int main(int argc, char* argv[])
{
hermes2d_initialize(&argc, argv);
info("SHAPESET TESTER");
info("num_components = %d", shapeset.get_num_components());
info("max_order = %d", shapeset.get_max_order());
precalc.set_quad_2d(&quad);
for (int mode = 0; mode <= 1; mode++)
{
shapeset.set_mode(mode);
quad.set_mode(mode);
precalc.set_mode(mode);
info(mode ? "\nTESTING QUADS\n" : "\nTESTING TRIANGLES\n");
//test_orders(&shapeset);
test_edge_rotation();
//test_edge_orientation(&shapeset);
//test_num_bubbles(&shapeset);
}
//info("\nALL OK!\n");
printf("\n");
hermes2d_finalize();
return 0;
}
static void old_projection(Element* e, int order, double2* proj, double* old[2])
{
int mo2 = quad2d.get_max_order();
int np = quad2d.get_num_points(mo2);
for (unsigned int k = 0; k < e->nvert; k++) // loop over vertices
{
// vertex basis functions in all integration points
double* vd;
int index_v = ref_map_shapeset.get_vertex_index(k);
ref_map_pss.set_active_shape(index_v);
ref_map_pss.set_quad_order(mo2);
vd = ref_map_pss.get_fn_values();
for (int m = 0; m < 2; m++) // part 0 or 1
for (int j = 0; j < np; j++)
old[m][j] += proj[k][m] * vd[j];
for (int ii = 0; ii < order - 1; ii++)
{
// edge basis functions in all integration points
double* ed;
int index_e = ref_map_shapeset.get_edge_index(k,0,ii+2);
ref_map_pss.set_active_shape(index_e);
ref_map_pss.set_quad_order(mo2);
ed = ref_map_pss.get_fn_values();
for (int m = 0; m < 2; m++) //part 0 or 1
for (int j = 0; j < np; j++)
old[m][j] += proj[e->nvert + k * (order-1) + ii][m] * ed[j];
}
}
}
void test_edge_rotation()
{
info("Testing edge rotation...");
int mode = shapeset.get_mode();
int ne = mode ? 4 : 3;
for (int ori = 0; ori <= 1; ori++)
{
for (int order = 0; order <= shapeset.get_max_order(); order++)
{
double *e01, *e02, *ee1, *ee2;
precalc.set_active_shape(shapeset.get_edge_index(0, ori, order));
precalc.set_quad_order(quad.get_edge_points(0));
e01 = precalc.get_fn_values(0);
if (nc > 1) e02 = precalc.get_fn_values(1);
for (int e = 1; e < ne; e++)
{
precalc.set_active_shape(shapeset.get_edge_index(e, ori, order));
precalc.set_quad_order(quad.get_edge_points(e));
ee1 = precalc.get_fn_values(0);
if (nc > 1) ee2 = precalc.get_fn_values(1);
int np = quad.get_num_points(quad.get_edge_points(0));
if (nc == 1)
{
for (int i = 0; i < np; i++)
if (!eq(e01[i], ee1[i]))
{
info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
}
}
else
{
for (int i = 0; i < np; i++)
{
double x = rot[mode][e][0][0] * ee1[i] + rot[mode][e][0][1] * ee2[i];
double y = rot[mode][e][1][0] * ee1[i] + rot[mode][e][1][1] * ee2[i];
if (!eq(e01[i], x) || !eq(e02[i], y))
{
info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
printf("x comp: 0-ta %g, %d-ta %g\n", e01[i], e, x);
printf("y comp: 0-ta %g, %d-ta %g\n\n", e02[i], e, y);
}
}
}
}
}
}
}
// preparation of projection matrices, Cholesky factorization
static void precalculate_cholesky_projection_matrix_edge()
{
int order = ref_map_shapeset.get_max_order();
int n = order - 1; // number of edge basis functions
edge_proj_matrix = new_matrix<double>(n, n);
// calculate projection matrix of maximum order
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
int o = i + j + 4;
double2* pt = quad1d.get_points(o);
double val = 0.0;
for (int k = 0; k < quad1d.get_num_points(o); k++)
{
double x = pt[k][0];
double fi = lob[i+2](x);
double fj = lob[j+2](x);
val += pt[k][1] * (fi * fj);
}
edge_proj_matrix[i][j] = edge_proj_matrix[j][i] = val;
}
}
// Cholesky factorization of the matrix
edge_p = new double[n];
choldc(edge_proj_matrix, n, edge_p);
}
void CurvMap::update_refmap_coefs(Element* e)
{
ref_map_pss.set_quad_2d(&quad2d);
//ref_map_pss.set_active_element(e);
// calculation of projection matrices
if (edge_proj_matrix == NULL) precalculate_cholesky_projection_matrix_edge();
if (bubble_proj_matrix_tri == NULL) precalculate_cholesky_projection_matrices_bubble();
ref_map_pss.set_mode(e->get_mode());
ref_map_shapeset.set_mode(e->get_mode());
// allocate projection coefficients
int nv = e->nvert;
int ne = order - 1;
int qo = e->is_quad() ? make_quad_order(order, order) : order;
int nb = ref_map_shapeset.get_num_bubbles(qo);
nc = nv + nv*ne + nb;
if (coefs != NULL) delete [] coefs;
coefs = new double2[nc];
// WARNING: do not change the format of the array 'coefs'. If it changes,
// RefMap::set_active_element() has to be changed too.
