static ppl_Constraint_t
cloog_matrix_to_ppl_constraint (CloogMatrix *matrix, int row)
{
int j;
ppl_Constraint_t cstr;
ppl_Coefficient_t coef;
ppl_Linear_Expression_t expr;
ppl_dimension_type dim = matrix->NbColumns - 2;
ppl_new_Coefficient (&coef);
ppl_new_Linear_Expression_with_dimension (&expr, dim);
for (j = 1; j < matrix->NbColumns - 1; j++)
{
ppl_assign_Coefficient_from_mpz_t (coef, matrix->p[row][j]);
ppl_Linear_Expression_add_to_coefficient (expr, j - 1, coef);
}
ppl_assign_Coefficient_from_mpz_t (coef,
matrix->p[row][matrix->NbColumns - 1]);
ppl_Linear_Expression_add_to_inhomogeneous (expr, coef);
ppl_delete_Coefficient (coef);
if (value_zero_p (matrix->p[row][0]))
ppl_new_Constraint (&cstr, expr, PPL_CONSTRAINT_TYPE_EQUAL);
else
ppl_new_Constraint (&cstr, expr, PPL_CONSTRAINT_TYPE_GREATER_OR_EQUAL);
ppl_delete_Linear_Expression (expr);
return cstr;
}
/*
* 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 */
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;
}
enum lp_result PL_polyhedron_opt(Polyhedron *P, Value *obj, Value denom,
enum lp_dir dir, Value *opt)
{
int i;
int first = 1;
Value val, d;
enum lp_result res = lp_empty;
POL_ENSURE_VERTICES(P);
if (emptyQ(P))
return res;
value_init(val);
value_init(d);
for (i = 0; i < P->NbRays; ++ i) {
Inner_Product(P->Ray[i]+1, obj, P->Dimension+1, &val);
if (value_zero_p(P->Ray[i][0]) && value_notzero_p(val)) {
res = lp_unbounded;
break;
}
if (value_zero_p(P->Ray[i][1+P->Dimension])) {
if ((dir == lp_min && value_neg_p(val)) ||
(dir == lp_max && value_pos_p(val))) {
res = lp_unbounded;
break;
}
} else {
res = lp_ok;
value_multiply(d, denom, P->Ray[i][1+P->Dimension]);
if (dir == lp_min)
mpz_cdiv_q(val, val, d);
else
mpz_fdiv_q(val, val, d);
if (first || (dir == lp_min ? value_lt(val, *opt) :
value_gt(val, *opt)))
value_assign(*opt, val);
first = 0;
}
}
value_clear(d);
value_clear(val);
return res;
}
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 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 __isl_give isl_mat *extract_equalities(isl_ctx *ctx, Matrix *M)
{
int i, j;
int n;
isl_val *v;
isl_mat *eq;
n = 0;
for (i = 0; i < M->NbRows; ++i)
if (value_zero_p(M->p[i][0]))
++n;
eq = isl_mat_alloc(ctx, n, M->NbColumns - 1);
for (i = 0; i < M->NbRows; ++i) {
if (!value_zero_p(M->p[i][0]))
continue;
for (j = 0; j < M->NbColumns - 1; ++j) {
v = isl_val_int_from_gmp(ctx, M->p[i][1 + j]);
eq = isl_mat_set_element_val(eq, i, j, v);
}
}
return eq;
}
/** 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 */
/* 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;
}
/*
* 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 */
/*
* Basic hermite engine
*/
static int hermite(Matrix *H,Matrix *U,Matrix *Q) {
int nc, nr, i, j, k, rank, reduced, pivotrow;
Value pivot,x,aux;
Value *temp1, *temp2;
/* T -1 T */
/* Computes form: A = Q H and U A = H and U = Q */
if (!H) {
