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qpms/qpms/scatsystem.c

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#include <stdlib.h>
#include <cblas.h>
#include <lapacke.h>
#include "scatsystem.h"
#include "indexing.h"
#include "vswf.h"
#include "groups.h"
#include "symmetries.h"
#include <gsl/gsl_spline.h>
#include <assert.h>
#include <unistd.h>
#include "vectors.h"
#include "wigner.h"
#include <string.h>
#include "qpms_error.h"
#include "translations.h"
#include <pthread.h>
#define SQ(x) ((x)*(x))
#define QPMS_SCATSYS_LEN_RTOL 1e-13
#define QPMS_SCATSYS_TMATRIX_ATOL 1e-14
#define QPMS_SCATSYS_TMATRIX_RTOL 1e-12
qpms_tmatrix_t *qpms_tmatrix_init(const qpms_vswf_set_spec_t *bspec) {
qpms_tmatrix_t *t = malloc(sizeof(qpms_tmatrix_t));
if (!t) abort();
else {
t->spec = bspec;
size_t n = bspec->n;
t->m = calloc(n*n, sizeof(complex double));
if (!t->m) abort();
t->owns_m = true;
}
return t;
}
qpms_tmatrix_t *qpms_tmatrix_copy(const qpms_tmatrix_t *T) {
qpms_tmatrix_t *t = qpms_tmatrix_init(T->spec);
size_t n = T->spec->n;
for(size_t i = 0; i < n*n; ++i)
t->m = T->m;
return t;
}
void qpms_tmatrix_free(qpms_tmatrix_t *t){
if(t && t->owns_m) free(t->m);
free(t);
}
qpms_tmatrix_t *qpms_tmatrix_apply_symop_inplace(
qpms_tmatrix_t *T,
const complex double *M
)
{
//qpms_tmatrix_t *t = qpms_tmatrix_init(T->spec);
const size_t n = T->spec->n;
complex double tmp[n][n];
// tmp = M T
const complex double one = 1, zero = 0;
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasNoTrans,
n, n, n, &one, M, n, T->m, n, &zero, tmp, n);
// t->m = tmp M* = M T M*
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasConjTrans,
n, n, n, &one, tmp, n, M, n, &zero, T->m, n);
return T;
}
qpms_tmatrix_t *qpms_tmatrix_apply_symop(
const qpms_tmatrix_t *T,
const complex double *M
)
{
qpms_tmatrix_t *t = qpms_tmatrix_init(T->spec);
const size_t n = T->spec->n;
complex double tmp[n][n];
// tmp = M T
const complex double one = 1, zero = 0;
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasNoTrans,
n, n, n, &one, M, n, T->m, n, &zero, tmp, n);
// t->m = tmp M* = M T M*
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasConjTrans,
n, n, n, &one, tmp, n, M, n, &zero, t->m, n);
return t;
}
qpms_errno_t qpms_symmetrise_tmdata_irot3arr(
complex double *tmdata, const size_t tmcount,
const qpms_vswf_set_spec_t *bspec,
const size_t n_symops, const qpms_irot3_t *symops) {
const size_t n = bspec->n;
qpms_tmatrix_t *tmcopy = qpms_tmatrix_init(bspec);
complex double *symop_matrices = malloc(n*n*sizeof(complex double) * n_symops);
if(!symop_matrices) qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"malloc() failed.");
for (size_t i = 0; i < n_symops; ++i)
qpms_irot3_uvswfi_dense(symop_matrices + i*n*n, bspec, symops[i]);
complex double tmp[n][n];
const complex double one = 1, zero = 0;
for (size_t tmi = 0; tmi < tmcount; ++tmi) {
// Move the data in tmcopy; we will then write the sum directly into tmdata.
memcpy(tmcopy->m, tmdata+n*n*tmi, n*n*sizeof(complex double));
memset(tmdata+n*n*tmi, 0, n*n*sizeof(complex double));
for (size_t i = 0; i < n_symops; ++i) {
const complex double *const M = symop_matrices + i*n*n;
// tmp = M T
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
n, n, n, &one, M, n, tmcopy->m, n, &zero, tmp, n);
// tmdata[...] += tmp M* = M T M*
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans,
n, n, n, &one, tmp, n, M, n, &one, tmdata + tmi*n*n, n);
}
for (size_t ii = 0; ii < n*n; ++ii)
tmdata[n*n*tmi+ii] /= n_symops;
}
free(symop_matrices);
qpms_tmatrix_free(tmcopy);
return QPMS_SUCCESS;
}
qpms_errno_t qpms_symmetrise_tmdata_finite_group(
complex double *tmdata, const size_t tmcount,
const qpms_vswf_set_spec_t *bspec,
const qpms_finite_group_t *pointgroup) {
if (!(pointgroup->rep3d)) qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"This function requires pointgroup->rep3d to be set correctly!");
return qpms_symmetrise_tmdata_irot3arr(tmdata, tmcount, bspec,
pointgroup->order, pointgroup->rep3d);
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_irot3arr_inplace(
qpms_tmatrix_t *T,
size_t n_symops,
const qpms_irot3_t *symops
) {
if(qpms_symmetrise_tmdata_irot3arr(T->m, 1,
T->spec, n_symops, symops) != QPMS_SUCCESS)
return NULL;
else return T;
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_finite_group_inplace(
qpms_tmatrix_t *T,
const qpms_finite_group_t *pointgroup
) {
if(qpms_symmetrise_tmdata_finite_group(T->m, 1,
T->spec, pointgroup) != QPMS_SUCCESS)
return NULL;
else return T;
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_involution_inplace(
qpms_tmatrix_t *T,
const complex double *M
)
{
qpms_tmatrix_t *t = qpms_tmatrix_apply_symop(T, M);
const size_t n = T->spec->n;
for(size_t i = 0; i < n*n; ++i)
T->m[i] = 0.5 * (t->m[i] + T->m[i]);
qpms_tmatrix_free(t);
return T;
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_involution(
const qpms_tmatrix_t *T,
const complex double *M
)
{
qpms_tmatrix_t *t = qpms_tmatrix_init(T->spec);
const size_t n = T->spec->n;
complex double tmp[n][n];
// tmp = M T
const complex double one = 1, zero = 0;
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasNoTrans,
n, n, n, &one, M, n, T->m, n, &zero, tmp, n);
// t->m = tmp M* = M T M*
cblas_zgemm(CblasRowMajor,
CblasNoTrans,
CblasConjTrans,
n, n, n, &one, tmp, n, M, n, &zero, t->m, n);
for(size_t i = 0; i < n*n; ++i)
t->m[i] = 0.5 * (t->m[i] + T->m[i]);
return t;
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_inf(const qpms_tmatrix_t *T) {
qpms_tmatrix_t *t = qpms_tmatrix_copy(T);
return qpms_tmatrix_symmetrise_C_inf_inplace(t);
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_inf_inplace(qpms_tmatrix_t *T) {
const size_t n = T->spec->n;
for (size_t row = 0; row < n; row++) {
qpms_m_t rm = qpms_uvswfi2m(T->spec->ilist[row]);
for (size_t col = 0; col < n; col++) {
qpms_m_t cm = qpms_uvswfi2m(T->spec->ilist[col]);
if (rm == cm)
;// No-op // t->m[n*row + col] = T->m[n*row + col];
else
T->m[n*row + col] = 0;
}
}
return T;
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_N(const qpms_tmatrix_t *T, int N) {
qpms_tmatrix_t *t = qpms_tmatrix_copy(T);
return qpms_tmatrix_symmetrise_C_N_inplace(t, N);
}
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_N_inplace(qpms_tmatrix_t *T, int N) {
const size_t n = T->spec->n;
for (size_t row = 0; row < n; row++) {
qpms_m_t rm = qpms_uvswfi2m(T->spec->ilist[row]);
for (size_t col = 0; col < n; col++) {
qpms_m_t cm = qpms_uvswfi2m(T->spec->ilist[col]);
if (((rm - cm) % N) == 0)
; // T->m[n*row + col] = T->m[n*row + col];
else
T->m[n*row + col] = 0;
}
}
return T;
}
bool qpms_tmatrix_isclose(const qpms_tmatrix_t *A, const qpms_tmatrix_t *B,
const double rtol, const double atol)
{
if (!qpms_vswf_set_spec_isidentical(A->spec, B->spec))
return false;
if (A->m == B->m)
return true;
const size_t n = A->spec->n;
