_minus = (2.0*Rij0)*grad_Rij0 + Rij_minus*grad_abs_wi0 + absw*grad_Rij_minus;
				grad_b_minus = Sij_minus*grad_mij0 + mij0*grad_Sij_minus;
				grad_betaij_plus  = (1.0/(a_plus*a_plus + b_plus*b_plus))*(a_plus*grad_b_plus - b_plus*grad_a_plus);
				grad_betaij_minus = (1.0/(a_minus*a_minus + b_minus*b_minus))*(a_minus*grad_b_minus - b_minus*grad_a_minus);

				grad_betaij = grad_betaij_plus - grad_betaij_minus;

				tmp_k = gctl::kron(grad_betaij, mpara->nf[f]);
				k2 = k2 - sig*tmp_k;
			}
			else
			{
				if (std::abs(mij0) > mag_tolerance)
				{
					k3 += (-1.0/mij0)*(Sij_plus/Rij_plus - Sij_minus/Rij_minus);
				}
			}
		}

		if (k3 != 0.0)
		{
			tmp_k = gctl::kron(mpara->nf[f], mpara->nf[f]);
			k2 = k2 - k3*tmp_k;
		}

		// nT -> T 1e-9 / 4*pi*e-7 = 1/(400*pi)*100 = 1/(4*pi) -> A/m
		out_tensor = out_tensor - 1.0/(4.0*GCTL_Pi)*k2*mpara->mag_amp[f];
	}

    out_tensor = R*out_tensor*R_T;
    out_tensor[0][0] *= -1.0;
    out_tensor[0][1] *= -1.0;
    out_tensor[0][2] *= -1.0;
    out_tensor[1][0] *= -1.0;
    out_tensor[2][0] *= -1.0;
	return out_tensor;
}

void gctl::magkernel(matrix<double> &kernel, const array<magcone_ren17> &top_ele, 
    const array<magcone_ren17> &btm_ele, const array<point3ds> &obsp, 
    magnetic_field_type_e comp_type, verbose_type_e verbose)
{
    if (comp_type != Bx && comp_type != By && comp_type != Bz)
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Invalid magnetic componment type. Must be Bx, By or Bz.");
		return;
	}
	
	if (top_ele.size() != btm_ele.size())
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Elements' size don't equal.");
		return;
	}

    int i, j;
	int o_size = obsp.size();
	int e_size = top_ele.size();
	kernel.resize(o_size, e_size);

	array<tensor> Rs(o_size);
#pragma omp parallel for private (i) schedule(guided)
	for (i = 0; i < o_size; i++)
	{
		Rs[i] = transform_matrix(obsp[i]);
	}

	point3dc mag_b;
	gctl::progress_bar bar(o_size*2, "magkernel_componments");
	for (i = 0; i < o_size; i++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(i);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);

#pragma omp parallel for private (j, mag_b) shared(i) schedule(guided)
		for (j = 0; j < e_size; j++)
		{
			mag_b = magkernel_single(top_ele[j], obsp[i], Rs.get(i));
			if (comp_type == Bx) kernel[i][j] = mag_b.y;
			if (comp_type == By) kernel[i][j] = mag_b.z;
			if (comp_type == Bz) kernel[i][j] = mag_b.x;
		}
	}

	for (i = 0; i < o_size; i++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(i + o_size);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(i + o_size);

#pragma omp parallel for private (j, mag_b) shared(i) schedule(guided)
		for (j = 0; j < e_size; j++)
		{
			mag_b = magkernel_single(btm_ele[j], obsp[i], Rs.get(i));
			if (comp_type == Bx) kernel[i][j] -= mag_b.y;
			if (comp_type == By) kernel[i][j] -= mag_b.z;
			if (comp_type == Bz) kernel[i][j] -= mag_b.x;
		}
	}
	return;
}

void gctl::magkernel(spmat<double> &kernel, const array<magcone_ren17> &top_ele, 
    const array<magcone_ren17> &btm_ele, const array<point3ds> &obsp, 
    double cut_angle, magnetic_field_type_e comp_type, verbose_type_e verbose)
{
    if (comp_type != Bx && comp_type != By && comp_type != Bz)
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Invalid magnetic componment type. Must be Bx, By or Bz.");
		return;
	}
	
	if (top_ele.size() != btm_ele.size())
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Elements' size don't equal.");
		return;
	}

    int i, j;
	int o_size = obsp.size();
	int e_size = top_ele.size();

	array<tensor> Rs(o_size);
#pragma omp parallel for private (i) schedule(guided)
	for (i = 0; i < o_size; i++)
	{
		Rs[i] = transform_matrix(obsp[i]);
	}

	point3dc cen, mag_b;
	mat_node<double> tmp_plt;
	std::map<int, int> tri_idx;
	std::vector<mat_node<double>> triplts;

	gctl::progress_bar bar2(o_size, "initializing triplts");
	for (i = 0; i < o_size; i++)
	{
		if (verbose == gctl::FullMsg) bar2.progressed(i);
		else if (verbose == gctl::ShortMsg) bar2.progressed_simple(i);

		for (j = 0; j < e_size; j++)
		{
			cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
			if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
			{
				tmp_plt.r_id = i;
				tmp_plt.c_id = j;
				tmp_plt.val = 1.0;

				tri_idx[j + i*e_size] = triplts.size();
				triplts.push_back(tmp_plt);
			}
		}
	}

	gctl::progress_bar bar(o_size*2, "magkernel_componments");
	for (i = 0; i < o_size; i++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(i);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);

