int
LUfactor(Matrix A, int *indexarray)
{
int dim = A->dim, i, j, k, i_max, k_max;
Vector scale;
double mx, tmp;
scale = new_vector(dim);
for (i = 0; i < dim; i++)
indexarray[i] = i;
for (i = 0; i < dim; i++) {
mx = 0.;
for (j = 0; j < dim; j++) {
tmp = fabs(M_VAL(A, i, j));
if (mx < tmp)
mx = tmp;
}
scale->ve[i] = mx;
}
k_max = dim - 1;
for (k = 0; k < k_max; k++) {
mx = 0.;
i_max = -1;
for (i = k; i < dim; i++) {
if (fabs(scale->ve[i]) >= Tiny * fabs(M_VAL(A, i, k))) {
tmp = fabs(M_VAL(A, i, k)) / scale->ve[i];
if (mx < tmp) {
mx = tmp;
i_max = i;
}
}
}
if (i_max == -1) {
M_VAL(A, k, k) = 0.;
continue;
}
if (i_max != k) {
SWAPI(indexarray[i_max], indexarray[k]);
for (j = 0; j < dim; j++)
SWAPD(M_VAL(A, i_max, j), M_VAL(A, k, j));
}
for (i = k + 1; i < dim; i++) {
tmp = M_VAL(A, i, k) = M_VAL(A, i, k) / M_VAL(A, k, k);
for (j = k + 1; j < dim; j++)
M_VAL(A, i, j) -= tmp * M_VAL(A, k, j);
}
}
return 0;
}
static double
triang_area(double rx0, double ry0, double rx1, double ry1,
double tx0, double ty0, double tx1, double ty1,
int tt) {
/* rx0,ry0,rx1,ry1: rectangle boundaries */
/* tx0,ty0,tx1,ty1: triangle boundaries */
/* tt: triangle type */
double a,b,c,d;
double lx0,ly0,lx1,ly1;
/* Convert everything to a NW triangle */
if (tt & STH) {
double t;
SWAPI(ry0,ry1);
SWAPI(ty0,ty1);
}
if (tt & EST) {
double t;
SWAPI(rx0,rx1);
SWAPI(tx0,tx1);
}
/* Compute overlapping box */
if (tx0 > rx0)
rx0 = tx0;
if (ty0 > ry0)
ry0 = ty0;
if (tx1 < rx1)
rx1 = tx1;
if (ty1 < ry1)
ry1 = ty1;
if (rx1 <= rx0 || ry1 <= ry0)
return 0.0;
/* Need to compute diagonal line intersection with the box */
/* First compute co-efficients to formulas x = a + by and y = c + dx */
b = (tx1 - tx0)/(ty1 - ty0);
a = tx0 - b * ty0;
d = (ty1 - ty0)/(tx1 - tx0);
c = ty0 - d * tx0;
/* compute top or right intersection */
tt = 0;
ly1 = ry1;
lx1 = a + b * ly1;
if (lx1 <= rx0)
return (rx1 - rx0) * (ry1 - ry0);
else if (lx1 > rx1) {
/* could be right hand side */
lx1 = rx1;
ly1 = c + d * lx1;
if (ly1 <= ry0)
return (rx1 - rx0) * (ry1 - ry0);
tt = 1; /* right hand side intersection */
}
/* compute left or bottom intersection */
lx0 = rx0;
ly0 = c + d * lx0;
if (ly0 >= ry1)
return (rx1 - rx0) * (ry1 - ry0);
else if (ly0 < ry0) {
/* could be right hand side */
ly0 = ry0;
lx0 = a + b * ly0;
if (lx0 >= rx1)
return (rx1 - rx0) * (ry1 - ry0);
tt |= 2; /* bottom intersection */
}
if (tt == 0) {
/* top and left intersection */
/* rectangle minus triangle */
return ((rx1 - rx0) * (ry1 - ry0))
- (0.5 * (lx1 - rx0) * (ry1 - ly0));
} else if (tt == 1) {
/* right and left intersection */
return ((rx1 - rx0) * (ly0 - ry0))
+ (0.5 * (rx1 - rx0) * (ly1 - ly0));
} else if (tt == 2) {
/* top and bottom intersection */
return ((rx1 - lx1) * (ry1 - ry0))
+ (0.5 * (lx1 - lx0) * (ry1 - ry0));
} else {
/* tt == 3 */
/* right and bottom intersection */
/* triangle */
return (0.5 * (rx1 - lx0) * (ly1 - ry0));
}
}
int LLLoperations::doLLL(MutableMatrix *A,
MutableMatrix *Achange,
MutableMatrix *LLLstate,
int nsteps)
{
int n = A->n_cols();
if (n == 0) return COMP_DONE;
// Extract the state from LLLstate:
int k, kmax;
ring_elem a, alphaTop, alphaBottom;
buffer o;
if (LLLstate->get_entry(0,n,a))
k = globalZZ->coerce_to_int(a);
else
k = 0;
if (LLLstate->get_entry(0,n+1,a))
kmax = globalZZ->coerce_to_int(a);
else
kmax = 0;
LLLstate->get_entry(0,n+2,alphaTop); // Don't free alphaTop!
LLLstate->get_entry(0,n+3,alphaBottom);
while (k < n && nsteps != 0 && !system_interrupted())
{
if (M2_gbTrace >= 1)
{
o.reset();
o << ".";
if (M2_gbTrace >= 2)
o << k;
if (nsteps % 20 == 0)
o << newline;
emit(o.str());
}
nsteps--;
if (k > kmax)
{
if (M2_gbTrace == 1)
{
o.reset();
o << "." << k;
if (nsteps % 20 == 0)
o << newline;
emit(o.str());
}
kmax = k;
for (int j=0; j<=k; j++)
{
ring_elem u;
A->dot_product(k,j,u);
for (int i=0; i<=j-1; i++)
{
// u = (D#i * u - lambda#(k,i) * lambda#(j,i)) // D#(i-1)
ring_elem Di, mki, mji, Di1;
LLLstate->get_entry(i,i,Di);
globalZZ->mult_to(u, Di);
if (LLLstate->get_entry(i,k,mki) && LLLstate->get_entry(i,j,mji))
{
ring_elem t1 = globalZZ->mult(mki,mji);
globalZZ->subtract_to(u,t1);
}
if (i > 0)
{
LLLstate->get_entry(i-1,i-1,Di1); // Cannot be zero!!
ring_elem t1 = globalZZ->divide(u,Di1);
globalZZ->remove(u);
u = t1;
}
}
// At this point we have our element:
LLLstate->set_entry(j,k,u);
if (j == k && globalZZ->is_zero(u))
{
ERROR("LLL vectors not independent");
return COMP_ERROR;
}
}
} // end of the k>kmax initialization
REDI(k,k-1,A,Achange,LLLstate);
if (Lovasz(LLLstate,k,alphaTop,alphaBottom))
{
SWAPI(k,kmax,A,Achange,LLLstate);
k--;
if (k == 0) k = 1;
}
else
{
for (int ell=k-2; ell>=0; ell--)
REDI(k,ell,A,Achange,LLLstate);
k++;
}
}
// Before returning, reset k,kmax:
LLLstate->set_entry(0,n,globalZZ->from_int(k));
LLLstate->set_entry(0,n+1,globalZZ->from_int(kmax));
if (k >= n) return COMP_DONE;
if (nsteps == 0) return COMP_DONE_STEPS;
return COMP_INTERRUPTED;
}