for (size_t i = 0; i < n*n; ++i) {
const double tol = atol + rtol * (cabs(B->m[i]));
if ( cabs(B->m[i] - A->m[i]) > tol )
return false;
}
return true;
}
qpms_tmatrix_interpolator_t *qpms_tmatrix_interpolator_create(const size_t incount,
const double *freqs, const qpms_tmatrix_t *ta, const gsl_interp_type *iptype//, const bool copy_bspec
) {
if (incount <= 0) return NULL;
qpms_tmatrix_interpolator_t *ip = malloc(sizeof(qpms_tmatrix_interpolator_t));
/*
if (copy_bspec) {
ip->bspec = qpms_vswf_set_spec_copy(ta[0].spec);
ip->owns_bspec = true;
}
else {
*/
ip->bspec = ta[0].spec;
// ip->owns_bspec = false;
//}
const size_t n = ip->bspec->n;
// check if all matrices have the same bspec
for (size_t i = 0; i < incount; ++i)
if (!qpms_vswf_set_spec_isidentical(ip->bspec, ta[i].spec))
abort();
if (!(ip->splines_real = calloc(n*n,sizeof(gsl_spline *)))) abort();
if (!(ip->splines_imag = calloc(n*n,sizeof(gsl_spline *)))) abort();
for (size_t row = 0; row < n; ++row)
for (size_t col = 0; col < n; ++col) {
double y_real[incount], y_imag[incount];
bool n0_real = false, n0_imag = false;
for (size_t i = 0; i < incount; ++i) {
complex double telem = ta[i].m[n * row + col];
if ((y_real[i] = creal(telem))) n0_real = true;
if ((y_imag[i] = cimag(telem))) n0_imag = true;
}
if (n0_real) {
gsl_spline *s =
ip->splines_real[n * row + col] = gsl_spline_alloc(iptype, incount);
if (gsl_spline_init(s, freqs, y_real, incount) != 0 /*GSL_SUCCESS*/) abort();
}
else ip->splines_real[n * row + col] = NULL;
if (n0_imag) {
gsl_spline *s =
ip->splines_imag[n * row + col] = gsl_spline_alloc(iptype, incount);
if (gsl_spline_init(s, freqs, y_imag, incount) != 0 /*GSL_SUCCESS*/) abort();
}
else ip->splines_imag[n * row + col] = NULL;
}
return ip;
}
void qpms_tmatrix_interpolator_free(qpms_tmatrix_interpolator_t *ip) {
if (ip) {
const size_t n = ip->bspec->n;
for (size_t i = 0; i < n*n; ++i) {
if (ip->splines_real[i]) gsl_spline_free(ip->splines_real[i]);
if (ip->splines_imag[i]) gsl_spline_free(ip->splines_imag[i]);
}
//if (ip->owns_bspec)
// qpms_vswf_set_spec_free(ip->bspec);
free(ip);
}
}
qpms_tmatrix_t *qpms_tmatrix_interpolator_eval(const qpms_tmatrix_interpolator_t *ip, double freq) {
qpms_tmatrix_t *t = qpms_tmatrix_init(ip->bspec);
const size_t n = ip->bspec->n;
for (size_t i = 0; i < n*n; ++i){
if (ip->splines_real[i]) t->m[i] = gsl_spline_eval(ip->splines_real[i], freq, NULL /*does this work?*/);
if (ip->splines_imag[i]) t->m[i] += I* gsl_spline_eval(ip->splines_imag[i], freq, NULL /*does this work?*/);
}
return t;
}
// ------------ Stupid implementation of qpms_scatsys_apply_symmetry() -------------
#define MIN(x,y) (((x)<(y))?(x):(y))
#define MAX(x,y) (((x)>(y))?(x):(y))
// The following functions are just to make qpms_scatsys_apply_symmetry more readable.
// They are not to be used elsewhere, as they do not perform any array capacity checks etc.
/// Compare two orbit types in a scattering system.
static bool orbit_types_equal(const qpms_ss_orbit_type_t *a, const qpms_ss_orbit_type_t *b) {
if (a->size != b->size) return false;
if (memcmp(a->action, b->action, a->size*sizeof(qpms_ss_orbit_pi_t))) return false;
if (memcmp(a->tmatrices, b->tmatrices, a->size*sizeof(qpms_ss_tmi_t))) return false;
return true;
}
// Extend the action to all particles in orbit if only the action on the 0th
// particle has been filled.
static void extend_orbit_action(qpms_scatsys_t *ss, qpms_ss_orbit_type_t *ot) {
for(qpms_ss_orbit_pi_t src = 1; src < ot->size; ++src) {
// find any element g that sends 0 to src:
qpms_gmi_t g;
for (g = 0; g < ss->sym->order; ++g)
if (ot->action[g] == src) break;
assert(g < ss->sym->order);
// invg sends src to 0
qpms_gmi_t invg = qpms_finite_group_inv(ss->sym, g);
for (qpms_gmi_t f = 0; f < ss->sym->order; ++f)
// if f sends 0 to dest, then f * invg sends src to dest
ot->action[src * ss->sym->order +
qpms_finite_group_mul(ss->sym,f,invg)] = ot->action[f];
}
}
//Add orbit type to a scattering system, updating the ss->otspace_end pointer accordingly
static void add_orbit_type(qpms_scatsys_t *ss, const qpms_ss_orbit_type_t *ot_current) {
qpms_ss_orbit_type_t * const ot_new = & (ss->orbit_types[ss->orbit_type_count]);
ot_new->size = ot_current->size;
const qpms_vswf_set_spec_t *bspec = ss->tm[ot_current->tmatrices[0]]->spec;
const size_t bspecn = bspec->n;
ot_new->bspecn = bspecn;
const size_t actionsiz = sizeof(ot_current->action[0]) * ot_current->size
* ss->sym->order;
ot_new->action = (void *) (ss->otspace_end);
memcpy(ot_new->action, ot_current->action, actionsiz);
// N.B. we copied mostly garbage ^^^, most of it is initialized just now:
extend_orbit_action(ss, ot_new);
#ifdef DUMP_ORBIT_ACTION
fprintf(stderr, "Orbit action:\n");
for (qpms_gmi_t gmi = 0; gmi < ss->sym->order; ++gmi) {
const qpms_quat4d_t q = qpms_quat_4d_from_2c(ss->sym->rep3d[gmi].rot);
fprintf(stderr, "%+d[%g %g %g %g] ", (int)ss->sym->rep3d[gmi].det,
q.c1, q.ci, q.cj, q.ck);
fprintf(stderr, "%s\t", (ss->sym->permrep && ss->sym->permrep[gmi])?
ss->sym->permrep[gmi] : "");
for (qpms_ss_orbit_pi_t pi = 0; pi < ot_new->size; ++pi)
fprintf(stderr, "%d\t", (int) ot_new->action[gmi + pi*ss->sym->order]);
fprintf(stderr, "\n");
}
#endif
ss->otspace_end += actionsiz;
const size_t tmsiz = sizeof(ot_current->tmatrices[0]) * ot_current->size;
ot_new->tmatrices = (void *) (ss->otspace_end);
memcpy(ot_new->tmatrices, ot_current->tmatrices, tmsiz);
ss->otspace_end += tmsiz;
const size_t irbase_sizes_siz = sizeof(ot_new->irbase_sizes[0]) * ss->sym->nirreps;
ot_new->irbase_sizes = (void *) (ss->otspace_end);
ss->otspace_end += irbase_sizes_siz;
ot_new->irbase_cumsizes = (void *) (ss->otspace_end);
ss->otspace_end += irbase_sizes_siz;
ot_new->irbase_offsets = (void *) (ss->otspace_end);
ss->otspace_end += irbase_sizes_siz;
const size_t irbases_siz = sizeof(ot_new->irbases[0]) * SQ(ot_new->size * bspecn);
ot_new->irbases = (void *) (ss->otspace_end);
ss->otspace_end += irbases_siz;
size_t lastbs, bs_cumsum = 0;
for(qpms_iri_t iri = 0; iri < ss->sym->nirreps; ++iri) {
ot_new->irbase_offsets[iri] = bs_cumsum * bspecn * ot_new->size;
qpms_orbit_irrep_basis(&lastbs,
ot_new->irbases + bs_cumsum*ot_new->size*bspecn,
ot_new, bspec, ss->sym, iri);
ot_new->irbase_sizes[iri] = lastbs;
bs_cumsum += lastbs;
ot_new->irbase_cumsizes[iri] = bs_cumsum;
}
if(bs_cumsum != ot_new->size * bspecn)
qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"The cumulative size of the symmetry-adapted bases is wrong; "
"expected %d = %d * %d, got %d.",
ot_new->size * bspecn, ot_new->size, bspecn, bs_cumsum);
ot_new->instance_count = 0;
ss->orbit_type_count++;
}
// Almost 200 lines. This whole thing deserves a rewrite!
qpms_scatsys_t *qpms_scatsys_apply_symmetry(const qpms_scatsys_t *orig, const qpms_finite_group_t *sym) {
// TODO check data sanity
qpms_l_t lMax = 0; // the overall lMax of all base specs.
