polylib: matrix_addon.c Source File

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# matrix_addon.c

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    00001 /**
    00002  * $Id: matrix_addon.c,v 1.17 2007/03/18 18:49:08 skimo Exp $
    00003  *
    00004  * Polylib matrix addons
    00005  * Mainly, deals with polyhedra represented as a matrix (implicit form)
    00006  * @author Benoit Meister <meister@icps.u-strasbg.fr>
    00007  *
    00008  */
    00009
    00010 #include <stdlib.h>
    00011 #include<polylib/polylib.h>
    00012 #include <polylib/matrix_addon.h>
    00013
    00014 /** Creates a view of the constraints of a polyhedron as a Matrix * */
    00015 Matrix * constraintsView(Polyhedron * P) {
    00016   Matrix * view = (Matrix *)malloc(sizeof(Matrix));
    00017   view->NbRows = P->NbConstraints;
    00018   view->NbColumns = P->Dimension+2;
    00019   view->p = P->Constraint;
    00020   return view;
    00021 }
    00022
    00023 /** "Frees" a view of the constraints of a polyhedron */
    00024 void constraintsView_Free(Matrix * M) {
    00025   free(M);
    00026 }
    00027
    00028 /**
    00029  * splits a matrix of constraints M into a matrix of equalities Eqs and a
    00030  *  matrix of inequalities Ineqs allocs the new matrices.
    00031  * Allocates Eqs and Ineqs.
    00032 */
    00033 void split_constraints(Matrix const * M, Matrix ** Eqs, Matrix **Ineqs) {
    00034   unsigned int i, j, k_eq, k_ineq, nb_eqs=0;
    00035
    00036   /* 1- count the number of equations */
    00037   for (i=0; i< M->NbRows; i++)
    00038     if (value_zero_p(M->p[i][0])) nb_eqs++;
    00039
    00040   /* 2- extract the two matrices of equations */
    00041   (*Eqs) = Matrix_Alloc(nb_eqs, M->NbColumns);
    00042   (*Ineqs) = Matrix_Alloc(M->NbRows-nb_eqs, M->NbColumns);
    00043
    00044   k_eq = k_ineq = 0;
    00045   for(i=0; i< M->NbRows; i++) {
    00046     if (value_zero_p(M->p[i][0]))
    00047       {
    00048         for(j=0; j< M->NbColumns; j++)
    00049           value_assign((*Eqs)->p[k_eq][j], M->p[i][j]);
    00050         k_eq++;
    00051       }
    00052     else
    00053        {
    00054         for(j=0; j< M->NbColumns; j++)
    00055           value_assign((*Ineqs)->p[k_ineq][j], M->p[i][j]);
    00056         k_ineq++;
    00057       }
    00058   }
    00059 }
    00060
    00061
    00062 /* returns the dim-dimensional identity matrix */
    00063 Matrix * Identity_Matrix(unsigned int dim) {
    00064   Matrix * ret = Matrix_Alloc(dim, dim);
    00065   unsigned int i,j;
    00066   for (i=0; i< dim; i++) {
    00067     for (j=0; j< dim; j++) {
    00068       if (i==j)
    00069         { value_set_si(ret->p[i][j], 1); }
    00070       else value_set_si(ret->p[i][j], 0);
    00071     }
    00072   }
    00073   return ret;
    00074 } /* Identity_Matrix */
    00075
    00076
    00077 /**
    00078  * returns the dim-dimensional identity matrix.
    00079  * If I is set to NULL, allocates it first.
    00080  * Else, assumes an existing, allocated Matrix.
