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-rw-r--r--brill_data.c843
1 files changed, 0 insertions, 843 deletions
diff --git a/brill_data.c b/brill_data.c
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--- a/brill_data.c
+++ /dev/null
@@ -1,843 +0,0 @@
-/*
- * Copyright 2014 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/>.
- */
-
-#include <errno.h>
-#include <limits.h>
-#include <math.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include <gsl/gsl_blas.h>
-#include <gsl/gsl_linalg.h>
-
-#include <lapacke.h>
-
-#include "brill_data.h"
-
-#define ACC_TEST 1
-
-#define MAX(x, y) ((x) > (y) ? (x) : (y))
-#define MIN(x, y) ((x) > (y) ? (y) : (x))
-#define SQR(x) ((x) * (x))
-#define SGN(x) ((x) >= 0.0 ? 1.0 : -1.0)
-
-/*
- * small number to avoid r=0 singularities
- */
-#define EPS 1E-08
-
-/* a set of basis functions */
-typedef struct BasisSet {
- /* evaluate the idx-th basis function at the specified point*/
- long double (*eval) (long double coord, int idx, long double sf);
- /* evaluate the first derivative of the idx-th basis function at the specified point*/
- long double (*eval_diff1)(long double coord, int idx, long double sf);
- /* evaluate the second derivative of the idx-th basis function at the specified point*/
- long double (*eval_diff2)(long double coord, int idx, long double sf);
- /**
- * Get the idx-th collocation point for the specified order.
- * idx runs from 0 to order - 1 (inclusive)
- */
- long double (*colloc_point)(int order, int idx, long double sf);
-} BasisSet;
-
-typedef struct QFunc {
- double (*q)(struct BDContext *bd, double rho, double z);
- double (*dq_rho)(struct BDContext *bd, double rho, double z);
- double (*dq_z)(struct BDContext *bd, double rho, double z);
- double (*d2q_rho)(struct BDContext *bd, double rho, double z);
- double (*d2q_z)(struct BDContext *bd, double rho, double z);
- double (*d2q_rho_z)(struct BDContext *bd, double rho, double z);
-} QFunc;
-
-typedef struct BDPriv {
- const BasisSet *basis;
- const QFunc *q_func;
-
- int nb_colloc_points;
- int nb_colloc_points_rho;
- int nb_colloc_points_z;
-
- int colloc_grid_order_rho;
- int colloc_grid_order_z;
- int nb_coeffs;
-
- gsl_vector *coeffs;
-} BDPriv;
-
-/*
- * The basis of even (n = 2 * idx) SB functions (Boyd 2000, Ch 17.9)
- * SB(x, n) = sin((n + 1) arccot(|x| / L))
- * They are symmetric wrt origin and decay as 1/x in infinity.
- */
-
-static long double sb_even_eval(long double coord, int idx, long double sf)
-{
- long double val = atan2l(sf, coord);
-
- idx *= 2; // even only
-
- return sinl((idx + 1) * val);
-}
-
-static long double sb_even_eval_diff1(long double coord, int idx, long double sf)
-{
- long double val = atan2l(sf, coord);
-
- idx *= 2; // even only
-
- return - sf * (idx + 1) * SGN(coord) * cosl((idx + 1) * val) / (SQR(sf) + SQR(coord));
-}
-
-static long double sb_even_eval_diff2(long double coord, int idx, long double sf)
-{
- long double val = atan2l(sf, coord);
-
- idx *= 2; // even only
-
- return sf * (idx + 1) * SGN(coord) * (2 * fabsl(coord) * cosl((idx + 1) * val) - sf * (idx + 1) * sinl((idx + 1) * val)) / SQR(SQR(sf) + SQR(coord));
-}
-
-static long double sb_even_colloc_point(int order, int idx, long double sf)