qpms_normalisation_t normalisation = QPMS_NORMALISATION_UNDEF;
// First, determine the rough radius of the array; it should be nonzero
// in order to particle position equivalence work correctly
double lenscale = 0;
{
double minx = +INFINITY, miny = +INFINITY, minz = +INFINITY;
double maxx = -INFINITY, maxy = -INFINITY, maxz = -INFINITY;
for (qpms_ss_pi_t i = 0; i < orig->p_count; ++i) {
minx = MIN(minx,orig->p[i].pos.x);
miny = MIN(miny,orig->p[i].pos.y);
minz = MIN(minz,orig->p[i].pos.z);
maxx = MAX(maxx,orig->p[i].pos.x);
maxy = MAX(maxy,orig->p[i].pos.y);
maxz = MAX(maxz,orig->p[i].pos.z);
}
lenscale = (fabs(maxx)+fabs(maxy)+fabs(maxz)+(maxx-minx)+(maxy-miny)+(maxz-minz)) / 3;
}
// Second, check that there are no duplicit positions in the input system.
for (qpms_ss_pi_t i = 0; i < orig->p_count; ++i)
for (qpms_ss_pi_t j = 0; j < i; ++j)
assert(!cart3_isclose(orig->p[i].pos, orig->p[j].pos, 0, QPMS_SCATSYS_LEN_RTOL * lenscale));
// Allocate T-matrix, particle and particle orbit info arrays
qpms_scatsys_t *ss = malloc(sizeof(qpms_scatsys_t));
ss->lenscale = lenscale;
ss->sym = sym;
ss->tm_capacity = sym->order * orig->tm_count;
ss->tm = malloc(ss->tm_capacity * sizeof(qpms_tmatrix_t *));
ss->p_capacity = sym->order * orig->p_count;
ss->p = malloc(ss->p_capacity * sizeof(qpms_particle_tid_t));
ss->p_orbitinfo = malloc(ss->p_capacity * sizeof(qpms_ss_particle_orbitinfo_t));
for (qpms_ss_pi_t pi = 0; pi < ss->p_capacity; ++pi) {
ss->p_orbitinfo[pi].t = QPMS_SS_P_ORBITINFO_UNDEF;
ss->p_orbitinfo[pi].p = QPMS_SS_P_ORBITINFO_UNDEF;
}
// Copy T-matrices; checking for duplicities
ss->max_bspecn = 0; // We'll need it later.for memory alloc estimates.
qpms_ss_tmi_t tm_dupl_remap[ss->tm_capacity]; // Auxilliary array to label remapping the indices after ignoring t-matrix duplicities
ss->tm_count = 0;
for (qpms_ss_tmi_t i = 0; i < orig->tm_count; ++i) {
qpms_ss_tmi_t j;
for (j = 0; j < ss->tm_count; ++j)
if (qpms_tmatrix_isclose(orig->tm[i], ss->tm[j], QPMS_SCATSYS_TMATRIX_RTOL, QPMS_SCATSYS_TMATRIX_ATOL)) {
break;
}
if (j == ss->tm_count) { // duplicity not found, copy the t-matrix
ss->tm[j] = qpms_tmatrix_copy(orig->tm[i]);
ss->max_bspecn = MAX(ss->tm[j]->spec->n, ss->max_bspecn);
lMax = MAX(lMax, ss->tm[j]->spec->lMax);
++(ss->tm_count);
}
tm_dupl_remap[i] = j;
if (normalisation == QPMS_NORMALISATION_UNDEF)
normalisation = ss->tm[i]->spec->norm;
// We expect all bspec norms to be the same.
else QPMS_ENSURE(normalisation == ss->tm[j]->spec->norm,
"Normalisation convention must be the same for all T-matrices."
" %d != %d\n", normalisation, ss->tm[j]->spec->norm);
}
// Copy particles, remapping the t-matrix indices
for (qpms_ss_pi_t i = 0; i < orig->p_count; ++(i)) {
ss->p[i] = orig->p[i];
ss->p[i].tmatrix_id = tm_dupl_remap[ss->p[i].tmatrix_id];
}
ss->p_count = orig->p_count;
// allocate t-matrix symmetry map
ss->tm_sym_map = malloc(sizeof(qpms_ss_tmi_t) * sym->order * sym->order * ss->tm_count);
// Extend the T-matrices list by the symmetry operations
for (qpms_ss_tmi_t tmi = 0; tmi < ss->tm_count; ++tmi)
for (qpms_gmi_t gmi = 0; gmi < sym->order; ++gmi){
const size_t d = ss->tm[tmi]->spec->n;
complex double M[d][d]; // transformation matrix
qpms_irot3_uvswfi_dense(M[0], ss->tm[tmi]->spec, sym->rep3d[gmi]);
qpms_tmatrix_t *transformed = qpms_tmatrix_apply_symop(ss->tm[tmi], M[0]);
qpms_ss_tmi_t tmj;
for (tmj = 0; tmj < ss->tm_count; ++tmj)
if (qpms_tmatrix_isclose(transformed, ss->tm[tmj], QPMS_SCATSYS_TMATRIX_RTOL, QPMS_SCATSYS_TMATRIX_ATOL))
break;
if (tmj < ss->tm_count) { // HIT, transformed T-matrix already exists
qpms_tmatrix_free(transformed);
} else { // MISS, save the matrix and increment the count
ss->tm[ss->tm_count] = transformed;
++(ss->tm_count);
}
ss->tm_sym_map[gmi + tmi * sym->order] = tmj; // In any case, tmj now indexes the correct transformed matrix
}
// Possibly free some space using the new ss->tm_count instead of (old) ss->tm_count*sym->order
ss->tm_sym_map = realloc(ss->tm_sym_map, sizeof(qpms_ss_tmi_t) * sym->order * ss->tm_count);
// tm could be realloc'd as well, but those are just pointers, not likely many.
// allocate particle symmetry map
ss->p_sym_map = malloc(sizeof(qpms_ss_pi_t) * sym->order * sym->order * ss->p_count);
// allocate orbit type array (TODO realloc later if too long)
ss->orbit_type_count = 0;
ss->orbit_types = calloc(ss->p_count, sizeof(qpms_ss_orbit_type_t));
ss->otspace_end = ss->otspace = malloc( // reallocate later
(sizeof(qpms_ss_orbit_pi_t) * sym->order * sym->order
+ sizeof(qpms_ss_tmi_t) * sym->order
+ 3*sizeof(size_t) * sym->nirreps
+ sizeof(complex double) * SQ(sym->order * ss->max_bspecn)) * ss->p_count
);
// Workspace for the orbit type determination
qpms_ss_orbit_type_t ot_current;
qpms_ss_orbit_pi_t ot_current_action[sym->order * sym->order];
qpms_ss_tmi_t ot_current_tmatrices[sym->order];
qpms_ss_pi_t current_orbit[sym->order];
ot_current.action = ot_current_action;
ot_current.tmatrices = ot_current_tmatrices;
// Extend the particle list by the symmetry operations, check that particles mapped by symmetry ops on themselves
// have the correct symmetry
// TODO this could be sped up to O(npart * log(npart)); let's see later whether needed.
for (qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
const bool new_orbit = (ss->p_orbitinfo[pi].t == QPMS_SS_P_ORBITINFO_UNDEF); // TODO build the orbit!!!
if (new_orbit){
current_orbit[0] = pi;
ot_current.size = 1;
ot_current.tmatrices[0] = ss->p[pi].tmatrix_id;
#ifdef DUMP_PARTICLE_POSITIONS
cart3_t pos = ss->p[pi].pos;
fprintf(stderr, "An orbit [%.4g, %.4g, %.4g] => ", pos.x, pos.y, pos.z);
#endif
}
for (qpms_gmi_t gmi = 0; gmi < sym->order; ++gmi) {
cart3_t newpoint = qpms_irot3_apply_cart3(sym->rep3d[gmi], ss->p[pi].pos);
qpms_ss_tmi_t new_tmi = ss->tm_sym_map[gmi + ss->p[pi].tmatrix_id * sym->order]; // transformed t-matrix index
qpms_ss_pi_t pj;
for (pj = 0; pj < ss->p_count; ++pj)
if (cart3_isclose(newpoint, ss->p[pj].pos, 0, ss->lenscale * QPMS_SCATSYS_LEN_RTOL)) {
if (new_tmi != ss->p[pj].tmatrix_id)
qpms_pr_error("The %d. particle with coords (%lg, %lg, %lg) "
"is mapped to %d. another (or itself) with cords (%lg, %lg, %lg) "
"without having the required symmetry", (int)pi,
ss->p[pi].pos.x, ss->p[pi].pos.y, ss->p[pi].pos.z,
(int)pj, ss->p[pj].pos.x, ss->p[pj].pos.y, ss->p[pj].pos.z);
break;
}
if (pj < ss->p_count) { // HIT, the particle is transformed to an "existing" one.
