void clear()
{
clear_mp(v_target);
clear_mp(u_target);
clear_mp(crit_val_left);
clear_mp(crit_val_right);
if (num_projections>0) {
for (int ii=0; ii<num_projections; ii++) {
clear_vec_mp(pi[ii]);
}
free(pi);
}
}
int write_member_points_sc(vec_mp point_to_write)
{
FILE *OUT = NULL;
int ii;
remove("member_points");
OUT = safe_fopen_write("member_points");
vec_mp result;
init_vec_mp(result,0);
dehomogenize(&result,point_to_write);
fprintf(OUT,"2\n\n");
for(ii=0;ii<result->size;ii++)
{
print_mp(OUT,0,&result->coord[ii]); fprintf(OUT,"\n");
}
comp_mp temp; init_mp(temp);
fprintf(OUT,"\n");
for(ii=0;ii<result->size;ii++)
{
conjugate_mp(temp, &result->coord[ii]);
print_mp(OUT,0,temp); fprintf(OUT,"\n");
}
fclose(OUT);
clear_vec_mp(result); clear_mp(temp);
return 0;
}
void clear()
{
clear_vec_mp(checker_1_);
clear_vec_mp(checker_2_);
clear_mp(diff_);
mpf_clear(abs_);
mpf_clear(zerothresh_);
for (int ii=0; ii<num_projections_; ii++) {
clear_vec_mp(projections_[ii]);
}
free(projections_);
}
/**
\brief reset to empty state.
*/
void clear()
{
if (this->num_projections>0) {
for (int ii=0; ii<num_projections; ii++) {
clear_vec_mp(pi[ii]);
}
free(pi);
}
clear_mp(v_target);
clear_mp(u_target);
clear_mp(crit_val_left);
clear_mp(crit_val_right);
clear_mp(u_start);
clear_mp(v_start);
clear_mp(half);
clear_mp(one);
clear_mp(zero);
if (this->MPType==2){
if (this->num_projections>0) {
for (int ii=0; ii<num_projections; ii++) {
clear_vec_mp(pi_full_prec[ii]);
}
free(pi_full_prec);
}
clear_mp(v_target_full_prec);
clear_mp(u_target_full_prec);
clear_mp(crit_val_left_full_prec);
clear_mp(crit_val_right_full_prec);
clear_mp(u_start_full_prec);
clear_mp(v_start_full_prec);
clear_mp(half_full_prec);
clear_mp(one_full_prec);
clear_mp(zero_full_prec);
}
} // re: clear
void WitnessSet::sort_for_inside_sphere(comp_mp radius, vec_mp center)
{
int num_good_pts = 0;
std::vector<int> is_ok;
vec_mp temp_vec; init_vec_mp(temp_vec,0);
comp_mp temp; init_mp(temp);
for (unsigned int ii = 0; ii<num_points(); ++ii) {
dehomogenize(&temp_vec, point(ii),num_natty_vars_);
temp_vec->size = center->size;
norm_of_difference(temp->r, temp_vec, center);
if ( mpf_cmp(temp->r, radius->r) < 0 ){
is_ok.push_back(1);
num_good_pts++;
}
else
{
is_ok.push_back(0);
}
}
vec_mp *transferme = (vec_mp *)br_malloc(num_good_pts*sizeof(vec_mp));
int counter = 0;
for (unsigned int ii=0; ii<num_points(); ++ii) {
if (is_ok[ii]==1) {
init_vec_mp2(transferme[counter],0,1024); transferme[counter]->size = 0;
vec_cp_mp(transferme[counter], point(ii));
counter++;
}
}
if (counter!= num_good_pts) {
printf("counter mismatch\n");
br_exit(271);
}
for (unsigned int ii=0; ii<num_points(); ii++) {
clear_vec_mp(point(ii));
}
free(pts_mp_);
num_pts_ = num_good_pts;
pts_mp_ = transferme;
clear_vec_mp(temp_vec);
clear_mp(temp);
return;
}
int sphere_dehom(point_d out_d, point_mp out_mp, int *out_prec, point_d in_d, point_mp in_mp, int in_prec, void const *ED_d, void const *ED_mp)
{
sphere_eval_data_d *BED_d = NULL;
sphere_eval_data_mp *BED_mp = NULL;
*out_prec = in_prec;
if (in_prec < 64)
{ // compute out_d
sphere_eval_data_d *BED_d = (sphere_eval_data_d *)ED_d;
comp_d denom;
change_size_vec_d(out_d,in_d->size-1);
out_d->size = in_d->size-1;
set_d(denom, &in_d->coord[0]);
for (int ii=0; ii<BED_d->num_variables-1; ++ii) {
set_d(&out_d->coord[ii],&in_d->coord[ii+1]);
div_d(&out_d->coord[ii],&out_d->coord[ii],denom); // result[ii] = dehom_me[ii+1]/dehom_me[0].
