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/*
* Copyright 2014-2015 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/>.
*/
/**
* @file
* evaluation of the solution on a grid
*/
#include <errno.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "brill_data.h"
#include "internal.h"
int bd_eval_psi(const BDContext *bd,
const double *rho, int nb_coords_rho,
const double *z, int nb_coords_z,
const unsigned int diff_order[2],
double *psi, unsigned int psi_stride)
{
BDPriv *s = bd->priv;
const double sfr = bd->basis_scale_factor_rho, sfz = bd->basis_scale_factor_z;
double (*eval)(double coord, int idx, double sf);
double *basis_val_rho = NULL, *basis_val_z = NULL;
double add = 0.0;
int ret = 0;
if (diff_order[0] > 2 || diff_order[1] > 2) {
bdi_log(bd, 0, "Derivatives of higher order than 2 are not supported.\n");
return -ENOSYS;
}
if (diff_order[0] == 0 && diff_order[1] == 0)
add = 1.0;
/* precompute the basis values on the grid points */
basis_val_rho = malloc(sizeof(*basis_val_rho) * bd->nb_coeffs_rho * nb_coords_rho);
basis_val_z = malloc(sizeof(*basis_val_z) * bd->nb_coeffs_z * nb_coords_z);
if (!basis_val_rho || !basis_val_z) {
ret = -ENOMEM;
goto fail;
}
switch (diff_order[0]) {
case 0: eval = s->basis->eval; break;
case 1: eval = s->basis->eval_diff1; break;
case 2: eval = s->basis->eval_diff2; break;
}
for (int i = 0; i < nb_coords_rho; i++) {
double rrho = rho[i];
for (int j = 0; j < bd->nb_coeffs_rho; j++)
basis_val_rho[i * bd->nb_coeffs_rho + j] = eval(rrho, j, sfr);
}
switch (diff_order[1]) {
case 0: eval = s->basis->eval; break;
case 1: eval = s->basis->eval_diff1; break;
case 2: eval = s->basis->eval_diff2; break;
}
for (int i = 0; i < nb_coords_z; i++) {
double zz = z[i];
for (int j = 0; j < bd->nb_coeffs_z; j++)
basis_val_z[i * bd->nb_coeffs_z + j] = eval(zz, j, sfz);
}
for (int i = 0; i < nb_coords_z; i++) {
double *dst = psi + i * psi_stride;
for (int j = 0; j < nb_coords_rho; j++) {
double ppsi = add;
for (int m = 0; m < bd->nb_coeffs_z; m++)
for (int n = 0; n < bd->nb_coeffs_rho; n++)
ppsi += s->coeffs[m * bd->nb_coeffs_rho + n] * basis_val_rho[j * bd->nb_coeffs_rho + n] * basis_val_z[i * bd->nb_coeffs_z + m];
*dst++ = ppsi;
}
}
fail:
free(basis_val_rho);
free(basis_val_z);
return ret;
}
static void eval_metric(const BDContext *bd,
const double *rho, int nb_coords_rho,
const double *z, int nb_coords_z,
enum BDMetricComponent comp,
const unsigned int diff_order[2],
const double *psi,
const double *dpsi_rho, const double *dpsi_z,
const double *d2psi_rho, const double *d2psi_z, const double *d2psi_rho_z,
double *out, unsigned int out_stride)
{
const BDPriv *s = bd->priv;
if (comp != BD_METRIC_COMPONENT_RHORHO &&
comp != BD_METRIC_COMPONENT_ZZ &&
comp != BD_METRIC_COMPONENT_PHIPHI) {
memset(out, 0, out_stride * nb_coords_z * sizeof(*out));
return;
}
/* the template for the loop over the grid points */
#define EVAL_LOOP(DO_EVAL) \
do { \
for (int i = 0; i < nb_coords_z; i++) { \
const double zz = z[i]; \
double *dst = out + i * out_stride; \
\
for (int j = 0; j < nb_coords_rho; j++) { \
const double rrho = rho[j]; \
const double ppsi = psi[i * nb_coords_rho + j]; \
const double psi2 = SQR(ppsi); \
const double psi3 = psi2 * ppsi; \
const double psi4 = SQR(psi2); \
double val; \
\
DO_EVAL; \
\
*dst++ = val; \
} \
} \
} while (0)
#define GRID(arr) (arr[i * nb_coords_rho + j])
if (comp == BD_METRIC_COMPONENT_PHIPHI) {
switch (diff_order[0]) {
case 0:
switch (diff_order[1]) {
case 0: EVAL_LOOP(val = SQR(rrho) * psi4); break;
case 1: EVAL_LOOP(val = 4 * SQR(rrho) * psi3 * GRID(dpsi_z)); break; // ∂_z
case 2: EVAL_LOOP(val = 4 * SQR(rrho) * (GRID(d2psi_z) * psi3 + 3 * psi2 * SQR(GRID(dpsi_z)))); break; // ∂_z ∂_z
}
break;
case 1:
switch (diff_order[1]) {
case 0: EVAL_LOOP(val = 2 * rrho * psi4 + 4 * SQR(rrho) * psi3 * GRID(dpsi_rho)); break; // ∂_ρ
case 1: EVAL_LOOP(val = 8 * rrho * psi3 * GRID(dpsi_z) + 12 * SQR(rrho) * psi2 * GRID(dpsi_z) * GRID(dpsi_rho) + 4 * SQR(rrho) * psi3 * GRID(d2psi_rho_z)); break; // ∂_ρ ∂_z
}
break;
case 2: EVAL_LOOP(val = 4 * SQR(rrho) * psi3 * GRID(d2psi_rho) + 12 * SQR(rrho * ppsi * GRID(dpsi_rho)) + 16 * rrho * psi3 * GRID(dpsi_rho) + 2 * psi4); break; // ∂_ρ ∂_ρ
}
} else {
// γ_ρρ / γ_zz
/* a wrapper around the actual evaluation expression that provides the q function and its
* derivatives as needed */
#define DO_EVAL_Q_WRAPPER(DO_EVAL, eval_drho, eval_dz, eval_d2rho, eval_d2z, eval_d2rhoz) \
do { \
const double base = psi4 * exp(2 * s->q_func->q(bd, rrho, zz)); \
double drho, dz, d2rho, d2z, d2rho_z; \
\
if (eval_drho) drho = s->q_func->dq_rho(bd, rrho, zz) + 2 * GRID(dpsi_rho) / ppsi; \
if (eval_dz) dz = s->q_func->dq_z(bd, rrho, zz) + 2 * GRID(dpsi_z) / ppsi; \
if (eval_d2rho) d2rho = s->q_func->d2q_rho(bd, rrho, zz) + 2 * GRID(d2psi_rho) / ppsi - 2 * SQR(GRID(dpsi_rho) / ppsi); \
if (eval_d2z) d2z = s->q_func->d2q_z(bd, rrho, zz) + 2 * GRID(d2psi_z) / ppsi - 2 * SQR(GRID(dpsi_z) / ppsi); \
if (eval_d2rhoz) d2rho_z = s->q_func->d2q_rho_z(bd, rrho, zz) + 2 * GRID(d2psi_rho_z) / ppsi - 2 * GRID(dpsi_rho) * GRID(dpsi_z) / psi2; \
\
DO_EVAL; \
} while (0)
switch (diff_order[0]) {
case 0:
switch (diff_order[1]) {
case 0: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = base, 0, 0, 0, 0, 0)); break;
case 1: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = 2 * base * dz, 0, 1, 0, 0, 0)); break; // ∂_z
case 2: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = 4 * SQR(dz) * base + 2 * base * d2z, 0, 1, 0, 1, 0)); break; // ∂_z ∂_z
}
break;
case 1:
switch (diff_order[1]) {
case 0: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = 2 * base * drho, 1, 0, 0, 0, 0)); break; // ∂_ρ
case 1: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = 4 * base * drho * dz + 2 * base * d2rho_z, 1, 1, 0, 0, 1)); break; // ∂_ρ ∂_z
}
break;
case 2: EVAL_LOOP(DO_EVAL_Q_WRAPPER(val = 4 * SQR(drho) * base + 2 * base * d2rho, 1, 0, 1, 0, 0)); break; // ∂_ρ ∂_ρ
}
}
}
