Ewald summation – stupid implementation of alternative lattice sums
Former-commit-id: de2830e9e5b65fd679fcf5fd1e8ec3e13dba116a
This commit is contained in:
Marek Nečada
parent
68c1bf711a
commit
f660107925
156
qpms/ewald.c
156
qpms/ewald.c
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@ -239,6 +239,96 @@ int ewald32_sigma_long_shiftedpoints (
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return 0;
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return 0;
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}
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}
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int ewald32_sigma_long_points_and_shift (
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complex double *target, // must be c->nelem_sc long
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double *err,
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const qpms_ewald32_constants_t *c,
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const double eta, const double k, const double unitcell_area,
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const size_t npoints, const point2d *Kpoints,
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const point2d beta, // not needed
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const point2d particle_shift // target - src
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)
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{
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const qpms_y_t nelem_sc = c->nelem_sc;
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const qpms_l_t lMax = c->lMax;
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// Manual init of the ewald summation targets
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complex double *target_c = calloc(nelem_sc, sizeof(complex double));
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memset(target, 0, nelem_sc * sizeof(complex double));
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double *err_c = NULL;
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if (err) {
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err_c = calloc(nelem_sc, sizeof(double));
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memset(err, 0, nelem_sc * sizeof(double));
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}
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const double commonfac = 1/(k*k*unitcell_area); // used in the very end (CFC)
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assert(commonfac > 0);
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// space for Gamma_pq[j]'s
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qpms_csf_result Gamma_pq[lMax/2+1];
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// CHOOSE POINT BEGIN
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for (size_t i = 0; i < npoints; ++i) { // BEGIN POINT LOOP
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// Only these following two lines differ from ewald32_sigma_long_points_and_shift()!!!
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const point2d K_pq = Kpoints[i];
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const point2d beta_pq = {K_pq.x + beta.x, K_pq.y + beta.y};
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const double rbeta_pq = cart2norm(beta_pq);
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// CHOOSE POINT END
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const complex double phasefac = cexp(I*cart2_dot(K_pq,particle_shift)); // POINT-DEPENDENT (PFC) // !!!CHECKSIGN!!!
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const double arg_pq = atan2(beta_pq.y, beta_pq.x); // POINT-DEPENDENT
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// R-DEPENDENT BEGIN
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const complex double gamma_pq = lilgamma(rbeta_pq/k);
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const complex double z = csq(gamma_pq*k/(2*eta)); // Když o tom tak přemýšlím, tak tohle je vlastně vždy reálné
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for(qpms_l_t j = 0; j <= lMax/2; ++j) {
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int retval = complex_gamma_inc_e(0.5-j, z, Gamma_pq+j);
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// we take the other branch, cf. [Linton, p. 642 in the middle]: FIXME instead use the C11 CMPLX macros and fill in -O*I part to z in the line above
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if(creal(z) < 0)
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Gamma_pq[j].val = conj(Gamma_pq[j].val); //FIXME as noted above
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if(!(retval==0 ||retval==GSL_EUNDRFLW)) abort();
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}
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// R-DEPENDENT END
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// TODO optimisations: all the j-dependent powers can be done for each j only once, stored in array
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// and just fetched for each n, m pair
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for(qpms_l_t n = 0; n <= lMax; ++n)
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for(qpms_m_t m = -n; m <= n; ++m) {
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if((m+n) % 2 != 0) // odd coefficients are zero.
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continue;
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const qpms_y_t y = qpms_mn2y_sc(m, n);
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const complex double e_imalpha_pq = cexp(I*m*arg_pq);
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complex double jsum, jsum_c; ckahaninit(&jsum, &jsum_c);
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double jsum_err, jsum_err_c; kahaninit(&jsum_err, &jsum_err_c); // TODO do I really need to kahan sum errors?
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assert((n-abs(m))/2 == c->s1_jMaxes[y]);
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for(qpms_l_t j = 0; j <= c->s1_jMaxes[y]/*(n-abs(m))/2*/; ++j) { // FIXME </<= ?
