static Polyhedron *partition2polyhedron(Matrix *A,
struct barvinok_options *options)
{
int i;
unsigned nvar, nparam;
Matrix *M;
Polyhedron *P;
nvar = A->NbColumns;
nparam = A->NbRows;
M = Matrix_Alloc(nvar + nparam, 1 + nvar + nparam + 1);
assert(M);
for (i = 0; i < nparam; ++i) {
Vector_Copy(A->p[i], M->p[i] + 1, nvar);
value_set_si(M->p[i][1 + nvar + i], -1);
}
for (i = 0; i < nvar; ++i) {
value_set_si(M->p[nparam + i][0], 1);
value_set_si(M->p[nparam + i][1 + i], 1);
}
P = Constraints2Polyhedron(M, options->MaxRays);
Matrix_Free(M);
return P;
}
/**
* Eliminate the columns corresponding to a list of eliminated parameters.
* @param M the constraints matrix whose columns are to be removed
* @param nbVars an offset to be added to the ranks of the variables to be
* removed
* @param elimParms the list of ranks of the variables to be removed
* @param newM (output) the matrix without the removed columns
*/
void Constraints_removeElimCols(Matrix * M, unsigned int nbVars,
unsigned int *elimParms, Matrix ** newM) {
unsigned int i, j, k;
if (elimParms[0]==0) {
Matrix_clone(M, newM);
return;
}
if ((*newM)==NULL) {
(*newM) = Matrix_Alloc(M->NbRows, M->NbColumns - elimParms[0]);
}
else {
assert ((*newM)->NbColumns==M->NbColumns - elimParms[0]);
}
for (i=0; i< M->NbRows; i++) {
value_assign((*newM)->p[i][0], M->p[i][0]); /* kind of cstr */
k=0;
Vector_Copy(&(M->p[i][1]), &((*newM)->p[i][1]), nbVars);
for (j=0; j< M->NbColumns-2-nbVars; j++) {
if (j!=elimParms[k+1]) {
value_assign((*newM)->p[i][j-k+nbVars+1], M->p[i][j+nbVars+1]);
}
else {
k++;
}
}
value_assign((*newM)->p[i][(*newM)->NbColumns-1],
M->p[i][M->NbColumns-1]); /* cst part */
}
} /* Constraints_removeElimCols */
static Matrix *Polyhedron2standard_form(Polyhedron *P, Matrix **T)
{
int i, j;
int rows;
unsigned dim = P->Dimension;
Matrix *M2;
Matrix *H, *U;
Matrix M;
assert(P->NbEq == 0);
Polyhedron_Remove_Positivity_Constraint(P);
for (i = 0; i < P->NbConstraints; ++i)
assert(value_zero_p(P->Constraint[i][1+dim]));
Polyhedron_Matrix_View(P, &M, P->NbConstraints);
H = standard_constraints(&M, 0, &rows, &U);
*T = homogenize(U);
Matrix_Free(U);
M2 = Matrix_Alloc(rows, 2+dim+rows);
for (i = dim; i < H->NbRows; ++i) {
Vector_Copy(H->p[i], M2->p[i-dim]+1, dim);
value_set_si(M2->p[i-dim][1+i], -1);
}
for (i = 0, j = H->NbRows-dim; i < dim; ++i) {
if (First_Non_Zero(H->p[i], i) == -1)
continue;
Vector_Oppose(H->p[i], M2->p[j]+1, dim);
value_set_si(M2->p[j][1+j+dim], 1);
++j;
}
Matrix_Free(H);
return M2;
}
/**
* Computes the overall period of the variables I for (MI) mod |d|, where M is
* a matrix and |d| a vector. Produce a diagonal matrix S = (s_k) where s_k is
* the overall period of i_k
* @param M the set of affine functions of I (row-vectors)
* @param d the column-vector representing the modulos
*/
Matrix * affine_periods(Matrix * M, Matrix * d) {
Matrix * S;
unsigned int i,j;
Value tmp;
Value * periods = (Value *)malloc(sizeof(Value) * M->NbColumns);
value_init(tmp);
for(i=0; i< M->NbColumns; i++) {
value_init(periods[i]);
value_set_si(periods[i], 1);
}
for (i=0; i<M->NbRows; i++) {
for (j=0; j< M->NbColumns; j++) {
value_gcd(tmp, d->p[i][0], M->p[i][j]);
value_divexact(tmp, d->p[i][0], tmp);
value_lcm(periods[j], periods[j], tmp);
}
}
value_clear(tmp);
/* 2- build S */
S = Matrix_Alloc(M->NbColumns, M->NbColumns);
for (i=0; i< M->NbColumns; i++)
for (j=0; j< M->NbColumns; j++)
if (i==j) value_assign(S->p[i][j],periods[j]);
else value_set_si(S->p[i][j], 0);
/* 3- clean up */
for(i=0; i< M->NbColumns; i++) value_clear(periods[i]);
free(periods);
return S;
} /* affine_periods */
/* Return
* T 0
* 0 1
*/
static Matrix *homogenize(Matrix *T)
{
int i;
Matrix *H = Matrix_Alloc(T->NbRows+1, T->NbColumns+1);
for (i = 0; i < T->NbRows; ++i)
Vector_Copy(T->p[i], H->p[i], T->NbColumns);
value_set_si(H->p[T->NbRows][T->NbColumns], 1);
return H;
}
static Matrix *VectorArray2Matrix(VectorArray array, unsigned cols)
{
int i, j;
Matrix *M = Matrix_Alloc(array->Size, cols+1);
for (i = 0; i < array->Size; ++i) {
for (j = 0; j < cols; ++j)
value_set_si(M->p[i][j], array->Data[i][j]);
value_set_si(M->p[i][cols], 1);
}
return M;
}
/**
* Computes the intersection of two linear lattices, whose base vectors are
* respectively represented in A and B.
* If I and/or Lb is set to NULL, then the matrix is allocated.
* Else, the matrix is assumed to be allocated already.
* I and Lb are rk x rk, where rk is the rank of A (or B).
* @param A the full-row rank matrix whose column-vectors are the basis for the
* first linear lattice.
* @param B the matrix whose column-vectors are the basis for the second linear
* lattice.
* @param Lb the matrix such that B.Lb = I, where I is the intersection.
* @return their intersection.
*/
static void linearInter(Matrix * A, Matrix * B, Matrix ** I, Matrix **Lb) {
Matrix * AB=NULL;
int rk = A->NbRows;
int a = A->NbColumns;
int b = B->NbColumns;
int i,j, z=0;
Matrix * H, *U, *Q;
/* ensure that the spanning vectors are in the same space */
assert(B->NbRows==rk);
/* 1- build the matrix
* (A 0 1)
* (0 B 1)
*/
AB = Matrix_Alloc(2*rk, a+b+rk);
Matrix_copySubMatrix(A, 0, 0, rk, a, AB, 0, 0);
Matrix_copySubMatrix(B, 0, 0, rk, b, AB, rk, a);
for (i=0; i< rk; i++) {
value_set_si(AB->p[i][a+b+i], 1);
value_set_si(AB->p[i+rk][a+b+i], 1);
}
if (dbgCompParm) {
show_matrix(AB);
}
/* 2- Compute its left Hermite normal form. AB.U = [H 0] */
left_hermite(AB, &H, &Q, &U);
Matrix_Free(AB);
Matrix_Free(Q);
/* count the number of non-zero colums in H */
for (z=H->NbColumns-1; value_zero_p(H->p[H->NbRows-1][z]); z--);
z++;
if (dbgCompParm) {
show_matrix(H);
printf("z=%d\n", z);
}
Matrix_Free(H);
/* if you split U in 9 submatrices, you have:
* A.U_13 = -U_33
* B.U_23 = -U_33,
* where the nb of cols of U_{*3} equals the nb of zero-cols of H
* U_33 is a (the smallest) combination of col-vectors of A and B at the same
* time: their intersection.
