void ns_concluding_modifications(SolverOutput & solve_out,
const WitnessSet & W,
NullspaceConfiguration * ns_config)
{
solve_out.num_variables = ns_config->num_natural_vars + ns_config->num_v_vars;
solve_out.num_natural_vars = W.num_natural_variables();
solve_out.add_patch(ns_config->v_patch);
for (int ii=0; ii< ns_config->num_additional_linears; ii++) {
solve_out.add_linear(ns_config->additional_linears_terminal[ii]);
}
}
void WitnessSet::merge(const WitnessSet & W_in, tracker_config_t * T)
{
//error checking first
if ( (num_vars_==0) && (W_in.num_vars_!=0) && (num_points()==0)) {
num_vars_ = W_in.num_vars_;
num_natty_vars_ = W_in.num_natty_vars_;
}
if (W_in.num_natty_vars_ != this->num_natty_vars_) {
std::stringstream ss;
ss << "merging two witness sets with differing numbers of natural variables. "<< W_in.num_natural_variables() <<" merging set, "<< this->num_natural_variables() << " existing\n",
throw std::logic_error(ss.str());
}
//just mindlessly add the linears. up to user to ensure linears get merged correctly. no way to know what they want...
for (unsigned int ii = 0; ii<W_in.num_linears(); ii++) {
WitnessSet::add_linear(W_in.linear(ii));
}
for (unsigned int ii = 0; ii<W_in.num_points(); ii++) {
int is_new = 1;
vec_mp & in_point = W_in.point(ii);
for (unsigned int jj = 0; jj<num_points(); jj++){
vec_mp & curr_point = this->point(jj);
//cache the sizes
int in_size = in_point->size;
int curr_size = curr_point->size;
in_point->size = this->num_natural_variables();
curr_point->size = this->num_natural_variables();
if (isSamePoint_homogeneous_input(curr_point, in_point, T->final_tol_times_mult)) {
is_new = 0;
in_point->size = in_size;
curr_point->size = curr_size;
break;
}
// restore the sizes
in_point->size = in_size;
curr_point->size = curr_size;
}
if (is_new==1)
WitnessSet::add_point( (in_point) );
}
for (unsigned int ii = 0; ii<W_in.num_patches(); ii++) {
int is_new = 1;
for (unsigned int jj = 0; jj<this->num_patches(); jj++){
if ( this->patch(jj)->size == W_in.patch(ii)->size) {
if (isSamePoint_inhomogeneous_input(patch(jj), W_in.patch(ii), T->final_tol_times_mult)) {
is_new = 0;
break;
}
}
}
if (is_new==1)
WitnessSet::add_patch(W_in.patch(ii));
}
return;
}//re: merge_witness_sets
void nullspace_config_setup_right(NullspaceConfiguration *ns_config,
vec_mp *pi, // an array of projections, the number of which is the target dimensions
int ambient_dim,
int *max_degree, // a pointer to the value
std::shared_ptr<SystemRandomizer> randomizer,
const WitnessSet & W,
SolverConfiguration & solve_options)
{
ns_config->set_side(nullspace_handedness::RIGHT);
int toss;
parse_input_file(W.input_filename(), &toss); // re-create the parsed files for the stuffs (namely the SLP).
ns_config->set_randomizer(randomizer); // set the pointer. this randomizer is for the underlying system.
*max_degree = randomizer->max_degree()-1; // minus one for differentiated degree
ns_config->max_degree = *max_degree;
// set some integers
ns_config->num_projections = ambient_dim;
ns_config->num_v_vars = W.num_natural_variables()-1;
ns_config->num_synth_vars = W.num_synth_vars(); // this may get a little crazy if we chain into this more than once. this code is written to be called into only one time beyond the first.
ns_config->num_natural_vars = W.num_natural_variables();
ns_config->ambient_dim = ambient_dim;
ns_config->target_projection = (vec_mp *) br_malloc(ns_config->num_projections * sizeof(vec_mp));
for (int ii=0; ii<ns_config->num_projections; ii++) {
init_vec_mp2(ns_config->target_projection[ii], W.num_variables(),solve_options.T.AMP_max_prec);
ns_config->target_projection[ii]->size = W.num_variables();
vec_cp_mp(ns_config->target_projection[ii], pi[ii]);
}
ns_config->num_jac_equations = (ns_config->num_natural_vars - 1);// N-1; the subtraction of 1 is for the 1 hom-var.