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complex double summand = pow(rbeta_pq/k, n-2*j)
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* e_imalpha_pq * c->legendre0[gsl_sf_legendre_array_index(n,abs(m))] * min1pow_m_neg(m) // This line can actually go outside j-loop
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* cpow(gamma_pq, 2*j-1) // * Gamma_pq[j] bellow (GGG) after error computation
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* c->s1_constfacs[y][j];
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if(err) {
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// FIXME include also other errors than Gamma_pq's relative error
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kahanadd(&jsum_err, &jsum_err_c, Gamma_pq[j].err * cabs(summand));
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}
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summand *= Gamma_pq[j].val; // GGG
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ckahanadd(&jsum, &jsum_c, summand);
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}
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jsum *= phasefac; // PFC
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ckahanadd(target + y, target_c + y, jsum);
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if(err) kahanadd(err + y, err_c + y, jsum_err);
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}
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} // END POINT LOOP
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free(err_c);
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free(target_c);
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for(qpms_y_t y = 0; y < nelem_sc; ++y) // CFC common factor from above
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target[y] *= commonfac;
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if(err)
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for(qpms_y_t y = 0; y < nelem_sc; ++y)
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err[y] *= commonfac;
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return 0;
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}
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struct sigma2_integrand_params {
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struct sigma2_integrand_params {
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int n;
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int n;
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@ -339,6 +429,72 @@ int ewald32_sigma_short_shiftedpoints(
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return 0;
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return 0;
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}
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}
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int ewald32_sigma_short_points_and_shift(
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complex double *target, // must be c->nelem_sc long
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double *err,
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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const double eta, const double k,
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const size_t npoints, const point2d *Rpoints,
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const point2d beta,
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const point2d particle_shift // used only in the very end to multiply it by the phase
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)
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{
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const qpms_y_t nelem_sc = c->nelem_sc;
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const qpms_l_t lMax = c->lMax;
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gsl_integration_workspace *workspace =
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gsl_integration_workspace_alloc(INTEGRATION_WORKSPACE_LIMIT);
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// Manual init of the ewald summation targets
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complex double * const target_c = calloc(nelem_sc, sizeof(complex double));
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memset(target, 0, nelem_sc * sizeof(complex double));
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double *err_c = NULL;
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if (err) {
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err_c = calloc(nelem_sc, sizeof(double));
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memset(err, 0, nelem_sc * sizeof(double));
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}
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// CHOOSE POINT BEGIN
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for (size_t i = 0; i < npoints; ++i) { // BEGIN POINT LOOP
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//const point2d Rpq_shifted = Rpoints_plus_particle_shift[i];
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const point2d Rpq_shifted = cart2_add(Rpoints[i], cart2_scale(-1,particle_shift)); // CHECKSIGN!!!!
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const double r_pq_shifted = cart2norm(Rpq_shifted);
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// CHOOSE POINT END
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const double Rpq_shifted_arg = atan2(Rpq_shifted.y, Rpq_shifted.x); // POINT-DEPENDENT
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const complex double e_beta_Rpq = cexp(I*cart2_dot(beta, Rpq_shifted)); // POINT-DEPENDENT
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for(qpms_l_t n = 0; n <= lMax; ++n) {
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const double complex prefacn = - I * pow(2./k, n+1) * M_2_SQRTPI / 2; // TODO put outside the R-loop and multiply in the end
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const double R_pq_pown = pow(r_pq_shifted, n);
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// TODO the integral here
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double intres, interr;
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int retval = ewald32_sr_integral(r_pq_shifted, k, n, eta,
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&intres, &interr, workspace);
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if (retval) abort();
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for (qpms_m_t m = -n; m <= n; ++m){
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if((m+n) % 2 != 0) // odd coefficients are zero.