errormsg1("Domlib", "nullH", "hermite: ? Null H");
return -1;
}
nc = H->NbColumns;
nr = H->NbRows;
temp1 = (Value *) malloc(nc * sizeof(Value));
temp2 = (Value *) malloc(nr * sizeof(Value));
if (!temp1 ||!temp2) {
errormsg1("Domlib", "outofmem", "out of memory space");
return -1;
}
/* Initialize all the 'Value' variables */
value_init(pivot); value_init(x);
value_init(aux);
for(i=0;i<nc;i++)
value_init(temp1[i]);
for(i=0;i<nr;i++)
value_init(temp2[i]);
#ifdef DEBUG
fprintf(stderr,"Start -----------\n");
Matrix_Print(stderr,0,H);
#endif
for (k=0, rank=0; k<nc && rank<nr; k=k+1) {
reduced = 1; /* go through loop the first time */
#ifdef DEBUG
fprintf(stderr, "Working on col %d. Rank=%d ----------\n", k+1, rank+1);
#endif
while (reduced) {
reduced=0;
/* 1. find pivot row */
value_absolute(pivot,H->p[rank][k]);
/* the kth-diagonal element */
pivotrow = rank;
/* find the row i>rank with smallest nonzero element in col k */
for (i=rank+1; i<nr; i++) {
value_absolute(x,H->p[i][k]);
if (value_notzero_p(x) &&
(value_lt(x,pivot) || value_zero_p(pivot))) {
value_assign(pivot,x);
pivotrow = i;
}
}
/* 2. Bring pivot to diagonal (exchange rows pivotrow and rank) */
if (pivotrow != rank) {
Vector_Exchange(H->p[pivotrow],H->p[rank],nc);
if (U)
Vector_Exchange(U->p[pivotrow],U->p[rank],nr);
if (Q)
Vector_Exchange(Q->p[pivotrow],Q->p[rank],nr);
#ifdef DEBUG
fprintf(stderr,"Exchange rows %d and %d -----------\n", rank+1, pivotrow+1);
Matrix_Print(stderr,0,H);
#endif
}
value_assign(pivot,H->p[rank][k]); /* actual ( no abs() ) pivot */
/* 3. Invert the row 'rank' if pivot is negative */
if (value_neg_p(pivot)) {
value_oppose(pivot,pivot); /* pivot = -pivot */
for (j=0; j<nc; j++)
value_oppose(H->p[rank][j],H->p[rank][j]);
/* H->p[rank][j] = -(H->p[rank][j]); */
if (U)
for (j=0; j<nr; j++)
value_oppose(U->p[rank][j],U->p[rank][j]);
/* U->p[rank][j] = -(U->p[rank][j]); */
if (Q)
for (j=0; j<nr; j++)
value_oppose(Q->p[rank][j],Q->p[rank][j]);
/* Q->p[rank][j] = -(Q->p[rank][j]); */
#ifdef DEBUG
fprintf(stderr,"Negate row %d -----------\n", rank+1);
Matrix_Print(stderr,0,H);
#endif
}
if (value_notzero_p(pivot)) {
/* 4. Reduce the column modulo the pivot */
/* This eventually zeros out everything below the */
/* diagonal and produces an upper triangular matrix */
for (i=rank+1;i<nr;i++) {
value_assign(x,H->p[i][k]);
if (value_notzero_p(x)) {
value_modulus(aux,x,pivot);
/* floor[integer division] (corrected for neg x) */
if (value_neg_p(x) && value_notzero_p(aux)) {
/* x=(x/pivot)-1; */
value_division(x,x,pivot);
value_decrement(x,x);
}
else
value_division(x,x,pivot);
for (j=0; j<nc; j++) {
value_multiply(aux,x,H->p[rank][j]);
value_subtract(H->p[i][j],H->p[i][j],aux);
}
/* U->p[i][j] -= (x * U->p[rank][j]); */
if (U)
for (j=0; j<nr; j++) {
value_multiply(aux,x,U->p[rank][j]);
value_subtract(U->p[i][j],U->p[i][j],aux);
}
/* Q->p[rank][j] += (x * Q->p[i][j]); */
