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Complex k support for new ewald sums. 

Basic tests give good results (only up to rounding error differences
compared to the previous versions), the time increase is almost negligible.


Former-commit-id: 0907517ca94f130a0d8b140ba7b525653e24090f
This commit is contained in:
Marek Nečada 2018-12-21 19:05:52 +00:00
parent d2b34f9407
commit fd1aed02ca
2 changed files with 38 additions and 26 deletions
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58
qpms/ewald.c
View File

@ -176,11 +176,11 @@ void qpms_ewald32_constants_free(qpms_ewald32_constants_t *c) {
int ewald3_sigma0(complex double *result, double *err, int ewald3_sigma0(complex double *result, double *err,
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k) const double eta, const complex double k)
{ {
qpms_csf_result gam; qpms_csf_result gam;
int retval = complex_gamma_inc_e(-0.5, -sq(k/(2*eta)), &gam); int retval = complex_gamma_inc_e(-0.5, -csq(k/(2*eta)), &gam);
gam.val = conj(gam.val); // We take the other branch, cf. [Linton, p. 642 in the middle] // FIXME DO THIS CORRECTLY gam.val = conj(gam.val); // We take the other branch, cf. [Linton, p. 642 in the middle]
if (0 != retval) if (0 != retval)
abort(); abort();
*result = gam.val * c->legendre0[gsl_sf_legendre_array_index(0,0)] / 2 / M_SQRTPI; *result = gam.val * c->legendre0[gsl_sf_legendre_array_index(0,0)] / 2 / M_SQRTPI;
@ -381,7 +381,7 @@ int ewald3_21_xy_sigma_long (
complex double *target, // must be c->nelem_sc long complex double *target, // must be c->nelem_sc long
double *err, double *err,
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k /* TODO COMPLEX */, const double eta, const complex double k,
const double unitcell_volume /* with the corresponding lattice dimensionality */, const double unitcell_volume /* with the corresponding lattice dimensionality */,
const LatticeDimensionality latdim, const LatticeDimensionality latdim,
PGen *pgen_K, const bool pgen_generates_shifted_points PGen *pgen_K, const bool pgen_generates_shifted_points
@ -394,6 +394,7 @@ int ewald3_21_xy_sigma_long (
const cart3_t particle_shift const cart3_t particle_shift
) )
{ {
const bool k_is_real = (cimag(k) == 0);
assert((latdim & LAT_XYONLY) && (latdim & SPACE3D)); assert((latdim & LAT_XYONLY) && (latdim & SPACE3D));
assert((latdim & LAT1D) || (latdim & LAT2D)); assert((latdim & LAT1D) || (latdim & LAT2D));
const qpms_y_t nelem_sc = c->nelem_sc; const qpms_y_t nelem_sc = c->nelem_sc;
@ -408,8 +409,9 @@ int ewald3_21_xy_sigma_long (
memset(err, 0, nelem_sc * sizeof(double)); memset(err, 0, nelem_sc * sizeof(double));
} }
const double commonfac = 1/(k*k*unitcell_volume); // used in the very end (CFC) //TODO COMPLEX const complex double commonfac = 1/(k*k*unitcell_volume); // used in the very end (CFC)
assert(commonfac > 0); if (k_is_real)
assert(creal(commonfac) > 0);
PGenSphReturnData pgen_retdata; PGenSphReturnData pgen_retdata;
#ifndef NDEBUG #ifndef NDEBUG
@ -418,7 +420,7 @@ int ewald3_21_xy_sigma_long (
// recycleable values if rbeta_pq stays the same: // recycleable values if rbeta_pq stays the same:
complex double gamma_pq; complex double gamma_pq;
complex double z; complex double z;
