/*
* Replaces constraint a x >= c by x >= ceil(c/a)
* where "a" is a common factor in the coefficients
* old is the constraint; v points to an initialized
* value that this procedure can use.
* Return non-zero if something changed.
* Result is placed in newp.
*/
int ConstraintSimplify(Value *old, Value *newp, int len, Value* v)
{
/* first remove common factor of all coefficients (including "c") */
Vector_Gcd(old+1, len - 1, v);
if (value_notone_p(*v))
Vector_AntiScale(old+1, newp+1, *v, len-1);
Vector_Gcd(old+1, len - 2, v);
if (value_one_p(*v))
return 0;
Vector_AntiScale(old+1, newp+1, *v, len-2);
value_pdivision(newp[len-1], old[len-1], *v);
return 1;
}
/**
* Given a system of equalities, looks if it has an integer solution in the
* combined space, and if yes, returns one solution.
* <p>pre-condition: the equalities are full-row rank (without the constant
* part)</p>
* @param Eqs the system of equations (as constraints)
* @param I a feasible integer solution if it exists, else NULL. Allocated if
* initially set to NULL, else reused.
*/
void Equalities_integerSolution(Matrix * Eqs, Matrix **I) {
Matrix * Hm, *H=NULL, *U, *Q, *M=NULL, *C=NULL, *Hi;
Matrix *Ip;
int i;
Value mod;
unsigned int rk;
if (Eqs==NULL){
if ((*I)!=NULL) Matrix_Free(*I);
I = NULL;
return;
}
/* we use: AI = C = (Ha 0).Q.I = (Ha 0)(I' 0)^T */
/* with I = Qinv.I' = U.I'*/
/* 1- compute I' = Hainv.(-C) */
/* HYP: the equalities are full-row rank */
rk = Eqs->NbRows;
Matrix_subMatrix(Eqs, 0, 1, rk, Eqs->NbColumns-1, &M);
left_hermite(M, &Hm, &Q, &U);
Matrix_Free(M);
Matrix_subMatrix(Hm, 0, 0, rk, rk, &H);
if (dbgCompParmMore) {
show_matrix(Hm);
show_matrix(H);
show_matrix(U);
}
Matrix_Free(Q);
Matrix_Free(Hm);
Matrix_subMatrix(Eqs, 0, Eqs->NbColumns-1, rk, Eqs->NbColumns, &C);
Matrix_oppose(C);
Hi = Matrix_Alloc(rk, rk+1);
MatInverse(H, Hi);
if (dbgCompParmMore) {
show_matrix(C);
show_matrix(Hi);
}
/* put the numerator of Hinv back into H */
Matrix_subMatrix(Hi, 0, 0, rk, rk, &H);
Ip = Matrix_Alloc(Eqs->NbColumns-2, 1);
/* fool Matrix_Product on the size of Ip */
Ip->NbRows = rk;
Matrix_Product(H, C, Ip);
Ip->NbRows = Eqs->NbColumns-2;
Matrix_Free(H);
Matrix_Free(C);
value_init(mod);
for (i=0; i< rk; i++) {
/* if Hinv.C is not integer, return NULL (no solution) */
value_pmodulus(mod, Ip->p[i][0], Hi->p[i][rk]);
if (value_notzero_p(mod)) {
if ((*I)!=NULL) Matrix_Free(*I);
value_clear(mod);
Matrix_Free(U);
Matrix_Free(Ip);
Matrix_Free(Hi);
I = NULL;
return;
}
else {
value_pdivision(Ip->p[i][0], Ip->p[i][0], Hi->p[i][rk]);
}
}
/* fill the rest of I' with zeros */
for (i=rk; i< Eqs->NbColumns-2; i++) {
value_set_si(Ip->p[i][0], 0);
}
value_clear(mod);
Matrix_Free(Hi);
/* 2 - Compute the particular solution I = U.(I' 0) */
ensureMatrix((*I), Eqs->NbColumns-2, 1);
Matrix_Product(U, Ip, (*I));
Matrix_Free(U);
Matrix_Free(Ip);
if (dbgCompParm) {
show_matrix(*I);
}
}
/**
* Tests Constraints_fullDimensionize by comparing the Ehrhart polynomials
* @param A the input set of constraints
* @param B the corresponding context
* @param the number of samples to generate for the test
* @return 1 if the Ehrhart polynomial had the same value for the
* full-dimensional and non-full-dimensional sets of constraints, for their
* corresponding sample parameters values.
*/
int test_Constraints_fullDimensionize(Matrix * A, Matrix * B,
unsigned int nbSamples) {
Matrix * Eqs= NULL, *ParmEqs=NULL, *VL=NULL;
unsigned int * elimVars=NULL, * elimParms=NULL;
Matrix * sample, * smallerSample=NULL;
Matrix * transfSample=NULL;
Matrix * parmVL=NULL;
unsigned int i, j, r, nbOrigParms, nbParms;
Value div, mod, *origVal=NULL, *fullVal=NULL;
Matrix * VLInv;
Polyhedron * P, *PC;
Matrix * M, *C;
Enumeration * origEP, * fullEP=NULL;
const char **fullNames = NULL;
int isOk = 1; /* holds the result */
/* compute the origial Ehrhart polynomial */
M = Matrix_Copy(A);
C = Matrix_Copy(B);
P = Constraints2Polyhedron(M, maxRays);
PC = Constraints2Polyhedron(C, maxRays);
origEP = Polyhedron_Enumerate(P, PC, maxRays, origNames);
Matrix_Free(M);
Matrix_Free(C);
Polyhedron_Free(P);
Polyhedron_Free(PC);
/* compute the full-dimensional polyhedron corresponding to A and its Ehrhart
polynomial */
M = Matrix_Copy(A);
C = Matrix_Copy(B);
nbOrigParms = B->NbColumns-2;
Constraints_fullDimensionize(&M, &C, &VL, &Eqs, &ParmEqs,
&elimVars, &elimParms, maxRays);
if ((Eqs->NbRows==0) && (ParmEqs->NbRows==0)) {
Matrix_Free(M);
Matrix_Free(C);
Matrix_Free(Eqs);
Matrix_Free(ParmEqs);
free(elimVars);
free(elimParms);
return 1;
}
nbParms = C->NbColumns-2;
P = Constraints2Polyhedron(M, maxRays);
PC = Constraints2Polyhedron(C, maxRays);
namesWithoutElim(origNames, nbOrigParms, elimParms, &fullNames);
fullEP = Polyhedron_Enumerate(P, PC, maxRays, fullNames);
Matrix_Free(M);
Matrix_Free(C);
Polyhedron_Free(P);
Polyhedron_Free(PC);
/* make a set of sample parameter values and compare the corresponding
Ehrhart polnomials */
sample = Matrix_Alloc(1,nbOrigParms);
transfSample = Matrix_Alloc(1, nbParms);
Lattice_extractSubLattice(VL, nbParms, &parmVL);
VLInv = Matrix_Alloc(parmVL->NbRows, parmVL->NbRows+1);
MatInverse(parmVL, VLInv);
if (dbg) {
show_matrix(parmVL);
show_matrix(VLInv);
}
srand(nbSamples);
value_init(mod);
value_init(div);
for (i = 0; i< nbSamples; i++) {
/* create a random sample */
for (j=0; j< nbOrigParms; j++) {
value_set_si(sample->p[0][j], rand()%100);
}
/* compute the corresponding value for the full-dimensional
constraints */
valuesWithoutElim(sample, elimParms, &smallerSample);
/* (N' i' 1)^T = VLinv.(N i 1)^T*/
for (r = 0; r < nbParms; r++) {
Inner_Product(&(VLInv->p[r][0]), smallerSample->p[0], nbParms,
&(transfSample->p[0][r]));
/* add the constant part */
value_addto(transfSample->p[0][r], transfSample->p[0][r],
VLInv->p[r][VLInv->NbColumns-2]);
value_pdivision(div, transfSample->p[0][r],
VLInv->p[r][VLInv->NbColumns-1]);
value_subtract(mod, transfSample->p[0][r], div);
/* if the parameters value does not belong to the validity lattice, the
Ehrhart polynomial is zero. */
if (!value_zero_p(mod)) {
fullEP = Enumeration_zero(nbParms, maxRays);
break;
}
}
/* compare the two forms of the Ehrhart polynomial.*/
if (origEP ==NULL) break; /* NULL has loose semantics for EPs */
origVal = compute_poly(origEP, sample->p[0]);
fullVal = compute_poly(fullEP, transfSample->p[0]);
if (!value_eq(*origVal, *fullVal)) {
isOk = 0;
printf("EPs don't match. \n Original value = ");
value_print(stdout, VALUE_FMT, *origVal);
printf("\n Original sample = [");
for (j=0; j<sample->NbColumns; j++) {
value_print(stdout, VALUE_FMT, sample->p[0][j]);
printf(" ");
}
printf("] \n EP = ");
if(origEP!=NULL) {
print_evalue(stdout, &(origEP->EP), origNames);
}
else {
printf("NULL");
}
printf(" \n Full-dimensional value = ");
value_print(stdout, P_VALUE_FMT, *fullVal);
printf("\n full-dimensional sample = [");
for (j=0; j<sample->NbColumns; j++) {
value_print(stdout, VALUE_FMT, transfSample->p[0][j]);
printf(" ");
}
printf("] \n EP = ");
if(origEP!=NULL) {
print_evalue(stdout, &(origEP->EP), fullNames);
}
else {
printf("NULL");
}
}
if (dbg) {
printf("\nOriginal value = ");
value_print(stdout, VALUE_FMT, *origVal);
printf("\nFull-dimensional value = ");
value_print(stdout, P_VALUE_FMT, *fullVal);
printf("\n");
}
value_clear(*origVal);
value_clear(*fullVal);
}
value_clear(mod);
value_clear(div);
Matrix_Free(sample);
Matrix_Free(smallerSample);
Matrix_Free(transfSample);
Enumeration_Free(origEP);
Enumeration_Free(fullEP);
return isOk;
} /* test_Constraints_fullDimensionize */