if (Q)
for(j=0;j<nr;j++) {
value_addmul(Q->p[rank][j], x, Q->p[i][j]);
}
reduced = 1;
#ifdef DEBUG
fprintf(stderr,
"row %d = row %d - %d row %d -----------\n", i+1, i+1, x, rank+1);
Matrix_Print(stderr,0,H);
#endif
} /* if (x) */
} /* for (i) */
} /* if (pivot != 0) */
} /* while (reduced) */
/* Last finish up this column */
/* 5. Make pivot column positive (above pivot row) */
/* x should be zero for i>k */
if (value_notzero_p(pivot)) {
for (i=0; i<rank; i++) {
value_assign(x,H->p[i][k]);
if (value_notzero_p(x)) {
value_modulus(aux,x,pivot);
/* floor[integer division] (corrected for neg x) */
if (value_neg_p(x) && value_notzero_p(aux)) {
value_division(x,x,pivot);
value_decrement(x,x);
/* x=(x/pivot)-1; */
}
else
value_division(x,x,pivot);
/* H->p[i][j] -= x * H->p[rank][j]; */
for (j=0; j<nc; j++) {
value_multiply(aux,x,H->p[rank][j]);
value_subtract(H->p[i][j],H->p[i][j],aux);
}
/* U->p[i][j] -= x * U->p[rank][j]; */
if (U)
for (j=0; j<nr; j++) {
value_multiply(aux,x,U->p[rank][j]);
value_subtract(U->p[i][j],U->p[i][j],aux);
}
/* Q->p[rank][j] += x * Q->p[i][j]; */
if (Q)
for (j=0; j<nr; j++) {
value_addmul(Q->p[rank][j], x, Q->p[i][j]);
}
#ifdef DEBUG
fprintf(stderr,
"row %d = row %d - %d row %d -----------\n", i+1, i+1, x, rank+1);
Matrix_Print(stderr,0,H);
#endif
} /* if (x) */
} /* for (i) */
rank++;
} /* if (pivot!=0) */
} /* for (k) */
/* Clear all the 'Value' variables */
value_clear(pivot); value_clear(x);
value_clear(aux);
for(i=0;i<nc;i++)
value_clear(temp1[i]);
for(i=0;i<nr;i++)
value_clear(temp2[i]);
free(temp2);
free(temp1);
return rank;
} /* Hermite */
/**
* 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 */
/* GaussSimplify --
Given Mat1, a matrix of equalities, performs Gaussian elimination.
Find a minimum basis, Returns the rank.
Mat1 is context, Mat2 is reduced in context of Mat1
*/
int GaussSimplify(Matrix *Mat1,Matrix *Mat2) {
int NbRows = Mat1->NbRows;
int NbCols = Mat1->NbColumns;
int *column_index;
int i, j, k, n, t, pivot, Rank;
Value gcd, tmp, *cp;
column_index=(int *)malloc(NbCols * sizeof(int));
if (!column_index) {
errormsg1("GaussSimplify", "outofmem", "out of memory space\n");
Pol_status = 1;
return 0;
}
/* Initialize all the 'Value' variables */
value_init(gcd); value_init(tmp);
Rank=0;
for (j=0; j<NbCols; j++) { /* for each column starting at */
for (i=Rank; i<NbRows; i++) /* diagonal, look down to find */
if (value_notzero_p(Mat1->p[i][j])) /* the first non-zero entry */
break;
if (i!=NbRows) { /* was one found ? */
if (i!=Rank) /* was it found below the diagonal?*/
Vector_Exchange(Mat1->p[Rank],Mat1->p[i],NbCols);
/* Normalize the pivot row */
Vector_Gcd(Mat1->p[Rank],NbCols,&gcd);
/* If (gcd >= 2) */
value_set_si(tmp,2);
if (value_ge(gcd,tmp)) {
cp = Mat1->p[Rank];
for (k=0; k<NbCols; k++,cp++)
value_division(*cp,*cp,gcd);
}
if (value_neg_p(Mat1->p[Rank][j])) {
cp = Mat1->p[Rank];