*/
Matrix_subMatrix(U, a+b, z, U->NbColumns, U->NbColumns, I);
Matrix_subMatrix(U, a, z, a+b, U->NbColumns, Lb);
if (dbgCompParm) {
show_matrix(U);
}
Matrix_Free(U);
} /* linearInter */
Matrix *pluto_matrix_to_polylib(const PlutoMatrix *mat)
{
int r, c;
Matrix *polymat;
polymat = Matrix_Alloc(mat->nrows, mat->ncols);
for (r=0; r<mat->nrows; r++) {
for (c=0; c<mat->ncols; c++) {
polymat->p[r][c] = mat->val[r][c];
}
}
return polymat;
}
/**
* Given a full-row-rank nxm matrix M made of m row-vectors), computes the
* basis K (made of n-m column-vectors) of the integer kernel of the rows of M
* so we have: M.K = 0
*/
Matrix * int_ker(Matrix * M) {
Matrix *U, *Q, *H, *H2, *K=NULL;
int i, j, rk;
if (dbgCompParm)
show_matrix(M);
/* eliminate redundant rows : UM = H*/
right_hermite(M, &H, &Q, &U);
for (rk=H->NbRows-1; (rk>=0) && Vector_IsZero(H->p[rk], H->NbColumns); rk--);
rk++;
if (dbgCompParmMore) {
printf("rank = %d\n", rk);
}
/* there is a non-null kernel if and only if the dimension m of
the space spanned by the rows
is inferior to the number n of variables */
if (M->NbColumns <= rk) {
Matrix_Free(H);
Matrix_Free(Q);
Matrix_Free(U);
K = Matrix_Alloc(M->NbColumns, 0);
return K;
}
Matrix_Free(U);
Matrix_Free(Q);
/* fool left_hermite by giving NbRows =rank of M*/
H->NbRows=rk;
/* computes MU = [H 0] */
left_hermite(H, &H2, &Q, &U);
if (dbgCompParmMore) {
printf("-- Int. Kernel -- \n");
show_matrix(M);
printf(" = \n");
show_matrix(H2);
show_matrix(U);
}
H->NbRows==M->NbRows;
Matrix_Free(H);
/* the Integer Kernel is made of the last n-rk columns of U */
Matrix_subMatrix(U, 0, rk, U->NbRows, U->NbColumns, &K);
/* clean up */
Matrix_Free(H2);
Matrix_Free(U);
Matrix_Free(Q);
return K;
} /* int_ker */
/**
* Given an integer matrix B with m rows and integer m-vectors C and d,
* computes the basis of the integer solutions to (BN+C) mod d = 0 (1).
* This is an affine lattice (G): (N 1)^T= G(N' 1)^T, forall N' in Z^b.
* If there is no solution, returns NULL.
* @param B B, a (m x b) matrix
* @param C C, a (m x 1) integer matrix
* @param d d, a (1 x m) integer matrix
* @param imb the affine (b+1)x(b+1) basis of solutions, in the homogeneous
* form. Allocated if initially set to NULL, reused if not.
*/
void Equalities_intModBasis(Matrix * B, Matrix * C, Matrix * d, Matrix ** imb) {
int b = B->NbColumns;
/* FIXME: treat the case d=0 as a regular equality B_kN+C_k = 0: */
/* OPT: could keep only equalities for which d>1 */
int nbEqs = B->NbRows;
unsigned int i;
/* 1- buid the problem DI+BN+C = 0 */
Matrix * eqs = Matrix_Alloc(nbEqs, nbEqs+b+1);
for (i=0; i< nbEqs; i++) {
value_assign(eqs->p[i][i], d->p[0][i]);
}
Matrix_copySubMatrix(B, 0, 0, nbEqs, b, eqs, 0, nbEqs);
Matrix_copySubMatrix(C, 0, 0, nbEqs, 1, eqs, 0, nbEqs+b);
/* 2- the solution is the validity lattice of the equalities */
Equalities_validityLattice(eqs, nbEqs, imb);
Matrix_Free(eqs);
} /* Equalities_intModBasis */
void count_new(Value* cb, int lanes[NLANES][L],int filaments,int noconsts){
//clock_t t1 = clock();
Polyhedron *A;
int i,j;
Matrix *M;
//printf("inside count we have the following lanes for %d filaments and %d noconsts:\n",filaments,noconsts);
//dump_lanes(lanes);
M=Matrix_Alloc(noconsts,filaments+2);
//lock_t t2 = clock();
int** constraints;
constraints= malloc(noconsts*sizeof(int *));
//clock_t t3 = clock();
//printf("%lu\n",(filaments+2)*(noconsts));
for (i=0;i<noconsts;i++){
constraints[i]=(int*)malloc(sizeof(int)*(filaments+2));
for(j=0;j<filaments+2;j++){
constraints[i][j]=0;
//printf("%d %d %d\n",i,j,constraints[i][j]);
}
}
//clock_t t4 = clock();
//printf("from count: fils %d noconsts %d\n",filaments,noconsts);
gen_constraints(constraints,lanes,filaments,noconsts);
//clock_t t5 = clock();
struct barvinok_options *options = barvinok_options_new_with_defaults();
Matrix_Init(M,constraints);
//clock_t t6 = clock();
A=Constraints2Polyhedron(M,options->MaxRays);
//clock_t t7 = clock();
barvinok_count_with_options(A, cb, options);
//clock_t t8 = clock();
//printf("timings at count: t2=%f, t3=%f, t4=%f, t5=%f, t6=%f, t7=%f, t8=%f\n",(double)(t2-t1)/CLOCKS_PER_SEC,(double)(t3-t1)/CLOCKS_PER_SEC,(double)(t4-t1)/CLOCKS_PER_SEC,(double)(t5-t1)/CLOCKS_PER_SEC,(double)(t6-t1)/CLOCKS_PER_SEC,(double)(t7-t1)/CLOCKS_PER_SEC,(double)(t8-t1)/CLOCKS_PER_SEC);
Polyhedron_Free(A);
barvinok_options_free(options);
Matrix_Free(M);
for (i=0;i<noconsts;i++){
free(constraints[i]);
}
free(constraints);
}
/**
* Eliminates certain parameters from a vector of values for parameters
* @param origParms the initial vector of values of parameters
* @param elimParms the list of parameters to be eliminated in the vector
* @param newParms the vector of values without the eliminated ones.
*/
void valuesWithoutElim(Matrix * origParms, unsigned int * elimParms,
Matrix ** newParms) {
unsigned int i, j=0;
if (*newParms==NULL) {
*newParms = Matrix_Alloc(1, origParms->NbColumns-elimParms[0]);
} /* else assume enough space is allocated */
if (elimParms[0] ==0) {
for (i=0; i< origParms->NbColumns; i++) {
value_assign((*newParms)->p[0][i], origParms->p[0][i]);
}
}
for (i=0; i< origParms->NbColumns; i++) {
if (i!=elimParms[j+1]) {
value_assign((*newParms)->p[0][i-j], origParms->p[0][i]);
}
else {
j++;
}
}
}/* valuesWithoutElim */
PlutoMatrix *pluto_matrix_inverse(PlutoMatrix *mat)
{
assert(mat->nrows == mat->ncols);
PlutoMatrix *inv;
int dim = mat->nrows;
Matrix *pinv = Matrix_Alloc(dim, dim);
Matrix *pmat = pluto_matrix_to_polylib(mat);
Matrix_Inverse(pmat, pinv);
inv = polylib_matrix_to_pluto(pinv);
Matrix_Free(pmat);
Matrix_Free(pinv);
return inv;
}
/*
* Read the contents of the matrix 'Mat' from standard input.
* A '#' in the first column is a comment line
*/
Matrix *Matrix_Read(void) {
Matrix *Mat;
unsigned NbRows, NbColumns;
char s[1024];
if (fgets(s, 1024, stdin) == NULL)
return NULL;
while ((*s=='#' || *s=='\n') ||
(sscanf(s, "%d %d", &NbRows, &NbColumns)<2)) {
if (fgets(s, 1024, stdin) == NULL)
return NULL;
}
Mat = Matrix_Alloc(NbRows,NbColumns);
if(!Mat) {
errormsg1("Matrix_Read", "outofmem", "out of memory space");
return(NULL);
}
Matrix_Read_Input(Mat);
return Mat;
} /* Matrix_Read */
/**
* Given a matrix that defines a full-dimensional affine lattice, returns the
* affine sub-lattice spanned in the k first dimensions.
* Useful for instance when you only look for the parameters' validity lattice.