int bd_eval_metric(const BDContext *bd, const double *rho, int nb_coords_rho,
const double *z, int nb_coords_z,
int nb_comp, const enum BDMetricComponent *comp,
const unsigned int (*diff_order)[2],
double **out, unsigned int *out_strides)
{
const int nb_coords = nb_coords_rho * nb_coords_z;
double *psi = NULL, *dpsi_rho = NULL, *dpsi_z = NULL, *d2psi_rho = NULL, *d2psi_rho_z = NULL, *d2psi_z = NULL;
int ret = 0;
/* check the parameters for validity */
for (int i = 0; i < nb_comp; i++) {
if (comp[i] >= 9 || comp[i] < 0) {
bdi_log(bd, 0, "Invalid component %d: %d\n", i, comp[i]);
return -EINVAL;
}
if (diff_order[i][0] + diff_order[i][1] > 2) {
bdi_log(bd, 0, "At most second order derivatives are supported.\n");
return -ENOSYS;
}
}
/* evaluate the conformal factor and its derivatives as necessary */
#define EVAL_PSI(arr, order) \
do { \
if (arr) \
break; \
\
arr = malloc(nb_coords * sizeof(*arr)); \
if (!arr) { \
ret = -ENOMEM; \
goto fail; \
} \
\
ret = bd_eval_psi(bd, rho, nb_coords_rho, z, nb_coords_z, \
order, arr, nb_coords_rho); \
if (ret < 0) \
goto fail; \
} while (0)
for (int i = 0; i < nb_comp; i++) {
if (comp[i] != BD_METRIC_COMPONENT_RHORHO &&
comp[i] != BD_METRIC_COMPONENT_ZZ &&
comp[i] != BD_METRIC_COMPONENT_PHIPHI)
continue;
EVAL_PSI(psi, ((unsigned int[2]){ 0, 0 }));
if (diff_order[i][0])
EVAL_PSI(dpsi_rho, ((unsigned int[2]){ 1, 0 }));
if (diff_order[i][0] > 1)
EVAL_PSI(d2psi_rho, ((unsigned int[2]){ 2, 0 }));
if (diff_order[i][1])
EVAL_PSI(dpsi_z, ((unsigned int[2]){ 0, 1 }));
if (diff_order[i][1] > 1)
EVAL_PSI(d2psi_z, ((unsigned int[2]){ 0, 2 }));
if (diff_order[i][0] && diff_order[i][1])
EVAL_PSI(d2psi_rho_z, ((unsigned int[2]){ 1, 1 }));
}
/* evaluate the requested metric components */
for (int i = 0; i < nb_comp; i++)
eval_metric(bd, rho, nb_coords_rho, z, nb_coords_z,
comp[i], diff_order[i],
psi, dpsi_rho, dpsi_z, d2psi_rho, d2psi_z, d2psi_rho_z,
out[i], out_strides[i]);
fail:
free(psi);
free(dpsi_rho);
free(dpsi_z);
free(d2psi_rho);
free(d2psi_rho_z);
free(d2psi_z);
return ret;
}
int bd_eval_q(const BDContext *bd, const double *rho, int nb_coords_rho,
const double *z, int nb_coords_z, const unsigned int diff_order[2],
double *out, unsigned int out_stride)
{
BDPriv *s = bd->priv;
double (*eval)(const struct BDContext *bd, double rho, double z);
if (diff_order[0] > 2 || diff_order[1] > 2) {
bdi_log(bd, 0, "Derivatives of higher order than 2 are not supported.\n");
return -ENOSYS;
}
switch (diff_order[0]) {
case 0:
switch (diff_order[1]) {
case 0: eval = s->q_func->q; break;
case 1: eval = s->q_func->dq_z; break;
case 2: eval = s->q_func->d2q_z; break;
}
break;
case 1:
switch (diff_order[1]) {
case 0: eval = s->q_func->dq_rho; break;
case 1: eval = s->q_func->d2q_rho_z; break;
}
break;
case 2: eval = s->q_func->d2q_rho; break;
}
for (int i = 0; i < nb_coords_z; i++) {
double *dst = out + i * out_stride;
for (int j = 0; j < nb_coords_rho; j++)
*dst++ = eval(bd, rho[j], z[i]);
}
return 0;
}
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