static double sc(basis_s *v,simplex *s, int k, int j) {
/* amount by which to scale up vector, for reduce_inner */
double labound;
static int lscale;
static double max_scale,
ldetbound,
Sb;
if (j<10) {
labound = logb(v->sqa)/2;
max_scale = exact_bits - labound - 0.66*(k-2)-1 -DELIFT;
if (max_scale<1) {
warning(-10, overshot exact arithmetic);
max_scale = 1;
}
if (j==0) {
int i;
neighbor *sni;
basis_s *snib;
ldetbound = DELIFT;
Sb = 0;
for (i=k-1,sni=s->neigh+k-1;i>0;i--,sni--) {
snib = sni->basis;
Sb += snib->sqb;
ldetbound += logb(snib->sqb)/2 + 1;
ldetbound -= snib->lscale;
}
}
}
if (ldetbound - v->lscale + logb(v->sqb)/2 + 1 < 0) {
DEBS(-2)
DEBTR(-2) DEBEXP(-2, ldetbound)
print_simplex_f(s, DFILE, &print_neighbor_full);
print_basis(DFILE,v);
EDEBS
return 0;
} else {
int main( int argc, char * argv[] )
{
// degree of polinomial parametrization
// warning: not set N to a value greater than 20!
// (10 in case you don't utilize the micro-basis)
// determinant computation becomes very expensive
unsigned int N = 4;
// max modulus of polynomial coefficients
unsigned int M = 1000;
if (argc > 1)
N = std::atoi(argv[1]);
if (argc > 2)
M = std::atoi(argv[2]);
Geom::SL::MVPoly1 f, g;
Geom::SL::basis_type b;
Geom::SL::MVPoly3 p, q;
Geom::SL::Matrix<Geom::SL::MVPoly2> B;
Geom::SL::MVPoly2 r;
// generate two univariate polynomial with degree N
// and coeffcient in the range [-M, M]
f = pick_multipoly_max<1>(N, M);
g = pick_multipoly_max<1>(N, M);
std::cout << "parametrization: \n";
std::cout << "f = " << f << std::endl;
std::cout << "g = " << g << "\n\n";
// computes the micro-basis
microbasis(b, f, g);
// in case you want utilize directly the initial basis
// you should uncomment the next row and comment
// the microbasis function call
//make_initial_basis(b, f, g);
std::cout << "generators in vector form : \n";
print_basis(b);
std::cout << std::endl;
// micro-basis generators
basis_to_poly(p, b[0]);
basis_to_poly(q, b[1]);
std::cout << "generators as polynomial in R[t,x,y] : \n";
std::cout << "p = " << p << std::endl;
std::cout << "q = " << q << "\n\n";
// make up the Bezout matrix and compute the determinant
B = make_bezout_matrix(p, q);
r = determinant_minor(B);
r.normalize();
std::cout << "Bezout matrix: (entries are bivariate polynomials) \n";
std::cout << "B = " << B << "\n\n";
std::cout << "determinant: \n";
std::cout << "r(x, y) = " << r << "\n\n";
return EXIT_SUCCESS;
}
int optimize_transport(BASIS *basis)
{
/** Declare |optimize_transport| scalars */
int i_enter,j_enter;
int arcindex;
int halfnodes;
int subroot;
int prev;
int orient;
int status;
double deltadual;
/** Declare |optimize_transport| arrays */
int *family;
int *pred;
int *brother;
int *son;
status=init_basis(basis); /* construct initial basis */
if (status) return status;
/** Define simplifications for |optimize_transport| */
family = basis->family;
pred = basis->pred;
brother = basis->brother;
son = basis->son;
halfnodes=basis->no_nodes/2;
deltadual=find_entering_arc(basis,&i_enter,&j_enter,&arcindex);
while(i_enter>=0){ /* there is an entering arc */
basis->pivot++;
#ifdef PRINT
printf("+-----------------------------------+\n");
printf("| pivot %3d |\n",basis->pivot);
printf("+-----------------------------------+\n");
#endif
subroot = find_cycle(basis,i_enter,j_enter,arcindex,&orient);
#ifdef PRINT
printf("\nentering arc : %d --> %d \n",i_enter,j_enter);
printf(" arcindex : %d\n",arcindex);
printf(" redcost : %8.4lf",deltadual);
#endif
/* update duals in the smaller subtrees */
if(family[subroot]<=halfnodes)
update_dual(basis,subroot,(orient>0)?deltadual:-deltadual);
else { /* separate trees, update duals, then reconnect */
basis->rerooted++;
prev = pred[subroot];
/* remove root from successors of prev */
son[prev]= brother[subroot];
update_dual(basis,0,(orient>0)?-deltadual:deltadual);
brother[subroot]=son[prev]; /* insert root to successors of prev */
son[prev]=subroot;
}
#ifdef PRINT
print_basis(basis);
#endif
deltadual=find_entering_arc(basis,&i_enter,&j_enter,&arcindex);
}
status=check_solution(basis);
return status;
}