-{
- long double t;
-
- idx = order - idx - 1;
-
- t = (idx + 2) * M_PI / (2 *(order + 2));
- return sf / tanl(t);
-}
-
-static const BasisSet sb_even_basis = {
- .eval = sb_even_eval,
- .eval_diff1 = sb_even_eval_diff1,
- .eval_diff2 = sb_even_eval_diff2,
- .colloc_point = sb_even_colloc_point,
-};
-
-static int brill_construct_matrix(BDContext *bd, gsl_matrix *mat,
- gsl_vector *rhs)
-{
- BDPriv *s = bd->priv;
- const long double sfr = bd->basis_scale_factor_rho, sfz = bd->basis_scale_factor_z;
-
- double *basis_val, *basis_dval, *basis_d2val;
- int idx_coeff_rho, idx_coeff_z, idx_grid_rho, idx_grid_z;
-
- /* precompute the basis values we will need */
- // FIXME: assumes same number of points in ρ and z directions
- basis_val = malloc(sizeof(*basis_val) * s->nb_colloc_points_rho * bd->nb_coeffs_rho);
- basis_dval = malloc(sizeof(*basis_dval) * s->nb_colloc_points_rho * bd->nb_coeffs_rho);
- basis_d2val = malloc(sizeof(*basis_d2val) * s->nb_colloc_points_rho * bd->nb_coeffs_rho);
- for (int i = 0; i < s->nb_colloc_points_rho; i++) {
- double coord = s->basis->colloc_point(s->colloc_grid_order_rho, i, sfr);
- for (int j = 0; j < bd->nb_coeffs_rho; j++) {
- basis_val [i * bd->nb_coeffs_rho + j] = s->basis->eval(coord, j, sfr);
- basis_dval [i * bd->nb_coeffs_rho + j] = s->basis->eval_diff1(coord, j, sfr);
- basis_d2val[i * bd->nb_coeffs_rho + j] = s->basis->eval_diff2(coord, j, sfr);
- }
- }
-
- for (idx_grid_z = 0; idx_grid_z < s->nb_colloc_points_z; idx_grid_z++) {
- double z_physical = s->basis->colloc_point(s->colloc_grid_order_z, idx_grid_z, sfz);
-
- for (idx_grid_rho = 0; idx_grid_rho < s->nb_colloc_points_rho; idx_grid_rho++) {
- double x_physical = s->basis->colloc_point(s->colloc_grid_order_rho, idx_grid_rho, sfr);
- double d2q = s->q_func->d2q_rho(bd, x_physical, z_physical) + s->q_func->d2q_z(bd, x_physical, z_physical);
- int idx_grid = idx_grid_z * s->nb_colloc_points_z + idx_grid_rho;
-
- for (idx_coeff_z = 0; idx_coeff_z < bd->nb_coeffs_z; idx_coeff_z++)
- for (idx_coeff_rho = 0; idx_coeff_rho < bd->nb_coeffs_rho; idx_coeff_rho++) {
- int idx_coeff = idx_coeff_z * bd->nb_coeffs_z + idx_coeff_rho;
-
- mat->data[idx_grid + mat->tda * idx_coeff] = basis_d2val[idx_grid_rho * bd->nb_coeffs_rho + idx_coeff_rho] * basis_val[idx_grid_z * bd->nb_coeffs_z + idx_coeff_z] +
- basis_d2val[idx_grid_z * bd->nb_coeffs_z + idx_coeff_z] * basis_val[idx_grid_rho * bd->nb_coeffs_rho + idx_coeff_rho] +
- basis_val [idx_grid_rho * bd->nb_coeffs_rho + idx_coeff_rho] * basis_val[idx_grid_z * bd->nb_coeffs_z + idx_coeff_z] * 0.25 * d2q;
- if (x_physical > EPS)
- mat->data[idx_grid + mat->tda * idx_coeff] += basis_dval [idx_grid_rho * bd->nb_coeffs_rho + idx_coeff_rho] * basis_val[idx_grid_z * bd->nb_coeffs_z + idx_coeff_z] / x_physical;
- else
- mat->data[idx_grid + mat->tda * idx_coeff] += basis_d2val [idx_grid_rho * bd->nb_coeffs_rho + idx_coeff_rho] * basis_val[idx_grid_z * bd->nb_coeffs_z + idx_coeff_z];
- }
- rhs->data[idx_grid] = -0.25 * d2q;
- }
- }
-
- free(basis_val);
- free(basis_dval);
- free(basis_d2val);
-
- return 0;
-}
-
-static int brill_solve_linear(gsl_matrix *mat, gsl_vector **px, gsl_vector **prhs)
-{
- int *ipiv;
- gsl_matrix *mat_f;