;
} else { // MISS, the symmetry transforms the particle to a new location, so add it.
qpms_particle_tid_t newparticle = {newpoint, new_tmi};
ss->p[ss->p_count] = newparticle;
++(ss->p_count);
#ifdef DUMP_PARTICLE_POSITIONS
if(new_orbit)
fprintf(stderr, "[%.4g, %.4g, %.4g] ", newpoint.x, newpoint.y, newpoint.z);
#endif
}
ss->p_sym_map[gmi + pi * sym->order] = pj;
if (new_orbit) {
// Now check whether the particle (result of the symmetry op) is already in the current orbit
qpms_ss_orbit_pi_t opj;
for (opj = 0; opj < ot_current.size; ++opj)
if (current_orbit[opj] == pj) break; // HIT, pj already on current orbit
if (opj == ot_current.size) { // MISS, pj is new on the orbit, extend the size and set the T-matrix id
current_orbit[opj] = pj;
++ot_current.size;
ot_current.tmatrices[opj] = ss->p[pj].tmatrix_id;
}
ot_current.action[gmi] = opj;
}
}
if (new_orbit) { // Now compare if the new orbit corresponds to some of the existing types.
#ifdef DUMP_PARTICLE_POSITIONS
fputc('\n', stderr);
#endif
qpms_ss_oti_t oti;
for(oti = 0; oti < ss->orbit_type_count; ++oti)
if (orbit_types_equal(&ot_current, &(ss->orbit_types[oti]))) break; // HIT, orbit type already exists
assert(0 == sym->order % ot_current.size);
if (oti == ss->orbit_type_count) // MISS, add the new orbit type
add_orbit_type(ss, &ot_current);
// Walk through the orbit again and set up the orbit info of the particles
for (qpms_ss_orbit_pi_t opi = 0; opi < ot_current.size; ++opi) {
const qpms_ss_pi_t pi_opi = current_orbit[opi];
ss->p_orbitinfo[pi_opi].t = oti;
ss->p_orbitinfo[pi_opi].p = opi;
ss->p_orbitinfo[pi_opi].osn = ss->orbit_types[oti].instance_count;
}
ss->orbit_types[oti].instance_count++;
}
}
// Possibly free some space using the new ss->p_count instead of (old) ss->p_count*sym->order
ss->p_sym_map = realloc(ss->p_sym_map, sizeof(qpms_ss_pi_t) * sym->order * ss->p_count);
ss->p = realloc(ss->p, sizeof(qpms_particle_tid_t) * ss->p_count);
ss->p_orbitinfo = realloc(ss->p_orbitinfo, sizeof(qpms_ss_particle_orbitinfo_t)*ss->p_count);
ss->p_capacity = ss->p_count;
{ // Reallocate the orbit type data space and update the pointers if needed.
size_t otspace_sz = ss->otspace_end - ss->otspace;
char *old_otspace = ss->otspace;
ss->otspace = realloc(ss->otspace, otspace_sz);
ptrdiff_t shift = ss->otspace - old_otspace;
if(shift) {
for (size_t oi = 0; oi < ss->orbit_type_count; ++oi) {
ss->orbit_types[oi].action = (void *)(((char *) (ss->orbit_types[oi].action)) + shift);
ss->orbit_types[oi].tmatrices = (void *)(((char *) (ss->orbit_types[oi].tmatrices)) + shift);
ss->orbit_types[oi].irbase_sizes = (void *)(((char *) (ss->orbit_types[oi].irbase_sizes)) + shift);
ss->orbit_types[oi].irbase_cumsizes = (void *)(((char *) (ss->orbit_types[oi].irbase_cumsizes)) + shift);
ss->orbit_types[oi].irbase_offsets = (void *)(((char *) (ss->orbit_types[oi].irbase_offsets)) + shift);
ss->orbit_types[oi].irbases = (void *)(((char *) (ss->orbit_types[oi].irbases)) + shift);
}
ss->otspace_end += shift;
}
}
// Set ss->fecv_size and ss->fecv_pstarts
ss->fecv_size = 0;
ss->fecv_pstarts = malloc(ss->p_count * sizeof(size_t));
for (qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
ss->fecv_pstarts[pi] = ss->fecv_size;
ss->fecv_size += ss->tm[ss->p[pi].tmatrix_id]->spec->n; // That's a lot of dereferencing!
}
ss->saecv_sizes = malloc(sizeof(size_t) * sym->nirreps); if (!ss->saecv_sizes) abort();
ss->saecv_ot_offsets = malloc(sizeof(size_t) * sym->nirreps * ss->orbit_type_count);
if (!ss->saecv_ot_offsets) abort();
for(qpms_iri_t iri = 0; iri < sym->nirreps; ++iri) {
ss->saecv_sizes[iri] = 0;
for(qpms_ss_oti_t oti = 0; oti < ss->orbit_type_count; ++oti) {
ss->saecv_ot_offsets[iri * ss->orbit_type_count + oti] = ss->saecv_sizes[iri];
const qpms_ss_orbit_type_t *ot = &(ss->orbit_types[oti]);
ss->saecv_sizes[iri] += ot->instance_count * ot->irbase_sizes[iri];
}
}
qpms_ss_pi_t p_ot_cumsum = 0;
for (qpms_ss_oti_t oti = 0; oti < ss->orbit_type_count; ++oti) {
qpms_ss_orbit_type_t *ot = ss->orbit_types + oti;
ot->p_offset = p_ot_cumsum;
p_ot_cumsum += ot->size * ot->instance_count;
}
// Set ss->p_by_orbit[]
QPMS_CRASHING_MALLOC(ss->p_by_orbit, sizeof(qpms_ss_pi_t) * ss->p_count);
for (qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
const qpms_ss_particle_orbitinfo_t *oi = ss->p_orbitinfo + pi;
const qpms_ss_oti_t oti = oi->t;
const qpms_ss_orbit_type_t *ot = ss->orbit_types + oti;
ss->p_by_orbit[ot->p_offset + ot->size * oi->osn + oi->p] = pi;
}
ss->c = qpms_trans_calculator_init(lMax, normalisation);
return ss;
}
void qpms_scatsys_free(qpms_scatsys_t *ss) {
if(ss) {
free(ss->tm);
free(ss->p);
free(ss->fecv_pstarts);
free(ss->tm_sym_map);
free(ss->p_sym_map);
free(ss->otspace);
free(ss->p_orbitinfo);
free(ss->orbit_types);
free(ss->saecv_sizes);
free(ss->p_by_orbit);
qpms_trans_calculator_free(ss->c);
}
free(ss);
}
// (copypasta from symmetries.c)
// TODO at some point, maybe support also other norms.
// (perhaps just use qpms_normalisation_t_factor() at the right places)
static inline void check_norm_compat(const qpms_vswf_set_spec_t *s)
{
switch (qpms_normalisation_t_normonly(s->norm)) {
case QPMS_NORMALISATION_POWER:
break;
case QPMS_NORMALISATION_SPHARM:
break;
default:
abort(); // Only SPHARM and POWER norms are supported right now.
}
}
complex double *qpms_orbit_action_matrix(complex double *target,
const qpms_ss_orbit_type_t *ot, const qpms_vswf_set_spec_t *bspec,
const qpms_finite_group_t *sym, const qpms_gmi_t g) {
assert(sym); assert(g < sym->order);
assert(sym->rep3d);
assert(ot); assert(ot->size > 0);
check_norm_compat(bspec);
const size_t n = bspec->n;
const qpms_gmi_t N = ot->size;
if (target == NULL)
target = malloc(n*n*N*N*sizeof(complex double));
if (target == NULL) abort();
memset(target, 0, n*n*N*N*sizeof(complex double));
complex double tmp[n][n]; // this is the 'per-particle' action
qpms_irot3_uvswfi_dense(tmp[0], bspec, sym->rep3d[g]);
for(qpms_gmi_t Col = 0; Col < ot->size; ++Col) {
// Row is the 'destination' of the symmetry operation, Col is the 'source'
const qpms_gmi_t Row = ot->action[sym->order * Col + g];
for(size_t row = 0; row < bspec->n; ++row)
for(size_t col = 0; col < bspec->n; ++col)
target[n*n*N*Row + n*Col + n*N*row + col] = conj(tmp[row][col]); //CHECKCONJ
}
#ifdef DUMP_ACTIONMATRIX
fprintf(stderr,"%d: %s\n",
(int) g, (sym->permrep && sym->permrep[g])?
