ddf_MatrixPtr ddf_BlockElimination(ddf_MatrixPtr M, ddf_colset delset, ddf_ErrorType *error)
/* Eliminate the variables (columns) delset by
the Block Elimination with ddf_DoubleDescription algorithm.
Given (where y is to be eliminated):
c1 + A1 x + B1 y >= 0
c2 + A2 x + B2 y = 0
1. First construct the dual system: z1^T B1 + z2^T B2 = 0, z1 >= 0.
2. Compute the generators of the dual.
3. Then take the linear combination of the original system with each generator.
4. Remove redundant inequalies.
*/
{
ddf_MatrixPtr Mdual=NULL, Mproj=NULL, Gdual=NULL;
ddf_rowrange i,h,m,mproj,mdual,linsize;
ddf_colrange j,k,d,dproj,ddual,delsize;
ddf_colindex delindex;
myfloat temp,prod;
ddf_PolyhedraPtr dualpoly;
ddf_ErrorType err=ddf_NoError;
ddf_boolean localdebug=ddf_FALSE;
*error=ddf_NoError;
m= M->rowsize;
d= M->colsize;
delindex=(long*)calloc(d+1,sizeof(long));
ddf_init(temp);
ddf_init(prod);
k=0; delsize=0;
for (j=1; j<=d; j++){
if (set_member(j, delset)){
k++; delsize++;
delindex[k]=j; /* stores the kth deletion column index */
}
}
if (localdebug) ddf_WriteMatrix(stdout, M);
linsize=set_card(M->linset);
ddual=m+1;
mdual=delsize + m - linsize; /* #equalitions + dimension of z1 */
/* setup the dual matrix */
Mdual=ddf_CreateMatrix(mdual, ddual);
Mdual->representation=ddf_Inequality;
for (i = 1; i <= delsize; i++){
set_addelem(Mdual->linset,i); /* equality */
for (j = 1; j <= m; j++) {
ddf_set(Mdual->matrix[i-1][j], M->matrix[j-1][delindex[i]-1]);
}
}
k=0;
for (i = 1; i <= m; i++){
if (!set_member(i, M->linset)){
/* set nonnegativity for the dual variable associated with
each non-linearity inequality. */
k++;
ddf_set(Mdual->matrix[delsize+k-1][i], ddf_one);
}
}
/* 2. Compute the generators of the dual system. */
dualpoly=ddf_DDMatrix2Poly(Mdual, &err);
Gdual=ddf_CopyGenerators(dualpoly);
/* 3. Take the linear combination of the original system with each generator. */
dproj=d-delsize;
mproj=Gdual->rowsize;
Mproj=ddf_CreateMatrix(mproj, dproj);
Mproj->representation=ddf_Inequality;
set_copy(Mproj->linset, Gdual->linset);
for (i=1; i<=mproj; i++){
k=0;
for (j=1; j<=d; j++){
if (!set_member(j, delset)){
k++; /* new index of the variable x_j */
ddf_set(prod, ddf_purezero);
for (h = 1; h <= m; h++){
ddf_mul(temp,M->matrix[h-1][j-1],Gdual->matrix[i-1][h]);
ddf_add(prod,prod,temp);
}
ddf_set(Mproj->matrix[i-1][k-1],prod);
}
}
}
if (localdebug) printf("Size of the projection system: %ld x %ld\n", mproj, dproj);
ddf_FreePolyhedra(dualpoly);
free(delindex);
ddf_clear(temp);
ddf_clear(prod);
ddf_FreeMatrix(Mdual);
ddf_FreeMatrix(Gdual);
return Mproj;
}
ddf_boolean ddf_DDFile2File(char *ifile, char *ofile, ddf_ErrorType *err)
{
/* The representation conversion from an input file to an outfile. */
/* modified by D. Avis to allow stdin/stdout */
ddf_boolean found=ddf_TRUE;
FILE *reading=NULL,*writing=NULL;
ddf_PolyhedraPtr poly;
ddf_MatrixPtr M, A, G;
if (strcmp(ifile,"**stdin") == 0 )
reading = stdin;
else if ( ( reading = fopen(ifile, "r") )!= NULL) {
fprintf(stderr,"input file %s is open\n", ifile);
}
else{
fprintf(stderr,"The input file %s not found\n",ifile);
found=ddf_FALSE;
*err=ddf_IFileNotFound;
goto _L99;
}
if (found){
if (strcmp(ofile,"**stdout") == 0 )
writing = stdout;
else if ( (writing = fopen(ofile, "w") ) != NULL){
fprintf(stderr,"output file %s is open\n",ofile);
found=ddf_TRUE;
} else {
fprintf(stderr,"The output file %s cannot be opened\n",ofile);
found=ddf_FALSE;
*err=ddf_OFileNotOpen;
goto _L99;
}
}
M=ddf_PolyFile2Matrix(reading, err);
if (*err!=ddf_NoError){
goto _L99;
} poly=ddf_DDMatrix2Poly(M, err); /* compute the second representation */ ddf_FreeMatrix(M);
if (*err==ddf_NoError) {
ddf_WriteRunningMode(writing, poly);
A=ddf_CopyInequalities(poly);
G=ddf_CopyGenerators(poly);
if (poly->representation==ddf_Inequality) {
ddf_WriteMatrix(writing,G);
} else {
ddf_WriteMatrix(writing,A);
}
ddf_FreePolyhedra(poly);
ddf_FreeMatrix(A);
ddf_FreeMatrix(G);
}
_L99: ;
if (*err!=ddf_NoError) ddf_WriteErrorMessages(stderr,*err);
if (reading!=NULL) fclose(reading);
if (writing!=NULL) fclose(writing);
return found;
ddf_MatrixPtr ddf_FourierElimination(ddf_MatrixPtr M,ddf_ErrorType *error)
/* Eliminate the last variable (column) from the given H-matrix using
the standard Fourier Elimination.