* @param lat the original full-dimensional lattice
* @param subLat the sublattice
*/
void Lattice_extractSubLattice(Matrix * lat, unsigned int k, Matrix ** subLat) {
Matrix * H, *Q, *U, *linLat = NULL;
unsigned int i;
dbgStart(Lattice_extractSubLattice);
/* if the dimension is already good, just copy the initial lattice */
if (k==lat->NbRows-1) {
if (*subLat==NULL) {
(*subLat) = Matrix_Copy(lat);
}
else {
Matrix_copySubMatrix(lat, 0, 0, lat->NbRows, lat->NbColumns, (*subLat), 0, 0);
}
return;
}
assert(k<lat->NbRows-1);
/* 1- Make the linear part of the lattice triangular to eliminate terms from
other dimensions */
Matrix_subMatrix(lat, 0, 0, lat->NbRows, lat->NbColumns-1, &linLat);
/* OPT: any integer column-vector elimination is ok indeed. */
/* OPT: could test if the lattice is already in triangular form. */
left_hermite(linLat, &H, &Q, &U);
if (dbgCompParmMore) {
show_matrix(H);
}
Matrix_Free(Q);
Matrix_Free(U);
Matrix_Free(linLat);
/* if not allocated yet, allocate it */
if (*subLat==NULL) {
(*subLat) = Matrix_Alloc(k+1, k+1);
}
Matrix_copySubMatrix(H, 0, 0, k, k, (*subLat), 0, 0);
Matrix_Free(H);
Matrix_copySubMatrix(lat, 0, lat->NbColumns-1, k, 1, (*subLat), 0, k);
for (i=0; i<k; i++) {
value_set_si((*subLat)->p[k][i], 0);
}
value_set_si((*subLat)->p[k][k], 1);
dbgEnd(Lattice_extractSubLattice);
} /* Lattice_extractSubLattice */
int main(int argc,char *argv[]) {
Matrix *C1, *P1;
Polyhedron *C, *P, *S;
Polyhedron *CC, *PP;
Enumeration *en;
Value *p;
int i,j,k;
int m,M;
char str[1024];
Value c;
/******* Read the input *********/
P1 = Matrix_Read();
C1 = Matrix_Read();
if(C1->NbColumns < 2) {
fprintf(stderr,"Not enough parameters !\n");
exit(0);
}
P = Constraints2Polyhedron(P1, MAXRAYS);
C = Constraints2Polyhedron(C1, MAXRAYS);
Matrix_Free(C1);
Matrix_Free(P1);
/******* Compute the true context *******/
CC = align_context(C,P->Dimension,MAXRAYS);
PP = DomainIntersection(P,CC,MAXRAYS);
Domain_Free(CC);
C1 = Matrix_Alloc(C->Dimension+1,P->Dimension+1);
for(i=0;i<C1->NbRows;i++)
for(j=0;j<C1->NbColumns;j++)
if(i==j-P->Dimension+C->Dimension)
value_set_si(C1->p[i][j],1);
else
value_set_si(C1->p[i][j],0);
CC = Polyhedron_Image(PP,C1,MAXRAYS);
Domain_Free(C);
Domain_Free(PP);
Matrix_Free(C1);
C = CC;
/******* Initialize parameters *********/
p = (Value *)malloc(sizeof(Value) * (P->Dimension+2));
for(i=0;i<=P->Dimension;i++) {
value_init(p[i]);
value_set_si(p[i],0);
}
value_init(p[i]);
value_set_si(p[i],1);
/*** S = scanning list of polyhedra ***/
S = Polyhedron_Scan(P,C,MAXRAYS);
value_init(c);
/******* Count now *********/
FOREVER {
fflush(stdin);
printf("Enter %d parameters : ",C->Dimension);
for(k=S->Dimension-C->Dimension+1;k<=S->Dimension;++k) {
scanf(" %s", str);
value_read(p[k],str);
}
printf("EP( ");
value_print(stdout,VALUE_FMT,p[S->Dimension-C->Dimension+1]);
for(k=S->Dimension-C->Dimension+2;k<=S->Dimension;++k) {
printf(", ");
value_print(stdout,VALUE_FMT,p[k]);
}
printf(" ) = ");
count_points(1,S,p,&c);
value_print(stdout,VALUE_FMT,c);
printf("\n");
}
for(i=0;i<=(P->Dimension+1);i++)
value_clear(p[i]);
value_clear(c);
return(0);
} /* main */
/**
* Eliminates all the equalities in a set of constraints and returns the set of
* constraints defining a full-dimensional polyhedron, such that there is a
* bijection between integer points of the original polyhedron and these of the
* resulting (projected) polyhedron).
* If VL is set to NULL, this funciton allocates it. Else, it assumes that
* (*VL) points to a matrix of the right size.
* <p> The following things are done:
* <ol>
* <li> remove equalities involving only parameters, and remove as many
* parameters as there are such equalities. From that, the list of
* eliminated parameters <i>elimParms</i> is built.
* <li> remove equalities that involve variables. This requires a compression
* of the parameters and of the other variables that are not eliminated.
* The affine compresson is represented by matrix VL (for <i>validity
* lattice</i>) and is such that (N I 1)^T = VL.(N' I' 1), where N', I'
* are integer (they are the parameters and variables after compression).
*</ol>
*</p>
*/
void Constraints_fullDimensionize(Matrix ** M, Matrix ** C, Matrix ** VL,
Matrix ** Eqs, Matrix ** ParmEqs,
unsigned int ** elimVars,
unsigned int ** elimParms,
int maxRays) {
unsigned int i, j;
Matrix * A=NULL, *B=NULL;
Matrix * Ineqs=NULL;
unsigned int nbVars = (*M)->NbColumns - (*C)->NbColumns;
unsigned int nbParms;
int nbElimVars;
Matrix * fullDim = NULL;
/* variables for permutations */
unsigned int * permutation;
Matrix * permutedEqs=NULL, * permutedIneqs=NULL;
/* 1- Eliminate the equalities involving only parameters. */
(*ParmEqs) = Constraints_removeParmEqs(M, C, 0, elimParms);
/* if the polyehdron is empty, return now. */
if ((*M)->NbColumns==0) return;
/* eliminate the columns corresponding to the eliminated parameters */
if (elimParms[0]!=0) {
Constraints_removeElimCols(*M, nbVars, (*elimParms), &A);
Matrix_Free(*M);
(*M) = A;
Constraints_removeElimCols(*C, 0, (*elimParms), &B);
Matrix_Free(*C);
(*C) = B;
if (dbgCompParm) {
printf("After false parameter elimination: \n");
show_matrix(*M);
show_matrix(*C);
}
}
nbParms = (*C)->NbColumns-2;
/* 2- Eliminate the equalities involving variables */
/* a- extract the (remaining) equalities from the poyhedron */
split_constraints((*M), Eqs, &Ineqs);
nbElimVars = (*Eqs)->NbRows;
/* if the polyhedron is already full-dimensional, return */
if ((*Eqs)->NbRows==0) {
Matrix_identity(nbParms+1, VL);
return;
}
/* b- choose variables to be eliminated */
permutation = find_a_permutation((*Eqs), nbParms);
if (dbgCompParm) {
printf("Permuting the vars/parms this way: [ ");
for (i=0; i< (*Eqs)->NbColumns-2; i++) {
printf("%d ", permutation[i]);
}
printf("]\n");
}
Constraints_permute((*Eqs), permutation, &permutedEqs);
Equalities_validityLattice(permutedEqs, (*Eqs)->NbRows, VL);
if (dbgCompParm) {
printf("Validity lattice: ");
show_matrix(*VL);
}
Constraints_compressLastVars(permutedEqs, (*VL));
Constraints_permute(Ineqs, permutation, &permutedIneqs);
if (dbgCompParmMore) {
show_matrix(permutedIneqs);
show_matrix(permutedEqs);
}
Matrix_Free(*Eqs);
Matrix_Free(Ineqs);
Constraints_compressLastVars(permutedIneqs, (*VL));
if (dbgCompParm) {
printf("After compression: ");
show_matrix(permutedIneqs);
}
/* c- eliminate the first variables */
assert(Constraints_eliminateFirstVars(permutedEqs, permutedIneqs));
if (dbgCompParmMore) {
