261 lines
10 KiB
C
261 lines
10 KiB
C
// c99 -ggdb -Wall -I ../ ewalds.c ../qpms/ewald.c ../qpms/ewaldsf.c ../qpms/lattices2d.c -lgsl -lm -lblas
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// implementation of the [LT(4.16)] test
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#include <math.h>
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#define M_SQRTPI 1.7724538509055160272981674833411452
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#include <qpms/ewald.h>
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#include <qpms/tiny_inlines.h>
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#include <qpms/indexing.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <float.h>
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#include <gsl/gsl_sf_legendre.h>
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typedef struct ewaldtest_triang_params {
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qpms_l_t lMax;
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point2d beta;
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double k;
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double a;
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double eta;
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double maxR;
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double maxK;
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double csphase;
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TriangularLatticeOrientation orientation;
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} ewaldtest_triang_params;
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typedef struct ewaldtest_triang_results {
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ewaldtest_triang_params p;
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complex double *sigmas_short,
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*sigmas_long,
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sigma0,
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*sigmas_total;
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double *err_sigmas_short,
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*err_sigmas_long,
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err_sigma0,
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*err_sigmas_total;
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complex double *regsigmas_416;
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} ewaldtest_triang_results;
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ewaldtest_triang_params paramslist[] = {
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// lMax, beta, k, a, eta, maxR, maxK, csphase, orientation
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#if 0
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{ 3, {1.1, 0.23}, 2.3, 0.97, 0.5, 20, 20, 1., TRIANGULAR_VERTICAL},
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{ 3, {1.1, 0.23}, 2.3, 0.97, 0.5, 30, 30, -1., TRIANGULAR_VERTICAL},
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{ 3, {1.1, 0.23}, 2.3, 0.97, 0.9, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 3, {1.1, 0.23}, 2.3, 0.97, 1.3, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 1.9, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 2.5, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 3.2, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 3.8, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 4.5, 30, 30, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 4.5, 40, 40, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 2.3, 100, 100, 1., TRIANGULAR_VERTICAL},
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{ 6, {1.1, 0.23}, 2.3, 0.97, 2.9, 100, 100, 1., TRIANGULAR_VERTICAL},
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#endif
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{ 2, {1.1, 0.23}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {-1.1, -0.23}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 1.1}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, -1.1}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {-1.1, 0}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 5.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 5.5, 10, 80, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 5.5, 5, 40, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 5.5, 2, 16, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 2.5, 10, 80, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 2.5, 5, 40, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 2.5, 2, 16, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 0.5, 10, 80, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 0.5, 5, 40, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 0}, 2.3, 0.97, 0.5, 2, 16, 1., TRIANGULAR_VERTICAL},
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{ 2, {0.3, 0}, 2.3, 0.97, 0.5, 2, 16, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, 2.3, 0.97, 0.5, 5, 40, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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// end:
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// { 0, {0, 0}, 0, 0, 0, 0, 0, 0, 0}
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};
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void ewaldtest_triang_results_free(ewaldtest_triang_results *r) {
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free(r->sigmas_short);
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free(r->sigmas_long);
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free(r->sigmas_total);
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free(r->err_sigmas_long);
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free(r->err_sigmas_total);
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free(r->err_sigmas_short);
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free(r->regsigmas_416);
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free(r);
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}
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void dump_points2d_rordered(const points2d_rordered_t *ps, char *filename) {
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FILE *f = fopen(filename, "w");
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for (size_t i = 0; i < ps->nrs; ++i) {