- double cond, ferr, berr, rpivot;
-
- gsl_vector *x = *px;
- gsl_vector *rhs = *prhs;
- char equed = 'N';
- int ret = 0;
-
- ipiv = malloc(mat->size1 * sizeof(*ipiv));
- mat_f = gsl_matrix_alloc(mat->size1, mat->size2);
- if (!ipiv || !mat_f) {
- ret = -ENOMEM;
- goto fail;
- }
-
- LAPACKE_dgesvx(LAPACK_COL_MAJOR, 'N', 'N', mat->size1, 1,
- mat->data, mat->tda, mat_f->data, mat_f->tda, ipiv, &equed,
- NULL, NULL, rhs->data, rhs->size, x->data, x->size,
- &cond, &ferr, &berr, &rpivot);
-
- fprintf(stderr, "LU factorization solution to a %zdx%zd matrix: "
- "condition number %16.16g; forward error %16.16g backward error %16.16g\n",
- mat->size1, mat->size2, cond, ferr, berr);
-fail:
- gsl_matrix_free(mat_f);
- free(ipiv);
-
- return ret;
-}
-
-static int brill_solve_svd(gsl_matrix *mat, gsl_vector **px, gsl_vector **prhs)
-{
- double *sv;
- int rank;
-
- gsl_vector *x = *px;
- gsl_vector *rhs = *prhs;
-
- sv = malloc(sizeof(*sv) * x->size);
- if (!sv)
- return -ENOMEM;
-
- LAPACKE_dgelsd(LAPACK_COL_MAJOR, rhs->size, x->size, 1, mat->data, mat->tda,
- rhs->data, rhs->size, sv, -1, &rank);
-
- fprintf(stderr, "Least squares SVD solution to a %zdx%zd matrix: "
- "rank %d, condition number %16.16g\n", mat->size1, mat->size2,
- rank, sv[x->size - 1] / sv[0]);
-
- gsl_vector_free(x);
-
- *px = rhs;
- (*px)->size = mat->size1;
- *prhs = NULL;
-
- free(sv);
-
- return 0;
-}
-
-/*
- * Solve the equation
- * Δψ + ¼ ψ (∂²q/∂r² + ∂²q/∂z²) = 0
- * for the coefficients of spectral approximation of ψ:
- * ψ(r, z) = 1 + ΣaᵢⱼTᵢ(r)Tⱼ(z)
- * where i = { 0, ... , bd->nb_coeffs_rho };
- * j = { 0, ... , bd->nb_coeffs_z };
- * q(r, z) and Tᵢ(x) are defined by bd->q_func, bd->laplace_q_func and
- * bd->basis.
- *
- * The cofficients are exported in bd->priv->coeffs
- */
-static int brill_solve(BDContext *bd)
-{
- BDPriv *s = bd->priv;
- gsl_matrix *mat = NULL;
- gsl_vector *coeffs = NULL, *rhs = NULL;
-
-#if ACC_TEST
- gsl_vector *rhs_bkp = NULL;
- gsl_matrix *mat_bkp = NULL;
-#endif
-
- int ret = 0;
-
- /* allocate and fill the pseudospectral matrix */
- mat = gsl_matrix_alloc (s->nb_coeffs, s->nb_colloc_points); // inverted order for lapack
- coeffs = gsl_vector_alloc (s->nb_coeffs);
- rhs = gsl_vector_calloc(s->nb_colloc_points);
- if (!mat || !coeffs || !rhs) {
- ret = -ENOMEM;
- goto fail;
- }
-
- /* fill the matrix */
- ret = brill_construct_matrix(bd, mat, rhs);
- if (ret < 0)
- goto fail;
-
-#if ACC_TEST
- /* make backups of the matrix and RHS, since they might be destroyed later */
- mat_bkp = gsl_matrix_alloc(mat->size2, mat->size1);
- rhs_bkp = gsl_vector_alloc(rhs->size);
- if (!mat_bkp || !rhs_bkp) {
- ret = -ENOMEM;
- goto fail;
- }
-
- gsl_vector_memcpy(rhs_bkp, rhs);
- gsl_matrix_transpose_memcpy(mat_bkp, mat);
-#endif
-
- /* solve for the coeffs */
- if (s->nb_colloc_points > s->nb_coeffs)
- ret = brill_solve_svd(mat, &coeffs, &rhs);
- else
- ret = brill_solve_linear(mat, &coeffs, &rhs);
-
- /* export the result */
- s->coeffs = coeffs;
-
-#if ACC_TEST
- {
- double min, max, rmin, rmax;
-
- gsl_vector_minmax(rhs_bkp, &rmin, &rmax);
- gsl_blas_dgemv(CblasNoTrans, 1.0, mat_bkp, coeffs, -1.0, rhs_bkp);
- gsl_vector_minmax(rhs_bkp, &min, &max);
-
- fprintf(stderr, "max(|A·x - rhs|) / max(|rhs|): %16.16g\n",
