/**
* 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 */
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;
}
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;
}
int Vector_IsZero(Value * v, unsigned length) {
unsigned i;
if (value_notzero_p(v[0])) return 0;
else {
value_set_si(v[0], 1);
for (i=length-1; value_zero_p(v[i]); i--);
value_set_si(v[0], 0);
return (i==0);
}
}
/**
* Computes the validity lattice of a set of equalities. I.e., the lattice
* induced on the last <tt>b</tt> variables by the equalities involving the
* first <tt>a</tt> integer existential variables. The submatrix of Eqs that
* concerns only the existential variables (so the first a columns) is assumed
* to be full-row rank.
* @param Eqs the equalities
* @param a the number of existential integer variables, placed as first
* variables
* @param vl the (returned) validity lattice, in homogeneous form. It is
* allocated if initially set to null, or reused if already allocated.
*/
void Equalities_validityLattice(Matrix * Eqs, int a, Matrix** vl) {
unsigned int b = Eqs->NbColumns-2-a;
unsigned int r = Eqs->NbRows;
Matrix * A=NULL, * B=NULL, *I = NULL, *Lb=NULL, *sol=NULL;
Matrix *H, *U, *Q;
unsigned int i;
if (dbgCompParm) {
printf("Computing validity lattice induced by the %d first variables of:"
,a);
show_matrix(Eqs);
}
if (b==0) {
ensureMatrix((*vl), 1, 1);
value_set_si((*vl)->p[0][0], 1);
return;
}
/* 1- check that there is an integer solution to the equalities */
/* OPT: could change integerSolution's profile to allocate or not*/
Equalities_integerSolution(Eqs, &sol);
/* if there is no integer solution, there is no validity lattice */
if (sol==NULL) {
if ((*vl)!=NULL) Matrix_Free(*vl);
return;
}
Matrix_subMatrix(Eqs, 0, 1, r, 1+a, &A);
Matrix_subMatrix(Eqs, 0, 1+a, r, 1+a+b, &B);
linearInter(A, B, &I, &Lb);
Matrix_Free(A);
Matrix_Free(B);
Matrix_Free(I);
if (dbgCompParm) {
show_matrix(Lb);
}
/* 2- The linear part of the validity lattice is the left HNF of Lb */
left_hermite(Lb, &H, &Q, &U);
Matrix_Free(Lb);
Matrix_Free(Q);
Matrix_Free(U);
/* 3- build the validity lattice */
ensureMatrix((*vl), b+1, b+1);
Matrix_copySubMatrix(H, 0, 0, b, b, (*vl), 0,0);
Matrix_Free(H);
for (i=0; i< b; i++) {
value_assign((*vl)->p[i][b], sol->p[0][a+i]);
}
Matrix_Free(sol);
Vector_Set((*vl)->p[b],0, b);
value_set_si((*vl)->p[b][b], 1);
} /* validityLattice */
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 */
/*---------------------------------------------------------------------*/
static int exist_points(int pos,Polyhedron *Pol,Value *context) {
Value LB, UB, k,tmp;
value_init(LB); value_init(UB);
value_init(k); value_init(tmp);
value_set_si(LB,0);
value_set_si(UB,0);
/* Problem if UB or LB is INFINITY */
if (lower_upper_bounds(pos,Pol,context,&LB,&UB) !=0) {
errormsg1("exist_points", "infdom", "infinite domain");
value_clear(LB);
value_clear(UB);
value_clear(k);
value_clear(tmp);
return -1;
}
value_set_si(context[pos],0);
if(value_lt(UB,LB)) {
value_clear(LB);
value_clear(UB);
value_clear(k);
value_clear(tmp);
return 0;
}
if (!Pol->next) {
value_subtract(tmp,UB,LB);
value_increment(tmp,tmp);
value_clear(UB);
value_clear(LB);
value_clear(k);
return (value_pos_p(tmp));
}
for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) {
/* insert k in context */
value_assign(context[pos],k);
if (exist_points(pos+1,Pol->next,context) > 0 ) {
value_clear(LB); value_clear(UB);
value_clear(k); value_clear(tmp);
return 1;
}
}
/* Reset context */
value_set_si(context[pos],0);
value_clear(UB); value_clear(LB);
value_clear(k); value_clear(tmp);
return 0;
}
/*
* Compute n!