double factor1d = 1; // the "additional" factor for the 1D case (then it is not 1) complex double factor1d = 1; // the "additional" factor for the 1D case (then it is not 1)
// space for Gamma_pq[j]'s // space for Gamma_pq[j]'s
qpms_csf_result Gamma_pq[lMax/2+1]; qpms_csf_result Gamma_pq[lMax/2+1];
@ -452,18 +454,18 @@ int ewald3_21_xy_sigma_long (
// R-DEPENDENT BEGIN // R-DEPENDENT BEGIN
if (new_rbeta_pq) { if (new_rbeta_pq) {
gamma_pq = lilgamma(rbeta_pq/k /*TODO COMPLEX*/); gamma_pq = clilgamma(rbeta_pq/k);
z = csq(gamma_pq*k/(2*eta)); // Když o tom tak přemýšlím, tak tohle je vlastně vždy reálné z = csq(gamma_pq*k/(2*eta));
for(qpms_l_t j = 0; j <= lMax/2; ++j) { for(qpms_l_t j = 0; j <= lMax/2; ++j) {
// TODO COMPLEX FIXME check the branches in the old lilgamma case // TODO COMPLEX FIXME check the branches in the old lilgamma case
int retval = complex_gamma_inc_e(0.5-j, z, Gamma_pq+j); int retval = complex_gamma_inc_e(0.5-j, z, Gamma_pq+j);
// 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 // 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
if(creal(z) < 0) //if(creal(z) < 0)
Gamma_pq[j].val = conj(Gamma_pq[j].val); //FIXME as noted above // Gamma_pq[j].val = conj(Gamma_pq[j].val); //FIXME as noted above
if(!(retval==0 || retval==GSL_EUNDRFLW)) abort(); if(!(retval==0 || retval==GSL_EUNDRFLW)) abort();
} }
if (latdim & LAT1D) if (latdim & LAT1D)
factor1d = k /*TODO COMPLEX */ * M_SQRT1_2 * .5 * gamma_pq; factor1d = M_SQRT1_2 * .5 * k * gamma_pq;
} }
// R-DEPENDENT END // R-DEPENDENT END
@ -479,7 +481,7 @@ int ewald3_21_xy_sigma_long (
double jsum_err, jsum_err_c; kahaninit(&jsum_err, &jsum_err_c); // TODO do I really need to kahan sum errors? double jsum_err, jsum_err_c; kahaninit(&jsum_err, &jsum_err_c); // TODO do I really need to kahan sum errors?
assert((n-abs(m))/2 == c->s1_jMaxes[y]); assert((n-abs(m))/2 == c->s1_jMaxes[y]);
for(qpms_l_t j = 0; j <= c->s1_jMaxes[y]/*(n-abs(m))/2*/; ++j) { // FIXME </<= ? for(qpms_l_t j = 0; j <= c->s1_jMaxes[y]/*(n-abs(m))/2*/; ++j) { // FIXME </<= ?
complex double summand = pow(rbeta_pq/k, n-2*j) complex double summand = cpow(rbeta_pq/k, n-2*j)
* 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 * 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
* cpow(gamma_pq, 2*j-1) // * Gamma_pq[j] bellow (GGG) after error computation * cpow(gamma_pq, 2*j-1) // * Gamma_pq[j] bellow (GGG) after error computation
* c->s1_constfacs[y][j]; * c->s1_constfacs[y][j];
@ -516,7 +518,7 @@ int ewald3_1_z_sigma_long (
complex double *target, // must be c->nelem_sc long complex double *target, // must be c->nelem_sc long
double *err, double *err,
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k, const double eta, const complex double k,
const double unitcell_volume /* length (periodicity) in this case */, const double unitcell_volume /* length (periodicity) in this case */,
const LatticeDimensionality latdim, const LatticeDimensionality latdim,
PGen *pgen_K, const bool pgen_generates_shifted_points PGen *pgen_K, const bool pgen_generates_shifted_points
@ -573,13 +575,13 @@ int ewald3_1_z_sigma_long (
const complex double phasefac = cexp(I * K_z * particle_shift_z); // POINT-DEPENDENT (PFC) // !!!CHECKSIGN!!! const complex double phasefac = cexp(I * K_z * particle_shift_z); // POINT-DEPENDENT (PFC) // !!!CHECKSIGN!!!