    00081 */
    00082 void Matrix_identity(unsigned int dim, Matrix ** I) {
    00083   int i,j;
    00084   if (*I==NULL) {
    00085     (*I) = Identity_Matrix(dim);
    00086   }
    00087   else {
    00088     assert((*I)->NbRows>=dim && (*I)->NbColumns>=dim);
    00089     for (i=0; i< dim; i++) {
    00090       for (j=0; j< dim; j++) {
    00091         if (i==j) {
    00092             value_set_si((*I)->p[i][j], 1);
    00093           }
    00094         else {
    00095           value_set_si((*I)->p[i][j], 0);
    00096         }
    00097       }
    00098     }
    00099   }
    00100 } /* Matrix_identity */
    00101
    00102
    00103 /** given a n x n integer transformation matrix transf, compute its inverse
    00104     M/g, where M is a nxn integer matrix.  g is a common denominator for
    00105     elements of (transf^{-1}) */
    00106 void mtransformation_inverse(Matrix * transf, Matrix ** inverse, Value * g) {
    00107   Value factor;
    00108   unsigned int i,j;
    00109   Matrix *tmp, *inv;
    00110
    00111   value_init(*g);
    00112   value_set_si(*g,1);
    00113
    00114   /* a - compute the inverse as usual (n x (n+1) matrix) */
    00115   tmp = Matrix_Copy(transf);
    00116   inv = Matrix_Alloc(transf->NbRows, transf->NbColumns+1);
    00117   MatInverse(tmp, inv);
    00118   Matrix_Free(tmp);
    00119
    00120   /* b - as it is rational, put it to the same denominator*/
    00121   (*inverse) = Matrix_Alloc(transf->NbRows, transf->NbRows);
    00122   for (i=0; i< inv->NbRows; i++)
    00123     value_lcm(*g, *g, inv->p[i][inv->NbColumns-1]);
    00124   for (i=0; i< inv->NbRows; i++) {
    00125     value_division(factor, *g, inv->p[i][inv->NbColumns-1]);
    00126     for (j=0; j< (*inverse)->NbColumns; j++)
    00127       value_multiply((*inverse)->p[i][j], inv->p[i][j],  factor);
    00128   }
    00129
    00130   /* c- clean up */
    00131   value_clear(factor);
    00132   Matrix_Free(inv);
    00133 } /* mtransformation_inverse */
    00134
    00135
    00136 /** takes a transformation matrix, and expands it to a higher dimension with
    00137     the identity matrix regardless of it homogeneousness */
    00138 Matrix * mtransformation_expand_left_to_dim(Matrix * M, int new_dim) {
    00139   Matrix * ret = Identity_Matrix(new_dim);
    00140   int offset = new_dim-M->NbRows;
    00141   unsigned int i,j;
    00142
    00143   assert(new_dim>=M->NbColumns);
    00144   assert(M->NbRows==M->NbColumns);
    00145
    00146   for (i=0; i< M->NbRows; i++)
    00147     for (j=0; j< M->NbRows; j++)
    00148       value_assign(ret->p[offset+i][offset+j], M->p[i][j]);
    00149   return ret;
    00150 } /* mtransformation_expand_left_to_dim */
    00151
    00152
    00153 /** simplify a matrix seen as a polyhedron, by dividing its rows by the gcd of
    00154    their elements. */
    00155 void mpolyhedron_simplify(Matrix * polyh) {
    00156   int i, j;
    00157   Value cur_gcd;
    00158   value_init(cur_gcd);
    00159   for (i=0; i< polyh->NbRows; i++) {
    00160     Vector_Gcd(polyh->p[i]+1, polyh->NbColumns-1, &cur_gcd);
    00161     printf(" gcd[%d] = ", i);
    00162     value_print(stdout, VALUE_FMT, cur_gcd);printf("\n");
    00163     Vector_AntiScale(polyh->p[i]+1, polyh->p[i]+1, cur_gcd, polyh->NbColumns-1);
    00164   }
    00165   value_clear(cur_gcd);
    00166 } /* mpolyhedron_simplify */
    00167
    00168
    00169 /** inflates a polyhedron (represented as a matrix) P, so that the apx of its
    00170     Ehrhart Polynomial is an upper bound of the Ehrhart polynomial of P
    00171     WARNING: this inflation is supposed to be applied on full-dimensional
    00172     polyhedra. */
    00173 void mpolyhedron_inflate(Matrix * polyh, unsigned int nb_parms) {
    00174   unsigned int i,j;
    00175   unsigned nb_vars = polyh->NbColumns-nb_parms-2;
    00176   Value infl;
    00177   value_init(infl);
    00178   /* subtract the sum of the negative coefficients of each inequality */
    00179   for (i=0; i< polyh->NbRows; i++) {
    00180     value_set_si(infl, 0);
    00181     for (j=0; j< nb_vars; j++) {
    00182       if (value_neg_p(polyh->p[i][1+j]))
    00183         value_addto(infl, infl, polyh->p[i][1+j]);
    00184     }
    00185     /* here, we subtract a negative value */
    00186     value_subtract(polyh->p[i][polyh->NbColumns-1],
    00187                    polyh->p[i][polyh->NbColumns-1], infl);
    00188   }
    00189   value_clear(infl);
    00190 } /* mpolyhedron_inflate */
    00191
    00192
    00193 /** deflates a polyhedron (represented as a matrix) P, so that the apx of its
    00194     Ehrhart Polynomial is a lower bound of the Ehrhart polynomial of P WARNING:
    00195     this deflation is supposed to be applied on full-dimensional polyhedra. */
    00196 void mpolyhedron_deflate(Matrix * polyh, unsigned int nb_parms) {
    00197   unsigned int i,j;
    00198   unsigned nb_vars = polyh->NbColumns-nb_parms-2;
    00199   Value defl;
    00200   value_init(defl);
    00201   /* substract the sum of the negative coefficients of each inequality */
    00202   for (i=0; i< polyh->NbRows; i++) {
    00203     value_set_si(defl, 0);
    00204     for (j=0; j< nb_vars; j++) {
    00205       if (value_pos_p(polyh->p[i][1+j]))
    00206         value_addto(defl, defl, polyh->p[i][1+j]);
    00207     }
    00208     /* here, we substract a negative value */
    00209     value_subtract(polyh->p[i][polyh->NbColumns-1],
    00210                    polyh->p[i][polyh->NbColumns-1], defl);
    00211   }
    00212   value_clear(defl);
    00213 } /* mpolyhedron_deflate */
    00214
    00215
    00216 /** use an eliminator row to eliminate a variable in a victim row (without
    00217  * changing the sign of the victim row -> important if it is an inequality).