printf("After elimination of the variables: ");
show_matrix(permutedIneqs);
}
/* d- get rid of the first (zero) columns,
which are now useless, and put the parameters back at the end */
fullDim = Matrix_Alloc(permutedIneqs->NbRows,
permutedIneqs->NbColumns-nbElimVars);
for (i=0; i< permutedIneqs->NbRows; i++) {
value_set_si(fullDim->p[i][0], 1);
for (j=0; j< nbParms; j++) {
value_assign(fullDim->p[i][j+fullDim->NbColumns-nbParms-1],
permutedIneqs->p[i][j+nbElimVars+1]);
}
for (j=0; j< permutedIneqs->NbColumns-nbParms-2-nbElimVars; j++) {
value_assign(fullDim->p[i][j+1],
permutedIneqs->p[i][nbElimVars+nbParms+j+1]);
}
value_assign(fullDim->p[i][fullDim->NbColumns-1],
permutedIneqs->p[i][permutedIneqs->NbColumns-1]);
}
Matrix_Free(permutedIneqs);
} /* Constraints_fullDimensionize */
/* INDEX = 1 .... Dimension */
int PolyhedronLTQ (Polyhedron *Pol1,Polyhedron *Pol2,int INDEX, int PDIM, int NbMaxConstrs) {
int res, dim, i, j, k;
Polyhedron *Q1, *Q2, *Q3, *Q4, *Q;
Matrix *Mat;
if (Pol1->next || Pol2->next) {
errormsg1("PolyhedronLTQ", "compoly", "Can only compare polyhedra");
return 0;
}
if (Pol1->Dimension != Pol2->Dimension) {
errormsg1("PolyhedronLTQ","diffdim","Polyhedra are not same dimension");
return 0;
}
dim = Pol1->Dimension+2;
POL_ENSURE_FACETS(Pol1);
POL_ENSURE_VERTICES(Pol1);
POL_ENSURE_FACETS(Pol2);
POL_ENSURE_VERTICES(Pol2);
#ifdef DEBUG
fprintf(stdout, "P1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Pol1);
fprintf(stdout, "P2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Pol2);
#endif
/* Create the Line to add */
k = Pol1->Dimension-INDEX+1-PDIM;
Mat = Matrix_Alloc(k,dim);
Vector_Set(Mat->p_Init,0,dim*k);
for(j=0,i=INDEX;j<k;i++,j++)
value_set_si(Mat->p[j][i],1);
Q1 = AddRays(Mat->p[0],k,Pol1,NbMaxConstrs);
Q2 = AddRays(Mat->p[0],k,Pol2,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q1);
fprintf(stdout, "Q2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q2);
#endif
Matrix_Free(Mat);
Q = DomainIntersection(Q1,Q2,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q);
#endif
Domain_Free(Q1);
Domain_Free(Q2);
if (emptyQ(Q)) res = 0; /* not comparable */
else {
Q1 = DomainIntersection(Pol1,Q,NbMaxConstrs);
Q2 = DomainIntersection(Pol2,Q,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q1);
fprintf(stdout, "Q2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q2);
#endif
k = Q1->NbConstraints + Q2->NbConstraints;
Mat = Matrix_Alloc(k, dim);
Vector_Set(Mat->p_Init,0,k*dim);
/* First compute surrounding polyhedron */
j=0;
for (i=0; i<Q1->NbConstraints; i++) {
if ((value_one_p(Q1->Constraint[i][0])) && (value_pos_p(Q1->Constraint[i][INDEX]))) {
/* keep Q1's lower bounds */
for (k=0; k<dim; k++)
value_assign(Mat->p[j][k],Q1->Constraint[i][k]);
j++;
}
}
for (i=0; i<Q2->NbConstraints; i++) {
if ((value_one_p(Q2->Constraint[i][0])) && (value_neg_p(Q2->Constraint[i][INDEX]))) {
/* and keep Q2's upper bounds */
for (k=0; k<dim; k++)
value_assign(Mat->p[j][k],Q2->Constraint[i][k]);
j++;
}
}
Q4 = AddConstraints(Mat->p[0], j, Q, NbMaxConstrs);
Matrix_Free(Mat);
#ifdef debug
fprintf(stderr, "Q4 surrounding polyhedron\n");
Polyhderon_Print(stderr,P_VALUE_FMT, Q4);
#endif
/* if surrounding polyhedron is empty, D1>D2 */
if (emptyQ(Q4)) {
res = 1;
#ifdef debug
fprintf(stderr, "Surrounding polyhedron is empty\n");
#endif
goto LTQdone2;
}
/* Test if Q1 < Q2 */
/* Build a constraint array for >= Q1 and <= Q2 */
Mat = Matrix_Alloc(2,dim);
Vector_Set(Mat->p_Init,0,2*dim);
/* Choose a contraint from Q1 */
for (i=0; i<Q1->NbConstraints; i++) {
if (value_zero_p(Q1->Constraint[i][0])) {
/* Equality */
if (value_zero_p(Q1->Constraint[i][INDEX])) {
/* Ignore side constraint (they are in Q) */
continue;
}
else if (value_neg_p(Q1->Constraint[i][INDEX])) {
/* copy -constraint to Mat */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[0][k],Q1->Constraint[i][k]);
}
else {
/* Copy constraint to Mat */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_assign(Mat->p[0][k],Q1->Constraint[i][k]);
}
}
else if(value_neg_p(Q1->Constraint[i][INDEX])) {
/* Upper bound -- make a lower bound from it */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[0][k],Q1->Constraint[i][k]);
}
else {
/* Lower or side bound -- ignore it */
continue;
}
/* Choose a constraint from Q2 */
for (j=0; j<Q2->NbConstraints; j++) {
if (value_zero_p(Q2->Constraint[j][0])) { /* equality */
if (value_zero_p(Q2->Constraint[j][INDEX])) {
/* Ignore side constraint (they are in Q) */
continue;
}
else if (value_pos_p(Q2->Constraint[j][INDEX])) {
/* Copy -constraint to Mat */
value_set_si(Mat->p[1][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[1][k],Q2->Constraint[j][k]);
}
else {
/* Copy constraint to Mat */
value_set_si(Mat->p[1][0],1);
for (k=1; k<dim; k++)
value_assign(Mat->p[1][k],Q2->Constraint[j][k]);
};
}
else if (value_pos_p(Q2->Constraint[j][INDEX])) {
/* Lower bound -- make an upper bound from it */
value_set_si(Mat->p[1][0],1);
for(k=1;k<dim;k++)
value_oppose(Mat->p[1][k],Q2->Constraint[j][k]);
}
else {
/* Upper or side bound -- ignore it */
continue;
};
#ifdef DEBUG
fprintf(stdout, "i=%d j=%d M=\n", i+1, j+1);
Matrix_Print(stdout,P_VALUE_FMT,Mat);
#endif
/* Add Mat to Q and see if anything is made */
Q3 = AddConstraints(Mat->p[0],2,Q,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q3\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q3);
#endif
if (!emptyQ(Q3)) {
Domain_Free(Q3);
#ifdef DEBUG
fprintf(stdout, "not empty\n");
#endif
res = -1;
goto LTQdone;
}
#ifdef DEBUG
fprintf(stdout,"empty\n");
#endif
Domain_Free(Q3);
} /* end for j */
} /* end for i */
res = 1;
LTQdone:
Matrix_Free(Mat);
LTQdone2:
Domain_Free(Q4);
Domain_Free(Q1);
Domain_Free(Q2);
}
Domain_Free(Q);
#ifdef DEBUG
fprintf(stdout, "res = %d\n", res);
#endif
return res;
} /* PolyhedronLTQ */
/**
* 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);
}
}
/*
* Given a Z-polyhderon 'A' and a Z-domain 'Head', return a new Z-domain with
* 'A' added to it. If the new Z-polyhedron 'A', is already included in the
* Z-domain 'Head', it is not added in the list. Othewise, the function checks
* if the new Z-polyhedron 'A' to be added to the Z-domain 'Head' has a common
* lattice with some other Z-polyhderon already present in the Z-domain. If it
* is so, it takes the union of the underlying polyhdera; domains and returns.
* The function tries to make sure that the added Z-polyhedron 'A' is in the
* canonical form.
*/
static ZPolyhedron *AddZPolytoZDomain(ZPolyhedron *A, ZPolyhedron *Head) {
ZPolyhedron *Zpol, *temp, *temp1;
Polyhedron *i;
Bool Added;
if ((A == NULL) || (isEmptyZPolyhedron(A)))
return Head;
/* For each "underlying" Pol, find the Cnf and add Zpol in Cnf*/
for(i=A->P; i!= NULL; i=i->next) {
ZPolyhedron *Z, *Z1;
Polyhedron *Image;
Matrix *H, *U;
Lattice *Lat ;
Added = False;
Image = Domain_Copy(i);
Domain_Free(Image->next);
Image->next = NULL;
Z1 = ZPolyhedron_Alloc(A->Lat,Image);
Domain_Free(Image);
CanonicalForm(Z1,&Z,&H);
ZDomain_Free(Z1);
Lat = (Lattice *)Matrix_Alloc(H->NbRows,Z->Lat->NbColumns);
Matrix_Product(H,Z->Lat,(Matrix *)Lat);
Matrix_Free(H);
AffineHermite(Lat,(Lattice **)&H,&U);
Image = DomainImage(Z->P,U,MAXNOOFRAYS);
ZDomain_Free(Z);
Zpol=ZPolyhedron_Alloc((Lattice *)H,Image);
Domain_Free(Image);
Matrix_Free((Matrix *)Lat);
Matrix_Free(H);
Matrix_Free(U);
if ((Head == NULL) || (isEmptyZPolyhedron (Head))) {
Head = Zpol;
continue;
}
temp1 = temp = Head;
/* Check if the curr pol is included in the zpol or vice versa. */
for(; temp != NULL; temp = temp->next) {
if (ZPolyhedronIncludes(Zpol, temp) == True) {
ZPolyhedron_Free (Zpol);
Added = True;
break;
}
else if (ZPolyhedronIncludes(temp, Zpol) == True) {
if (temp == Head) {
Zpol->next = temp->next;
Head = Zpol;
ZPolyhedron_Free (temp);
Added = True;
break;
}
temp1->next = Zpol;
Zpol->next = temp->next;
ZPolyhedron_Free (temp);
Added = True;
break ;
}
temp1 = temp ;
}
if(Added == True)
continue ;
for(temp = Head; temp != NULL; temp = temp->next) {
if(sameLattice(temp->Lat, Zpol->Lat) == True) {
Polyhedron *Union;
Union = DomainUnion (temp->P,Zpol->P,MAXNOOFRAYS);
if (!Union)
fprintf (stderr,"\n In AddZPolytoZDomain: Out of memory\n");
else {
Domain_Free(temp->P);
temp->P = Union;
Added = True;
ZPolyhedron_Free(Zpol);
}
break ;
}
temp1 = temp;
}
if (Added == False)
temp1->next = Zpol;
}
return Head ;
} /* AddZPolytoZDomain */
/**
* 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 */
void right_hermite(Matrix *A,Matrix **Hp,Matrix **Up,Matrix **Qp) {
Matrix *H, *Q, *U;
int i, j, nr, nc, rank;
Value tmp;
/* Computes form: A = QH , UA = H */
nc = A->NbColumns;
nr = A->NbRows;
/* H = A */
*Hp = H = Matrix_Alloc(nr,nc);
if (!H) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
return;
}
/* Initialize all the 'Value' variables */
value_init(tmp);
Vector_Copy(A->p_Init,H->p_Init,nr*nc);
/* U = I */
if (Up) {
*Up = U = Matrix_Alloc(nr, nr);
if (!U) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(U->p_Init,0,nr*nr); /* zero's */
for(i=0;i<nr;i++) /* with diagonal of 1's */
value_set_si(U->p[i][i],1);
}
else
U = (Matrix *)0;
/* Q = I */
/* Actually I compute Q transpose... its easier */
if (Qp) {
*Qp = Q = Matrix_Alloc(nr,nr);
if (!Q) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(Q->p_Init,0,nr*nr); /* zero's */
for (i=0;i<nr;i++) /* with diagonal of 1's */
value_set_si(Q->p[i][i],1);
}
else
Q = (Matrix *)0;
rank = hermite(H,U,Q);
/* Q is returned transposed */
/* Transpose Q */
if (Q) {
for (i=0; i<nr; i++) {
for (j=i+1; j<nr; j++) {
value_assign(tmp,Q->p[i][j]);
value_assign(Q->p[i][j],Q->p[j][i] );
value_assign(Q->p[j][i],tmp);
}
}
}
value_clear(tmp);
return;
} /* right_hermite */
/** Removes the equalities that involve only parameters, by eliminating some
* parameters in the polyhedron's constraints and in the context.<p>
* <b>Updates M and Ctxt.</b>
* @param M1 the polyhedron's constraints
* @param Ctxt1 the constraints of the polyhedron's context
* @param renderSpace tells if the returned equalities must be expressed in the
* parameters space (renderSpace=0) or in the combined var/parms space
* (renderSpace = 1)
* @param elimParms the list of parameters that have been removed: an array
* whose 1st element is the number of elements in the list. (returned)
* @return the system of equalities that involve only parameters.
*/
Matrix * Constraints_Remove_parm_eqs(Matrix ** M1, Matrix ** Ctxt1,
int renderSpace,
unsigned int ** elimParms) {
int i, j, k, nbEqsParms =0;
int nbEqsM, nbEqsCtxt, allZeros, nbTautoM = 0, nbTautoCtxt = 0;
Matrix * M = (*M1);
Matrix * Ctxt = (*Ctxt1);
int nbVars = M->NbColumns-Ctxt->NbColumns;
Matrix * Eqs;
Matrix * EqsMTmp;
/* 1- build the equality matrix(ces) */
nbEqsM = 0;
for (i=0; i< M->NbRows; i++) {
k = First_Non_Zero(M->p[i], M->NbColumns);
/* if it is a tautology, count it as such */
if (k==-1) {
nbTautoM++;
}
else {
/* if it only involves parameters, count it */
if (k>= nbVars+1) nbEqsM++;
}
}
nbEqsCtxt = 0;
for (i=0; i< Ctxt->NbRows; i++) {
if (value_zero_p(Ctxt->p[i][0])) {
if (First_Non_Zero(Ctxt->p[i], Ctxt->NbColumns)==-1) {
nbTautoCtxt++;
}
else {
nbEqsCtxt ++;
}
}
}
nbEqsParms = nbEqsM + nbEqsCtxt;
/* nothing to do in this case */
if (nbEqsParms+nbTautoM+nbTautoCtxt==0) {
(*elimParms) = (unsigned int*) malloc(sizeof(int));
(*elimParms)[0] = 0;
if (renderSpace==0) {
return Matrix_Alloc(0,Ctxt->NbColumns);
}
else {
return Matrix_Alloc(0,M->NbColumns);
}
}
Eqs= Matrix_Alloc(nbEqsParms, Ctxt->NbColumns);
EqsMTmp= Matrix_Alloc(nbEqsParms, M->NbColumns);
/* copy equalities from the context */
k = 0;
for (i=0; i< Ctxt->NbRows; i++) {
if (value_zero_p(Ctxt->p[i][0])
&& First_Non_Zero(Ctxt->p[i], Ctxt->NbColumns)!=-1) {
Vector_Copy(Ctxt->p[i], Eqs->p[k], Ctxt->NbColumns);
Vector_Copy(Ctxt->p[i]+1, EqsMTmp->p[k]+nbVars+1,
Ctxt->NbColumns-1);
k++;
}
}
for (i=0; i< M->NbRows; i++) {
j=First_Non_Zero(M->p[i], M->NbColumns);
/* copy equalities that involve only parameters from M */
if (j>=nbVars+1) {
Vector_Copy(M->p[i]+nbVars+1, Eqs->p[k]+1, Ctxt->NbColumns-1);
Vector_Copy(M->p[i]+nbVars+1, EqsMTmp->p[k]+nbVars+1,
Ctxt->NbColumns-1);
/* mark these equalities for removal */
value_set_si(M->p[i][0], 2);
k++;
}
/* mark the all-zero equalities for removal */
if (j==-1) {
value_set_si(M->p[i][0], 2);
}
}
/* 2- eliminate parameters until all equalities are used or until we find a
contradiction (overconstrained system) */
(*elimParms) = (unsigned int *) malloc((Eqs->NbRows+1) * sizeof(int));
(*elimParms)[0] = 0;
allZeros = 0;
for (i=0; i< Eqs->NbRows; i++) {
/* find a variable that can be eliminated */
k = First_Non_Zero(Eqs->p[i], Eqs->NbColumns);
if (k!=-1) { /* nothing special to do for tautologies */
/* if there is a contradiction, return empty matrices */
if (k==Eqs->NbColumns-1) {
printf("Contradiction in %dth row of Eqs: ",k);
show_matrix(Eqs);
Matrix_Free(Eqs);
Matrix_Free(EqsMTmp);
(*M1) = Matrix_Alloc(0, M->NbColumns);
Matrix_Free(M);
(*Ctxt1) = Matrix_Alloc(0,Ctxt->NbColumns);
Matrix_Free(Ctxt);
free(*elimParms);
(*elimParms) = (unsigned int *) malloc(sizeof(int));
(*elimParms)[0] = 0;
if (renderSpace==1) {
return Matrix_Alloc(0,(*M1)->NbColumns);
}
else {
return Matrix_Alloc(0,(*Ctxt1)->NbColumns);
}
}
/* if we have something we can eliminate, do it in 3 places:
Eqs, Ctxt, and M */
else {
k--; /* k is the rank of the variable, now */
(*elimParms)[0]++;
(*elimParms)[(*elimParms[0])]=k;
for (j=0; j< Eqs->NbRows; j++) {
if (i!=j) {
eliminate_var_with_constr(Eqs, i, Eqs, j, k);
eliminate_var_with_constr(EqsMTmp, i, EqsMTmp, j, k+nbVars);
}
}
for (j=0; j< Ctxt->NbRows; j++) {
if (value_notzero_p(Ctxt->p[i][0])) {
eliminate_var_with_constr(Eqs, i, Ctxt, j, k);
}
}
for (j=0; j< M->NbRows; j++) {
if (value_cmp_si(M->p[i][0], 2)) {
eliminate_var_with_constr(EqsMTmp, i, M, j, k+nbVars);
}
}
}
}
/* if (k==-1): count the tautologies in Eqs to remove them later */
else {
allZeros++;
}
}
/* elimParms may have been overallocated. Now we know how many parms have
been eliminated so we can reallocate the right amount of memory. */
if (!realloc((*elimParms), ((*elimParms)[0]+1)*sizeof(int))) {
fprintf(stderr, "Constraints_Remove_parm_eqs > cannot realloc()");
}
Matrix_Free(EqsMTmp);
/* 3- remove the "bad" equalities from the input matrices
and copy the equalities involving only parameters */
EqsMTmp = Matrix_Alloc(M->NbRows-nbEqsM-nbTautoM, M->NbColumns);
k=0;
for (i=0; i< M->NbRows; i++) {
if (value_cmp_si(M->p[i][0], 2)) {
Vector_Copy(M->p[i], EqsMTmp->p[k], M->NbColumns);
k++;
}
}
Matrix_Free(M);
(*M1) = EqsMTmp;
EqsMTmp = Matrix_Alloc(Ctxt->NbRows-nbEqsCtxt-nbTautoCtxt, Ctxt->NbColumns);
k=0;
for (i=0; i< Ctxt->NbRows; i++) {
if (value_notzero_p(Ctxt->p[i][0])) {
Vector_Copy(Ctxt->p[i], EqsMTmp->p[k], Ctxt->NbColumns);
k++;
}
}
Matrix_Free(Ctxt);
(*Ctxt1) = EqsMTmp;
if (renderSpace==0) {/* renderSpace=0: equalities in the parameter space */
EqsMTmp = Matrix_Alloc(Eqs->NbRows-allZeros, Eqs->NbColumns);
k=0;
for (i=0; i<Eqs->NbRows; i++) {
if (First_Non_Zero(Eqs->p[i], Eqs->NbColumns)!=-1) {
Vector_Copy(Eqs->p[i], EqsMTmp->p[k], Eqs->NbColumns);
k++;
}
}
}
else {/* renderSpace=1: equalities rendered in the combined space */
EqsMTmp = Matrix_Alloc(Eqs->NbRows-allZeros, (*M1)->NbColumns);
k=0;
for (i=0; i<Eqs->NbRows; i++) {
if (First_Non_Zero(Eqs->p[i], Eqs->NbColumns)!=-1) {
Vector_Copy(Eqs->p[i], &(EqsMTmp->p[k][nbVars]), Eqs->NbColumns);
k++;
}
}
}
Matrix_Free(Eqs);
Eqs = EqsMTmp;
return Eqs;
} /* Constraints_Remove_parm_eqs */
/*
* Return the Z-polyhderon 'Zpol' in canonical form: 'Result' (for the Z-poly-
* hedron in canonical form) and Basis 'Basis' (for the basis with respect to
* which 'Result' is in canonical form.
*/
void CanonicalForm(ZPolyhedron *Zpol,ZPolyhedron **Result,Matrix **Basis) {
Matrix *B1 = NULL, *B2=NULL, *T1 , *B2inv;
int i, l1, l2;
Value tmp;
Polyhedron *Image, *ImageP;
Matrix *H, *U, *temp, *Hprime, *Uprime, *T2;
#ifdef DOMDEBUG
FILE *fp;
fp = fopen("_debug", "a");
fprintf(fp,"\nEntered CANONICALFORM\n");
fclose(fp);
#endif
if(isEmptyZPolyhedron (Zpol)) {
Basis[0] = Identity(Zpol->Lat->NbRows);
Result[0] = ZDomain_Copy (Zpol);
return ;
}
value_init(tmp);
l1 = FindHermiteBasisofDomain(Zpol->P,&B1);
Image = DomainImage (Zpol->P,(Matrix *)Zpol->Lat,MAXNOOFRAYS);
l2 = FindHermiteBasisofDomain(Image,&B2);
if (l1 != l2)
fprintf(stderr,"In CNF : Something wrong with the Input Zpolyhedra \n");
B2inv = Matrix_Alloc(B2->NbRows, B2->NbColumns);
temp = Matrix_Copy(B2);
Matrix_Inverse(temp,B2inv);
Matrix_Free(temp);
temp = Matrix_Alloc(B2inv->NbRows,Zpol->Lat->NbColumns);
T1 = Matrix_Alloc(temp->NbRows,B1->NbColumns);
Matrix_Product(B2inv,(Matrix *)Zpol->Lat,temp);
Matrix_Product(temp,B1,T1);
Matrix_Free(temp);
T2 = ChangeLatticeDimension(T1,l1);
temp = ChangeLatticeDimension(T2,T2->NbRows+1);
/* Adding the affine part */
for(i = 0; i < l1; i ++)
value_assign(temp->p[i][temp->NbColumns-1],T1->p[i][T1->NbColumns-1]);
AffineHermite(temp,&H,&U);
Hprime = ChangeLatticeDimension(H,Zpol->Lat->NbRows);
/* Exchanging the Affine part */
for(i = 0; i < l1; i ++) {
value_assign(tmp,Hprime->p[i][Hprime->NbColumns-1]);
value_assign(Hprime->p[i][Hprime->NbColumns-1],Hprime->p[i][H->NbColumns-1]);
value_assign(Hprime->p[i][H->NbColumns-1],tmp);
}
Uprime = ChangeLatticeDimension(U,Zpol->Lat->NbRows);
/* Exchanging the Affine part */
for (i = 0;i < l1; i++) {
value_assign(tmp,Uprime->p[i][Uprime->NbColumns-1]);
value_assign(Uprime->p[i][Uprime->NbColumns-1],Uprime->p[i][U->NbColumns-1]);
value_assign(Uprime->p[i][U->NbColumns-1],tmp);
}
Polyhedron_Free (Image);
Matrix_Free (B2inv);
B2inv = Matrix_Alloc(B1->NbRows, B1->NbColumns);
Matrix_Inverse(B1,B2inv);
ImageP = DomainImage(Zpol->P, B2inv, MAXNOOFRAYS);
Matrix_Free(B2inv);
Image = DomainImage(ImageP, Uprime, MAXNOOFRAYS);
Domain_Free(ImageP);
Result[0] = ZPolyhedron_Alloc(Hprime, Image);
Basis[0] = Matrix_Copy(B2);
/* Free the variables */
Polyhedron_Free (Image);
Matrix_Free (B1);
Matrix_Free (B2);
Matrix_Free (temp);
Matrix_Free (T1);
Matrix_Free (T2);
Matrix_Free (H);
Matrix_Free (U);
Matrix_Free (Hprime);
Matrix_Free (Uprime);
value_clear(tmp);
return;
} /* CanonicalForm */
int main(int argc, char **argv)
{
isl_ctx *ctx;
int i, nbPol, nbVec, nbMat, func, j, n;
Polyhedron *A, *B, *C, *D, *E, *F, *G;
char s[128];
struct barvinok_options *options = barvinok_options_new_with_defaults();
argc = barvinok_options_parse(options, argc, argv, ISL_ARG_ALL);
ctx = isl_ctx_alloc_with_options(&barvinok_options_args, options);
nbPol = nbVec = nbMat = 0;
fgets(s, 128, stdin);
while ((*s=='#') ||
((sscanf(s, "D %d", &nbPol) < 1) &&
(sscanf(s, "V %d", &nbVec) < 1) &&
(sscanf(s, "M %d", &nbMat) < 1)))
fgets(s, 128, stdin);
for (i = 0; i < nbPol; ++i) {
Matrix *M = Matrix_Read();
A = Constraints2Polyhedron(M, options->MaxRays);
Matrix_Free(M);
fgets(s, 128, stdin);
while ((*s=='#') || (sscanf(s, "F %d", &func)<1))
fgets(s, 128, stdin);
switch(func) {
case 0: {
Value cb, ck;
value_init(cb);
value_init(ck);
fgets(s, 128, stdin);
/* workaround for apparent bug in older gmps */
*strchr(s, '\n') = '\0';
while ((*s=='#') || (value_read(ck, s) != 0)) {
fgets(s, 128, stdin);
/* workaround for apparent bug in older gmps */
*strchr(s, '\n') = '\0';
}
barvinok_count_with_options(A, &cb, options);
if (value_ne(cb, ck))
return -1;
value_clear(cb);
value_clear(ck);
break;
}
case 1:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
B = Polyhedron_Polar(A, options->MaxRays);
Polyhedron_Print(stdout, P_VALUE_FMT, B);
C = Polyhedron_Polar(B, options->MaxRays);
Polyhedron_Print(stdout, P_VALUE_FMT, C);
Polyhedron_Free(C);
Polyhedron_Free(B);
break;
case 2:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
for (j = 0; j < A->NbRays; ++j) {
B = supporting_cone(A, j);
Polyhedron_Print(stdout, P_VALUE_FMT, B);
Polyhedron_Free(B);
}
break;
case 3:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
C = B = NULL;
barvinok_decompose(A,&B,&C);
puts("Pos:");
Polyhedron_Print(stdout, P_VALUE_FMT, B);
puts("Neg:");
Polyhedron_Print(stdout, P_VALUE_FMT, C);
Domain_Free(B);
Domain_Free(C);
break;
case 4: {
Value cm, cb;
struct tms tms_before, tms_between, tms_after;
value_init(cm);
value_init(cb);
Polyhedron_Print(stdout, P_VALUE_FMT, A);
times(&tms_before);
manual_count(A, &cm);
times(&tms_between);
barvinok_count(A, &cb, 100);
times(&tms_after);
printf("manual: ");
value_print(stdout, P_VALUE_FMT, cm);
puts("");
time_diff(&tms_before, &tms_between);
printf("Barvinok: ");
value_print(stdout, P_VALUE_FMT, cb);
puts("");
time_diff(&tms_between, &tms_after);
value_clear(cm);
value_clear(cb);
break;
}
case 5:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
B = triangulate_cone(A, 100);
Polyhedron_Print(stdout, P_VALUE_FMT, B);
check_triangulization(A, B);
Domain_Free(B);
break;
case 6:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
B = remove_equalities(A, options->MaxRays);
Polyhedron_Print(stdout, P_VALUE_FMT, B);
Polyhedron_Free(B);
break;
case 8: {
evalue *EP;
Matrix *M = Matrix_Read();
const char **param_name;
C = Constraints2Polyhedron(M, options->MaxRays);
Matrix_Free(M);
Polyhedron_Print(stdout, P_VALUE_FMT, A);
Polyhedron_Print(stdout, P_VALUE_FMT, C);
EP = barvinok_enumerate_with_options(A, C, options);
param_name = Read_ParamNames(stdin, C->Dimension);
print_evalue(stdout, EP, (const char**)param_name);
evalue_free(EP);
Polyhedron_Free(C);
}
case 9:
Polyhedron_Print(stdout, P_VALUE_FMT, A);