// me must omit any previously added synthetic vars.
ns_config->num_additional_linears = ambient_dim-1;
ns_config->num_v_linears = ns_config->num_jac_equations;
// this check is correct.
int check_num_func = randomizer->num_rand_funcs() + ns_config->num_jac_equations + ns_config->num_additional_linears + W.num_patches() + 1; // +1 for v patch from this incoming computation
int check_num_vars = ns_config->num_natural_vars + ns_config->num_synth_vars + ns_config->num_v_vars;
if (check_num_func != check_num_vars) {
std::cout << color::red();
std::cout << "mismatch in number of equations...\n" << std::endl;
std::cout << "left: " << check_num_func << " right " << check_num_vars << std::endl;
std::cout << color::console_default();
throw std::logic_error("logic error in nullspace_left");
}
// set up the linears in $v$ ( the M_i linears)
ns_config->v_linears = (vec_mp *)br_malloc(ns_config->num_v_linears*sizeof(vec_mp));
for (int ii=0; ii<ns_config->num_v_linears; ii++) {
init_vec_mp2(ns_config->v_linears[ii],ns_config->num_v_vars,solve_options.T.AMP_max_prec);
ns_config->v_linears[ii]->size = ns_config->num_v_vars;
for (int jj=0; jj<ns_config->num_v_vars; jj++){
get_comp_rand_mp(&ns_config->v_linears[ii]->coord[jj]); // should this be real? no.
}
}
// the last of the linears will be used for the slicing, and passed on to later routines
int offset = 1;
ns_config->additional_linears_terminal = (vec_mp *)br_malloc((ns_config->num_additional_linears)*sizeof(vec_mp));
ns_config->additional_linears_starting = (vec_mp *)br_malloc((ns_config->num_additional_linears)*sizeof(vec_mp));
for (int ii=0; ii<ns_config->num_additional_linears; ii++) {
init_vec_mp2(ns_config->additional_linears_terminal[ii],W.num_variables(),solve_options.T.AMP_max_prec);
ns_config->additional_linears_terminal[ii]->size = W.num_variables();
for (int jj=0; jj<W.num_natural_variables(); jj++){
get_comp_rand_mp(&ns_config->additional_linears_terminal[ii]->coord[jj]); // should this be real? no.
}
for (int jj=W.num_natural_variables(); jj<W.num_variables(); jj++) {
set_zero_mp(&ns_config->additional_linears_terminal[ii]->coord[jj]);
}
init_vec_mp2(ns_config->additional_linears_starting[ii],W.num_variables(),solve_options.T.AMP_max_prec);
ns_config->additional_linears_starting[ii]->size = W.num_variables();
vec_cp_mp(ns_config->additional_linears_starting[ii], W.linear(ii+offset));
}
// set up the patch in $v$. we will include this in an inversion matrix to get the starting $v$ values.
init_vec_mp2(ns_config->v_patch,ns_config->num_v_vars,solve_options.T.AMP_max_prec);
ns_config->v_patch->size = ns_config->num_v_vars;
for (int ii=0; ii<ns_config->num_v_vars; ii++) {
get_comp_rand_mp(&ns_config->v_patch->coord[ii]);
}
mat_mp temp_getter; init_mat_mp2(temp_getter,0, 0,solve_options.T.AMP_max_prec);
temp_getter->rows = 0; temp_getter->cols = 0;
//the 'ns_config->starting_linears' will be used for the x variables. we will homotope to these 1 at a time
ns_config->starting_linears = (vec_mp **)br_malloc( randomizer->num_rand_funcs()*sizeof(vec_mp *));
for (int ii=0; ii<randomizer->num_rand_funcs(); ii++) {
int curr_degree = std::max(0,randomizer->randomized_degree(ii)-1);
ns_config->starting_linears[ii] = (vec_mp *) br_malloc(curr_degree*sizeof(vec_mp));
make_matrix_random_mp(temp_getter,curr_degree, W.num_natural_variables(), solve_options.T.AMP_max_prec); // this matrix is nearly orthogonal
for (unsigned int jj=0; jj<curr_degree; jj++) {
init_vec_mp2(ns_config->starting_linears[ii][jj],W.num_variables(),solve_options.T.AMP_max_prec);
ns_config->starting_linears[ii][jj]->size = W.num_variables();
for (int kk=0; kk<W.num_natural_variables(); kk++) {
set_mp(&ns_config->starting_linears[ii][jj]->coord[kk], &temp_getter->entry[jj][kk]);
}
for (int kk=W.num_natural_variables(); kk<W.num_variables(); kk++) {
set_zero_mp(&ns_config->starting_linears[ii][jj]->coord[kk]);
}
}
}
clear_mat_mp(temp_getter);
return;
}
int compute_crit_nullspace_right(SolverOutput & solve_out, // the returned value
const WitnessSet & W,
std::shared_ptr<SystemRandomizer> randomizer,
vec_mp *pi, // an array of projections, the number of which is the target dimensions
int ambient_dim,
BertiniRealConfig & program_options,
SolverConfiguration & solve_options,
NullspaceConfiguration *ns_config)
{
//many of the 1's here should be replaced by the number of patch equations, or the number of variable_groups
// get the max degree of the derivative functions. this is unique to the left nullspace formulation, as the functions become mixed together
int max_degree;
nullspace_config_setup_right(ns_config,
pi,
ambient_dim,
&max_degree,
randomizer,
W,
solve_options);
if (max_degree==0) {
// this will probably need tweaking when the dimension is higher than 1. but who really is going to decompose a linear surface?