    00218  * @param Eliminator the matrix containing the eliminator row
    00219  * @param eliminator_row the index of the eliminator row in <tt>Eliminator</tt>
    00220  * @param Victim the matrix containing the row to be eliminated
    00221  * @param victim_row the row to be eliminated in <tt>Victim</tt>
    00222  * @param var_to_elim the variable to be eliminated.
    00223  */
    00224 void eliminate_var_with_constr(Matrix * Eliminator,
    00225                                unsigned int eliminator_row, Matrix * Victim,
    00226                                unsigned int victim_row,
    00227                                unsigned int var_to_elim) {
    00228   Value cur_lcm, mul_a, mul_b;
    00229   Value tmp, tmp2;
    00230   int k;
    00231
    00232   value_init(cur_lcm);
    00233   value_init(mul_a);
    00234   value_init(mul_b);
    00235   value_init(tmp);
    00236   value_init(tmp2);
    00237   /* if the victim coefficient is not zero */
    00238   if (value_notzero_p(Victim->p[victim_row][var_to_elim+1])) {
    00239     value_lcm(cur_lcm, Eliminator->p[eliminator_row][var_to_elim+1],
    00240               Victim->p[victim_row][var_to_elim+1]);
    00241     /* multiplication factors */
    00242     value_division(mul_a, cur_lcm,
    00243                    Eliminator->p[eliminator_row][var_to_elim+1]);
    00244     value_division(mul_b, cur_lcm,
    00245                    Victim->p[victim_row][var_to_elim+1]);
    00246     /* the multiplicator for the vitim row has to be positive */
    00247     if (value_pos_p(mul_b)) {
    00248       value_oppose(mul_a, mul_a);
    00249     }
    00250     else {
    00251       value_oppose(mul_b, mul_b);
    00252     }
    00253     value_clear(cur_lcm);
    00254     /* now we have a.mul_a = -(b.mul_b) and mul_a > 0 */
    00255     for (k=1; k<Victim->NbColumns; k++) {
    00256       value_multiply(tmp, Eliminator->p[eliminator_row][k], mul_a);
    00257       value_multiply(tmp2, Victim->p[victim_row][k], mul_b);
    00258       value_addto(Victim->p[victim_row][k], tmp, tmp2);
    00259     }
    00260   }
    00261   value_clear(mul_a);
    00262   value_clear(mul_b);
    00263   value_clear(tmp);
    00264   value_clear(tmp2);
    00265 }
    00266 /* eliminate_var_with_constr */
    00267
    00268
    00269 /* STUFF WITH PARTIAL MAPPINGS (Mappings to a subset of the
    00270    variables/parameters) : on the first or last variables/parameters */
    00271
    00272 /** compress the last vars/pars of the polyhedron M expressed as a polylib
    00273     matrix
    00274  - adresses the full-rank compressions only
    00275  - modfies M */
    00276 void mpolyhedron_compress_last_vars(Matrix * M, Matrix * compression) {
    00277   unsigned int i, j, k;
    00278   unsigned int offset = M->NbColumns - compression->NbRows;
    00279   /* the computations on M will begin on column "offset" */
    00280
    00281   Matrix * M_tmp = Matrix_Alloc(1, M->NbColumns);
    00282   assert(compression->NbRows==compression->NbColumns);
    00283   /* basic matrix multiplication (using a temporary row instead of a whole
    00284      temporary matrix), but with a column offset */
    00285   for(i=0; i< M->NbRows; i++) {
    00286     for (j=0; j< compression->NbRows; j++) {
    00287       value_set_si(M_tmp->p[0][j], 0);
    00288       for (k=0; k< compression->NbRows; k++) {
    00289         value_addmul(M_tmp->p[0][j], M->p[i][k+offset],compression->p[k][j]);
    00290       }
    00291     }
    00292     for (j=0; j< compression->NbRows; j++)
    00293       value_assign(M->p[i][j+offset], M_tmp->p[0][j]);
    00294   }
    00295   Matrix_Free(M_tmp);
    00296 } /* mpolyhedron_compress_last_vars */
    00297
    00298
    00299 /** use a set of m equalities Eqs to eliminate m variables in the polyhedron
    00300     Ineqs represented as a matrix
    00301  eliminates the m first variables
    00302  - assumes that Eqs allow to eliminate the m equalities
    00303  - modifies Eqs and Ineqs */
    00304 unsigned int mpolyhedron_eliminate_first_variables(Matrix * Eqs,