Polyhedron_Polarize(A);
C = B = NULL;
barvinok_decompose(A,&B,&C);
for (D = B; D; D = D->next)
Polyhedron_Polarize(D);
for (D = C; D; D = D->next)
Polyhedron_Polarize(D);
puts("Pos:");
Polyhedron_Print(stdout, P_VALUE_FMT, B);
puts("Neg:");
Polyhedron_Print(stdout, P_VALUE_FMT, C);
Domain_Free(B);
Domain_Free(C);
break;
case 10: {
evalue *EP;
Value cb, ck;
value_init(cb);
value_init(ck);
fgets(s, 128, stdin);
sscanf(s, "%d", &n);
for (j = 0; j < n; ++j) {
Polyhedron *P;
M = Matrix_Read();
P = Constraints2Polyhedron(M, options->MaxRays);
Matrix_Free(M);
A = DomainConcat(P, A);
}
fgets(s, 128, stdin);
/* workaround for apparent bug in older gmps */
*strchr(s, '\n') = '\0';
while ((*s=='#') || (value_read(ck, s) != 0)) {
fgets(s, 128, stdin);
/* workaround for apparent bug in older gmps */
*strchr(s, '\n') = '\0';
}
C = Universe_Polyhedron(0);
EP = barvinok_enumerate_union(A, C, options->MaxRays);
value_set_double(cb, compute_evalue(EP, &ck)+.25);
if (value_ne(cb, ck))
return -1;
Domain_Free(C);
value_clear(cb);
value_clear(ck);
evalue_free(EP);
break;
}
case 11: {
isl_space *dim;
isl_basic_set *bset;
isl_pw_qpolynomial *expected, *computed;
unsigned nparam;
expected = isl_pw_qpolynomial_read_from_file(ctx, stdin);
nparam = isl_pw_qpolynomial_dim(expected, isl_dim_param);
dim = isl_space_set_alloc(ctx, nparam, A->Dimension - nparam);
bset = isl_basic_set_new_from_polylib(A, dim);
computed = isl_basic_set_lattice_width(bset);
computed = isl_pw_qpolynomial_sub(computed, expected);
if (!isl_pw_qpolynomial_is_zero(computed))
return -1;
isl_pw_qpolynomial_free(computed);
break;
}
case 12: {
Vector *sample;
int has_sample;
fgets(s, 128, stdin);
sscanf(s, "%d", &has_sample);
sample = Polyhedron_Sample(A, options);
if (!sample && has_sample)
return -1;
if (sample && !has_sample)
return -1;
if (sample && !in_domain(A, sample->p))
return -1;
Vector_Free(sample);
}
}
Domain_Free(A);
}
for (i = 0; i < nbVec; ++i) {
int ok;
Vector *V = Vector_Read();
Matrix *M = Matrix_Alloc(V->Size, V->Size);
Vector_Copy(V->p, M->p[0], V->Size);
ok = unimodular_complete(M, 1);
assert(ok);
Matrix_Print(stdout, P_VALUE_FMT, M);
Matrix_Free(M);
Vector_Free(V);
}
for (i = 0; i < nbMat; ++i) {
Matrix *U, *V, *S;
Matrix *M = Matrix_Read();
Smith(M, &U, &V, &S);
Matrix_Print(stdout, P_VALUE_FMT, U);
Matrix_Print(stdout, P_VALUE_FMT, V);
Matrix_Print(stdout, P_VALUE_FMT, S);
Matrix_Free(M);
Matrix_Free(U);
Matrix_Free(V);
Matrix_Free(S);
}
isl_ctx_free(ctx);
return 0;
}
/* Assumes C is a linear cone (i.e. with apex zero).
* All equalities are removed first to speed up the computation
* in zsolve.
*/
Matrix *Cone_Hilbert_Basis(Polyhedron *C, unsigned MaxRays)
{
unsigned dim;
int i;
Matrix *M2, *M3, *T;
Matrix *CV = NULL;
LinearSystem initialsystem;
ZSolveMatrix matrix;
ZSolveVector rhs;
ZSolveContext ctx;
remove_all_equalities(&C, NULL, NULL, &CV, 0, MaxRays);
dim = C->Dimension;
for (i = 0; i < C->NbConstraints; ++i)
assert(value_zero_p(C->Constraint[i][1+dim]) ||
First_Non_Zero(C->Constraint[i]+1, dim) == -1);
M2 = Polyhedron2standard_form(C, &T);
matrix = Matrix2zsolve(M2);
Matrix_Free(M2);
rhs = createVector(matrix->Height);
for (i = 0; i < matrix->Height; i++)
rhs[i] = 0;
initialsystem = createLinearSystem();
setLinearSystemMatrix(initialsystem, matrix);
deleteMatrix(matrix);
setLinearSystemRHS(initialsystem, rhs);
deleteVector(rhs);
setLinearSystemLimit(initialsystem, -1, 0, MAXINT, 0);
setLinearSystemEquationType(initialsystem, -1, EQUATION_EQUAL, 0);
ctx = createZSolveContextFromSystem(initialsystem, NULL, 0, 0, NULL, NULL);
zsolveSystem(ctx, 0);
M2 = VectorArray2Matrix(ctx->Homs, C->Dimension);
deleteZSolveContext(ctx, 1);
Matrix_Transposition(T);
M3 = Matrix_Alloc(M2->NbRows, M2->NbColumns);
Matrix_Product(M2, T, M3);
Matrix_Free(M2);
Matrix_Free(T);
if (CV) {
Matrix *T, *M;
T = Transpose(CV);
M = Matrix_Alloc(M3->NbRows, T->NbColumns);
Matrix_Product(M3, T, M);
Matrix_Free(M3);
Matrix_Free(CV);
Matrix_Free(T);
Polyhedron_Free(C);
M3 = M;
}
return M3;
}
void left_hermite(Matrix *A,Matrix **Hp,Matrix **Qp,Matrix **Up) {
Matrix *H, *HT, *Q, *U;
int i, j, nc, nr, rank;
Value tmp;
/* Computes left form: A = HQ , AU = H ,
T T T T T T
using right form A = Q H , U A = H */
nr = A->NbRows;
nc = A->NbColumns;
/* HT = A transpose */
HT = Matrix_Alloc(nc, nr);
if (!HT) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
return;
}
value_init(tmp);
for (i=0; i<nr; i++)
for (j=0; j<nc; j++)
value_assign(HT->p[j][i],A->p[i][j]);
/* U = I */
if (Up) {
*Up = U = Matrix_Alloc(nc,nc);
if (!U) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(U->p_Init,0,nc*nc); /* zero's */
for (i=0;i<nc;i++) /* with diagonal of 1's */
value_set_si(U->p[i][i],1);
}
else U=(Matrix *)0;
/* Q = I */
if (Qp) {
*Qp = Q = Matrix_Alloc(nc, nc);
if (!Q) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(Q->p_Init,0,nc*nc); /* zero's */
for (i=0;i<nc;i++) /* with diagonal of 1's */
value_set_si(Q->p[i][i],1);
}
else Q=(Matrix *)0;
rank = hermite(HT,U,Q);
/* H = HT transpose */
*Hp = H = Matrix_Alloc(nr,nc);
if (!H) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
for (i=0; i<nr; i++)
for (j=0;j<nc;j++)
value_assign(H->p[i][j],HT->p[j][i]);
Matrix_Free(HT);
/* Transpose U */
if (U) {
for (i=0; i<nc; i++) {
for (j=i+1; j<nc; j++) {
value_assign(tmp,U->p[i][j]);
value_assign(U->p[i][j],U->p[j][i] );
value_assign(U->p[j][i],tmp);
}
}
}
value_clear(tmp);
} /* left_hermite */
/**
* Given a matrix with m parameterized equations, compress the nb_parms
* parameters and n-m variables so that m variables are integer, and transform
* the variable space into a n-m space by eliminating the m variables (using
* the equalities) the variables to be eliminated are chosen automatically by
* the function.