}
// print_point_to_screen_matlab(in_d,"in");
// print_point_to_screen_matlab(out_d,"out");
}
else
{ // compute out_mp
sphere_eval_data_mp *BED_mp = (sphere_eval_data_mp *)ED_mp;
setprec_point_mp(out_mp, *out_prec);
comp_mp denom; init_mp(denom);
change_size_vec_mp(out_mp,in_mp->size-1);
out_mp->size = in_mp->size-1;
set_mp(denom, &in_mp->coord[0]);
for (int ii=0; ii<BED_mp->num_variables-1; ++ii) {
set_mp(&out_mp->coord[ii],&in_mp->coord[ii+1]);
div_mp(&out_mp->coord[ii],&out_mp->coord[ii],denom); // result[ii] = dehom_me[ii+1]/dehom_me[0].
}
clear_mp(denom);
// set prec on out_mp
// print_point_to_screen_matlab(in_mp,"in");
// print_point_to_screen_matlab(out_mp,"out");
}
BED_d = NULL;
BED_mp = NULL;
return 0;
}
//this derived from basic_eval_d
int sphere_eval_mp(point_mp funcVals, point_mp parVals, vec_mp parDer, mat_mp Jv, mat_mp Jp, point_mp current_variable_values, comp_mp pathVars, void const *ED)
{ // evaluates a special homotopy type, built for bertini_real
// print_comp_mp_matlab(pathVars,"pathvars");
sphere_eval_data_mp *BED = (sphere_eval_data_mp *)ED; // to avoid having to cast every time
BED->SLP_memory.set_globals_to_this();
int ii, jj, mm; // counters
int offset;
comp_mp one_minus_s, gamma_s;
comp_mp temp, temp2;
comp_mp func_val_sphere, func_val_start;
init_mp(one_minus_s); init_mp(gamma_s);
init_mp(temp); init_mp(temp2);
init_mp(func_val_start);
init_mp(func_val_sphere);
set_one_mp(one_minus_s);
sub_mp(one_minus_s, one_minus_s, pathVars); // one_minus_s = (1 - s)
mul_mp(gamma_s, BED->gamma, pathVars); // gamma_s = gamma * s
vec_mp patchValues; init_vec_mp(patchValues, 0);
vec_mp temp_function_values; init_vec_mp(temp_function_values,0);
vec_mp AtimesF; init_vec_mp(AtimesF,BED->randomizer()->num_rand_funcs()); AtimesF->size = BED->randomizer()->num_rand_funcs();// declare // initialize
mat_mp temp_jacobian_functions; init_mat_mp(temp_jacobian_functions,BED->randomizer()->num_base_funcs(),BED->num_variables);
temp_jacobian_functions->rows = BED->randomizer()->num_base_funcs(); temp_jacobian_functions->cols = BED->num_variables;
mat_mp temp_jacobian_parameters; init_mat_mp(temp_jacobian_parameters,0,0);
mat_mp Jv_Patch; init_mat_mp(Jv_Patch, 0, 0);
mat_mp AtimesJ; init_mat_mp(AtimesJ,BED->randomizer()->num_rand_funcs(),BED->num_variables);
AtimesJ->rows = BED->randomizer()->num_rand_funcs(); AtimesJ->cols = BED->num_variables;
//set the sizes
change_size_vec_mp(funcVals,BED->num_variables); funcVals->size = BED->num_variables;
change_size_mat_mp(Jv, BED->num_variables, BED->num_variables); Jv->rows = Jv->cols = BED->num_variables; // -> this should be square!!!
for (ii=0; ii<BED->num_variables; ii++)
for (jj=0; jj<BED->num_variables; jj++)
set_zero_mp(&Jv->entry[ii][jj]);
// evaluate the SLP to get the system's whatnot.
evalProg_mp(temp_function_values, parVals, parDer, temp_jacobian_functions, temp_jacobian_parameters, current_variable_values, pathVars, BED->SLP);
// evaluate the patch
patch_eval_mp(patchValues, parVals, parDer, Jv_Patch, Jp, current_variable_values, pathVars, &BED->patch); // Jp is ignored
// we assume that the only parameter is s = t and setup parVals & parDer accordingly.