- MAX(fabs(min), fabs(max)) / MAX(fabs(rmin), fabs(rmax)));
- }
-#endif
-
-fail:
-
-#if ACC_TEST
- gsl_matrix_free(mat_bkp);
- gsl_vector_free(rhs_bkp);
-#endif
-
- if (ret < 0)
- gsl_vector_free(coeffs);
-
- gsl_vector_free(rhs);
- gsl_matrix_free(mat);
-
- return ret;
-}
-
-// q function form from PHYSICAL REVIEW D 88, 103009 (2013)
-// with σ and ρ_0 hardcoded to 1 for now
-static double q_gundlach(BDContext *bd, double rho, double z)
-{
- return bd->amplitude * SQR(rho) * exp(- (SQR(rho) + SQR(z)));
-}
-
-static double dq_rho_gundlach(BDContext *bd, double rho, double z)
-{
- return bd->amplitude * 2 * rho * exp(-SQR(rho) - SQR(z)) * (1 - SQR(rho));
-}
-
-static double d2q_rho_gundlach(BDContext *bd, double rho, double z)
-{
- double rho2 = SQR(rho);
- return bd->amplitude * 2 * exp(-rho2 - SQR(z)) * ((1 - rho2) * (1 - 2 * rho2) - 2 * rho2);
-}
-
-static double d2q_rho_z_gundlach(BDContext *bd, double rho, double z)
-{
- return -bd->amplitude * 4 * z * rho * exp(-SQR(rho) - SQR(z)) * (1 - SQR(rho));
-}
-
-static double dq_z_gundlach(BDContext *bd, double rho, double z)
-{
- return - bd->amplitude * 2 * z * SQR(rho) * exp(-SQR(rho) - SQR(z));
-}
-
-static double d2q_z_gundlach(BDContext *bd, double rho, double z)
-{
- return bd->amplitude * 2 * SQR(rho) * exp(-SQR(rho) - SQR(z)) * (2 * SQR(z) - 1);
-}
-
-static const QFunc q_func_gundlach = {
- .q = q_gundlach,
- .dq_rho = dq_rho_gundlach,
- .dq_z = dq_z_gundlach,
- .d2q_rho = d2q_rho_gundlach,
- .d2q_z = d2q_z_gundlach,
- .d2q_rho_z = d2q_rho_z_gundlach,
-};
-
-static double q_eppley(BDContext *bd, double rho, double z)
-{
- double r2 = SQR(rho) + SQR(z);
- return bd->amplitude * SQR(rho) / (1.0 + pow(r2, bd->eppley_n / 2.0));
-}
-
-static double dq_rho_eppley(BDContext *bd, double rho, double z)
-{
- double A = bd->amplitude;
- double n = bd->eppley_n;
- double rho2 = SQR(rho);
- double z2 = SQR(z);
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
- double rnm2 = pow(r, n - 2);
-
- return A * rho * (2 * (1 + rnm2 * r2) - n * rho2 * rnm2) / SQR(1 + rnm2 * r2);
-}
-
-static double dq_z_eppley(BDContext *bd, double rho, double z)
-{
- double A = bd->amplitude;
- double n = bd->eppley_n;
- double rho2 = SQR(rho);
- double z2 = SQR(z);
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
- double rnm2 = pow(r, n - 2);
-
- return - A * n * rho2 * z * rnm2 / SQR(1 + rnm2 * r2);
-}
-
-static double d2q_rho_eppley(BDContext *bd, double rho, double z)
-{
- double A = bd->amplitude;
- double n = bd->eppley_n;
- double rho2 = SQR(rho);
- double z2 = SQR(z);
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
- double rnm4 = pow(r, n - 4);
- double rn = rnm4 * SQR(r2);
- double rnp1 = 1 + rn;
-
- return A * (SQR(n) * SQR(rho2) * rnm4 * (rn - 1) - n * rho2 * rnm4 * (3 * rho2 + 5 * z2) * rnp1 + 2 * SQR(rnp1)) / (rnp1 * SQR(rnp1));
-}
-
-static double d2q_z_eppley(BDContext *bd, double rho, double z)
-{
- double A = bd->amplitude;
- double n = bd->eppley_n;
- double rho2 = SQR(rho);
- double z2 = SQR(z);
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
- double rnm4 = pow(r, n - 4);
- double rn = rnm4 * SQR(r2);
- double rnp1 = 1 + rn;
-
- return A * n * rho2 * rnm4 * (z2 - rho2 - n * z2 + rn * ((1 + n) * z2 - rho2)) / (rnp1 * SQR(rnp1));