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continue; // nothing needed, already done by memset
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const complex double e_imf = cexp(I*m*Rpq_shifted_arg);
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const double leg = c->legendre0[gsl_sf_legendre_array_index(n, abs(m))];
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const qpms_y_t y = qpms_mn2y_sc(m,n);
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if(err)
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kahanadd(err + y, err_c + y, cabs(leg * (prefacn / I) * R_pq_pown
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* interr)); // TODO include also other errors
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ckahanadd(target + y, target_c + y,
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prefacn * R_pq_pown * leg * intres * e_beta_Rpq * e_imf * min1pow_m_neg(m));
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}
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}
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}
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gsl_integration_workspace_free(workspace);
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if(err) free(err_c);
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free(target_c);
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return 0;
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}
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#if 0
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#if 0
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@ -106,7 +106,7 @@ int ewald32_sigma_long_shiftedpoints (
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point2d beta,
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point2d beta,
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point2d particle_shift
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point2d particle_shift
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);
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);
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int ewald32_sigma_long_points_and_shift (//NI
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int ewald32_sigma_long_points_and_shift (
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complex double *target_sigmalr_y, // must be c->nelem_sc long
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complex double *target_sigmalr_y, // must be c->nelem_sc long
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double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
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double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c,
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const qpms_ewald32_constants_t *c,
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@ -133,12 +133,13 @@ int ewald32_sigma_short_shiftedpoints(
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point2d beta,
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point2d beta,
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point2d particle_shift // used only in the very end to multiply it by the phase
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point2d particle_shift // used only in the very end to multiply it by the phase
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);
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);
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int ewald32_sigma_short_points_and_shift(//NI
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int ewald32_sigma_short_points_and_shift(
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complex double *target_sigmasr_y, // must be c->nelem_sc long
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complex double *target_sigmasr_y, // must be c->nelem_sc long
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double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
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double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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double eta, double k,
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double eta, double k,
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size_t npoints, const point2d *Rpoints,