for (k=0; k<NbCols; k++,cp++)
value_oppose(*cp,*cp);
}
/* End of normalize */
pivot=i;
for (i=0;i<NbRows;i++) /* Zero out the rest of the column */
if (i!=Rank) {
if (value_notzero_p(Mat1->p[i][j])) {
Value a, a1, a2, a1abs, a2abs;
value_init(a); value_init(a1); value_init(a2);
value_init(a1abs); value_init(a2abs);
value_assign(a1,Mat1->p[i][j]);
value_absolute(a1abs,a1);
value_assign(a2,Mat1->p[Rank][j]);
value_absolute(a2abs,a2);
value_gcd(a, a1abs, a2abs);
value_divexact(a1, a1, a);
value_divexact(a2, a2, a);
value_oppose(a1,a1);
Vector_Combine(Mat1->p[i],Mat1->p[Rank],Mat1->p[i],a2,
a1,NbCols);
Vector_Normalize(Mat1->p[i],NbCols);
value_clear(a); value_clear(a1); value_clear(a2);
value_clear(a1abs); value_clear(a2abs);
}
}
column_index[Rank]=j;
Rank++;
}
} /* end of Gauss elimination */
if (Mat2) { /* Mat2 is a transformation matrix (i,j->f(i,j))....
can't scale it because can't scale both sides of -> */
/* normalizes an affine transformation */
/* priority of forms */
/* 1. i' -> i (identity) */
/* 2. i' -> i + constant (uniform) */
/* 3. i' -> constant (broadcast) */
/* 4. i' -> j (permutation) */
/* 5. i' -> j + constant ( ) */
/* 6. i' -> i + j + constant (non-uniform) */
for (k=0; k<Rank; k++) {
j = column_index[k];
for (i=0; i<(Mat2->NbRows-1);i++) { /* all but the last row 0...0 1 */
if ((i!=j) && value_notzero_p(Mat2->p[i][j])) {
/* Remove dependency of i' on j */
Value a, a1, a1abs, a2, a2abs;
value_init(a); value_init(a1); value_init(a2);
value_init(a1abs); value_init(a2abs);
value_assign(a1,Mat2->p[i][j]);
value_absolute(a1abs,a1);
value_assign(a2,Mat1->p[k][j]);
value_absolute(a2abs,a2);
value_gcd(a, a1abs, a2abs);
value_divexact(a1, a1, a);
value_divexact(a2, a2, a);
value_oppose(a1,a1);
if (value_one_p(a2)) {
Vector_Combine(Mat2->p[i],Mat1->p[k],Mat2->p[i],a2,
a1,NbCols);
/* Vector_Normalize(Mat2->p[i],NbCols); -- can't do T */
} /* otherwise, can't do it without mult lhs prod (2i,3j->...) */
value_clear(a); value_clear(a1); value_clear(a2);
value_clear(a1abs); value_clear(a2abs);
}
else if ((i==j) && value_zero_p(Mat2->p[i][j])) {
/* 'i' does not depend on j */
for (n=j+1; n < (NbCols-1); n++) {
if (value_notzero_p(Mat2->p[i][n])) { /* i' depends on some n */
value_set_si(tmp,1);
Vector_Combine(Mat2->p[i],Mat1->p[k],Mat2->p[i],tmp,
tmp,NbCols);
break;
} /* if 'i' depends on just a constant, then leave it alone.*/
}
}
}
}
/* Check last row of transformation Mat2 */
for (j=0; j<(NbCols-1); j++)
if (value_notzero_p(Mat2->p[Mat2->NbRows-1][j])) {
errormsg1("GaussSimplify", "corrtrans", "Corrupted transformation\n");
break;
}
if (value_notone_p(Mat2->p[Mat2->NbRows-1][NbCols-1])) {
errormsg1("GaussSimplify", "corrtrans", "Corrupted transformation\n");
}
}
value_clear(gcd); value_clear(tmp);
free(column_index);
return Rank;
} /* GaussSimplify */
/* 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 */