solve_out.copy_patches(W);
ns_concluding_modifications(solve_out, W, ns_config);
std::cout << "the highest degree of any derivative equation is 0. Returning empty SolverOutput." << std::endl;
//then there cannot possibly be any critical points, with respect to ANY projection. simply return an empty but complete set.
return 0;
}
//
///
///// end setup
////////
//////////////
///////////////////////////
int offset;
WitnessSet Wtemp, Wtemp2;
// 2. Do a bunch of homotopies in $x$, each set of which will be followed by a single linear solve in $v$.
if (program_options.verbose_level()>=3) {
std::cout << "building up linprod start system for left nullspace" << std::endl;
}
// setup for the multilin moves
// these are for feeding into the multilin solver -- and that's it. the majority will be overridden in the while loop as the start x linears
vec_mp *multilin_linears = (vec_mp *) br_malloc(W.num_linears()*sizeof(vec_mp)); // target dim is the number of linears in the input witness set
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
init_vec_mp2(multilin_linears[ii],W.num_variables(), solve_options.T.AMP_max_prec);
multilin_linears[ii]->size = W.num_variables();
vec_cp_mp(multilin_linears[ii], W.linear(ii));
}
MultilinConfiguration ml_config(solve_options,randomizer);
// this is for performing the matrix inversion to get ahold of the $v$ values corresponding to $x$
mat_mp tempmat; init_mat_mp2(tempmat, ns_config->num_v_vars, ns_config->num_v_vars,solve_options.T.AMP_max_prec);
tempmat->rows = tempmat->cols = ns_config->num_v_vars;
offset = ns_config->num_v_vars-1;
for (int jj=0; jj<ns_config->num_v_vars; jj++)
set_mp(&tempmat->entry[offset][jj], &ns_config->v_patch->coord[jj]);
// for holding the result of the matrix inversion
vec_mp result; init_vec_mp2(result,ns_config->num_v_vars,solve_options.T.AMP_max_prec); result->size = ns_config->num_v_vars;
// use this for the matrix inversion
vec_mp invert_wrt_me;
init_vec_mp2(invert_wrt_me,ns_config->num_v_vars,solve_options.T.AMP_max_prec); invert_wrt_me->size = ns_config->num_v_vars;
for (int ii=0; ii<ns_config->num_v_vars-1; ii++)
set_zero_mp(&invert_wrt_me->coord[ii]); // set zero
set_one_mp(&invert_wrt_me->coord[ns_config->num_v_vars-1]); // the last entry is set to 1 for the patch equation
vec_mp temppoint; init_vec_mp2(temppoint, ns_config->num_natural_vars +ns_config->num_synth_vars + ns_config->num_v_vars,solve_options.T.AMP_max_prec);
temppoint->size = ns_config->num_natural_vars + ns_config->num_synth_vars + ns_config->num_v_vars;
WitnessSet W_step_one;
W_step_one.set_num_variables(W.num_variables());
W_step_one.set_num_natural_variables(W.num_natural_variables());
W_step_one.copy_patches(W);
W_step_one.copy_names(W);
WitnessSet W_linprod;
W_linprod.set_num_variables(ns_config->num_natural_vars + ns_config->num_v_vars + ns_config->num_synth_vars);
W_linprod.set_num_natural_variables(W.num_natural_variables());
if (program_options.quick_run()<=1)
solve_options.robust = true;
else
solve_options.robust = false;
for (int ii=0; ii<randomizer->num_rand_funcs(); ii++) {
int differentiated_degree = randomizer->randomized_degree(ii)-1; // the -1 is for differentiating. this could be 0.