Nurbs** nurbs;
if (toplevel == false)
{
ref_map_pss.set_active_element(e);
ref_map_pss.set_transform(part);
nurbs = parent->cm->nurbs;
}
else
{
ref_map_pss.reset_transform();
nurbs = e->cm->nurbs;
}
ctm = *(ref_map_pss.get_ctm());
ref_map_pss.reset_transform(); // fixme - do we need this?
// calculation of new projection coefficients
ref_map_projection(e, nurbs, order, coefs);
}
static void precalculate_cholesky_projection_matrices_bubble()
{
// *** triangles ***
ref_map_pss.set_mode(MODE_TRIANGLE);
int order = ref_map_shapeset.get_max_order();
// calculate projection matrix of maximum order
int nb = ref_map_shapeset.get_num_bubbles(order);
int* indices = ref_map_shapeset.get_bubble_indices(order);
bubble_proj_matrix_tri = calculate_bubble_projection_matrix(nb, indices);
// cholesky factorization of the matrix
bubble_tri_p = new double[nb];
choldc(bubble_proj_matrix_tri, nb, bubble_tri_p);
// *** quads ***
ref_map_pss.set_mode(MODE_QUAD);
order = ref_map_shapeset.get_max_order();
order = make_quad_order(order, order);
// calculate projection matrix of maximum order
nb = ref_map_shapeset.get_num_bubbles(order);
indices = ref_map_shapeset.get_bubble_indices(order);
bubble_proj_matrix_quad = calculate_bubble_projection_matrix(nb, indices);
// cholesky factorization of the matrix
bubble_quad_p = new double[nb];
choldc(bubble_proj_matrix_quad, nb, bubble_quad_p);
}
#include "hermes2d.h"
#ifndef COMPLEX
//H1ShapesetOrtho shapeset;
H1ShapesetBeuchler shapeset;
#else
HcurlShapesetLegendre shapeset;
//HcurlShapesetGradLeg shapeset;
#endif
PrecalcShapeset precalc(&shapeset);
Quad2DStd quad;
int nc = shapeset.get_num_components();
const double eps = 1e-13;
inline bool eq(double a, double b) { return fabs(a - b) < eps; }
//inline bool eq(double a, double b) { return a == b; }
double2x2 rot[2][4] =
{
{ {{1,0},{0,1}}, {{-0.5,0.5},{-0.5,-0.5}}, {{0,-1},{1,0}} },
{ {{1,0},{0,1}}, {{0,1},{-1,0}}, {{-1,0},{0,-1}}, {{0,-1},{1,0}} }
};
static void calc_bubble_projection(Element* e, Nurbs** nurbs, int order, double2* proj)
{
ref_map_pss.set_active_element(e);
int i, j, k;
int mo2 = quad2d.get_max_order();
int np = quad2d.get_num_points(mo2);
int qo = e->is_quad() ? make_quad_order(order, order) : order;
int nb = ref_map_shapeset.get_num_bubbles(qo);
AUTOLA_OR(double2, fn, np);
memset(fn, 0, sizeof(double2) * np);
double* rhside[2];
double* old[2];
for (i = 0; i < 2; i++) {
rhside[i] = new double[nb];
old[i] = new double[np];
memset(rhside[i], 0, sizeof(double) * nb);
memset(old[i], 0, sizeof(double) * np);
}
// compute known part of projection (vertex and edge part)
old_projection(e, order, proj, old);
// fn values of both components of nonpolynomial function
double3* pt = quad2d.get_points(mo2);
for (j = 0; j < np; j++) // over all integration points
{
double2 a;
a[0] = ctm.m[0] * pt[j][0] + ctm.t[0];
a[1] = ctm.m[1] * pt[j][1] + ctm.t[1];
calc_ref_map(e, nurbs, a[0], a[1], fn[j]);
}
double2* result = proj + e->nvert + e->nvert * (order - 1);
for (k = 0; k < 2; k++)
{
for (i = 0; i < nb; i++) // loop over bubble basis functions
{
// bubble basis functions in all integration points
double *bfn;
int index_i = ref_map_shapeset.get_bubble_indices(qo)[i];
ref_map_pss.set_active_shape(index_i);
ref_map_pss.set_quad_order(mo2);
bfn = ref_map_pss.get_fn_values();
for (j = 0; j < np; j++) // over all integration points
rhside[k][i] += pt[j][2] * (bfn[j] * (fn[j][k] - old[k][j]));
}
// solve
if (e->nvert == 3)
cholsl(bubble_proj_matrix_tri, nb, bubble_tri_p, rhside[k], rhside[k]);
else
cholsl(bubble_proj_matrix_quad, nb, bubble_quad_p, rhside[k], rhside[k]);
for (i = 0; i < nb; i++)
result[i][k] = rhside[k][i];
}
for (i = 0; i < 2; i++) {
delete [] rhside[i];
delete [] old[i];
}
}