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fprintf(f, "# r = %.16g\n", ps->rs[i]);
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for (ptrdiff_t j = ps->r_offsets[i]; j < ps->r_offsets[i+1]; ++j)
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fprintf(f, "%.16g %.16g\n", ps->base[j].x, ps->base[j].y);
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}
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fclose(f);
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}
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static inline double san(double x) {
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return fabs(x) < 1e-13 ? 0 : x;
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}
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ewaldtest_triang_results *ewaldtest_triang(const ewaldtest_triang_params p);
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int main() {
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gsl_set_error_handler(IgnoreUnderflowsGSLErrorHandler);
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for (size_t i = 0; i < sizeof(paramslist)/sizeof(ewaldtest_triang_params); ++i) {
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ewaldtest_triang_params p = paramslist[i];
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ewaldtest_triang_results *r = ewaldtest_triang(p);
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// TODO print per-test header here
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printf("===============================\n");
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printf("a = %g, K = %g, Kmax = %g, Rmax = %g, lMax = %d, eta = %g, k = %g, beta = (%g,%g), csphase = %g\n",
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p.a, 4*M_PI/sqrt(3)/p.a, p.maxK, p.maxR, p.lMax, p.eta, p.k, p.beta.x, p.beta.y, p.csphase);
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printf("sigma0: %.16g%+.16gj\n", creal(r->sigma0), cimag(r->sigma0));
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for (qpms_l_t n = 0; n <= p.lMax; ++n) {
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for (qpms_m_t m = -n; m <= n; ++m){
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if ((m+n)%2) continue;
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qpms_y_t y = qpms_mn2y_sc(m,n);
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qpms_y_t y_conj = qpms_mn2y_sc(-m,n);
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// y n m sigma_total (err), regsigmas_416 regsigmas_415_recon
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printf("%zd %d %d: T:%.16g%+.16gj(%.3g) L:%.16g%+.16gj(%.3g) S:%.16g%+.16gj(%.3g) \n| predict %.16g%+.16gj \n| actual %.16g%+.16gj\n",
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y, n, m, creal(san(r->sigmas_total[y])), san(cimag(r->sigmas_total[y])),
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r->err_sigmas_total[y],
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san(creal(r->sigmas_long[y])), san(cimag(r->sigmas_long[y])),
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r->err_sigmas_long[y],
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san(creal(r->sigmas_short[y])), san(cimag(r->sigmas_short[y])),
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r->err_sigmas_short[y],
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san(creal(r->regsigmas_416[y])), san(cimag(r->regsigmas_416[y])),
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san(creal(r->sigmas_total[y]) + creal(r->sigmas_total[y_conj])),
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san(cimag(r->sigmas_total[y]) - cimag(r->sigmas_total[y_conj]))
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);
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}
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}
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ewaldtest_triang_results_free(r);
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}
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return 0;
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}
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int ewaldtest_counter = 0;
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ewaldtest_triang_results *ewaldtest_triang(const ewaldtest_triang_params p) {
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const double a = p.a; //const double a = p.h * sqrt(3);
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const double A = sqrt(3) * a * a / 2.; // unit cell size
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const double K_len = 4*M_PI/a/sqrt(3); // reciprocal vector length
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ewaldtest_triang_results *results = malloc(sizeof(ewaldtest_triang_results));
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results->p = p;
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triangular_lattice_gen_t *Rlg = triangular_lattice_gen_init(a, p.orientation, false, 0); // N.B. orig is not included (not directly usable for the honeycomb lattice)
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triangular_lattice_gen_extend_to_r(Rlg, p.maxR + a);
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triangular_lattice_gen_t *Klg = triangular_lattice_gen_init(K_len, reverseTriangularLatticeOrientation(p.orientation), true, 0);
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triangular_lattice_gen_extend_to_r(Klg, p.maxK + K_len);
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point2d *Rpoints = Rlg->ps.base; //point2d *Kpoints = Klg->ps.base;
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size_t nR = Rlg->ps.r_offsets[Rlg->ps.nrs],
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nK = Klg->ps.r_offsets[Klg->ps.nrs];
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qpms_y_t nelem_sc = qpms_lMax2nelem_sc(p.lMax);
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results->sigmas_short = malloc(sizeof(complex double)*nelem_sc);
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results->sigmas_long = malloc(sizeof(complex double)*nelem_sc);
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results->sigmas_total = malloc(sizeof(complex double)*nelem_sc);