// note that you can only really do this AFTER you are done calling other evaluators.
// set parVals & parDer correctly
// i.e. these must remain here, or below. \/
change_size_point_mp(parVals, 1);
change_size_vec_mp(parDer, 1);
change_size_mat_mp(Jp, BED->num_variables, 1); Jp->rows = BED->num_variables; Jp->cols = 1;
for (ii=0; ii<BED->num_variables; ii++)
set_zero_mp(&Jp->entry[ii][0]);
parVals->size = parDer->size = 1;
set_mp(&parVals->coord[0], pathVars); // s = t
set_one_mp(&parDer->coord[0]); // ds/dt = 1
///////////////////////////
//
// the original (randomized) functions.
//
///////////////////////////////////
BED->randomizer()->randomize(AtimesF,AtimesJ,temp_function_values,temp_jacobian_functions,¤t_variable_values->coord[0]);
for (ii=0; ii<AtimesF->size; ii++) // for each function, after (real orthogonal) randomization
set_mp(&funcVals->coord[ii], &AtimesF->coord[ii]);
for (ii = 0; ii < BED->randomizer()->num_rand_funcs(); ii++)
for (jj = 0; jj < BED->num_variables; jj++)
set_mp(&Jv->entry[ii][jj],&AtimesJ->entry[ii][jj]);
//Jp is 0 for the equations.
///////////////////
//
// the sphere equation.
//
//////////////////////////
offset = BED->randomizer()->num_rand_funcs();
mul_mp(func_val_sphere, BED->radius, BED->radius);
neg_mp(func_val_sphere, func_val_sphere);
mul_mp(func_val_sphere, func_val_sphere, ¤t_variable_values->coord[0]);
mul_mp(func_val_sphere, func_val_sphere, ¤t_variable_values->coord[0]);
//f_sph = -r^2*h^2
for (int ii=1; ii<BED->num_natural_vars; ii++) {
mul_mp(temp2, &BED->center->coord[ii-1], ¤t_variable_values->coord[0]); // temp2 = c_{i-1}*h
sub_mp(temp, ¤t_variable_values->coord[ii], temp2); // temp = x_i - h*c_{i-1}
mul_mp(temp2, temp, temp); // temp2 = (x_i - h*c_{i-1})^2
add_mp(func_val_sphere, func_val_sphere, temp2); // f_sph += (x_i - h*c_{i-1})^2
}
set_one_mp(func_val_start);
for (mm=0; mm<2; ++mm) {
dot_product_mp(temp, BED->starting_linear[mm], current_variable_values);
mul_mp(func_val_start, func_val_start, temp);
//f_start *= L_i (x)
}
// combine the function values
mul_mp(temp, one_minus_s, func_val_sphere);
mul_mp(temp2, gamma_s, func_val_start);
add_mp(&funcVals->coord[offset], temp, temp2);
// f = (1-t) f_sph + gamma t f_start
//// / / / / / / now the derivatives wrt x
// first we store the derivatives of the target function, the sphere. then we will add the part for the linear product start.
//ddx for sphere
for (int ii=1; ii<BED->num_natural_vars; ii++) {
mul_mp(temp2, &BED->center->coord[ii-1], ¤t_variable_values->coord[0]); // temp2 = c_{i-1}*h
sub_mp(temp, ¤t_variable_values->coord[ii], temp2) // temp = x_i - c_{i-1}*h
mul_mp(&Jv->entry[offset][ii], BED->two, temp); // Jv = 2*(x_i - c_{i-1}*h)
mul_mp(&Jv->entry[offset][ii], &Jv->entry[offset][ii], one_minus_s); // Jv = (1-t)*2*(x_i - c_{i-1}*h)
mul_mp(temp2, &BED->center->coord[ii-1], temp); // temp2 = c_{i-1} * ( x_i - c_{i-1} * h )
add_mp(&Jv->entry[offset][0], &Jv->entry[offset][0], temp2); // Jv[0] += c_{i-1} * ( x_i - c_{i-1} * h )
}
// multiply these entries by (1-t)
// the homogenizing var deriv
mul_mp(temp, ¤t_variable_values->coord[0], BED->radius);
mul_mp(temp, temp, BED->radius); // temp = r^2 h
add_mp(&Jv->entry[offset][0], &Jv->entry[offset][0], temp); // Jv[0] = \sum_{i=1}^n {c_{i-1} * ( x_i - c_{i-1} * h )} + r^2 h
neg_mp(&Jv->entry[offset][0], &Jv->entry[offset][0]); // Jv[0] = -Jv[0]
mul_mp(&Jv->entry[offset][0], &Jv->entry[offset][0], BED->two); // Jv[0] *= 2
mul_mp(&Jv->entry[offset][0], &Jv->entry[offset][0], one_minus_s); // Jv[0] *= (1-t)
// f = \sum{ ( x_i - c_{i-1} * h )^2 } - r^2 h^2
//Jv = -2(1-t) ( \sum_{i=1}^n { c_{i-1} * ( x_i - c_{i-1} * h ) } + r^2 h )
// a hardcoded product rule for the two linears.