*/
{
ddf_MatrixPtr Mnew=NULL;
ddf_rowrange i,inew,ip,in,iz,m,mpos=0,mneg=0,mzero=0,mnew;
ddf_colrange j,d,dnew;
ddf_rowindex posrowindex, negrowindex,zerorowindex;
myfloat temp1,temp2;
ddf_boolean localdebug=ddf_FALSE;
*error=ddf_NoError;
m= M->rowsize;
d= M->colsize;
if (d<=1){
*error=ddf_ColIndexOutOfRange;
if (localdebug) {
printf("The number of column is too small: %ld for Fourier's Elimination.\n",d);
}
goto _L99;
}
if (M->representation==ddf_Generator){
*error=ddf_NotAvailForV;
if (localdebug) {
printf("Fourier's Elimination cannot be applied to a V-polyhedron.\n");
}
goto _L99;
}
if (set_card(M->linset)>0){
*error=ddf_CannotHandleLinearity;
if (localdebug) {
printf("The Fourier Elimination function does not handle equality in this version.\n");
}
goto _L99;
}
/* Create temporary spaces to be removed at the end of this function */
posrowindex=(long*)calloc(m+1,sizeof(long));
negrowindex=(long*)calloc(m+1,sizeof(long));
zerorowindex=(long*)calloc(m+1,sizeof(long));
ddf_init(temp1);
ddf_init(temp2);
for (i = 1; i <= m; i++) {
if (ddf_Positive(M->matrix[i-1][d-1])){
mpos++;
posrowindex[mpos]=i;
} else if (ddf_Negative(M->matrix[i-1][d-1])) {
mneg++;
negrowindex[mneg]=i;
} else {
mzero++;
zerorowindex[mzero]=i;
}
} /*of i*/
if (localdebug) {
ddf_WriteMatrix(stdout, M);
printf("No of (+ - 0) rows = (%ld, %ld, %ld)\n", mpos,mneg, mzero);
}
/* The present code generates so many redundant inequalities and thus
is quite useless, except for very small examples
*/
mnew=mzero+mpos*mneg; /* the total number of rows after elimination */
dnew=d-1;
Mnew=ddf_CreateMatrix(mnew, dnew);
ddf_CopyArow(Mnew->rowvec, M->rowvec, dnew);
/* set_copy(Mnew->linset,M->linset); */
Mnew->numbtype=M->numbtype;
Mnew->representation=M->representation;
Mnew->objective=M->objective;
/* Copy the inequalities independent of x_d to the top of the new matrix. */
for (iz = 1; iz <= mzero; iz++){
for (j = 1; j <= dnew; j++) {
ddf_set(Mnew->matrix[iz-1][j-1], M->matrix[zerorowindex[iz]-1][j-1]);
}
}
/* Create the new inequalities by combining x_d positive and negative ones. */
inew=mzero; /* the index of the last x_d zero inequality */
for (ip = 1; ip <= mpos; ip++){
for (in = 1; in <= mneg; in++){
inew++;
ddf_neg(temp1, M->matrix[negrowindex[in]-1][d-1]);
for (j = 1; j <= dnew; j++) {
ddf_LinearComb(temp2,M->matrix[posrowindex[ip]-1][j-1],temp1,\
M->matrix[negrowindex[in]-1][j-1],\
M->matrix[posrowindex[ip]-1][d-1]);
ddf_set(Mnew->matrix[inew-1][j-1],temp2);
}
ddf_Normalize(dnew,Mnew->matrix[inew-1]);
}
}
free(posrowindex);
free(negrowindex);
free(zerorowindex);
ddf_clear(temp1);
ddf_clear(temp2);
_L99:
return Mnew;
}