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results->err_sigmas_short = malloc(sizeof(double)*nelem_sc);
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results->err_sigmas_long = malloc(sizeof(double)*nelem_sc);
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results->err_sigmas_total = malloc(sizeof(double)*nelem_sc);
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qpms_ewald3_constants_t *c = qpms_ewald3_constants_init(p.lMax, p.csphase);
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points2d_rordered_t *Kpoints_plus_beta = points2d_rordered_shift(&(Klg->ps), p.beta,
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8*DBL_EPSILON, 8*DBL_EPSILON);
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char filename[BUFSIZ];
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sprintf(filename, "betalattice_%d.out", ewaldtest_counter);
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dump_points2d_rordered(Kpoints_plus_beta, filename);
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point2d particle_shift = {0,0}; // TODO make this a parameter
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if (0!=ewald32_sigma_long_shiftedpoints(results->sigmas_long,
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results->err_sigmas_long, c, p.eta, p.k, A,
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nK, Kpoints_plus_beta->base,
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p.beta,
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particle_shift))
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abort();
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if (0!=ewald32_sigma_short_shiftedpoints(
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results->sigmas_short, results->err_sigmas_short, c,
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p.eta, p.k,
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nR, Rpoints, p.beta, particle_shift))
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abort();
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if (0!=ewald32_sigma0(&(results->sigma0), &(results->err_sigma0), c, p.eta, p.k))
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abort();
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for(qpms_y_t y = 0; y < nelem_sc; ++y) {
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results->sigmas_total[y] = results->sigmas_short[y] + results->sigmas_long[y];
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results->err_sigmas_total[y] = results->err_sigmas_short[y] + results->err_sigmas_long[y];
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}
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results->sigmas_total[0] += results->sigma0;
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results->err_sigmas_total[0] += results->err_sigma0;
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// Now calculate the reference values [LT(4.16)]
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results->regsigmas_416 = calloc(nelem_sc, sizeof(complex double));
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results->regsigmas_416[0] = -2 * c->legendre0[gsl_sf_legendre_array_index(0,0)];
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{
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double legendres[gsl_sf_legendre_array_n(p.lMax)];
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points2d_rordered_t sel =
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points2d_rordered_annulus(Kpoints_plus_beta, 0, true, p.k, false);
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if (0 != sel.nrs)
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{
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point2d *beta_pq_lessthan_k = sel.base + sel.r_offsets[0];
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size_t beta_pq_lessthan_k_count = sel.r_offsets[sel.nrs] - sel.r_offsets[0];
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for(size_t i = 0; i < beta_pq_lessthan_k_count; ++i) {
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point2d beta_pq = beta_pq_lessthan_k[i];
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double rbeta_pq = cart2norm(beta_pq);
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double arg_pq = atan2(beta_pq.y, beta_pq.x);
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double denom = sqrt(p.k*p.k - rbeta_pq*rbeta_pq);
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if( gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,
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p.lMax, denom/p.k, p.csphase, legendres) != 0)
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abort();
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for (qpms_y_t y = 0; y < nelem_sc; ++y) {
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qpms_l_t n; qpms_m_t m;
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qpms_y2mn_sc_p(y, &m, &n);
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if ((m+n)%2 != 0)
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continue;
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complex double eimf = cexp(I*m*arg_pq);
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results->regsigmas_416[y] +=
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4*M_PI*ipow(n)/p.k/A
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* eimf * legendres[gsl_sf_legendre_array_index(n,abs(m))] * min1pow_m_neg(m)
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/ denom;
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}
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}
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}
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}
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points2d_rordered_free(Kpoints_plus_beta);
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qpms_ewald3_constants_free(c);
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triangular_lattice_gen_free(Klg);
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triangular_lattice_gen_free(Rlg);
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++ewaldtest_counter;
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return results;
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}
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