-}
-
-static double d2q_rho_z_eppley(BDContext *bd, double rho, double z)
-{
- double A = bd->amplitude;
- double n = bd->eppley_n;
- double rho2 = SQR(rho);
- double z2 = SQR(z);
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
- double rnm4 = pow(r, n - 4);
- double rn = rnm4 * SQR(r2);
- double rnp1 = 1 + rn;
-
- return A * n * rho * z * rnm4 * (rn * (n * rho2 - 2 * z2) - 2 * z2 - n * rho2) / (rnp1 * SQR(rnp1));
-}
-
-static const QFunc q_func_eppley = {
- .q = q_eppley,
- .dq_rho = dq_rho_eppley,
- .dq_z = dq_z_eppley,
- .d2q_rho = d2q_rho_eppley,
- .d2q_z = d2q_z_eppley,
- .d2q_rho_z = d2q_rho_z_eppley,
-};
-
-static double d2q_eppley(BDContext *bd, double rho, double z)
-{
- double rho2 = SQR(rho);
- double z2 = SQR(z);
- double rho4 = SQR(rho2);
- double z4 = SQR(z2);
- double z6 = z4 * z2;
-
- double r2 = rho2 + z2;
- double r = sqrt(r2);
-
- return bd->amplitude * (2.0 + r2 * (7 * rho4 * rho4 + 23 * rho4 * rho2 * z2 + 27 * rho4 * z4 + rho2 * (13 * z6 - 41 * r) + 2 * z2 * (z6 + 2 * r))) / pow(1.0 + r2 * r2 * r, 3);
-}
-
-static int brill_init_check_options(BDContext *bd)
-{
- BDPriv *s = bd->priv;
-
- switch (bd->q_func_type) {
- case BD_Q_FUNC_GUNDLACH:
- s->q_func = &q_func_gundlach;
- break;
- case BD_Q_FUNC_EPPLEY:
- if (bd->eppley_n < 4) {
- fprintf(stderr, "Invalid n: %d < 4\n", bd->eppley_n);
- return -EINVAL;
- }
-
- s->q_func = &q_func_eppley;
- break;
- default:
- fprintf(stderr, "Unknown q function type: %d\n", bd->q_func_type);
- return -EINVAL;
- }
-
- if (!bd->nb_coeffs_z)
- bd->nb_coeffs_z = bd->nb_coeffs_rho;
-
- if (bd->nb_coeffs_rho != bd->nb_coeffs_z) {
- fprintf(stderr, "Different ρ and z basis orders are not supported.\n");
- return -EINVAL;
- }
-
- s->basis = &sb_even_basis;
-
- s->nb_coeffs = bd->nb_coeffs_rho * bd->nb_coeffs_z;
-
- s->nb_colloc_points_rho = bd->nb_coeffs_rho + bd->overdet_rho;
- s->nb_colloc_points_z = bd->nb_coeffs_z + bd->overdet_z;
-
- s->nb_colloc_points = s->nb_colloc_points_rho * s->nb_colloc_points_z;
-
- s->colloc_grid_order_rho = bd->nb_coeffs_rho + bd->colloc_grid_offset_rho;
- s->colloc_grid_order_z = bd->nb_coeffs_z + bd->colloc_grid_offset_z;
-
- return 0;
-}
-
-int bd_solve(BDContext *bd)
-{
- BDPriv *s = bd->priv;
- int ret;
-
- if (bd->psi_minus1_coeffs) {
- fprintf(stderr, "Solve called multiple times on the same context.\n");
- return -EINVAL;
- }
-
- ret = brill_init_check_options(bd);
- if (ret < 0)
- return ret;
-
- ret = brill_solve(bd);
- if (ret < 0)
- return ret;
-
- bd->psi_minus1_coeffs = s->coeffs->data;
- bd->stride = bd->nb_coeffs_rho;
-
- return 0;
-}
-
-BDContext *bd_context_alloc(void)
-{
- BDContext *bd = calloc(1, sizeof(*bd));
-
- if (!bd)
- return NULL;
-
- bd->q_func_type = BD_Q_FUNC_GUNDLACH;
- bd->amplitude = 1.0;
- bd->eppley_n = 5;
-
- bd->nb_coeffs_rho = 80;
- bd->nb_coeffs_z = 0;
-
- bd->colloc_grid_offset_rho = 3;
- bd->colloc_grid_offset_z = 3;
-
- bd->basis_scale_factor_rho = 3.0;
- bd->basis_scale_factor_z = 3.0;
-
- bd->priv = calloc(1, sizeof(BDPriv));
- if (!bd->priv) {
- free(bd);
- return NULL;
- }
-
- return bd;
-}
-
-void bd_context_free(BDContext **pbd)
-{
- BDContext *bd = *pbd;
- BDPriv *s;
-
- if (!bd)
- return;
-
- s = bd->priv;
-
- gsl_vector_free(s->coeffs);
-
- free(bd->priv);
- free(bd);
- *pbd = NULL;
-}
-
-int bd_eval_psi(BDContext *bd, const double *rho, int nb_coords_rho,
- const double *z, int nb_coords_z,
- const unsigned int diff_order[2],
- double *psi)
-{
- BDPriv *s = bd->priv;
- const long double sfr = bd->basis_scale_factor_rho, sfz = bd->basis_scale_factor_z;
- long double (*eval)(long double coord, int idx, long double sf);
-
- long double *basis_val_rho, *basis_val_z;
-
- long double add = 0.0;
-
- if (diff_order[0] > 2 || diff_order[1] > 2) {
- fprintf(stderr, "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);
-
- 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++)
- for (int j = 0; j < nb_coords_rho; j++) {
- long 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->data[m * bd->nb_coeffs_rho + n] * basis_val_rho[j * bd->nb_coeffs_rho + n] * basis_val_z[i * bd->nb_coeffs_z + m];
-
- psi[i * nb_coords_rho + j] = ppsi;
- }
-
- free(basis_val_rho);
- free(basis_val_z);
-
- return 0;
-
-}
-
-int bd_eval_metric(BDContext *bd, const double *rho, int nb_coords_rho,
- const double *z, int nb_coords_z,
- const unsigned int comp[2], const unsigned int diff_order[2],
- double *out)
-{
- BDPriv *s = bd->priv;
- 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 */
- if (comp[0] > 2 || comp[1] > 2) {
- fprintf(stderr, "Invalid component indices: %d%d\n", comp[0], comp[1]);
- return -EINVAL;
- }
-
- if (comp[0] != comp[1]) {
- memset(out, 0, nb_coords * sizeof(*out));
- return 0;
- }
-
- if (diff_order[0] + diff_order[1] > 2) {
- fprintf(stderr, "At most second order derivatives are supported.\n");
- return -ENOSYS;
- }
-
- /* evaluate the conformal factor and its derivatives if necessary */
-#define EVAL_PSI(arr, order) \
-do { \
- 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); \
- if (ret < 0) \
- goto fail; \
-} while (0)
-
- EVAL_PSI(psi, ((unsigned int[2]){ 0, 0 }));
- if (diff_order[0])
- EVAL_PSI(dpsi_rho, ((unsigned int[2]){ 1, 0 }));
- if (diff_order[0] > 1)
- EVAL_PSI(d2psi_rho, ((unsigned int[2]){ 2, 0 }));
- if (diff_order[1])
- EVAL_PSI(dpsi_z, ((unsigned int[2]){ 0, 1 }));
- if (diff_order[1] > 1)
- EVAL_PSI(d2psi_z, ((unsigned int[2]){ 0, 2 }));
- if (diff_order[0] && diff_order[1])
- EVAL_PSI(d2psi_rho_z, ((unsigned int[2]){ 1, 1 }));
-
-/* 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]; \
- \
- 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; \
- \
- out[i * nb_coords_rho + j] = val; \
- } \
- } \
-} while (0)
-
-#define GRID(arr) (arr[i * nb_coords_rho + j])
-
- if (comp[0] == 2) {
- // γ_φφ
- 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
- }
- }
-
-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(BDContext *bd, const double *rho, int nb_coords_rho,
- const double *z, int nb_coords_z, const unsigned int diff_order[2],
- double *out)
-{
- BDPriv *s = bd->priv;
- double (*eval)(struct BDContext *bd, double rho, double z);
-
- if (diff_order[0] > 2 || diff_order[1] > 2) {
- fprintf(stderr, "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++)
- for (int j = 0; j < nb_coords_rho; j++)
- out[i * nb_coords_rho + j] = eval(bd, rho[j], z[i]);
-
- return 0;
-}
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