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size_t npoints, const point2d *Rpoints,
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point2d beta,
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point2d particle_shift
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point2d particle_shift
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);
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);
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int ewald32_sigma_short_points_rordered(//NI
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int ewald32_sigma_short_points_rordered(//NI
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@ -0,0 +1,329 @@
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// c99 -ggdb -Wall -I ../ ewaldshift2.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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point2d particle_shift;
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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, shift, k, a, eta, maxR, maxK, csphase, orientation
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/*
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{ 2, {2.7, 1}, {0.5,0.1325}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, {0.5,0.1325}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, {0.5,0.1325}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {2.7, 1}, {0.5,0.1325}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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*/
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 1}, {0.5,0.1325}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 2.1}, {0.5,0.1325}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 2.1}, {0.5,0.1325}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 2.1}, {0.5,0.1325}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {1.1, 2.1}, {0.5,0.1325}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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/*
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{ 2, {0, 3.1}, {0.5,0}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, {0.5,0}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, {0.5,0}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 3.1}, {0.5,0}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 1.1}, {0.5,0}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 1.1}, {0.5,0}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 1.1}, {0.5,0}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {0, 1.1}, {0.5,0}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
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{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 2, {1.1,0}, {0,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1,0}, {0,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1,0}, {0,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1,0}, {0,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1,0}, {0,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
*/
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.8,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.8,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.8,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.8,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.8,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.8,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.8,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.8,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
// Poloviční posun oproti přodchozímu
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.4,0.25}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.4,0.25}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.4,0.25}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {3.1*0.5,-3.1*0.8}, {0.4,0.25}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.4,0.25}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.4,0.25}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.4,0.25}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {1.1*0.5,-1.1*0.8}, {0.4,0.25}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
// miniposun
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {0.004,0.0025}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {3.1*0.5,-3.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 3, {1.1*0.5,-1.1*0.8}, {-0.004,-0.0025}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