sym->permrep[g] : "");
for (size_t Row = 0; Row < ot->size; ++Row) {
fprintf(stderr, "--------------------------\n");
for (size_t row = 0; row < bspec->n; ++row) {
for (size_t Col = 0; Col < ot->size; ++Col) {
fprintf(stderr, "| ");
for (size_t col = 0; col < bspec->n; ++col)
fprintf(stderr, "%+2.3f%+2.3fj ", creal(target[n*n*N*Row + n*Col + n*N*row + col]),cimag(target[n*n*N*Row + n*Col + n*N*row + col]));
}
fprintf(stderr, "|\n");
}
}
fprintf(stderr, "-------------------------------\n\n");
#endif
return target;
}
complex double *qpms_orbit_irrep_projector_matrix(complex double *target,
const qpms_ss_orbit_type_t *ot, const qpms_vswf_set_spec_t *bspec,
const qpms_finite_group_t *sym, const qpms_iri_t iri) {
assert(sym);
assert(sym->rep3d);
assert(ot); assert(ot->size > 0);
assert(iri < sym->nirreps); assert(sym->irreps);
check_norm_compat(bspec);
const size_t n = bspec->n;
const qpms_gmi_t N = ot->size;
if (target == NULL)
target = malloc(n*n*N*N*sizeof(complex double));
if (target == NULL) abort();
memset(target, 0, n*n*N*N*sizeof(complex double));
// Workspace for the orbit group action matrices
complex double *tmp = malloc(n*n*N*N*sizeof(complex double));
const int d = sym->irreps[iri].dim;
double prefac = d / (double) sym->order;
for(int partner = 0; partner < d; ++partner) {
for(qpms_gmi_t g = 0; g < sym->order; ++g) {
// We use the diagonal elements of D_g
complex double D_g_conj = sym->irreps[iri].m[g*d*d + partner*d + partner];
#ifdef DUMP_ACTIONMATRIX
fprintf(stderr,"(factor %+g%+gj) ", creal(D_g_conj), cimag(D_g_conj));
#endif
qpms_orbit_action_matrix(tmp, ot, bspec, sym, g);
// TODO kahan sum?
for(size_t i = 0; i < n*n*N*N; ++i)
target[i] += prefac * D_g_conj * tmp[i];
}
}
free(tmp);
#ifdef DUMP_PROJECTORMATRIX
fprintf(stderr,"Projector %d (%s):\n", (int) iri,
sym->irreps[iri].name?sym->irreps[iri].name:"");
for (size_t Row = 0; Row < ot->size; ++Row) {
fprintf(stderr, "--------------------------\n");
for (size_t row = 0; row < bspec->n; ++row) {
for (size_t Col = 0; Col < ot->size; ++Col) {
fprintf(stderr, "| ");
for (size_t col = 0; col < bspec->n; ++col)
fprintf(stderr, "%+2.3f%+2.3fj ", creal(target[n*n*N*Row + n*Col + n*N*row + col]),cimag(target[n*n*N*Row + n*Col + n*N*row + col]));
}
fprintf(stderr, "|\n");
}
}
fprintf(stderr, "-------------------------------\n\n");
#endif
return target;
}
#define SVD_ATOL 1e-8
complex double *qpms_orbit_irrep_basis(size_t *basis_size,
complex double *target,
const qpms_ss_orbit_type_t *ot, const qpms_vswf_set_spec_t *bspec,
const qpms_finite_group_t *sym, const qpms_iri_t iri) {
assert(sym);
assert(sym->rep3d);
assert(ot); assert(ot->size > 0);
assert(iri < sym->nirreps); assert(sym->irreps);
check_norm_compat(bspec);
const size_t n = bspec->n;
const qpms_gmi_t N = ot->size;
const bool newtarget = (target == NULL);
if (newtarget)
QPMS_CRASHING_MALLOC(target,n*n*N*N*sizeof(complex double));
if (target == NULL) abort();
memset(target, 0, n*n*N*N*sizeof(complex double));
// Get the projector (also workspace for right sg. vect.)
complex double *projector = qpms_orbit_irrep_projector_matrix(NULL,
ot, bspec, sym, iri);
if(!projector) abort();
// Workspace for the right singular vectors.
complex double *V_H = malloc(n*n*N*N*sizeof(complex double));
if(!V_H) abort();
// THIS SHOULD NOT BE NECESSARY
complex double *U = malloc(n*n*N*N*sizeof(complex double));
if(!U) abort();
double *s = malloc(n*N*sizeof(double)); if(!s) abort();
int info = LAPACKE_zgesdd(LAPACK_ROW_MAJOR,
'A', // jobz; overwrite projector with left sg.vec. and write right into V_H
n*N /* m */, n*N /* n */, projector /* a */, n*N /* lda */,
s /* s */, U /* u */, n*N /* ldu, irrelev. */, V_H /* vt */,
n*N /* ldvt */);
if (info) qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"Something went wrong with the SVD.");
size_t bs;
for(bs = 0; bs < n*N; ++bs) {
#if 0
qpms_pr_debug_at_flf(__FILE__, __LINE__, __func__,
"%d. irrep, %zd. SV: %.16lf", (int) iri, bs, s[bs]);
#endif
if(s[bs] > 1 + SVD_ATOL) qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"%zd. SV too large: %.16lf", bs, s[bs]);
if(s[bs] > SVD_ATOL && fabs(1-s[bs]) > SVD_ATOL)
qpms_pr_error_at_flf(__FILE__, __LINE__, __func__,
"%zd. SV in the 'wrong' interval: %.16lf", bs, s[bs]);
if(s[bs] < SVD_ATOL) break;
}
memcpy(target, V_H, bs*N*n*sizeof(complex double));
if(newtarget) QPMS_CRASHING_REALLOC(target, bs*N*n*sizeof(complex double));
if(basis_size) *basis_size = bs;
free(U);
free(V_H);
free(projector);
return target;
}
complex double *qpms_scatsys_irrep_transform_matrix(complex double *U,
const qpms_scatsys_t *ss, qpms_iri_t iri) {
const size_t packedlen = ss->saecv_sizes[iri];
const size_t full_len = ss->fecv_size;
if (U == NULL)
QPMS_CRASHING_MALLOC(U,full_len * packedlen * sizeof(complex double));
memset(U, 0, full_len * packedlen * sizeof(complex double));
size_t fullvec_offset = 0;
for(qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
const qpms_ss_oti_t oti = ss->p_orbitinfo[pi].t;
const qpms_ss_orbit_type_t *const ot = ss->orbit_types + oti;
const qpms_ss_osn_t osn = ss->p_orbitinfo[pi].osn;
const qpms_ss_orbit_pi_t opi = ss->p_orbitinfo[pi].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offset = ss->saecv_ot_offsets[iri*ss->orbit_type_count + oti]
+ osn * ot->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsize = ot->size * ot->bspecn;
const size_t orbit_packedsize = ot->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *om = ot->irbases + ot->irbase_offsets[iri];
for (size_t prow = 0; prow < orbit_packedsize; ++prow)
for (size_t pcol = 0; pcol < ot->bspecn; ++pcol)
U[full_len * (packed_orbit_offset + prow) + (fullvec_offset + pcol)]
= om[orbit_fullsize * prow + (opi * ot->bspecn + pcol)];
fullvec_offset += ot->bspecn;
}
return U;
}
complex double *qpms_scatsys_irrep_pack_matrix_stupid(complex double *target_packed,
const complex double *orig_full, const qpms_scatsys_t *ss,
qpms_iri_t iri){
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) // THIS IS A BIT PROBLEMATIC, TODO how to deal with empty irreps?
return target_packed;
const size_t full_len = ss->fecv_size;
if (target_packed == NULL)
target_packed = malloc(SQ(packedlen)*sizeof(complex double));
if (target_packed == NULL) abort();
memset(target_packed, 0, SQ(packedlen)*sizeof(complex double));
// Workspace for the intermediate matrix
complex double *tmp;
QPMS_CRASHING_MALLOC(tmp, full_len * packedlen * sizeof(complex double));
complex double *U = qpms_scatsys_irrep_transform_matrix(NULL, ss, iri);
const complex double one = 1, zero = 0;
// tmp = F U*
cblas_zgemm(
CblasRowMajor, CblasNoTrans, CblasConjTrans,
full_len /*M*/, packedlen /*N*/, full_len /*K*/,
&one /*alpha*/, orig_full/*A*/, full_len/*ldA*/,
U /*B*/, full_len/*ldB*/,
&zero /*beta*/, tmp /*C*/, packedlen /*LDC*/);
// target = U tmp
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
packedlen /*M*/, packedlen /*N*/, full_len /*K*/,
&one /*alpha*/, U/*A*/, full_len/*ldA*/,
tmp /*B*/, packedlen /*ldB*/, &zero /*beta*/,
target_packed /*C*/, packedlen /*ldC*/);
free(tmp);
free(U);
return target_packed;
}
/// Transforms a big "packed" matrix into the full basis (trivial implementation).
complex double *qpms_scatsys_irrep_unpack_matrix_stupid(complex double *target_full,
const complex double *orig_packed, const qpms_scatsys_t *ss,
qpms_iri_t iri, bool add){
const size_t packedlen = ss->saecv_sizes[iri];
const size_t full_len = ss->fecv_size;
if (target_full == NULL)
target_full = malloc(SQ(full_len)*sizeof(complex double));
if (target_full == NULL) abort();
if(!add) memset(target_full, 0, SQ(full_len)*sizeof(complex double));
if(!packedlen) return target_full; // Empty irrep, do nothing.
