void ProjBasedSelector::calc_projection_errors(Element* e, const CandsInfo& info_h, const CandsInfo& info_p, const CandsInfo& info_aniso, Solution* rsln, CandElemProjError herr[4], CandElemProjError perr, CandElemProjError anisoerr[4]) {
assert_msg(info_h.is_empty() || (H2D_GET_H_ORDER(info_h.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_h.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of H-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_h.max_quad_order), H2D_GET_V_ORDER(info_h.max_quad_order));
assert_msg(info_p.is_empty() || (H2D_GET_H_ORDER(info_p.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_p.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of P-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_p.max_quad_order), H2D_GET_V_ORDER(info_p.max_quad_order));
assert_msg(info_aniso.is_empty() || (H2D_GET_H_ORDER(info_aniso.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_aniso.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of ANISO-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_aniso.max_quad_order), H2D_GET_V_ORDER(info_aniso.max_quad_order));
int mode = e->get_mode();
// select quadrature, obtain integration points and weights
Quad2D* quad = &g_quad_2d_std;
quad->set_mode(mode);
rsln->set_quad_2d(quad);
double3* gip_points = quad->get_points(H2DRS_INTR_GIP_ORDER);
int num_gip_points = quad->get_num_points(H2DRS_INTR_GIP_ORDER);
// everything is done on the reference domain
rsln->enable_transform(false);
// obtain reference solution values on all four refined sons
scalar** rval[H2D_MAX_ELEMENT_SONS];
Element* base_element = rsln->get_mesh()->get_element(e->id);
assert(!base_element->active);
for (int son = 0; son < H2D_MAX_ELEMENT_SONS; son++)
{
//set element
Element* e = base_element->sons[son];
assert(e != NULL);
//obtain precalculated values
rval[son] = precalc_ref_solution(son, rsln, e, H2DRS_INTR_GIP_ORDER);
}
//retrieve transformations
Trf* trfs = NULL;
int num_noni_trfs = 0;
if (mode == H2D_MODE_TRIANGLE) {
trfs = tri_trf;
num_noni_trfs = H2D_TRF_TRI_NUM;
}
else {
trfs = quad_trf;
num_noni_trfs = H2D_TRF_QUAD_NUM;
}
// precalculate values of shape functions
TrfShape empty_shape_vals;
if (!cached_shape_vals_valid[mode]) {
precalc_ortho_shapes(gip_points, num_gip_points, trfs, num_noni_trfs, shape_indices[mode], max_shape_inx[mode], cached_shape_ortho_vals[mode]);
precalc_shapes(gip_points, num_gip_points, trfs, num_noni_trfs, shape_indices[mode], max_shape_inx[mode], cached_shape_vals[mode]);
cached_shape_vals_valid[mode] = true;
//issue a warning if ortho values are defined and the selected cand_list might benefit from that but it cannot because elements do not have uniform orders
if (!warn_uniform_orders && mode == H2D_MODE_QUAD && !cached_shape_ortho_vals[mode][H2D_TRF_IDENTITY].empty()) {
warn_uniform_orders = true;
if (cand_list == H2D_H_ISO || cand_list == H2D_H_ANISO || cand_list == H2D_P_ISO || cand_list == H2D_HP_ISO || cand_list == H2D_HP_ANISO_H) {
warn_if(!info_h.uniform_orders || !info_aniso.uniform_orders || !info_p.uniform_orders, "Possible inefficiency: %s might be more efficient if the input mesh contains elements with uniform orders strictly.", get_cand_list_str(cand_list));
}
}
}
TrfShape& svals = cached_shape_vals[mode];
TrfShape& ortho_svals = cached_shape_ortho_vals[mode];
//H-candidates
if (!info_h.is_empty()) {
Trf* p_trf_identity[1] = { &trfs[H2D_TRF_IDENTITY] };
std::vector<TrfShapeExp>* p_trf_svals[1] = { &svals[H2D_TRF_IDENTITY] };
std::vector<TrfShapeExp>* p_trf_ortho_svals[1] = { &ortho_svals[H2D_TRF_IDENTITY] };
for(int son = 0; son < H2D_MAX_ELEMENT_SONS; son++) {
scalar **sub_rval[1] = { rval[son] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 1, &base_element->sons[son], p_trf_identity, sub_rval
, p_trf_svals, p_trf_ortho_svals
, info_h, herr[son]);
}
}
//ANISO-candidates
if (!info_aniso.is_empty()) {
const int sons[4][2] = { {0,1}, {3,2}, {0,3}, {1,2} }; //indices of sons for sub-areas
const int tr[4][2] = { {6,7}, {6,7}, {4,5}, {4,5} }; //indices of ref. domain transformations for sub-areas
for(int version = 0; version < 4; version++) { // 2 elements for vertical split, 2 elements for horizontal split
Trf* sub_trfs[2] = { &trfs[tr[version][0]], &trfs[tr[version][1]] };
Element* sub_domains[2] = { base_element->sons[sons[version][0]], base_element->sons[sons[version][1]] };
scalar **sub_rval[2] = { rval[sons[version][0]], rval[sons[version][1]] };
std::vector<TrfShapeExp>* sub_svals[2] = { &svals[tr[version][0]], &svals[tr[version][1]] };
std::vector<TrfShapeExp>* sub_ortho_svals[2] = { &ortho_svals[tr[version][0]], &ortho_svals[tr[version][1]] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 2, sub_domains, sub_trfs, sub_rval
, sub_svals, sub_ortho_svals
, info_aniso, anisoerr[version]);
}
}
//P-candidates
if (!info_p.is_empty()) {
Trf* sub_trfs[4] = { &trfs[0], &trfs[1], &trfs[2], &trfs[3] };
scalar **sub_rval[4] = { rval[0], rval[1], rval[2], rval[3] };
std::vector<TrfShapeExp>* sub_svals[4] = { &svals[0], &svals[1], &svals[2], &svals[3] };
std::vector<TrfShapeExp>* sub_ortho_svals[4] = { &ortho_svals[0], &ortho_svals[1], &ortho_svals[2], &ortho_svals[3] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 4, base_element->sons, sub_trfs, sub_rval
, sub_svals, sub_ortho_svals
, info_p, perr);
}
}
void ProjBasedSelector::calc_error_cand_element(const int mode
, double3* gip_points, int num_gip_points
, const int num_sub, Element** sub_domains, Trf** sub_trfs, scalar*** sub_rvals
, std::vector<TrfShapeExp>** sub_nonortho_svals, std::vector<TrfShapeExp>** sub_ortho_svals
, const CandsInfo& info
, CandElemProjError errors_squared
) {
//allocate space
int max_num_shapes = next_order_shape[mode][current_max_order];
scalar* right_side = new scalar[max_num_shapes];
int* shape_inxs = new int[max_num_shapes];
int* indx = new int[max_num_shapes]; //solver data
double* d = new double[max_num_shapes]; //solver data
double** proj_matrix = new_matrix<double>(max_num_shapes, max_num_shapes);
ProjMatrixCache& proj_matrices = proj_matrix_cache[mode];
std::vector<ShapeInx>& full_shape_indices = shape_indices[mode];
//check whether ortho-svals are available
bool ortho_svals_available = true;
for(int i = 0; i < num_sub && ortho_svals_available; i++)
ortho_svals_available &= !sub_ortho_svals[i]->empty();
//clenup of the cache
for(int i = 0; i <= max_shape_inx[mode]; i++) {
nonortho_rhs_cache[i] = ValueCacheItem<scalar>();
ortho_rhs_cache[i] = ValueCacheItem<scalar>();
}
//calculate for all orders
double sub_area_corr_coef = 1.0 / num_sub;
OrderPermutator order_perm(info.min_quad_order, info.max_quad_order, mode == H2D_MODE_TRIANGLE || info.uniform_orders);
do {
int quad_order = order_perm.get_quad_order();
int order_h = H2D_GET_H_ORDER(quad_order), order_v = H2D_GET_V_ORDER(quad_order);
//build a list of shape indices from the full list
int num_shapes = 0;
unsigned int inx_shape = 0;
while (inx_shape < full_shape_indices.size()) {
ShapeInx& shape = full_shape_indices[inx_shape];
if (order_h >= shape.order_h && order_v >= shape.order_v) {
assert_msg(num_shapes < max_num_shapes, "more shapes than predicted, possible incosistency");
shape_inxs[num_shapes] = shape.inx;
num_shapes++;
}
inx_shape++;
}
//continue only if there are shapes to process
if (num_shapes > 0) {
bool use_ortho = ortho_svals_available && order_perm.get_order_h() == order_perm.get_order_v();
//error_if(!use_ortho, "Non-ortho"); //DEBUG
//select a cache
std::vector< ValueCacheItem<scalar> >& rhs_cache = use_ortho ? ortho_rhs_cache : nonortho_rhs_cache;
std::vector<TrfShapeExp>** sub_svals = use_ortho ? sub_ortho_svals : sub_nonortho_svals;
//calculate projection matrix iff no ortho is used
if (!use_ortho) {
//error_if(!use_ortho, "Non-ortho"); //DEBUG
if (proj_matrices[order_h][order_v] == NULL)
proj_matrices[order_h][order_v] = build_projection_matrix(gip_points, num_gip_points, shape_inxs, num_shapes);
copy_matrix(proj_matrix, proj_matrices[order_h][order_v], num_shapes, num_shapes); //copy projection matrix because original matrix will be modified
}
//build right side (fill cache values that are missing)
for(int inx_sub = 0; inx_sub < num_sub; inx_sub++) {
Element* this_sub_domain = sub_domains[inx_sub];
ElemSubTrf this_sub_trf = { sub_trfs[inx_sub], 1 / sub_trfs[inx_sub]->m[0], 1 / sub_trfs[inx_sub]->m[1] };
ElemGIP this_sub_gip = { gip_points, num_gip_points, sub_rvals[inx_sub] };
std::vector<TrfShapeExp>& this_sub_svals = *(sub_svals[inx_sub]);
for(int k = 0; k < num_shapes; k++) {
int shape_inx = shape_inxs[k];
ValueCacheItem<scalar>& shape_rhs_cache = rhs_cache[shape_inx];
if (!shape_rhs_cache.is_valid()) {
TrfShapeExp empty_sub_vals;
ElemSubShapeFunc this_sub_shape = { shape_inx, this_sub_svals.empty() ? empty_sub_vals : this_sub_svals[shape_inx] };
shape_rhs_cache.set(shape_rhs_cache.get() + evaluate_rhs_subdomain(this_sub_domain, this_sub_gip, this_sub_trf, this_sub_shape));
}
}
}
//copy values from cache and apply area correction coefficient
for(int k = 0; k < num_shapes; k++) {
ValueCacheItem<scalar>& rhs_cache_value = rhs_cache[shape_inxs[k]];
right_side[k] = sub_area_corr_coef * rhs_cache_value.get();
rhs_cache_value.mark();
}
//solve iff no ortho is used
if (!use_ortho) {
//error_if(!use_ortho, "Non-ortho"); //DEBUG
ludcmp(proj_matrix, num_shapes, indx, d);
lubksb<scalar>(proj_matrix, num_shapes, indx, right_side);
}
//calculate error
double error_squared = 0;
for(int inx_sub = 0; inx_sub < num_sub; inx_sub++) {
Element* this_sub_domain = sub_domains[inx_sub];
ElemSubTrf this_sub_trf = { sub_trfs[inx_sub], 1 / sub_trfs[inx_sub]->m[0], 1 / sub_trfs[inx_sub]->m[1] };
ElemGIP this_sub_gip = { gip_points, num_gip_points, sub_rvals[inx_sub] };
ElemProj elem_proj = { shape_inxs, num_shapes, *(sub_svals[inx_sub]), right_side, quad_order };
error_squared += evaluate_error_squared_subdomain(this_sub_domain, this_sub_gip, this_sub_trf, elem_proj);
}
errors_squared[order_h][order_v] = error_squared * sub_area_corr_coef; //apply area correction coefficient
}
} while (order_perm.next());
//clenaup
delete[] proj_matrix;
delete[] right_side;
delete[] shape_inxs;
delete[] indx;
delete[] d;
}
void Orderizer::process_solution(Space* space)
{
// sanity check
if (space == NULL) error("Space is NULL in Orderizer:process_solution().");
if (!space->is_up_to_date())
error("The space is not up to date.");
int type = 1;
nv = nt = ne = nl = 0;
del_slot = -1;
// estimate the required number of vertices and triangles
Mesh* mesh = space->get_mesh();
if (mesh == NULL) {
error("Mesh is NULL in Orderizer:process_solution().");
}
int nn = mesh->get_num_active_elements();
int ev = 77 * nn, et = 64 * nn, ee = 16 * nn, el = nn + 10;
// reuse or allocate vertex, triangle and edge arrays
lin_init_array(verts, double3, cv, ev);
lin_init_array(tris, int3, ct, et);
lin_init_array(edges, int3, ce, ee);
lin_init_array(lvert, int, cl1, el);
lin_init_array(ltext, char*, cl2, el);
lin_init_array(lbox, double2, cl3, el);
info = NULL;
int oo, o[6];
RefMap refmap;
refmap.set_quad_2d(&quad_ord);
// make a mesh illustrating the distribution of polynomial orders over the space
Element* e;
for_all_active_elements(e, mesh)
{
oo = o[4] = o[5] = space->get_element_order(e->id);
for (unsigned int k = 0; k < e->nvert; k++)
o[k] = space->get_edge_order(e, k);
refmap.set_active_element(e);
double* x = refmap.get_phys_x(type);
double* y = refmap.get_phys_y(type);
double3* pt = quad_ord.get_points(type);
int np = quad_ord.get_num_points(type);
int id[80];
assert(np <= 80);
#define make_vert(index, x, y, val) \
{ (index) = add_vertex(); \
verts[index][0] = (x); \
verts[index][1] = (y); \
verts[index][2] = (val); }
int mode = e->get_mode();
if (e->is_quad())
{
o[4] = H2D_GET_H_ORDER(oo);
o[5] = H2D_GET_V_ORDER(oo);
}
make_vert(lvert[nl], x[0], y[0], o[4]);
for (int i = 1; i < np; i++)
make_vert(id[i-1], x[i], y[i], o[(int) pt[i][2]]);
for (int i = 0; i < num_elem[mode][type]; i++)
add_triangle(id[ord_elem[mode][type][i][0]], id[ord_elem[mode][type][i][1]], id[ord_elem[mode][type][i][2]]);
for (int i = 0; i < num_edge[mode][type]; i++)
{
if (e->en[ord_edge[mode][type][i][2]]->bnd || (y[ord_edge[mode][type][i][0] + 1] < y[ord_edge[mode][type][i][1] + 1]) ||
((y[ord_edge[mode][type][i][0] + 1] == y[ord_edge[mode][type][i][1] + 1]) &&
(x[ord_edge[mode][type][i][0] + 1] < x[ord_edge[mode][type][i][1] + 1])))
{
add_edge(id[ord_edge[mode][type][i][0]], id[ord_edge[mode][type][i][1]], 0);
}
}
double xmin = 1e100, ymin = 1e100, xmax = -1e100, ymax = -1e100;
for (unsigned int k = 0; k < e->nvert; k++)
{
if (e->vn[k]->x < xmin) xmin = e->vn[k]->x;
if (e->vn[k]->x > xmax) xmax = e->vn[k]->x;
if (e->vn[k]->y < ymin) ymin = e->vn[k]->y;
if (e->vn[k]->y > ymax) ymax = e->vn[k]->y;
}
lbox[nl][0] = xmax - xmin;
lbox[nl][1] = ymax - ymin;
ltext[nl++] = labels[o[4]][o[5]];
}