/*
|
||||||
|
{ 2, {0, 3.1}, {0,0.5}, 2.3, 0.97, 0.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {0, 3.1}, {0,0.5}, 2.3, 0.97, 1.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {0, 3.1}, {0,0.5}, 2.3, 0.97, 2.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
{ 2, {0, 3.1}, {0,0.5}, 2.3, 0.97, 3.5, 20, 160, 1., TRIANGULAR_VERTICAL},
|
||||||
|
*/
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// end:
|
||||||
|
// { 0, {0, 0}, 0, 0, 0, 0, 0, 0, 0}
|
||||||
|
};
|
||||||
|
|
||||||
|
void ewaldtest_triang_results_free(ewaldtest_triang_results *r) {
|
||||||
|
free(r->sigmas_short);
|
||||||
|
free(r->sigmas_long);
|
||||||
|
free(r->sigmas_total);
|
||||||
|
free(r->err_sigmas_long);
|
||||||
|
free(r->err_sigmas_total);
|
||||||
|
free(r->err_sigmas_short);
|
||||||
|
free(r->regsigmas_416);
|
||||||
|
free(r);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void dump_points2d_rordered(const points2d_rordered_t *ps, char *filename) {
|
||||||
|
FILE *f = fopen(filename, "w");
|
||||||
|
for (size_t i = 0; i < ps->nrs; ++i) {
|
||||||
|
fprintf(f, "# r = %.16g\n", ps->rs[i]);
|
||||||
|
for (ptrdiff_t j = ps->r_offsets[i]; j < ps->r_offsets[i+1]; ++j)
|
||||||
|
fprintf(f, "%.16g %.16g\n", ps->base[j].x, ps->base[j].y);
|
||||||
|
}
|
||||||
|
fclose(f);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline double san(double x) {
|
||||||
|
return fabs(x) < 1e-13 ? 0 : x;
|
||||||
|
}
|
||||||
|
|
||||||
|
ewaldtest_triang_results *ewaldtest_triang(const ewaldtest_triang_params p);
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
gsl_set_error_handler(IgnoreUnderflowsGSLErrorHandler);
|
||||||
|
for (size_t i = 0; i < sizeof(paramslist)/sizeof(ewaldtest_triang_params); ++i) {
|
||||||
|
ewaldtest_triang_params p = paramslist[i];
|
||||||
|
ewaldtest_triang_results *r = ewaldtest_triang(p);
|
||||||
|
// TODO print per-test header here
|
||||||
|
printf("===============================\n");
|
||||||
|
printf("a = %g, K = %g, Kmax = %g, Rmax = %g, lMax = %d, eta = %g, k = %g, beta = (%g,%g), ps = (%g,%g), csphase = %g\n",
|
||||||
|
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.particle_shift.x, p.particle_shift.y, p.csphase);
|
||||||
|
printf("sigma0: %.16g%+.16gj\n", creal(r->sigma0), cimag(r->sigma0));
|
||||||
|
for (qpms_l_t n = 0; n <= p.lMax; ++n) {
|
||||||
|
for (qpms_m_t m = -n; m <= n; ++m){
|
||||||
|
if ((m+n)%2) continue;
|
||||||
|
qpms_y_t y = qpms_mn2y_sc(m,n);
|
||||||
|
qpms_y_t y_conj = qpms_mn2y_sc(-m,n);
|
||||||
|
// y n m sigma_total (err), regsigmas_416 regsigmas_415_recon
|
||||||
|
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"
|
||||||
|
,
|
||||||
|
y, n, m, creal(san(r->sigmas_total[y])), san(cimag(r->sigmas_total[y])),
|
||||||
|
r->err_sigmas_total[y],
|
||||||
|
san(creal(r->sigmas_long[y])), san(cimag(r->sigmas_long[y])),
|
||||||
|
r->err_sigmas_long[y],
|
||||||
|
san(creal(r->sigmas_short[y])), san(cimag(r->sigmas_short[y])),
|
||||||
|
r->err_sigmas_short[y]
|
||||||
|
//san(creal(r->regsigmas_416[y])), san(cimag(r->regsigmas_416[y])),
|
||||||
|
//san(creal(r->sigmas_total[y]) + creal(r->sigmas_total[y_conj])),
|
||||||
|
//san(cimag(r->sigmas_total[y]) - cimag(r->sigmas_total[y_conj]))
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
ewaldtest_triang_results_free(r);
|
||||||
|
}
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
int ewaldtest_counter = 0;
|
||||||
|
|
||||||
|
|
||||||
|
ewaldtest_triang_results *ewaldtest_triang(const ewaldtest_triang_params p) {
|
||||||
|
const double a = p.a; //const double a = p.h * sqrt(3);
|
||||||
|
|
||||||
|
const double A = sqrt(3) * a * a / 2.; // unit cell size
|
||||||
|
const double K_len = 4*M_PI/a/sqrt(3); // reciprocal vector length
|
||||||
|
|
||||||
|
|
||||||
|
ewaldtest_triang_results *results = malloc(sizeof(ewaldtest_triang_results));
|
||||||
|
results->p = p;
|
||||||
|
|
||||||
|
triangular_lattice_gen_t *Rlg = triangular_lattice_gen_init(a, p.orientation, true, 0); // N.B. orig is included
|
||||||
|
triangular_lattice_gen_extend_to_r(Rlg, p.maxR + a);
|
||||||
|
triangular_lattice_gen_t *Klg = triangular_lattice_gen_init(K_len, reverseTriangularLatticeOrientation(p.orientation), true, 0);
|
||||||
|