// R-DEPENDENT BEGIN // R-DEPENDENT BEGIN
complex double gamma_pq = lilgamma(rbeta_mu/k); // For real beta and k this is real or pure imaginary ... complex double gamma_pq = clilgamma(rbeta_mu/k); // For real beta and k this is real or pure imaginary ...
const complex double z = csq(gamma_pq*k/(2*eta));// ... so the square (this) is in fact real. const complex double z = csq(gamma_pq*k/(2*eta));// ... so the square (this) is in fact real.
for(qpms_l_t j = 0; j <= lMax/2; ++j) { for(qpms_l_t j = 0; j <= lMax/2; ++j) {
int retval = complex_gamma_inc_e(0.5-j, z, Gamma_pq+j); int retval = complex_gamma_inc_e(0.5-j, z, Gamma_pq+j);
// 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 // 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
if(creal(z) < 0) //if(creal(z) < 0)
Gamma_pq[j].val = conj(Gamma_pq[j].val); //FIXME as noted above // Gamma_pq[j].val = conj(Gamma_pq[j].val); //FIXME as noted above
if(!(retval==0 || retval==GSL_EUNDRFLW)) abort(); if(!(retval==0 || retval==GSL_EUNDRFLW)) abort();
} }
// R-DEPENDENT END // R-DEPENDENT END
@ -632,7 +634,7 @@ int ewald3_sigma_long (
complex double *target, // must be c->nelem_sc long complex double *target, // must be c->nelem_sc long
double *err, double *err,
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k, const double eta, const complex double k,
const double unitcell_volume /* with the corresponding lattice dimensionality */, const double unitcell_volume /* with the corresponding lattice dimensionality */,
const LatticeDimensionality latdim, const LatticeDimensionality latdim,
PGen *pgen_K, const bool pgen_generates_shifted_points PGen *pgen_K, const bool pgen_generates_shifted_points
@ -880,7 +882,7 @@ int ewald3_sigma_short(
complex double *target, // must be c->nelem_sc long complex double *target, // must be c->nelem_sc long
double *err, // must be c->nelem_sc long or NULL double *err, // must be c->nelem_sc long or NULL
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k /* TODO COMPLEX */, const double eta, const complex double k /* TODO COMPLEX */,
const LatticeDimensionality latdim, // apart from asserts and possible optimisations ignored, as the SR formula stays the same const LatticeDimensionality latdim, // apart from asserts and possible optimisations ignored, as the SR formula stays the same
PGen *pgen_R, const bool pgen_generates_shifted_points PGen *pgen_R, const bool pgen_generates_shifted_points
/* If false, the behaviour corresponds to the old ewald32_sigma_short_points_and_shift, /* If false, the behaviour corresponds to the old ewald32_sigma_short_points_and_shift,
@ -893,6 +895,8 @@ int ewald3_sigma_short(
const cart3_t particle_shift const cart3_t particle_shift
) )
{ {
const bool k_is_real = (cimag(k) == 0); // TODO check how the compiler optimises the loops
const double kreal = creal(k);
const qpms_y_t nelem_sc = c->nelem_sc; const qpms_y_t nelem_sc = c->nelem_sc;
const qpms_l_t lMax = c->lMax; const qpms_l_t lMax = c->lMax;
gsl_integration_workspace *workspace = gsl_integration_workspace *workspace =
@ -916,6 +920,7 @@ int ewald3_sigma_short(
#endif #endif
// recyclable variables if r_pq_shifted stays the same: // recyclable variables if r_pq_shifted stays the same:
double intres[lMax+1], interr[lMax+1]; double intres[lMax+1], interr[lMax+1];
complex double cintres[lMax+1];
// CHOOSE POINT BEGIN // CHOOSE POINT BEGIN
// TODO check whether _next_sph is the optimal coordinate system choice here // TODO check whether _next_sph is the optimal coordinate system choice here
@ -971,11 +976,18 @@ int ewald3_sigma_short(
} }
for(qpms_l_t n = 0; n <= lMax; ++n) { for(qpms_l_t n = 0; n <= lMax; ++n) {
const double complex prefacn = - I * pow(2./k /*TODO COMPLEX*/, n+1) * M_2_SQRTPI / 2; // profiling TODO put outside the R-loop and multiply in the end? const double complex prefacn = - I * (k_is_real ? pow(2./creal(k),n+1) : cpow(2./k, n+1)) * M_2_SQRTPI / 2; // profiling TODO put outside the R-loop and multiply in the end?