*/
void Factorial(int n, Value *fact) {
int i;
Value tmp;
value_init(tmp);
value_set_si(*fact,1);
for (i=1;i<=n;i++) {
value_set_si(tmp,i);
value_multiply(*fact,*fact,tmp);
}
value_clear(tmp);
} /* Factorial */
void
insert_constraint_into_matrix (CloogMatrix *m, int row,
ppl_const_Constraint_t cstr)
{
ppl_Coefficient_t c;
ppl_dimension_type i, dim, nb_cols = m->NbColumns;
ppl_Constraint_space_dimension (cstr, &dim);
ppl_new_Coefficient (&c);
for (i = 0; i < dim; i++)
{
ppl_Constraint_coefficient (cstr, i, c);
ppl_Coefficient_to_mpz_t (c, m->p[row][i + 1]);
}
for (i = dim; i < nb_cols - 1; i++)
value_set_si (m->p[row][i + 1], 0);
ppl_Constraint_inhomogeneous_term (cstr, c);
ppl_Coefficient_to_mpz_t (c, m->p[row][nb_cols - 1]);
value_set_si (m->p[row][0], 1);
switch (ppl_Constraint_type (cstr))
{
case PPL_CONSTRAINT_TYPE_LESS_THAN:
oppose_constraint (m, row);
case PPL_CONSTRAINT_TYPE_GREATER_THAN:
value_sub_int (m->p[row][nb_cols - 1],
m->p[row][nb_cols - 1], 1);
break;
case PPL_CONSTRAINT_TYPE_LESS_OR_EQUAL:
oppose_constraint (m, row);
case PPL_CONSTRAINT_TYPE_GREATER_OR_EQUAL:
break;
case PPL_CONSTRAINT_TYPE_EQUAL:
value_set_si (m->p[row][0], 0);
break;
default:
/* Not yet implemented. */
gcc_unreachable();
}
ppl_delete_Coefficient (c);
}
/*
* Given matrices 'Mat1' and 'Mat2', compute the matrix product and store in
* matrix 'Mat3'
*/
void Matrix_Product(Matrix *Mat1,Matrix *Mat2,Matrix *Mat3) {
int Size, i, j, k;
unsigned NbRows, NbColumns;
Value **q1, **q2, *p1, *p3,sum;
NbRows = Mat1->NbRows;
NbColumns = Mat2->NbColumns;
Size = Mat1->NbColumns;
if(Mat2->NbRows!=Size||Mat3->NbRows!=NbRows||Mat3->NbColumns!=NbColumns) {
fprintf(stderr, "? Matrix_Product : incompatable matrix dimension\n");
return;
}
value_init(sum);
p3 = Mat3->p_Init;
q1 = Mat1->p;
q2 = Mat2->p;
/* Mat3[i][j] = Sum(Mat1[i][k]*Mat2[k][j] where sum is over k = 1..nbrows */
for (i=0;i<NbRows;i++) {
for (j=0;j<NbColumns;j++) {
p1 = *(q1+i);
value_set_si(sum,0);
for (k=0;k<Size;k++) {
value_addmul(sum, *p1, *(*(q2+k)+j));
p1++;
}
value_assign(*p3,sum);
p3++;
}
}
value_clear(sum);
return;
} /* Matrix_Product */
static double compute_enode(enode *p, Value *list_args) {
int i;
Value m, param;
double res=0.0;
if (!p)
return(0.);
value_init(m);
value_init(param);
if (p->type == polynomial) {
if (p->size > 1)
value_assign(param,list_args[p->pos-1]);
/* Compute the polynomial using Horner's rule */
for (i=p->size-1;i>0;i--) {
res +=compute_evalue(&p->arr[i],list_args);
res *=VALUE_TO_DOUBLE(param);
}
res +=compute_evalue(&p->arr[0],list_args);
}
else if (p->type == periodic) {
value_assign(m,list_args[p->pos-1]);
/* Choose the right element of the periodic */
value_set_si(param,p->size);
value_pmodulus(m,m,param);
res = compute_evalue(&p->arr[VALUE_TO_INT(m)],list_args);
}
value_clear(m);
value_clear(param);
return res;
} /* compute_enode */
/*
* Return the component of 'p' with minimum non-zero absolute value. 'index'
* points to the component index that has the minimum value. If no such value
* and index is found, Value 1 is returned.