triangular_lattice_gen_extend_to_r(Klg, p.maxK + K_len);
|
||||||
|
|
||||||
|
point2d *Rpoints = Rlg->ps.base;
|
||||||
|
point2d *Kpoints = Klg->ps.base;
|
||||||
|
size_t nR = Rlg->ps.r_offsets[Rlg->ps.nrs],
|
||||||
|
nK = Klg->ps.r_offsets[Klg->ps.nrs];
|
||||||
|
|
||||||
|
point2d particle_shift = p.particle_shift;
|
||||||
|
point2d minus_ps = {-particle_shift.x, -particle_shift.y};
|
||||||
|
point2d Rpoints_plus_shift[nR];
|
||||||
|
for(size_t i = 0; i < nR; ++i){
|
||||||
|
Rpoints_plus_shift[i].x = Rpoints[i].x - particle_shift.x;
|
||||||
|
Rpoints_plus_shift[i].y = Rpoints[i].y - particle_shift.y;
|
||||||
|
}
|
||||||
|
|
||||||
|
qpms_y_t nelem_sc = qpms_lMax2nelem_sc(p.lMax);
|
||||||
|
|
||||||
|
results->sigmas_short = malloc(sizeof(complex double)*nelem_sc);
|
||||||
|
results->sigmas_long = malloc(sizeof(complex double)*nelem_sc);
|
||||||
|
results->sigmas_total = malloc(sizeof(complex double)*nelem_sc);
|
||||||
|
results->err_sigmas_short = malloc(sizeof(double)*nelem_sc);
|
||||||
|
results->err_sigmas_long = malloc(sizeof(double)*nelem_sc);
|
||||||
|
results->err_sigmas_total = malloc(sizeof(double)*nelem_sc);
|
||||||
|
|
||||||
|
qpms_ewald32_constants_t *c = qpms_ewald32_constants_init(p.lMax, p.csphase);
|
||||||
|
|
||||||
|
points2d_rordered_t *Kpoints_plus_beta = points2d_rordered_shift(&(Klg->ps), p.beta,
|
||||||
|
8*DBL_EPSILON, 8*DBL_EPSILON);
|
||||||
|
|
||||||
|
char filename[BUFSIZ];
|
||||||
|
sprintf(filename, "betalattice_%d.out", ewaldtest_counter);
|
||||||
|
dump_points2d_rordered(Kpoints_plus_beta, filename);
|
||||||
|
|
||||||
|
|
||||||
|
if (0!=ewald32_sigma_long_points_and_shift(results->sigmas_long,
|
||||||
|
results->err_sigmas_long, c, p.eta, p.k, A,
|
||||||
|
nK, Kpoints,
|
||||||
|
p.beta,
|
||||||
|
particle_shift /*minus_ps*/ ))
|
||||||
|
abort();
|
||||||
|
if (0!=ewald32_sigma_short_points_and_shift(
|
||||||
|
results->sigmas_short, results->err_sigmas_short, c,
|
||||||
|
p.eta, p.k,
|
||||||
|
nR, Rpoints, p.beta, particle_shift))
|
||||||
|
abort();
|
||||||
|
if (0!=ewald32_sigma0(&(results->sigma0), &(results->err_sigma0), c, p.eta, p.k))
|
||||||
|
abort();
|
||||||
|
for(qpms_y_t y = 0; y < nelem_sc; ++y) {
|
||||||
|
results->sigmas_total[y] = results->sigmas_short[y] + results->sigmas_long[y];
|
||||||
|
results->err_sigmas_total[y] = results->err_sigmas_short[y] + results->err_sigmas_long[y];
|
||||||
|
}
|
||||||
|
results->sigmas_total[0] += results->sigma0;
|
||||||
|
results->err_sigmas_total[0] += results->err_sigma0;
|
||||||
|
|
||||||
|
// Now calculate the reference values [LT(4.16)]
|
||||||
|
results->regsigmas_416 = calloc(nelem_sc, sizeof(complex double));
|
||||||
|
results->regsigmas_416[0] = -2 * c->legendre0[gsl_sf_legendre_array_index(0,0)];
|
||||||
|
|
||||||
|
{
|
||||||
|
double legendres[gsl_sf_legendre_array_n(p.lMax)];
|
||||||
|
points2d_rordered_t sel =
|
||||||
|
points2d_rordered_annulus(Kpoints_plus_beta, 0, true, p.k, false);
|
||||||
|
if (0 != sel.nrs)
|
||||||
|
{
|
||||||
|
point2d *beta_pq_lessthan_k = sel.base + sel.r_offsets[0];
|
||||||
|
size_t beta_pq_lessthan_k_count = sel.r_offsets[sel.nrs] - sel.r_offsets[0];
|
||||||
|
for(size_t i = 0; i < beta_pq_lessthan_k_count; ++i) {
|
||||||
|
point2d beta_pq = beta_pq_lessthan_k[i];
|
||||||
|
double rbeta_pq = cart2norm(beta_pq);
|
||||||
|
double arg_pq = atan2(beta_pq.y, beta_pq.x);
|
||||||
|
double denom = sqrt(p.k*p.k - rbeta_pq*rbeta_pq);
|
||||||
|
if( gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,
|
||||||
|
p.lMax, denom/p.k, p.csphase, legendres) != 0)
|
||||||
|
abort();
|
||||||
|
for (qpms_y_t y = 0; y < nelem_sc; ++y) {
|
||||||
|
qpms_l_t n; qpms_m_t m;
|
||||||
|
qpms_y2mn_sc_p(y, &m, &n);
|
||||||
|
if ((m+n)%2 != 0)
|
||||||
|
continue;
|
||||||
|
complex double eimf = cexp(I*m*arg_pq);
|
||||||
|
results->regsigmas_416[y] +=
|
||||||
|
4*M_PI*ipow(n)/p.k/A
|
||||||
|
* eimf * legendres[gsl_sf_legendre_array_index(n,abs(m))] * min1pow_m_neg(m)
|
||||||
|
/ denom;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
points2d_rordered_free(Kpoints_plus_beta);
|
||||||
|
qpms_ewald32_constants_free(c);
|
||||||
|
triangular_lattice_gen_free(Klg);
|
||||||
|
triangular_lattice_gen_free(Rlg);
|
||||||
|
++ewaldtest_counter;
|
||||||
|
return results;
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue