static void MakeQ(int n, int spl, const Matrix_t **endo)
{
int i;
int dim = endo[0]->Nor;
Matrix_t *q = MatAlloc(endo[0]->Field,spl,dim*dim);
char fn[200];
for (i = 0; i < spl; ++i)
{
int j;
Matrix_t *y = MatInverse(Trans[n]), *x;
MatMul(y,endo[i]);
x = MatTransposed(y);
MatFree(y);
for (j = 0; j < dim; ++j)
MatCopyRegion(q,i,j * dim,x,j,0,1,-1);
MatFree(x);
}
sprintf(fn,"%s.q.%d",TkiName,n+1);
MESSAGE(2,("Writing %s\n",fn));
#if 0
if (InfoM.Cf[TKInfo.CfIndex[0][n]].peakword < 0)
MatMulScalar(q,FF_ZERO);
#endif
MatSave(q,fn);
MatFree(q);
}
static void update_matrix(struct Transform *transform)
{
make_transform_matrix(transform->transform_order, transform->rotate_order,
transform->translate[0], transform->translate[1], transform->translate[2],
transform->rotate[0], transform->rotate[1], transform->rotate[2],
transform->scale[0], transform->scale[1], transform->scale[2],
transform->matrix);
MatInverse(transform->inverse, transform->matrix);
}
static void MakePQ(int n, int mj, int nj)
{
MatRep_t *rep_m;
Matrix_t *estar[MAXENDO], *endo[MAXENDO], *e, *ei;
char fn[200];
int dim = InfoM.Cf[mj].dim;
int spl = InfoM.Cf[mj].spl;
int i;
Matrix_t *p;
MESSAGE(1,("Condensing %s%s x ",InfoM.BaseName,Lat_CfName(&InfoM,mj)));
MESSAGE(1,("%s%s, [E:k]=%d\n",InfoN.BaseName,Lat_CfName(&InfoN,nj),spl));
/* Read the generators for the constituent of M and make the
endomorphism ring.
--------------------------------------------------------- */
rep_m = Lat_ReadCfGens(&InfoM,mj,InfoM.Cf[mj].peakword >= 0 ? LAT_RG_STD : 0);
MESSAGE(2,("Calculating endomorphism ring\n"));
MkEndo(rep_m,InfoM.Cf + mj,endo,MAXENDO);
MrFree(rep_m);
/* Calculate the Q matrix
---------------------- */
MESSAGE(2,("Calculating embedding of E\n"));
MakeQ(n,spl,(const Matrix_t **)endo);
/* Calculate the E* matrices
Note: We should use the symmetry under i<-->k here!
--------------------------------------------------- */
MESSAGE(2,("Calculating projection on E\n"));
MESSAGE(2,(" E* matrices\n"));
e = MatAlloc(FfOrder,spl,spl);
for (i = 0; i < spl; ++i)
{
PTR pptr = MatGetPtr(e,i);
int k;
for (k = 0; k < spl; ++k)
{
FEL f;
Matrix_t *x = MatDup(endo[i]);
MatMul(x,endo[k]);
f = MatTrace(x);
FfInsert(pptr,k,f);
MatFree(x);
}
}
ei = MatInverse(e);
MatFree(e);
for (i = 0; i < spl; ++i)
{
int k;
PTR p;
estar[i] = MatAlloc(FfOrder,dim,dim);
p = MatGetPtr(ei,i);
for (k = 0; k < spl; ++k)
MatAddMul(estar[i],endo[k],FfExtract(p,k));
}
MatFree(ei);
/* Transpose the E* matrices. This simplifies the
calculation of tr(z E*) below.
----------------------------------------------- */
MESSAGE(2,(" Transposing E* matrices\n"));
for (i = 0; i < spl; ++i)
{
Matrix_t *x = MatTransposed(estar[i]);
MatFree(estar[i]);
estar[i] = x;
}
/* Calculate the P matrix
---------------------- */
MESSAGE(2,(" P matrix\n"));
p = MatAlloc(FfOrder,dim*dim,spl);
for (i = 0; i < dim; ++i)
{
int j;
for (j = 0; j < dim; ++j)
{
int r;
PTR pptr = MatGetPtr(p,i*dim + j);
Matrix_t *x = MatAlloc(FfOrder,dim,dim);
MatCopyRegion(x,0,i,Trans[n],0,j,dim,1);
for (r = 0; r < spl; ++r)
{
FEL f = MatProd(x,estar[r]);
FfInsert(pptr,r,f);
}
MatFree(x);
}
}
sprintf(fn,"%s.p.%d",TkiName,n+1);
MESSAGE(2,("Writing %s\n",fn));
#if 0
if (InfoM.Cf[mj].peakword < 0)
MatMulScalar(p,FF_ZERO);
#endif
MatSave(p,fn);
/* Clean up
-------- */
MatFree(p);
for (i = 0; i < spl; ++i)
MatFree(endo[i]);
}
/**
* 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 */
static void kond(int mod, int cf)
{
const Lat_Info *li = &ModList[mod].Info;
char fn[LAT_MAXBASENAME+10];
Matrix_t *peakword, *kern, *m, *k, *pw;
int j, pwr;
/* Make the peak word, find its stable power,
and calculate both kernel and image.
------------------------------------------ */
peakword = WgMakeWord(ModList[mod].Wg,li->Cf[cf].peakword);
MatInsert_(peakword,li->Cf[cf].peakpol);
pw = MatDup(peakword);
StablePower_(peakword,&pwr,&kern);
MESSAGE(0,("pwr=%d, nul=%d, ",pwr,kern->Nor));
if (kern->Nor != li->Cf[cf].mult * li->Cf[cf].spl)
MTX_ERROR("Something is wrong here!");
MatEchelonize(peakword);
/* Write out the image
------------------- */
if (!opt_n)
{
sprintf(fn,"%s%s.im",li->BaseName,Lat_CfName(li,cf));
MatSave(peakword,fn);
}
/* Write out the `uncondense matrix'
--------------------------------- */
m = QProjection(peakword,kern);
k = MatInverse(m);
MatFree(m);
MatMul(k,kern);
sprintf(fn,"%s%s.k",li->BaseName,Lat_CfName(li,cf));
MatSave(k,fn);
/* Condense all generators
----------------------- */
MESSAGE(1,("("));
for (j = 0; j < li->NGen; ++j)
{
sprintf(fn,"%dk",j+1);
gkond(li,cf,peakword,k,ModList[mod].Rep->Gen[j],fn);
MESSAGE(1,("%d",j+1));
}
MESSAGE(1,(")"));
/* Condense the peak word
---------------------- */
gkond(li,cf,peakword,k,pw,"np");
/* Calculate the semisimplicity basis.
----------------------------------- */
if (opt_b)
{
Matrix_t *seed, *partbas;
int pos = CfPosition(li,cf);
seed = MatNullSpace_(pw,0);
partbas = SpinUp(seed,ModList[mod].Rep,SF_EACH|SF_COMBINE|SF_STD,NULL,NULL);
MatFree(seed);
MESSAGE(0,(", %d basis vectors",partbas->Nor));
if (MatCopyRegion(ModList[mod].SsBasis,pos,0,partbas,0,0,-1,-1) != 0)
{
MTX_ERROR1("Error making basis - '%s' is possibly not semisimple",
li->BaseName);
}
MatFree(partbas);
}
MatFree(pw);
MESSAGE(0,("\n"));
MatFree(k);
MatFree(kern);
MatFree(peakword);
}