for (int ii=0; ii<BED->num_variables; ii++) {
dot_product_mp(temp, BED->starting_linear[0], current_variable_values);
mul_mp(temp, temp, &BED->starting_linear[1]->coord[ii]);
dot_product_mp(temp2, BED->starting_linear[1], current_variable_values);
mul_mp(temp2, temp2, &BED->starting_linear[0]->coord[ii]);
add_mp(temp, temp, temp2);
mul_mp(temp2, temp, gamma_s);
//temp2 = gamma s * (L_1(x) * L_0[ii] + L_0(x) * L_1[ii])
//temp2 now has the value of the derivative of the start system wrt x_i
add_mp(&Jv->entry[offset][ii], &Jv->entry[offset][ii], temp2);
}
// finally, the Jp entry for sphere equation's homotopy.
//Jp = -f_sph + gamma f_start
neg_mp(&Jp->entry[offset][0], func_val_sphere);
mul_mp(temp, BED->gamma, func_val_start);
add_mp(&Jp->entry[offset][0], &Jp->entry[offset][0], temp);
//////////////
//
// function values for the static linears
//
////////////////////
offset++;
for (mm=0; mm<BED->num_static_linears; ++mm) {
dot_product_mp(&funcVals->coord[mm+offset], BED->static_linear[mm], current_variable_values);
}
for (mm=0; mm<BED->num_static_linears; ++mm) {
for (ii=0; ii<BED->num_variables; ii++) {
set_mp(&Jv->entry[offset+mm][ii], &BED->static_linear[mm]->coord[ii]);
}
}
//Jp is 0 for the static linears
//////////////
//
// the entries for the patch equations.
//
////////////////////
if (offset+BED->num_static_linears != BED->num_variables-BED->patch.num_patches) {
std::cout << color::red() << "mismatch in offset!\nleft: " <<
offset+BED->num_static_linears << " right " << BED->num_variables-BED->patch.num_patches << color::console_default() << std::endl;
mypause();
}
offset = BED->num_variables-BED->patch.num_patches;
for (ii=0; ii<BED->patch.num_patches; ii++)
set_mp(&funcVals->coord[ii+offset], &patchValues->coord[ii]);
for (ii = 0; ii<BED->patch.num_patches; ii++) // for each patch equation
{ // Jv = Jv_Patch
for (jj = 0; jj<BED->num_variables; jj++) // for each variable
set_mp(&Jv->entry[ii+offset][jj], &Jv_Patch->entry[ii][jj]);
}
//Jp is 0 for the patch.
// done! yay!
if (BED->verbose_level()==16 || BED->verbose_level()==-16) {
//uncomment to see screen output of important variables at each solve step.
print_comp_matlab(pathVars, "t_mp");
print_comp_matlab(BED->gamma, "gamma_mp");
print_point_to_screen_matlab(current_variable_values,"currvars_mp");
print_point_to_screen_matlab(funcVals,"F_mp");
print_matrix_to_screen_matlab(Jv,"Jv_mp");
print_matrix_to_screen_matlab(Jp,"Jp_mp");
}
BED->SLP_memory.set_globals_null();
clear_mp(temp);
clear_mp(temp2);
clear_mp(gamma_s);
clear_mp(one_minus_s);
clear_mp(func_val_sphere);
clear_mp(func_val_start);
clear_vec_mp(patchValues);
clear_vec_mp(temp_function_values);
clear_vec_mp(AtimesF);
clear_mat_mp(temp_jacobian_functions);
clear_mat_mp(temp_jacobian_parameters);
clear_mat_mp(Jv_Patch);
clear_mat_mp(AtimesJ);
return 0;
}