#pragma omp parallel for private (j, mag_b, cen) shared(i, cut_angle) schedule(guided)
		for (j = 0; j < e_size; j++)
		{
			cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
			if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
			{
				mag_b = magkernel_single(top_ele[j], obsp[i], Rs.get(i));
				if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val = mag_b.y;
				if (comp_type == By) triplts[tri_idx[j + i*e_size]].val = mag_b.z;
				if (comp_type == Bz) triplts[tri_idx[j + i*e_size]].val = mag_b.x;
			}
		}
	}

	for (i = 0; i < o_size; i++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(i + o_size);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(i + o_size);

#pragma omp parallel for private (j, mag_b, cen) shared(i, cut_angle) schedule(guided)
		for (j = 0; j < e_size; j++)
		{
			cen = 1.0/3.0*(*btm_ele[j].vert[0] + *btm_ele[j].vert[1] + *btm_ele[j].vert[2]);
			if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
			{
				mag_b = magkernel_single(btm_ele[j], obsp[i], Rs.get(i));
				if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val -= mag_b.y;
				if (comp_type == By) triplts[tri_idx[j + i*e_size]].val -= mag_b.z;
				if (comp_type == Bz) triplts[tri_idx[j + i*e_size]].val -= mag_b.x;
			}
		}
	}

	kernel.malloc(o_size, e_size, 0.0);
	kernel.set_triplts(triplts);
	return;
}

void gctl::magobser(array<point3dc> &out_obs, const array<magcone_ren17> &top_ele, 
    const array<magcone_ren17> &btm_ele, const array<point3ds> &obsp, 
    const array<double> &sus, verbose_type_e verbose)
{
    if (top_ele.size() != btm_ele.size())
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Elements' size don't equal.");
		return;
	}
	
    int i, j;
	int o_size = obsp.size();
	int e_size = top_ele.size();

	out_obs.resize(o_size, point3dc(0.0, 0.0, 0.0));
	array<tensor> Rs(o_size);
#pragma omp parallel for private (i) schedule(guided)
	for (i = 0; i < o_size; i++)
	{
		Rs[i] = transform_matrix(obsp[i]);
	}

	gctl::progress_bar bar(e_size*2, "magobser_componments");
	for (j = 0; j < e_size; j++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(j);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(j);

#pragma omp parallel for private (i) shared (j) schedule(guided)
		for (i = 0; i < o_size; i++)
		{
			out_obs[i] = out_obs[i] + sus[j] * magkernel_single(top_ele[j], obsp[i], Rs.get(i));
		}
	}

	for (j = 0; j < e_size; j++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(j + e_size);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(j + e_size);

#pragma omp parallel for private (i) shared (j) schedule(guided)
		for (i = 0; i < o_size; i++)
		{
			out_obs[i] = out_obs[i] - sus[j] * magkernel_single(btm_ele[j], obsp[i], Rs.get(i));
		}
	}
    return;
}

void gctl::magobser(array<tensor> &out_obs, const array<magcone_ren17> &top_ele, 
    const array<magcone_ren17> &btm_ele, const array<point3ds> &obsp, 
    const array<double> &sus, verbose_type_e verbose)
{
    if (top_ele.size() != btm_ele.size())
	{
		throw std::runtime_error("[gctl_potential::magcone_ren17] Elements' size don't equal.");
		return;
	}
	
    int i, j;
	int o_size = obsp.size();
	int e_size = top_ele.size();

	out_obs.resize(o_size, tensor(0.0));
	array<tensor> Rs(o_size);
#pragma omp parallel for private (i) schedule(guided)
	for (i = 0; i < o_size; i++)
	{
		Rs[i] = transform_matrix(obsp[i]);
	}

	gctl::progress_bar bar(e_size*2, "magobser_componments");
	for (j = 0; j < e_size; j++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(j);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(j);

#pragma omp parallel for private (i) shared (j) schedule(guided)
		for (i = 0; i < o_size; i++)
		{
			out_obs[i] = out_obs[i] + sus[j] * magkernel_single_tensor(top_ele[j], obsp[i], Rs.get(i));
		}
	}

	for (j = 0; j < e_size; j++)
	{
		if (verbose == gctl::FullMsg) bar.progressed(j + e_size);
		else if (verbose == gctl::ShortMsg) bar.progressed_simple(j + e_size);

#pragma omp parallel for private (i) shared (j) schedule(guided)
		for (i = 0; i < o_size; i++)
		{
			out_obs[i] = out_obs[i] - sus[j] * magkernel_single_tensor(btm_ele[j], obsp[i], Rs.get(i));
		}
	}
    return;
}