// Workspace for the intermediate matrix result
complex double *tmp;
QPMS_CRASHING_MALLOC(tmp, full_len * packedlen * sizeof(complex double));
complex double *U = qpms_scatsys_irrep_transform_matrix(NULL, ss, iri);
const complex double one = 1, zero = 0;
// tmp = P U
cblas_zgemm(
CblasRowMajor, CblasNoTrans, CblasNoTrans,
packedlen /*M*/, full_len /*N*/, packedlen /*K*/,
&one /*alpha*/, orig_packed/*A*/, packedlen/*ldA*/,
U /*B*/, full_len/*ldB*/,
&zero /*beta*/, tmp /*C*/, full_len /*LDC*/);
// target += U* tmp
cblas_zgemm(CblasRowMajor, CblasConjTrans, CblasNoTrans,
full_len /*M*/, full_len /*N*/, packedlen /*K*/,
&one /*alpha*/, U/*A*/, full_len/*ldA*/,
tmp /*B*/, full_len /*ldB*/, &one /*beta*/,
target_full /*C*/, full_len /*ldC*/);
free(tmp);
free(U);
return target_full;
}
complex double *qpms_scatsys_irrep_pack_matrix(complex double *target_packed,
const complex double *orig_full, const qpms_scatsys_t *ss,
qpms_iri_t iri){
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) // THIS IS A BIT PROBLEMATIC, TODO how to deal with empty irreps?
return target_packed;
const size_t full_len = ss->fecv_size;
if (target_packed == NULL)
target_packed = malloc(SQ(packedlen)*sizeof(complex double));
if (target_packed == NULL) abort();
memset(target_packed, 0, SQ(packedlen)*sizeof(complex double));
// Workspace for the intermediate particle-orbit matrix result
complex double *tmp = malloc(sizeof(complex double) * SQ(ss->max_bspecn)
* ss->sym->order); if (!tmp) abort();
const complex double one = 1, zero = 0;
size_t fullvec_offsetR = 0;
for(qpms_ss_pi_t piR = 0; piR < ss->p_count; ++piR) { //Row loop
const qpms_ss_oti_t otiR = ss->p_orbitinfo[piR].t;
const qpms_ss_orbit_type_t *const otR = ss->orbit_types + otiR;
const qpms_ss_osn_t osnR = ss->p_orbitinfo[piR].osn;
const qpms_ss_orbit_pi_t opiR = ss->p_orbitinfo[piR].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetR =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiR]
+ osnR * otR->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsizeR = otR->size * otR->bspecn;
const size_t particle_fullsizeR = otR->bspecn;
const size_t orbit_packedsizeR = otR->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omR = otR->irbases + otR->irbase_offsets[iri];
size_t fullvec_offsetC = 0;
if(orbit_packedsizeR) { // avoid zgemm crash on empty irrep
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) { //Column loop
const qpms_ss_oti_t otiC = ss->p_orbitinfo[piC].t;
const qpms_ss_orbit_type_t *const otC = ss->orbit_types + otiC;
const qpms_ss_osn_t osnC = ss->p_orbitinfo[piC].osn;
const qpms_ss_orbit_pi_t opiC = ss->p_orbitinfo[piC].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetC =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiC]
+ osnC * otC->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsizeC = otC->size * otC->bspecn;
const size_t particle_fullsizeC = otC->bspecn;
const size_t orbit_packedsizeC = otC->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omC = otC->irbases + otC->irbase_offsets[iri];
if(orbit_packedsizeC) { // avoid zgemm crash on empty irrep
// tmp[oiR|piR,piC] = ∑_K M[piR,K] U*[K,piC]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans,
particle_fullsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeC /*K*/,
&one /*alpha*/, orig_full + full_len*fullvec_offsetR + fullvec_offsetC/*A*/,
full_len/*ldA*/,
omC + opiC*particle_fullsizeC /*B*/,
orbit_fullsizeC/*ldB*/, &zero /*beta*/,
tmp /*C*/, orbit_packedsizeC /*LDC*/);
// target[oiR|piR,oiC|piC] += U[...] tmp[...]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
orbit_packedsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeR /*K*/,
&one /*alpha*/, omR + opiR*particle_fullsizeR/*A*/,
orbit_fullsizeR/*ldA*/,
tmp /*B*/, orbit_packedsizeC /*ldB*/, &one /*beta*/,
target_packed + packedlen*packed_orbit_offsetR + packed_orbit_offsetC /*C*/,
packedlen /*ldC*/);
}
fullvec_offsetC += otC->bspecn;
}
}
fullvec_offsetR += otR->bspecn;
}
free(tmp);
return target_packed;
}
/// Transforms a big "packed" matrix into the full basis.
/** TODO doc */
complex double *qpms_scatsys_irrep_unpack_matrix(complex double *target_full,
const complex double *orig_packed, const qpms_scatsys_t *ss,
qpms_iri_t iri, bool add){
const size_t packedlen = ss->saecv_sizes[iri];
const size_t full_len = ss->fecv_size;
if (target_full == NULL)
target_full = malloc(SQ(full_len)*sizeof(complex double));
if (target_full == NULL) abort();
if(!add) memset(target_full, 0, SQ(full_len)*sizeof(complex double));
if(!packedlen) return target_full; // Empty irrep, do nothing.
// Workspace for the intermediate particle-orbit matrix result
complex double *tmp = malloc(sizeof(complex double) * SQ(ss->max_bspecn)
* ss->sym->order); if (!tmp) abort();
const complex double one = 1, zero = 0;
size_t fullvec_offsetR = 0;
for(qpms_ss_pi_t piR = 0; piR < ss->p_count; ++piR) { //Row loop
const qpms_ss_oti_t otiR = ss->p_orbitinfo[piR].t;
const qpms_ss_orbit_type_t *const otR = ss->orbit_types + otiR;
const qpms_ss_osn_t osnR = ss->p_orbitinfo[piR].osn;
const qpms_ss_orbit_pi_t opiR = ss->p_orbitinfo[piR].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetR =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiR]
+ osnR * otR->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsizeR = otR->size * otR->bspecn;
const size_t particle_fullsizeR = otR->bspecn;
const size_t orbit_packedsizeR = otR->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omR = otR->irbases + otR->irbase_offsets[iri];
size_t fullvec_offsetC = 0;
if (orbit_packedsizeR) // avoid crash on empty irrep
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) { //Column loop
const qpms_ss_oti_t otiC = ss->p_orbitinfo[piC].t;
const qpms_ss_orbit_type_t *const otC = ss->orbit_types + otiC;
const qpms_ss_osn_t osnC = ss->p_orbitinfo[piC].osn;
const qpms_ss_orbit_pi_t opiC = ss->p_orbitinfo[piC].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetC =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiC]
+ osnC * otC->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsizeC = otC->size * otC->bspecn;
const size_t particle_fullsizeC = otC->bspecn;
const size_t orbit_packedsizeC = otC->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omC = otC->irbases + otC->irbase_offsets[iri];
if (orbit_packedsizeC) { // avoid crash on empty irrep
// tmp = P U
// tmp[oiR|piR,piC] = ∑_K M[piR,K] U[K,piC]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
orbit_packedsizeR /*M*/, particle_fullsizeC /*N*/, orbit_packedsizeC /*K*/,
&one /*alpha*/, orig_packed + packedlen*packed_orbit_offsetR + packed_orbit_offsetC/*A*/,
packedlen/*ldA*/,
omC + opiC*particle_fullsizeC /*B*/,
orbit_fullsizeC/*ldB*/, &zero /*beta*/,
tmp /*C*/, particle_fullsizeC /*LDC*/);
// target[oiR|piR,oiC|piC] += U*[...] tmp[...]
cblas_zgemm(CblasRowMajor, CblasConjTrans, CblasNoTrans,
particle_fullsizeR /*M*/, particle_fullsizeC /*N*/, orbit_packedsizeR /*K*/,
&one /*alpha*/, omR + opiR*particle_fullsizeR/*A*/,
orbit_fullsizeR/*ldA*/,
tmp /*B*/, particle_fullsizeC /*ldB*/, &one /*beta*/,
target_full + full_len*fullvec_offsetR + fullvec_offsetC /*C*/,
full_len /*ldC*/);
}
fullvec_offsetC += otC->bspecn;
}
fullvec_offsetR += otR->bspecn;
}
free(tmp);
return target_full;
}
/// Projects a "big" vector onto an irrep.
/** TODO doc */
complex double *qpms_scatsys_irrep_pack_vector(complex double *target_packed,
const complex double *orig_full, const qpms_scatsys_t *ss,
const qpms_iri_t iri) {
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) return target_packed; // Empty irrep
if (target_packed == NULL)
target_packed = malloc(packedlen*sizeof(complex double));
if (target_packed == NULL) abort();
memset(target_packed, 0, packedlen*sizeof(complex double));
const complex double one = 1;
size_t fullvec_offset = 0;
for(qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
const qpms_ss_oti_t oti = ss->p_orbitinfo[pi].t;
const qpms_ss_orbit_type_t *const ot = ss->orbit_types + oti;
const qpms_ss_osn_t osn = ss->p_orbitinfo[pi].osn;
const qpms_ss_orbit_pi_t opi = ss->p_orbitinfo[pi].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offset = ss->saecv_ot_offsets[iri*ss->orbit_type_count + oti]
+ osn * ot->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsize = ot->size * ot->bspecn;
const size_t particle_fullsize = ot->bspecn;
const size_t orbit_packedsize = ot->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *om = ot->irbases + ot->irbase_offsets[iri];
if (orbit_packedsize) // avoid crash on empty irrep
cblas_zgemv(CblasRowMajor/*order*/, CblasNoTrans/*transA*/,
orbit_packedsize/*M*/, particle_fullsize/*N*/, &one/*alpha*/,
om + opi*particle_fullsize/*A*/, orbit_fullsize/*lda*/,
orig_full+fullvec_offset/*X*/, 1/*incX*/,
&one/*beta*/, target_packed+packed_orbit_offset/*Y*/, 1/*incY*/);
fullvec_offset += ot->bspecn;
}
return target_packed;
}
/// Transforms a big "packed" vector into the full basis.