const double R_pq_pown = pow(r_pq_shifted, n); // profiling TODO: maybe put this into the new_r_pq_shifted condition as well? const double R_pq_pown = pow(r_pq_shifted, n); // profiling TODO: maybe put this into the new_r_pq_shifted condition as well?
if (new_r_pq_shifted) { if (new_r_pq_shifted) {
int retval = ewald32_sr_integral(r_pq_shifted, k /*TODO COMPLEX*/, n, eta, int retval;
intres + n, interr + n, workspace); if (k_is_real) {
double intres_real;
retval = ewald32_sr_integral(r_pq_shifted, kreal, n, eta,
&intres_real, interr + n, workspace);
cintres[n] = intres_real;
} else
retval = ewald32_sr_integral_ck(r_pq_shifted, k, n, eta,
cintres+n, interr + n, workspace);
if (retval) abort(); if (retval) abort();
} // otherwise recycle the integrals } // otherwise recycle the integrals
for (qpms_m_t m = -n; m <= n; ++m){ for (qpms_m_t m = -n; m <= n; ++m){
@ -1000,7 +1012,7 @@ int ewald3_sigma_short(
kahanadd(err + y, err_c + y, cabs(leg * (prefacn / I) * R_pq_pown kahanadd(err + y, err_c + y, cabs(leg * (prefacn / I) * R_pq_pown
* interr[n])); // TODO include also other errors * interr[n])); // TODO include also other errors
ckahanadd(target + y, target_c + y, ckahanadd(target + y, target_c + y,
prefacn * R_pq_pown * leg * intres[n] * e_beta_Rpq * e_imf * min1pow_m_neg(m)); prefacn * R_pq_pown * leg * cintres[n] * e_beta_Rpq * e_imf * min1pow_m_neg(m));
} }
} }

6
qpms/ewald.h
View File

@ -145,14 +145,14 @@ int ewald32_sr_integral(double r, double k, double n, double eta, double *result
int ewald3_sigma0(complex double *result, double *err, int ewald3_sigma0(complex double *result, double *err,
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
double eta, double k double eta, complex double k
); );
int ewald3_sigma_short( int ewald3_sigma_short(
complex double *target_sigmasr_y, // must be c->nelem_sc long complex double *target_sigmasr_y, // must be c->nelem_sc long
double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k, const double eta, const complex double k,
const LatticeDimensionality latdim, // apart from asserts and possible optimisations ignored, as the SR formula stays the same const LatticeDimensionality latdim, // apart from asserts and possible optimisations ignored, as the SR formula stays the same
PGen *pgen_R, const bool pgen_generates_shifted_points PGen *pgen_R, const bool pgen_generates_shifted_points
/* If false, the behaviour corresponds to the old ewald32_sigma_short_points_and_shift, /* If false, the behaviour corresponds to the old ewald32_sigma_short_points_and_shift,
@ -169,7 +169,7 @@ int ewald3_sigma_long( // calls ewald3_21_sigma_long or ewald3_3_sigma_long, dep
complex double *target_sigmalr_y, // must be c->nelem_sc long complex double *target_sigmalr_y, // must be c->nelem_sc long
double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
const qpms_ewald32_constants_t *c, const qpms_ewald32_constants_t *c,
const double eta, const double k, const double eta, const complex double k,
const double unitcell_volume /* with the corresponding lattice dimensionality */, const double unitcell_volume /* with the corresponding lattice dimensionality */,
const LatticeDimensionality latdim, const LatticeDimensionality latdim,
PGen *pgen_K, const bool pgen_generates_shifted_points PGen *pgen_K, const bool pgen_generates_shifted_points