    00305                                                    Matrix *Ineqs) {
    00306   unsigned int i, j, k;
    00307   /* eliminate one variable (index i) after each other */
    00308   for (i=0; i< Eqs->NbRows; i++) {
    00309     /* find j, the first (non-marked) row of Eqs with a non-zero coefficient */
    00310     for (j=0; j<Eqs->NbRows && (Eqs->p[j][i+1]==0 ||
    00311                                 ( !value_cmp_si(Eqs->p[j][0],2) ));
    00312          j++);
    00313     /* if no row is found in Eqs that allows to eliminate variable i, return an
    00314        error code (0) */
    00315     if (j==Eqs->NbRows) return 0;
    00316     /* else, eliminate variable i in Eqs and Ineqs with the j^th row of Eqs
    00317        (and mark this row so we don't use it again for an elimination) */
    00318     for (k=j+1; k<Eqs->NbRows; k++)
    00319       eliminate_var_with_constr(Eqs, j, Eqs, k, i);
    00320     for (k=0; k< Ineqs->NbRows; k++)
    00321       eliminate_var_with_constr(Eqs, j, Ineqs, k, i);
    00322     /* mark the row */
    00323     value_set_si(Eqs->p[j][0],2);
    00324   }
    00325   /* un-mark all the rows */
    00326   for (i=0; i< Eqs->NbRows; i++) value_set_si(Eqs->p[i][0],0);
    00327   return 1;
    00328 } /* mpolyhedron_eliminate_first_variables */
    00329
    00330
    00331 /** returns a contiguous submatrix of a matrix.
    00332  * @param M the input matrix
    00333  * @param sr the index of the starting row
    00334  * @param sc the index of the starting column
    00335  * @param er the index ofthe ending row (excluded)
    00336  * @param ec the ined of the ending colummn (excluded)
    00337  * @param sub (returned), the submatrix. Allocated if set to NULL, assumed to
    00338  * be already allocated else.
    00339  */
    00340 void Matrix_subMatrix(Matrix * M, unsigned int sr, unsigned int sc,
    00341                           unsigned int er, unsigned int ec, Matrix ** sub) {
    00342   int i;
    00343   int nbR = er-sr;
    00344   int nbC = ec-sc;
    00345   assert (er<=M->NbRows && ec<=M->NbColumns);
    00346   if ((*sub)==NULL) {
    00347     (*sub) = Matrix_Alloc(nbR, nbC);
    00348   }
    00349   if (nbR==0 || nbC==0) return;
    00350   for (i=0; i< nbR; i++) {
    00351     Vector_Copy(&(M->p[i+sr][sc]), (*sub)->p[i], nbC);
    00352   }
    00353 }/* Matrix_subMatrix */
    00354
    00355
    00356 /**
    00357  * Cloning function. Similar to Matrix_Copy() but allocates the target matrix
    00358  * if it is set to NULL.
    00359  */
    00360 void Matrix_clone(Matrix * M, Matrix ** Cl) {
    00361   Matrix_subMatrix(M, 0,0, M->NbRows, M->NbColumns, Cl);
    00362 }
    00363
    00364
    00365 /**
    00366  * Copies a contiguous submatrix of M1 into M2, at the indicated position.
    00367  * M1 and M2 are assumed t be allocated already.
    00368  * @param M1 the source matrix
    00369  * @param sr1 the starting source row
    00370  * @param sc1 the starting source column
    00371  * @param nbR the number of rows
    00372  * @param nbC the number of columns
    00373  * @param M2 the target matrix
    00374  * @param sr2 the starting target row
    00375  * @param sc2 the starting target column
    00376 */
    00377 void Matrix_copySubMatrix(Matrix *M1,
    00378                           unsigned int sr1, unsigned int sc1,
    00379                           unsigned int nbR, unsigned int nbC,
    00380                           Matrix * M2,
    00381                           unsigned int sr2, unsigned int sc2) {
    00382   int i;
    00383   for (i=0; i< nbR; i++) {
    00384     Vector_Copy(&(M1->p[i+sr1][sc1]), &(M2->p[i+sr2][sc2]), nbC);
    00385   }
    00386 } /* Matrix_copySubMatrix */
    00387
    00388
    00389 /**
    00390  * transforms a matrix M into -M
    00391  */
    00392 void Matrix_oppose(Matrix * M) {
    00393   int i,j;
    00394   for (i=0; i<M->NbRows; i++) {
    00395     for (j=0; j< M->NbColumns; j++) {
    00396       value_oppose(M->p[i][j], M->p[i][j]);
    00397     }
    00398   }
    00399 }