/** TODO doc */
complex double *qpms_scatsys_irrep_unpack_vector(complex double *target_full,
const complex double *orig_packed, const qpms_scatsys_t *ss,
const qpms_iri_t iri, bool add) {
const size_t full_len = ss->fecv_size;
if (target_full == NULL)
target_full = malloc(full_len*sizeof(complex double));
if (target_full == NULL) abort();
if (!add) memset(target_full, 0, full_len*sizeof(complex double));
const complex double one = 1;
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) return target_full; // Completely empty irrep
size_t fullvec_offset = 0;
for(qpms_ss_pi_t pi = 0; pi < ss->p_count; ++pi) {
const qpms_ss_oti_t oti = ss->p_orbitinfo[pi].t;
const qpms_ss_orbit_type_t *const ot = ss->orbit_types + oti;
const qpms_ss_osn_t osn = ss->p_orbitinfo[pi].osn;
const qpms_ss_orbit_pi_t opi = ss->p_orbitinfo[pi].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offset = ss->saecv_ot_offsets[iri*ss->orbit_type_count + oti]
+ osn * ot->irbase_sizes[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsize = ot->size * ot->bspecn;
const size_t particle_fullsize = ot->bspecn;
const size_t orbit_packedsize = ot->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *om = ot->irbases + ot->irbase_offsets[iri];
if (orbit_packedsize) // empty irrep, avoid zgemv crashing.
cblas_zgemv(CblasRowMajor/*order*/, CblasConjTrans/*transA*/,
orbit_packedsize/*M*/, particle_fullsize/*N*/, &one/*alpha*/, om + opi*particle_fullsize/*A*/,
orbit_fullsize/*lda*/, orig_packed+packed_orbit_offset /*X*/, 1/*incX*/, &one/*beta*/,
target_full+fullvec_offset/*Y*/, 1/*incY*/);
fullvec_offset += ot->bspecn;
}
return target_full;
}
complex double *qpms_scatsys_build_translation_matrix_full(
/// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
complex double *target,
const qpms_scatsys_t *ss,
double k ///< Wave number to use in the translation matrix.
)
{
const size_t full_len = ss->fecv_size;
if(!target)
QPMS_CRASHING_MALLOC(target, SQ(full_len) * sizeof(complex double));
memset(target, 0, SQ(full_len) * sizeof(complex double)); //unnecessary?
{ // Non-diagonal part; M[piR, piC] = T[piR] S(piR<-piC)
size_t fullvec_offsetR = 0;
for(qpms_ss_pi_t piR = 0; piR < ss->p_count; ++piR) {
const qpms_vswf_set_spec_t *bspecR = ss->tm[ss->p[piR].tmatrix_id]->spec;
const cart3_t posR = ss->p[piR].pos;
size_t fullvec_offsetC = 0;
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) {
const qpms_vswf_set_spec_t *bspecC = ss->tm[ss->p[piC].tmatrix_id]->spec;
if(piC != piR) { // The diagonal will be dealt with later.
const cart3_t posC = ss->p[piC].pos;
QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_lc3p(ss->c,
target + fullvec_offsetR*full_len + fullvec_offsetC,
bspecR, full_len, bspecC, 1,
k, posR, posC));
}
fullvec_offsetC += bspecC->n;
}
assert(fullvec_offsetC = full_len);
fullvec_offsetR += bspecR->n;
}
assert(fullvec_offsetR == full_len);
}
return target;
}
complex double *qpms_scatsys_build_modeproblem_matrix_full(
/// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
complex double *target,
const qpms_scatsys_t *ss,
double k ///< Wave number to use in the translation matrix.
)
{
const size_t full_len = ss->fecv_size;
if(!target)
QPMS_CRASHING_MALLOC(target, SQ(full_len) * sizeof(complex double));
complex double *tmp;
QPMS_CRASHING_MALLOC(tmp, SQ(ss->max_bspecn) * sizeof(complex double));
memset(target, 0, SQ(full_len) * sizeof(complex double)); //unnecessary?
complex double one = 1, zero = 0;
{ // Non-diagonal part; M[piR, piC] = T[piR] S(piR<-piC)
size_t fullvec_offsetR = 0;
for(qpms_ss_pi_t piR = 0; piR < ss->p_count; ++piR) {
const qpms_vswf_set_spec_t *bspecR = ss->tm[ss->p[piR].tmatrix_id]->spec;
const cart3_t posR = ss->p[piR].pos;
size_t fullvec_offsetC = 0;
// dest particle T-matrix
const complex double *tmmR = ss->tm[ss->p[piR].tmatrix_id]->m;
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) {
const qpms_vswf_set_spec_t *bspecC = ss->tm[ss->p[piC].tmatrix_id]->spec;
if(piC != piR) { // The diagonal will be dealt with later.
const cart3_t posC = ss->p[piC].pos;
QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_lc3p(ss->c,
tmp, // tmp is S(piR<-piC)
bspecR, bspecC->n, bspecC, 1,
k, posR, posC));
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
bspecR->n /*m*/, bspecC->n /*n*/, bspecR->n /*k*/,
&one/*alpha*/, tmmR/*a*/, bspecR->n/*lda*/,
tmp/*b*/, bspecC->n/*ldb*/, &zero/*beta*/,
target + fullvec_offsetR*full_len + fullvec_offsetC /*c*/,
full_len /*ldc*/);
}
fullvec_offsetC += bspecC->n;
}
fullvec_offsetR += bspecR->n;
}
}
// diagonal part M[pi,pi] = -1
for (size_t i = 0; i < full_len; ++i) target[full_len * i + i] = -1;
free(tmp);
return target;
}
complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed(
/// Target memory with capacity for ss->saecv_sizes[iri]**2 elements. If NULL, new will be allocated.
complex double *target_packed,
const qpms_scatsys_t *ss, qpms_iri_t iri,
double k ///< Wave number to use in the translation matrix.
)
{
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) // THIS IS A BIT PROBLEMATIC, TODO how to deal with empty irreps?
return target_packed;
if (target_packed == NULL)
target_packed = malloc(SQ(packedlen)*sizeof(complex double));
if (target_packed == NULL) abort();
memset(target_packed, 0, SQ(packedlen)*sizeof(complex double));
// some of the following workspaces are probably redundant; TODO optimize later.
// workspaces for the uncompressed particle<-particle tranlation matrix block
// and the result of multiplying with a T-matrix
complex double *Sblock, *TSblock;
QPMS_CRASHING_MALLOC(Sblock, sizeof(complex double)*SQ(ss->max_bspecn));
QPMS_CRASHING_MALLOC(TSblock, sizeof(complex double)*SQ(ss->max_bspecn));
// Workspace for the intermediate particle-orbit matrix result
complex double *tmp;
QPMS_CRASHING_MALLOC(tmp, sizeof(complex double) * SQ(ss->max_bspecn) * ss->sym->order);
const complex double one = 1, zero = 0;
for(qpms_ss_pi_t piR = 0; piR < ss->p_count; ++piR) { //Row loop
const qpms_ss_oti_t otiR = ss->p_orbitinfo[piR].t;
const qpms_ss_orbit_type_t *const otR = ss->orbit_types + otiR;
const qpms_ss_osn_t osnR = ss->p_orbitinfo[piR].osn;
const qpms_ss_orbit_pi_t opiR = ss->p_orbitinfo[piR].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetR =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiR]
+ osnR * otR->irbase_sizes[iri];
const qpms_vswf_set_spec_t *bspecR = ss->tm[ss->p[piR].tmatrix_id]->spec;
// Orbit coeff vector's full size:
const size_t orbit_fullsizeR = otR->size * otR->bspecn;
const size_t particle_fullsizeR = otR->bspecn; // == bspecR->n
const size_t orbit_packedsizeR = otR->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omR = otR->irbases + otR->irbase_offsets[iri];
const cart3_t posR = ss->p[piR].pos;
if(orbit_packedsizeR) { // avoid zgemm crash on empty irrep
// dest particle T-matrix
const complex double *tmmR = ss->tm[ss->p[piR].tmatrix_id]->m;
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) { //Column loop
const qpms_ss_oti_t otiC = ss->p_orbitinfo[piC].t;
const qpms_ss_orbit_type_t *const otC = ss->orbit_types + otiC;
const qpms_ss_osn_t osnC = ss->p_orbitinfo[piC].osn;
const qpms_ss_orbit_pi_t opiC = ss->p_orbitinfo[piC].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetC =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiC]
+ osnC * otC->irbase_sizes[iri];
const qpms_vswf_set_spec_t *bspecC = ss->tm[ss->p[piC].tmatrix_id]->spec;
// Orbit coeff vector's full size:
const size_t orbit_fullsizeC = otC->size * otC->bspecn;
const size_t particle_fullsizeC = otC->bspecn; // == bspecC->n
const size_t orbit_packedsizeC = otC->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omC = otC->irbases + otC->irbase_offsets[iri];
if(orbit_packedsizeC) { // avoid zgemm crash on empty irrep
if(piC != piR) { // non-diagonal, calculate TS
const cart3_t posC = ss->p[piC].pos;
QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_lc3p(ss->c,
Sblock, // Sblock is S(piR->piC)
bspecR, bspecC->n, bspecC, 1,
k, posR, posC));
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
bspecR->n /*m*/, bspecC->n /*n*/, bspecR->n /*k*/,
&one/*alpha*/, tmmR/*a*/, bspecR->n/*lda*/,
Sblock/*b*/, bspecC->n/*ldb*/, &zero/*beta*/,
TSblock /*c*/, bspecC->n /*ldc*/);
} else { // diagonal, fill with diagonal -1
for (size_t row = 0; row < bspecR->n; ++row)
for (size_t col = 0; col < bspecC->n; ++col)
TSblock[row * bspecC->n + col] = (row == col)? -1 : 0;
}
// tmp[oiR|piR,piC] = ∑_K M[piR,K] U*[K,piC]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans,
particle_fullsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeC /*K*/,
&one /*alpha*/, TSblock/*A*/, particle_fullsizeC/*ldA*/,
omC + opiC*particle_fullsizeC /*B*/,
orbit_fullsizeC/*ldB*/, &zero /*beta*/,
tmp /*C*/, orbit_packedsizeC /*LDC*/);
// target[oiR|piR,oiC|piC] += U[...] tmp[...]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
orbit_packedsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeR /*K*/,
&one /*alpha*/, omR + opiR*particle_fullsizeR/*A*/, orbit_fullsizeR/*ldA*/,
tmp /*B*/, orbit_packedsizeC /*ldB*/, &one /*beta*/,
target_packed + packedlen*packed_orbit_offsetR + packed_orbit_offsetC /*C*/,
packedlen /*ldC*/);
}
}
}
}
free(tmp);
free(Sblock);
free(TSblock);
return target_packed;
}
complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(
/// Target memory with capacity for ss->saecv_sizes[iri]**2 elements. If NULL, new will be allocated.
complex double *target_packed,
const qpms_scatsys_t *ss, qpms_iri_t iri,
double k ///< Wave number to use in the translation matrix.
)
{
const size_t packedlen = ss->saecv_sizes[iri];
if (!packedlen) // THIS IS A BIT PROBLEMATIC, TODO how to deal with empty irreps?
return target_packed;
if (target_packed == NULL)
target_packed = malloc(SQ(packedlen)*sizeof(complex double));
if (target_packed == NULL) abort();
memset(target_packed, 0, SQ(packedlen)*sizeof(complex double));
// some of the following workspaces are probably redundant; TODO optimize later.
// workspaces for the uncompressed particle<-particle tranlation matrix block
// and the result of multiplying with a T-matrix
complex double *Sblock, *TSblock;
QPMS_CRASHING_MALLOC(Sblock, sizeof(complex double)*SQ(ss->max_bspecn));
QPMS_CRASHING_MALLOC(TSblock, sizeof(complex double)*SQ(ss->max_bspecn));
// Workspace for the intermediate particle-orbit matrix result
complex double *tmp;
QPMS_CRASHING_MALLOC(tmp, sizeof(complex double) * SQ(ss->max_bspecn) * ss->sym->order);
const complex double one = 1, zero = 0;
for(qpms_ss_pi_t opistartR = 0; opistartR < ss->p_count;
opistartR += ss->orbit_types[ss->p_orbitinfo[opistartR].t].size //orbit_p_countR; might write a while() instead
) {
const qpms_ss_pi_t orbitstartpiR = ss->p_by_orbit[opistartR];
const qpms_ss_oti_t otiR = ss->p_orbitinfo[orbitstartpiR].t;
const qpms_ss_osn_t osnR = ss->p_orbitinfo[orbitstartpiR].osn;
const qpms_ss_orbit_type_t *const otR = ss->orbit_types + otiR;
const qpms_ss_orbit_pi_t orbit_p_countR = otR->size;
const size_t orbit_packedsizeR = otR->irbase_sizes[iri];
if(orbit_packedsizeR) { // avoid zgemm crash on empty irrep
const size_t particle_fullsizeR = otR->bspecn; // == bspecR->n
const qpms_vswf_set_spec_t *bspecR = ss->tm[ss->p[orbitstartpiR].tmatrix_id]->spec;
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omR = otR->irbases + otR->irbase_offsets[iri];
// Orbit coeff vector's full size:
const size_t orbit_fullsizeR = otR->size * otR->bspecn;
// This is where the orbit starts in the "packed" vector:
const size_t packed_orbit_offsetR =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiR]
+ osnR * otR->irbase_sizes[iri];
for(qpms_ss_orbit_pi_t opiR = 0; opiR < orbit_p_countR; ++opiR) {
qpms_ss_pi_t piR = ss->p_by_orbit[opistartR + opiR];
assert(opiR == ss->p_orbitinfo[piR].p);
const qpms_ss_oti_t otiR = ss->p_orbitinfo[piR].t;
assert(ss->p_orbitinfo[piR].osn == osnR);
const cart3_t posR = ss->p[piR].pos;
// dest particle T-matrix
const complex double *tmmR = ss->tm[ss->p[piR].tmatrix_id]->m;
for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) { //Column loop
const qpms_ss_oti_t otiC = ss->p_orbitinfo[piC].t;
const qpms_ss_orbit_type_t *const otC = ss->orbit_types + otiC;
const qpms_ss_osn_t osnC = ss->p_orbitinfo[piC].osn;
const qpms_ss_orbit_pi_t opiC = ss->p_orbitinfo[piC].p;
// This is where the particle's orbit starts in the "packed" vector:
const size_t packed_orbit_offsetC =
ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiC]
+ osnC * otC->irbase_sizes[iri];
const qpms_vswf_set_spec_t *bspecC = ss->tm[ss->p[piC].tmatrix_id]->spec;
// Orbit coeff vector's full size:
const size_t orbit_fullsizeC = otC->size * otC->bspecn;
const size_t particle_fullsizeC = otC->bspecn; // == bspecC->n
const size_t orbit_packedsizeC = otC->irbase_sizes[iri];
// This is the orbit-level matrix projecting the whole orbit onto the irrep.
const complex double *omC = otC->irbases + otC->irbase_offsets[iri];
if(orbit_packedsizeC) { // avoid zgemm crash on empty irrep
if(piC != piR) { // non-diagonal, calculate TS
const cart3_t posC = ss->p[piC].pos;
QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_lc3p(ss->c,
Sblock, // Sblock is S(piR->piC)
bspecR, bspecC->n, bspecC, 1,
k, posR, posC));
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
bspecR->n /*m*/, bspecC->n /*n*/, bspecR->n /*k*/,
&one/*alpha*/, tmmR/*a*/, bspecR->n/*lda*/,
Sblock/*b*/, bspecC->n/*ldb*/, &zero/*beta*/,
TSblock /*c*/, bspecC->n /*ldc*/);
} else { // diagonal, fill with diagonal -1
for (size_t row = 0; row < bspecR->n; ++row)
for (size_t col = 0; col < bspecC->n; ++col)
TSblock[row * bspecC->n + col] = (row == col)? -1 : 0;
}
// tmp[oiR|piR,piC] = ∑_K M[piR,K] U*[K,piC]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans,
particle_fullsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeC /*K*/,
&one /*alpha*/, TSblock/*A*/, particle_fullsizeC/*ldA*/,
omC + opiC*particle_fullsizeC /*B*/,
orbit_fullsizeC/*ldB*/, &zero /*beta*/,
tmp /*C*/, orbit_packedsizeC /*LDC*/);
// target[oiR|piR,oiC|piC] += U[...] tmp[...]
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
orbit_packedsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeR /*K*/,
&one /*alpha*/, omR + opiR*particle_fullsizeR/*A*/, orbit_fullsizeR/*ldA*/,
tmp /*B*/, orbit_packedsizeC /*ldB*/, &one /*beta*/,
target_packed + packedlen*packed_orbit_offsetR + packed_orbit_offsetC /*C*/,
packedlen /*ldC*/);
}
}
}
}
}
free(tmp);
free(Sblock);
free(TSblock);
return target_packed;
}
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