if (differentiated_degree==0) {
continue;
}
else{
for (int jj=0; jj<differentiated_degree; jj++) {
//copy in the linear for the solve
vec_cp_mp(multilin_linears[0], ns_config->starting_linears[ii][jj]);
// the remainder of the linears are left alone (stay stationary).
if (program_options.verbose_level()>=6) {
std::cout << "moving FROM this set:\n";
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
print_point_to_screen_matlab(W.linear(ii),"L");
}
std::cout << "\nTO this set:\n";
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
print_point_to_screen_matlab(multilin_linears[ii],"ELL");
}
}
// actually solve WRT the linears
SolverOutput fillme;
multilin_solver_master_entry_point(W, // WitnessSet
fillme, // the new data is put here!
multilin_linears,
ml_config,
solve_options);
WitnessSet Wtemp;
fillme.get_noninfinite_w_mult_full(Wtemp); // should be ordered
W_step_one.merge(Wtemp, &solve_options.T);
Wtemp.reset();
}
int curr_index = 0;
for (int kk=0; kk<ns_config->num_v_vars; kk++) { // subtract one from upper limit because of the patch equation
if (kk!=ii) {
for (int mm=0; mm<ns_config->num_v_vars; mm++){
set_mp(&tempmat->entry[curr_index][mm], &ns_config->v_linears[kk]->coord[mm]);}
curr_index++;
}
}
// invert the matrix for the v variables.
matrixSolve_mp(result, tempmat, invert_wrt_me);
//set the bottom part of the temppoint, which will be a startpoint for the nullspace call later.
offset = ns_config->num_natural_vars+ns_config->num_synth_vars;
for (int mm=0; mm<ns_config->num_v_vars; mm++)
set_mp(&temppoint->coord[mm+offset], &result->coord[mm]);
//set the top part, x, of the start point, and copy it in.
for (unsigned int kk=0; kk<W_step_one.num_points(); kk++) {
for (int mm=0; mm<ns_config->num_natural_vars+ns_config->num_synth_vars; mm++) {
set_mp(&temppoint->coord[mm], & W_step_one.point(kk)->coord[mm]);
}
W_linprod.add_point(temppoint);
}
W_step_one.reset();
W_step_one.set_num_variables(W.num_variables());
W_step_one.set_num_natural_variables(W.num_natural_variables());
W_step_one.copy_patches(W); // necessary?
W_step_one.copy_names(W); // necessary?
}
}
for (int ii=0; ii<1; ii++)
clear_vec_mp(multilin_linears[ii]);
free(multilin_linears);
clear_vec_mp(temppoint);
int num_before = W_linprod.num_points();
W_linprod.sort_for_unique(&solve_options.T);
if (num_before - W_linprod.num_points()>0) {
std::cout << "there were non-unique start points" << std::endl;
mypause();
}
W_linprod.set_num_natural_variables(ns_config->num_v_vars+ns_config->num_synth_vars);
W_linprod.copy_patches(W);
W_linprod.copy_names(W);
//set some solver options
if (program_options.quick_run()<=0)
solve_options.robust = true;
else
solve_options.robust = false;
solve_options.use_midpoint_checker = 0;
if (program_options.verbose_level()>=6)
ns_config->print();
if (program_options.verbose_level()>=3) {
std::cout << "running nullspace right method" << std::endl;
}
nullspacejac_solver_master_entry_point(solve_options.T.MPType,
W_linprod, // carries with it the start points, but not the linears.
solve_out, // the created data goes in here.
ns_config,
solve_options);
ns_concluding_modifications(solve_out, W, ns_config);
clear_mat_mp(tempmat);
clear_vec_mp(invert_wrt_me);
clear_vec_mp(result);
return SUCCESSFUL;
}
int sphere_eval_data_d::setup(SphereConfiguration & config,
const WitnessSet & W,
SolverConfiguration & solve_options)
{
SLP_memory = config.SLP_memory;
// set up the vectors to hold the two linears.
mp_to_d(radius, config.radius);
vec_mp_to_d(center, config.center);
if (this->center->size < W.num_variables()) {
int old_size = this->center->size;
increase_size_vec_d(this->center, W.num_variables());
this->center->size = W.num_variables();
for (int ii=old_size; ii<W.num_variables(); ii++) {
set_zero_d(&this->center->coord[ii]);
}
}
if (this->num_static_linears==0) {
static_linear = (vec_d *) br_malloc(W.num_linears()*sizeof(vec_d));
}
else
{
static_linear = (vec_d *) br_realloc(static_linear, W.num_linears()*sizeof(vec_d));
}
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
init_vec_d(static_linear[ii],0);
vec_mp_to_d(static_linear[ii],W.linear(ii));
}
num_static_linears = W.num_linears();
num_natural_vars = W.num_natural_variables();
num_variables = W.num_variables();
for (int ii=0; ii<2; ii++) {
vec_mp_to_d(starting_linear[ii],config.starting_linear[ii]);
}
verbose_level(solve_options.verbose_level());
SolverDoublePrecision::setup(config.SLP, config.randomizer());
generic_setup_patch(&patch,W);
if (solve_options.use_gamma_trick==1)
get_comp_rand_d(this->gamma); // set gamma to be random complex value
else
set_one_d(this->gamma);
if (this->MPType==2)
{
this->BED_mp->setup(config, W, solve_options);
rat_to_d(this->gamma, this->BED_mp->gamma_rat);
}
return 0;
}
int sphere_eval_data_mp::setup(SphereConfiguration & config,
const WitnessSet & W,
SolverConfiguration & solve_options)
{
if (config.randomizer().use_count()==0) {
std::cout << "don't have randomizer set up!" << std::endl;
br_exit(-97621);
}
if (!config.have_mem) {
std::cout << "don't have memory!" << std::endl;
br_exit(-3231);
}
this->SLP_memory = config.SLP_memory;
num_natural_vars = W.num_natural_variables();
num_variables = W.num_variables();
// set up the vectors to hold the linears.
if (this->num_static_linears==0) {
static_linear = (vec_mp *) br_malloc(W.num_linears()*sizeof(vec_mp));
}
else
{
static_linear = (vec_mp *) br_realloc(static_linear, W.num_linears()*sizeof(vec_mp));
}
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
init_vec_mp(static_linear[ii],0);
vec_cp_mp(static_linear[ii],W.linear(ii));
}
set_mp(this->radius, config.radius);
vec_cp_mp(this->center, config.center);
if (this->center->size < W.num_variables()) {
int old_size = this->center->size;
increase_size_vec_mp(this->center, W.num_variables());
this->center->size = W.num_variables();
for (int ii=old_size; ii<W.num_variables(); ii++) {
set_zero_mp(&this->center->coord[ii]);
}
}
if (this->MPType==2) {
set_mp(this->radius_full_prec, config.radius);
vec_cp_mp(this->center_full_prec, config.center);
if (this->center_full_prec->size < W.num_variables()) {
int old_size = this->center_full_prec->size;
increase_size_vec_mp(this->center_full_prec, W.num_variables());
this->center_full_prec->size = W.num_variables();
for (int ii=old_size; ii<W.num_variables(); ii++) {
set_zero_mp(&this->center_full_prec->coord[ii]);
}
}
if (this->num_static_linears==0) {
static_linear_full_prec = (vec_mp *) br_malloc(W.num_linears()*sizeof(vec_mp));
}
else
{
static_linear_full_prec = (vec_mp *) br_realloc(static_linear_full_prec, W.num_linears()*sizeof(vec_mp));
}
for (unsigned int ii=0; ii<W.num_linears(); ii++) {
init_vec_mp2(static_linear_full_prec[ii],0,1024);
vec_cp_mp(static_linear_full_prec[ii], W.linear(ii));
}
}
this->num_static_linears = W.num_linears();
for (int ii=0; ii<2; ii++) {
vec_cp_mp( this->starting_linear[ii], config.starting_linear[ii]);
if (MPType==2) {
vec_cp_mp(this->starting_linear_full_prec[ii], config.starting_linear[ii]);
}
}
// the usual
verbose_level(solve_options.verbose_level());
SolverMultiplePrecision::setup(config.SLP, config.randomizer());
generic_setup_patch(&patch,W);
if (solve_options.use_gamma_trick==1)
get_comp_rand_mp(this->gamma); // set gamma to be random complex value
else{
set_one_mp(this->gamma);
}
comp_d temp;
if (this->MPType==2) {
if (solve_options.use_gamma_trick==1){
get_comp_rand_rat(temp, this->gamma, this->gamma_rat, 64, solve_options.T.AMP_max_prec, 0, 0);
}
else{
set_one_mp(this->gamma);
set_one_rat(this->gamma_rat);
}
}
return 0;
}