*/
void Vector_Min_Not_Zero(Value *p,unsigned length,int *index,Value *min)
{
Value aux;
int i;
i = First_Non_Zero(p, length);
if (i == -1) {
value_set_si(*min,1);
return;
}
*index = i;
value_absolute(*min, p[i]);
value_init(aux);
for (i = i+1; i < length; i++) {
if (value_zero_p(p[i]))
continue;
value_absolute(aux, p[i]);
if (value_lt(aux,*min)) {
value_assign(*min,aux);
*index = i;
}
}
value_clear(aux);
} /* Vector_Min_Not_Zero */
/*--------------------------------------------------------------*/
int Polyhedron_Not_Empty(Polyhedron *P,Polyhedron *C,int MAXRAYS) {
int res,i;
Value *context;
Polyhedron *L;
POL_ENSURE_FACETS(P);
POL_ENSURE_VERTICES(P);
POL_ENSURE_FACETS(C);
POL_ENSURE_VERTICES(C);
/* Create a context vector size dim+2 and set it to all zeros */
context = (Value *) malloc((P->Dimension+2)*sizeof(Value));
/* Initialize array 'context' */
for (i=0;i<(P->Dimension+2);i++)
value_init(context[i]);
Vector_Set(context,0,(P->Dimension+2));
/* Set context[P->Dimension+1] = 1 (the constant) */
value_set_si(context[P->Dimension+1],1);
L = Polyhedron_Scan(P,C,MAXRAYS);
res = exist_points(1,L,context);
Domain_Free(L);
/* Clear array 'context' */
for (i=0;i<(P->Dimension+2);i++)
value_clear(context[i]);
free(context);
return res;
}
static ppl_Pointset_Powerset_C_Polyhedron_t
dr_equality_constraints (graphite_dim_t dim,
graphite_dim_t pos, graphite_dim_t nb_subscripts)
{
ppl_Polyhedron_t subscript_equalities;
ppl_Pointset_Powerset_C_Polyhedron_t res;
Value v, v_op;
graphite_dim_t i;
value_init (v);
value_init (v_op);
value_set_si (v, 1);
value_set_si (v_op, -1);
ppl_new_C_Polyhedron_from_space_dimension (&subscript_equalities, dim, 0);
for (i = 0; i < nb_subscripts; i++)
{
ppl_Linear_Expression_t expr;
ppl_Constraint_t cstr;
ppl_Coefficient_t coef;
ppl_new_Coefficient (&coef);
ppl_new_Linear_Expression_with_dimension (&expr, dim);
ppl_assign_Coefficient_from_mpz_t (coef, v);
ppl_Linear_Expression_add_to_coefficient (expr, pos + i, coef);
ppl_assign_Coefficient_from_mpz_t (coef, v_op);
ppl_Linear_Expression_add_to_coefficient (expr, pos + i + nb_subscripts,
coef);
ppl_new_Constraint (&cstr, expr, PPL_CONSTRAINT_TYPE_EQUAL);
ppl_Polyhedron_add_constraint (subscript_equalities, cstr);
ppl_delete_Linear_Expression (expr);
ppl_delete_Constraint (cstr);
ppl_delete_Coefficient (coef);
}
ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron
(&res, subscript_equalities);
value_clear (v);
value_clear (v_op);
ppl_delete_Polyhedron (subscript_equalities);
return res;
}
/* 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;
}
/*
* Return the inner product of the two Vectors 'p1' and 'p2'
*/
void Inner_Product(Value *p1, Value *p2, unsigned length, Value *ip)
{
int i;
if (length != 0)
value_multiply(*ip, p1[0], p2[0]);
else
value_set_si(*ip, 0);
for(i = 1; i < length; i++)
value_addmul(*ip, p1[i], p2[i]);
} /* Inner_Product */
/*
* Assign 'n' to each component of Vector 'p'
*/
void Vector_Set(Value *p,int n,unsigned length) {
Value *cp;
int i;
cp = p;
for (i=0;i<length;i++) {
value_set_si(*cp,n);
cp++;
}
return;
} /* Vector_Set */
/**
* 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 */
Value *compute_poly(Enumeration *en,Value *list_args) {
Value *tmp;
/* double d; int i; */
tmp = (Value *) malloc (sizeof(Value));
assert(tmp != NULL);
value_init(*tmp);
value_set_si(*tmp,0);
if(!en)
return(tmp); /* no ehrhart polynomial */
if(en->ValidityDomain) {
if(!en->ValidityDomain->Dimension) { /* no parameters */
value_set_double(*tmp,compute_evalue(&en->EP,list_args)+.25);
return(tmp);
}
}
else
return(tmp); /* no Validity Domain */
while(en) {
if(in_domain(en->ValidityDomain,list_args)) {
#ifdef EVAL_EHRHART_DEBUG
Print_Domain(stdout,en->ValidityDomain,NULL);
print_evalue(stdout,&en->EP,NULL);
#endif
/* d = compute_evalue(&en->EP,list_args);
i = d;
printf("(double)%lf = %d\n", d, i ); */
value_set_double(*tmp,compute_evalue(&en->EP,list_args)+.25);
return(tmp);
}
else
en=en->next;
}
value_set_si(*tmp,0);
return(tmp); /* no compatible domain with the arguments */
} /* compute_poly */
static ppl_Constraint_t
build_pairwise_constraint (graphite_dim_t dim,
graphite_dim_t pos1, graphite_dim_t pos2,
int c, enum ppl_enum_Constraint_Type cstr_type)
{
ppl_Linear_Expression_t expr;
ppl_Constraint_t cstr;
ppl_Coefficient_t coef;
Value v, v_op, v_c;
value_init (v);
value_init (v_op);
value_init (v_c);
value_set_si (v, 1);
value_set_si (v_op, -1);
value_set_si (v_c, c);
ppl_new_Coefficient (&coef);
ppl_new_Linear_Expression_with_dimension (&expr, dim);
ppl_assign_Coefficient_from_mpz_t (coef, v);
ppl_Linear_Expression_add_to_coefficient (expr, pos1, coef);
ppl_assign_Coefficient_from_mpz_t (coef, v_op);
ppl_Linear_Expression_add_to_coefficient (expr, pos2, coef);
ppl_assign_Coefficient_from_mpz_t (coef, v_c);
ppl_Linear_Expression_add_to_inhomogeneous (expr, coef);
ppl_new_Constraint (&cstr, expr, cstr_type);
ppl_delete_Linear_Expression (expr);
ppl_delete_Coefficient (coef);
value_clear (v);
value_clear (v_op);
value_clear (v_c);
return cstr;
}
/*
* Return the number of ways to choose 'b' items from 'a' items, that is,
* return a!/(b!(a-b)!)
*/
void CNP(int a,int b, Value *result) {
int i;
Value tmp;
value_init(tmp);
value_set_si(*result,1);
/* If number of items is less than the number to be choosen, return 1 */
if(a <= b) {
value_clear(tmp);
return;
}
for(i=a;i>b;--i) {
value_set_si(tmp,i);
value_multiply(*result,*result,tmp);
}
for(i=1;i<=(a-b);++i) {
value_set_si(tmp,i);
value_division(*result,*result,tmp);
}
value_clear(tmp);
} /* CNP */
/*
* Compute n!/(p!(n-p)!)
*/
void Binomial(int n, int p, Value *result) {
int i;
Value tmp;
Value f;
value_init(tmp);value_init(f);
if (n-p<p)
p=n-p;
if (p!=0) {
value_set_si(*result,(n-p+1));
for (i=n-p+2;i<=n;i++) {
value_set_si(tmp,i);
value_multiply(*result,*result,tmp);
}
Factorial(p,&f);
value_division(*result,*result,f);
}
else
value_set_si(*result,1);
value_clear(f);value_clear(tmp);
} /* Binomial */
static void
extend_scattering (poly_bb_p pbb, int max_scattering)
{
ppl_dimension_type nb_old_dims, nb_new_dims;
int nb_added_dims, i;
ppl_Coefficient_t coef;
Value one;
nb_added_dims = max_scattering - pbb_nb_scattering_transform (pbb);
value_init (one);
value_set_si (one, 1);
ppl_new_Coefficient (&coef);
ppl_assign_Coefficient_from_mpz_t (coef, one);
gcc_assert (nb_added_dims >= 0);
nb_old_dims = pbb_nb_scattering_transform (pbb) + pbb_dim_iter_domain (pbb)
+ scop_nb_params (PBB_SCOP (pbb));
nb_new_dims = nb_old_dims + nb_added_dims;
ppl_insert_dimensions (PBB_TRANSFORMED_SCATTERING (pbb),
pbb_nb_scattering_transform (pbb), nb_added_dims);
PBB_NB_SCATTERING_TRANSFORM (pbb) += nb_added_dims;
/* Add identity matrix for the added dimensions. */
for (i = max_scattering - nb_added_dims; i < max_scattering; i++)
{
ppl_Constraint_t cstr;
ppl_Linear_Expression_t expr;
ppl_new_Linear_Expression_with_dimension (&expr, nb_new_dims);
ppl_Linear_Expression_add_to_coefficient (expr, i, coef);
ppl_new_Constraint (&cstr, expr, PPL_CONSTRAINT_TYPE_EQUAL);
ppl_Polyhedron_add_constraint (PBB_TRANSFORMED_SCATTERING (pbb), cstr);
ppl_delete_Constraint (cstr);
ppl_delete_Linear_Expression (expr);
}
ppl_delete_Coefficient (coef);
value_clear (one);
}
/**
* 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 */
/** 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 */
/**
* 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 */
/**
* 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 rational matrix 'Mat'(k x k), compute its inverse rational matrix
* 'MatInv' k x k.
* The output is 1,
* if 'Mat' is non-singular (invertible), otherwise the output is 0. Note::
* (1) Matrix 'Mat' is modified during the inverse operation.
* (2) Matrix 'MatInv' must be preallocated before passing into this function.
*/
int Matrix_Inverse(Matrix *Mat,Matrix *MatInv ) {
int i, k, j, c;
Value x, gcd, piv;
Value m1,m2;
Value *den;
if(Mat->NbRows != Mat->NbColumns) {
fprintf(stderr,"Trying to invert a non-square matrix !\n");
return 0;
}
/* Initialize all the 'Value' variables */
value_init(x); value_init(gcd); value_init(piv);
value_init(m1); value_init(m2);
k = Mat->NbRows;
/* Initialise MatInv */
Vector_Set(MatInv->p[0],0,k*k);
/* Initialize 'MatInv' to Identity matrix form. Each diagonal entry is set*/
/* to 1. Last column of each row (denominator of each entry in a row) is */
/* also set to 1. */
for(i=0;i<k;++i) {
value_set_si(MatInv->p[i][i],1);
/* value_set_si(MatInv->p[i][k],1); /* denum */
}
/* Apply Gauss-Jordan elimination method on the two matrices 'Mat' and */
/* 'MatInv' in parallel. */
for(i=0;i<k;++i) {
/* Check if the diagonal entry (new pivot) is non-zero or not */
if(value_zero_p(Mat->p[i][i])) {
/* Search for a non-zero pivot down the column(i) */
for(j=i;j<k;++j)
if(value_notzero_p(Mat->p[j][i]))
break;
/* If no non-zero pivot is found, the matrix 'Mat' is non-invertible */
/* Return 0. */
if(j==k) {
/* Clear all the 'Value' variables */
value_clear(x); value_clear(gcd); value_clear(piv);
value_clear(m1); value_clear(m2);
return 0;
}
/* Exchange the rows, row(i) and row(j) so that the diagonal element */
/* Mat->p[i][i] (pivot) is non-zero. Repeat the same operations on */
/* matrix 'MatInv'. */
for(c=0;c<k;++c) {
/* Interchange rows, row(i) and row(j) of matrix 'Mat' */
value_assign(x,Mat->p[j][c]);
value_assign(Mat->p[j][c],Mat->p[i][c]);
value_assign(Mat->p[i][c],x);
/* Interchange rows, row(i) and row(j) of matrix 'MatInv' */
value_assign(x,MatInv->p[j][c]);
value_assign(MatInv->p[j][c],MatInv->p[i][c]);
value_assign(MatInv->p[i][c],x);
}
}
/* Make all the entries in column(i) of matrix 'Mat' zero except the */
/* diagonal entry. Repeat the same sequence of operations on matrix */
/* 'MatInv'. */
for(j=0;j<k;++j) {
if (j==i) continue; /* Skip the pivot */
value_assign(x,Mat->p[j][i]);
if(value_notzero_p(x)) {
value_assign(piv,Mat->p[i][i]);
value_gcd(gcd, x, piv);
if (value_notone_p(gcd) ) {
value_divexact(x, x, gcd);
value_divexact(piv, piv, gcd);
}
for(c=((j>i)?i:0);c<k;++c) {
value_multiply(m1,piv,Mat->p[j][c]);
value_multiply(m2,x,Mat->p[i][c]);
value_subtract(Mat->p[j][c],m1,m2);
}
for(c=0;c<k;++c) {
value_multiply(m1,piv,MatInv->p[j][c]);
value_multiply(m2,x,MatInv->p[i][c]);
value_subtract(MatInv->p[j][c],m1,m2);
}
/* Simplify row(j) of the two matrices 'Mat' and 'MatInv' by */
/* dividing the rows with the common GCD. */
Vector_Gcd(&MatInv->p[j][0],k,&m1);
Vector_Gcd(&Mat->p[j][0],k,&m2);
value_gcd(gcd, m1, m2);
if(value_notone_p(gcd)) {
for(c=0;c<k;++c) {
value_divexact(Mat->p[j][c], Mat->p[j][c], gcd);
value_divexact(MatInv->p[j][c], MatInv->p[j][c], gcd);
}
}
}
}
}
/* Find common denom for each row */
den = (Value *)malloc(k*sizeof(Value));
value_set_si(x,1);
for(j=0 ; j<k ; ++j) {
value_init(den[j]);
value_assign(den[j],Mat->p[j][j]);
/* gcd is always positive */
Vector_Gcd(&MatInv->p[j][0],k,&gcd);
value_gcd(gcd, gcd, den[j]);
if (value_neg_p(den[j]))
value_oppose(gcd,gcd); /* make denominator positive */
if (value_notone_p(gcd)) {
for (c=0; c<k; c++)
value_divexact(MatInv->p[j][c], MatInv->p[j][c], gcd); /* normalize */
value_divexact(den[j], den[j], gcd);
}
value_gcd(gcd, x, den[j]);
value_divexact(m1, den[j], gcd);
value_multiply(x,x,m1);
}
if (value_notone_p(x))
for(j=0 ; j<k ; ++j) {
for (c=0; c<k; c++) {
value_division(m1,x,den[j]);
value_multiply(MatInv->p[j][c],MatInv->p[j][c],m1); /* normalize */
}
}
/* Clear all the 'Value' variables */
for(j=0 ; j<k ; ++j) {
value_clear(den[j]);
}
value_clear(x); value_clear(gcd); value_clear(piv);
value_clear(m1); value_clear(m2);
free(den);
return 1;
} /* Matrix_Inverse */
/* 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;
}