* <b>Deprecated.</b> Try to use Constraints_fullDimensionize instead.
* @param M the constraints
* @param the number of parameters
* @param validityLattice the the integer lattice underlying the integer
* solutions.
*/
Matrix * full_dimensionize(Matrix const * M, int nbParms,
Matrix ** validityLattice) {
Matrix * Eqs, * Ineqs;
Matrix * permutedEqs, * permutedIneqs;
Matrix * Full_Dim;
Matrix * WVL; /* The Whole Validity Lattice (vars+parms) */
unsigned int i,j;
int nbElimVars;
unsigned int * permutation, * permutationInv;
/* 0- Split the equalities and inequalities from each other */
split_constraints(M, &Eqs, &Ineqs);
/* 1- if the polyhedron is already full-dimensional, return it */
if (Eqs->NbRows==0) {
Matrix_Free(Eqs);
(*validityLattice) = Identity_Matrix(nbParms+1);
return Ineqs;
}
nbElimVars = Eqs->NbRows;
/* 2- put the vars to be eliminated at the first positions,
and compress the other vars/parms
-> [ variables to eliminate / parameters / variables to keep ] */
permutation = find_a_permutation(Eqs, nbParms);
if (dbgCompParm) {
printf("Permuting the vars/parms this way: [ ");
for (i=0; i< Eqs->NbColumns; i++) {
printf("%d ", permutation[i]);
}
printf("]\n");
}
permutedEqs = mpolyhedron_permute(Eqs, permutation);
WVL = compress_parms(permutedEqs, Eqs->NbColumns-2-Eqs->NbRows);
if (dbgCompParm) {
printf("Whole validity lattice: ");
show_matrix(WVL);
}
mpolyhedron_compress_last_vars(permutedEqs, WVL);
permutedIneqs = mpolyhedron_permute(Ineqs, permutation);
if (dbgCompParm) {
show_matrix(permutedEqs);
}
Matrix_Free(Eqs);
Matrix_Free(Ineqs);
mpolyhedron_compress_last_vars(permutedIneqs, WVL);
if (dbgCompParm) {
printf("After compression: ");
show_matrix(permutedIneqs);
}
/* 3- eliminate the first variables */
if (!mpolyhedron_eliminate_first_variables(permutedEqs, permutedIneqs)) {
fprintf(stderr,"full-dimensionize > variable elimination failed. \n");
return NULL;
}
if (dbgCompParm) {
printf("After elimination of the variables: ");
show_matrix(permutedIneqs);
}
/* 4- get rid of the first (zero) columns,
which are now useless, and put the parameters back at the end */
Full_Dim = Matrix_Alloc(permutedIneqs->NbRows,
permutedIneqs->NbColumns-nbElimVars);
for (i=0; i< permutedIneqs->NbRows; i++) {
value_set_si(Full_Dim->p[i][0], 1);
for (j=0; j< nbParms; j++)
value_assign(Full_Dim->p[i][j+Full_Dim->NbColumns-nbParms-1],
permutedIneqs->p[i][j+nbElimVars+1]);
for (j=0; j< permutedIneqs->NbColumns-nbParms-2-nbElimVars; j++)
value_assign(Full_Dim->p[i][j+1],
permutedIneqs->p[i][nbElimVars+nbParms+j+1]);
value_assign(Full_Dim->p[i][Full_Dim->NbColumns-1],
permutedIneqs->p[i][permutedIneqs->NbColumns-1]);
}
Matrix_Free(permutedIneqs);
/* 5- Keep only the the validity lattice restricted to the parameters */
*validityLattice = Matrix_Alloc(nbParms+1, nbParms+1);
for (i=0; i< nbParms; i++) {
for (j=0; j< nbParms; j++)
value_assign((*validityLattice)->p[i][j],
WVL->p[i][j]);
value_assign((*validityLattice)->p[i][nbParms],
WVL->p[i][WVL->NbColumns-1]);
}
for (j=0; j< nbParms; j++)
value_set_si((*validityLattice)->p[nbParms][j], 0);
value_assign((*validityLattice)->p[nbParms][nbParms],
WVL->p[WVL->NbColumns-1][WVL->NbColumns-1]);
/* 6- Clean up */
Matrix_Free(WVL);
return Full_Dim;
} /* full_dimensionize */
/* Compute integer hull of truncated linear cone C, i.e., of C with
* the origin removed.
* Here, we do this by first computing the Hilbert basis of C
* and then discarding elements from this basis that are rational
* overconvex combinations of other elements in the basis.
*/
Matrix *Cone_Hilbert_Integer_Hull(Polyhedron *C,
struct barvinok_options *options)
{
int i, j, k;
Matrix *hilbert = Cone_Hilbert_Basis(C, options->MaxRays);
Matrix *rays, *hull;
unsigned dim = C->Dimension;
Value tmp;
unsigned MaxRays = options->MaxRays;
/* When checking for redundant points below, we want to
* check if there are any _rational_ solutions.
*/
POL_UNSET(options->MaxRays, POL_INTEGER);
POL_ENSURE_VERTICES(C);
rays = Matrix_Alloc(C->NbRays-1, C->Dimension);
for (i = 0, j = 0; i < C->NbRays; ++i) {
if (value_notzero_p(C->Ray[i][1+C->Dimension]))
continue;
Vector_Copy(C->Ray[i]+1, rays->p[j++], C->Dimension);
}
/* We only sort the pointers into the big Value array */
qsort(rays->p, rays->NbRows, sizeof(Value *), lex_cmp);
qsort(hilbert->p, hilbert->NbRows, sizeof(Value *), lex_cmp);
/* Remove rays from Hilbert basis */
for (i = 0, j = 0, k = 0; i < hilbert->NbRows && j < rays->NbRows; ++i) {
if (Vector_Equal(hilbert->p[i], rays->p[j], C->Dimension))
++j;
else
hilbert->p[k++] = hilbert->p[i];
}
hilbert->NbRows = k;
/* Now remove points that are overconvex combinations of other points */
value_init(tmp);
for (i = 0; hilbert->NbRows > 1 && i < hilbert->NbRows; ++i) {
Matrix *LP;
Vector *obj;
int nray = rays->NbRows;
int npoint = hilbert->NbRows;
enum lp_result result;
LP = Matrix_Alloc(dim + 1 + nray + (npoint-1), 2 + nray + (npoint-1));
for (j = 0; j < dim; ++j) {
for (k = 0; k < nray; ++k)
value_assign(LP->p[j][k+1], rays->p[k][j]);
for (k = 0; k < npoint; ++k) {
if (k == i)
value_oppose(LP->p[j][1+nray+npoint-1], hilbert->p[k][j]);
else
value_assign(LP->p[j][1+nray+k-(k>i)], hilbert->p[k][j]);
}
}
value_set_si(LP->p[dim][0], 1);
for (k = 0; k < nray+npoint-1; ++k)
value_set_si(LP->p[dim][1+k], 1);
value_set_si(LP->p[dim][LP->NbColumns-1], -1);
for (k = 0; k < LP->NbColumns-2; ++k) {
value_set_si(LP->p[dim+1+k][0], 1);
value_set_si(LP->p[dim+1+k][1+k], 1);
}
/* Somewhat arbitrary objective function. */
obj = Vector_Alloc(LP->NbColumns-1);
value_set_si(obj->p[0], 1);
value_set_si(obj->p[obj->Size-1], 1);
result = constraints_opt(LP, obj->p, obj->p[0], lp_min, &tmp,
options);
/* If the LP is not empty, the point can be discarded */
if (result != lp_empty) {
hilbert->NbRows--;
if (i < hilbert->NbRows)
hilbert->p[i] = hilbert->p[hilbert->NbRows];
--i;
}
Matrix_Free(LP);
Vector_Free(obj);
}
value_clear(tmp);
hull = Matrix_Alloc(rays->NbRows + hilbert->NbRows, dim+1);
for (i = 0; i < rays->NbRows; ++i) {
Vector_Copy(rays->p[i], hull->p[i], dim);
value_set_si(hull->p[i][dim], 1);
}
for (i = 0; i < hilbert->NbRows; ++i) {
Vector_Copy(hilbert->p[i], hull->p[rays->NbRows+i], dim);
value_set_si(hull->p[rays->NbRows+i][dim], 1);
}
Matrix_Free(rays);
Matrix_Free(hilbert);
options->MaxRays = MaxRays;
return hull;
}
