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/*
* Teukolsky data -- template for the constraint equations definitions
* Copyright (C) 2017 Anton Khirnov <anton@khirnov.net>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#define L 1.0
#define R_0 0.0
static void EQNAME(double a,
unsigned int nb_coords[2], double *coords[2],
double *vars[TD_CONSTRAINT_VAR_NB][PSSOLVE_DIFF_ORDER_NB],
double *out)
{
for (int idx1 = 0; idx1 < nb_coords[1]; idx1++) {
const double coord1 = coords[1][idx1];
for (int idx0 = 0; idx0 < nb_coords[0]; idx0++) {
const double coord0 = coords[0][idx0];
const double r = coord0;
const double theta = coord1;
const int idx = idx1 * nb_coords[0] + idx0;
const double psi = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_00][idx] + 1.0;
const double K_rr = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_00][idx];
const double K_phiphi = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_00][idx];
const double dpsi_10 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_10][idx];
const double dpsi_01 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_01][idx];
const double dpsi_11 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_11][idx];
const double dpsi_20 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_20][idx];
const double dpsi_02 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_02][idx];
const double dK_rr_10 = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_10][idx];
const double dK_rr_01 = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_01][idx];
const double dK_phiphi_10 = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_10][idx];
const double dK_phiphi_01 = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_01][idx];
//const double K_rtheta_val = K_rtheta(a, r, theta);
//const double dK_rtheta_r_val = K_rtheta_dr(a, r, theta);
//const double dK_rtheta_theta_val = K_rtheta_dtheta(a, r, theta);
const double K_rtheta_val = eval_K_rtheta(a, L, R_0, coord0, coord1);
const double dK_rtheta_r_val = eval_dK_rtheta_r(a, L, R_0, coord0, coord1);
const double dK_rtheta_theta_val = eval_dK_rtheta_theta(a, L, R_0, coord0, coord1);
const double Km[3][3] = {{ K_rr, K_rtheta_val, 0 },
{ K_rtheta_val / SQR(r), -(K_rr + K_phiphi), 0 },
{ 0, 0, K_phiphi }};
#if 0
double gu[3][3];
double dgu[3][3][3], G[3][3][3], dG[3][3][3][3];
double Ric[3][3];
double g[3][3], dg[3][3][3], d2g[3][3][3][3];
eval_metric (a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, g);
for (int i = 0; i < 3; i++)
eval_dmetric[i] (a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, dg[i]);
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
eval_d2metric[i][j](a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, d2g[i][j]);
const double det = g[0][0] * g[1][1] * g[2][2] + 2 * g[0][1] * g[1][2] * g[0][2] - g[2][2] * SQR(g[0][1]) - SQR(g[0][2]) * g[1][1] - g[0][0] * SQR(g[1][2]);
// γ^{ij}
gu[0][0] = (g[1][1] * g[2][2] - SQR(g[1][2])) / det;
gu[1][1] = (g[0][0] * g[2][2] - SQR(g[0][2])) / det;
gu[2][2] = (g[0][0] * g[1][1] - SQR(g[0][1])) / det;
gu[0][1] = -(g[0][1] * g[2][2] - g[1][2] * g[0][2]) / det;
gu[0][2] = (g[0][1] * g[1][2] - g[1][1] * g[0][2]) / det;
gu[1][2] = -(g[0][0] * g[1][2] - g[0][1] * g[0][2]) / det;
gu[1][0] = gu[0][1];
gu[2][0] = gu[0][2];
gu[2][1] = gu[1][2];
// ∂_j γ^{kl}
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++) {
double val = 0.0;
for (int m = 0; m < 3; m++)
for (int n = 0; n < 3; n++)
val += -gu[k][m] * gu[l][n] * dg[j][m][n];
dgu[j][k][l] = val;
}
// Γ^j_{kl}
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++) {
double val = 0.0;
for (int m = 0; m < 3; m++)
val += 0.5 * gu[j][m] * (dg[k][l][m] + dg[l][k][m] - dg[m][k][l]);
G[j][k][l] = val;
}
// ∂_j Γ^k_{lm}
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++)
for (int m = 0; m < 3; m++) {
double val = 0.0;
for (int n = 0; n < 3; n++) {
val += dgu[j][k][n] * (dg [l][m][n] + dg [m][l][n] - dg [n][l][m]) +
gu [k][n] * (d2g[j][l][m][n] + d2g[j][m][l][n] - d2g[j][n][l][m]);
}
dG[j][k][l][m] = 0.5 * val;
}
// Ric_{jk}
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++) {
double val = 0.0;
for (int m = 0; m < 3; m++)
val += dG[m][m][j][k] - dG[k][m][j][m];
for (int m = 0; m < 3; m++)
for (int l = 0; l < 3; l++)
val += G[l][l][m] * G[m][j][k] - G[l][k][m] * G[m][j][l];
Ric[j][k] = val;
}
double Rscal = 0.0;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
Rscal += gu[i][j] * Ric[i][j];
const double dKm[3][3][3] = {
{
{ dK_rr_10, dK_rtheta_r_val, 0 },
{ gu[1][1] / gu[0][0] * dK_rtheta_r_val + dgu[0][1][1] / gu[0][0] * K_rtheta_val - dgu[0][0][0] / SQR(gu[0][0]) * gu[1][1] * K_rtheta_val,
-(dK_rr_10 + dK_phiphi_10), 0 },
{ 0, 0, dK_phiphi_10 },
},
{
{ dK_rr_01, dK_rtheta_theta_val, 0 },
{ gu[1][1] / gu[0][0] * dK_rtheta_theta_val + dgu[1][1][1] / gu[0][0] * K_rtheta_val - dgu[1][0][0] / SQR(gu[0][0]) * gu[1][1] * K_rtheta_val,
-(dK_rr_01 + dK_phiphi_01), 0 },
{ 0, 0, dK_phiphi_01 },
},
{ 0 },
};
#endif
if (EQUATION == TD_CONSTRAINT_EQ_HAM) {
double Rscal = eval_R_scalar(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20,
K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10);
double K2 = 0.0;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
K2 += Km[i][j] * Km[j][i];
out[idx] = Rscal - K2;
} else if (EQUATION == TD_CONSTRAINT_EQ_MOM_0) {
out[idx] = eval_Dcurv_m_r(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20,
K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10);
} else {
out[idx] = eval_Dcurv_m_t(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20,
K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10);
}
#if 0
} else {
int mom_comp = (EQUATION == TD_CONSTRAINT_EQ_MOM_0) ? 0 : 1;
double dKm_sum = 0.0;
for (int i = 0; i < 3; i++)
dKm_sum += dKm[i][i][mom_comp];
double Gterm1 = 0.0;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
Gterm1 += G[i][i][j] * Km[j][mom_comp];
double Gterm2 = 0.0;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
Gterm2 += G[j][i][mom_comp] * Km[i][j];
out[idx] = dKm_sum + Gterm1 - Gterm2;
}
#endif
}
}
}
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