void
adj_extreme(int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])
{
dd_PolyhedraPtr P;
dd_ErrorType err;
dd_MatrixPtr H,V;
dd_SetFamilyPtr A;
if (nrhs == 1 && nlhs == 2 && mxIsStruct(prhs[0])) {
dd_set_global_constants(); /* First, this must be called. */
H = FT_get_H_MatrixPtr(prhs[0]);
P = dd_DDMatrix2Poly(H, &err); /* compute the second representation */
if (err == dd_NoError) {
V = dd_CopyGenerators(P);
A = dd_CopyAdjacency(P);
plhs[0] = FT_set_V_MatrixPtr(V);
plhs[1] = FT_set_SetFamilyPtr(A);
dd_FreeMatrix(V);
dd_FreeSetFamily(A);
} else {
dd_WriteErrorMessages(stdout,err);
mexErrMsgTxt("CDD returned an error, see above(!) for details");
}
dd_FreeMatrix(H);
dd_FreePolyhedra(P);
return;
} else {
mexErrMsgTxt("adj_extreme expects an H input struct and produces a V output struct and the adjacency struct");
}
}
void
adjacency(int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])
{
dd_PolyhedraPtr P;
dd_ErrorType err;
dd_MatrixPtr V;
dd_SetFamilyPtr A;
if (mxIsStruct(prhs[0])) {
V = FT_get_V_MatrixPtr(prhs[0]);
dd_set_global_constants(); /* First, this must be called. */
P = dd_DDMatrix2Poly(V, &err); /* compute the second representation */
if (err == dd_NoError) {
A = dd_CopyInputAdjacency(P);
plhs[0] = FT_set_SetFamilyPtr(A);
dd_FreeSetFamily(A);
} else {
dd_WriteErrorMessages(stdout,err);
mexErrMsgTxt("CDD returned an error, see above(!) for details");
}
dd_FreeMatrix(V);
dd_FreePolyhedra(P);
}
}
void allvertices(int m_input, int d_input, double *a_input)
/* output vertices and incidences */
{
dd_PolyhedraPtr poly;
dd_MatrixPtr A=NULL,G=NULL;
dd_SetFamilyPtr GI=NULL;
dd_rowrange i,m;
dd_colrange j,d;
dd_ErrorType err;
m=(dd_rowrange)m_input; d=(dd_colrange)d_input;
A=dd_CreateMatrix(m,d);
for (i=0; i<m; i++){
for (j=0; j<d; j++) dd_set_d(A->matrix[i][j],a_input[i*d+j]);
}
A->representation=dd_Inequality;
poly=dd_DDMatrix2Poly(A, &err);
/* compute the second (generator) representation */
if (err==dd_NoError) {
G=dd_CopyGenerators(poly);
GI=dd_CopyIncidence(poly);
MLPutFunction(stdlink,"List",2);
dd_MLWriteMatrix(G);
dd_MLWriteSetFamily(GI);
} else {
dd_MLWriteError(poly);
}
dd_FreeMatrix(A);
dd_FreeMatrix(G);
dd_FreeSetFamily(GI);
}
void
hull(int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])
{
dd_PolyhedraPtr P;
dd_ErrorType err;
dd_MatrixPtr H,V;
if (nrhs == 1 && nlhs == 1 && mxIsStruct(prhs[0])) {
V = FT_get_V_MatrixPtr(prhs[0]);
dd_set_global_constants(); /* First, this must be called. */
P = dd_DDMatrix2Poly(V, &err); /* compute the second representation */
if (err == dd_NoError) {
H = dd_CopyInequalities(P);
plhs[0] = FT_set_H_MatrixPtr(H);
dd_FreeMatrix(H);
} else {
dd_WriteErrorMessages(stdout,err);
mexErrMsgTxt("CDD returned an error, see above(!) for details");
}
dd_FreeMatrix(V);
dd_FreePolyhedra(P);
return;
} else {
mexErrMsgTxt("hull expects a V input struct and produces an H output struct");
}
}
void allfacets(int n_input, int d_input, double *g_input)
/* output facets and incidences */
{
dd_PolyhedraPtr poly;
dd_MatrixPtr A=NULL,G=NULL;
dd_SetFamilyPtr AI=NULL;
dd_rowrange i,n;
dd_colrange j,d;
dd_ErrorType err;
n=(dd_rowrange)n_input; d=(dd_colrange)d_input;
G=dd_CreateMatrix(n,d);
for (i=0; i<n; i++){
for (j=0; j<d; j++) dd_set_d(G->matrix[i][j],g_input[i*d+j]);
}
G->representation=dd_Generator;
poly=dd_DDMatrix2Poly(G, &err);
/* compute the second (inequality) representation */
if (err==dd_NoError){
A=dd_CopyInequalities(poly);
AI=dd_CopyIncidence(poly);
MLPutFunction(stdlink,"List",2);
dd_MLWriteMatrix(A);
dd_MLWriteSetFamily(AI);
} else {
dd_MLWriteError(poly);
}
dd_FreeMatrix(A);
dd_FreeMatrix(G);
dd_FreeSetFamily(AI);
}
bool init()
{
V_ = FromEigen(v);
dd_ErrorType error = dd_NoError;
/*dd_rowset redset,impl_linset;
dd_rowindex newpos;
dd_MatrixCanonicalize(&V_, &impl_linset, &redset, &newpos, &error);
if(error != dd_NoError)
{
std::cout << ("can not reduce matrix") << std::endl;
}
fprintf(stdout, "\nRedundant rows: ");
set_fwrite(stdout, redset);
fprintf(stdout, "\n");
set_free(redset);
set_free(impl_linset);
free(newpos);
error = dd_NoError;*/
H_= dd_DDMatrix2Poly(V_, &error);
if(error != dd_NoError)
{
if(dd_debug)
std::cout << ("numerical instability in cddlib. ill formed polytope") << std::endl;
}
else
{
init_= true;
b_A = dd_CopyInequalities(H_);
// get equalities and add them as complementary inequality constraints
long elem;
std::vector<long> eq_rows;
for(elem=1;elem<=(long)(b_A->linset[0]);++elem)
{
if (set_member(elem,b_A->linset))
eq_rows.push_back(elem);
}
int rowsize = (int)b_A->rowsize;
A = matrix_t (rowsize + eq_rows.size(), (int)b_A->colsize-1);
b = vector_t (rowsize + eq_rows.size());
for(int i=0; i < rowsize; ++i)
{
b(i) = (value_type)(*(b_A->matrix[i][0]));
for(int j=1; j < b_A->colsize; ++j)
{
A(i, j-1) = -(value_type)(*(b_A->matrix[i][j]));
}
}
int i = 0;
for(std::vector<long int>::const_iterator cit = eq_rows.begin();
cit != eq_rows.end(); ++cit, ++i)
{
b(rowsize + i) = -b((int)(*cit));
A(rowsize + i) = -A((int)(*cit));
}
}
return init_;
}
/*
* Find the extreme vertices between lower_bound and upper_bound of the convex
* hull of ineqs.
*
* ineqs: row-major order matrix of total length nrow*ncols
* nrows: Number of rows in matrix
* ncols: Number of columns in matrix
* lower_bound: lower bound of solution space on x-axis
* upper_bound: upper bound of solution space on y-axis
* output size: Set to size of result
*
* Returns array representing 3 by (output_size/3) matrix, where each row is:
* x_i, y_i, l_i
* Where x_i, y_i are the coordinates of the vertex, and l_i is the index of
* the input inequality that constrains the solution space *to the right* of
* vertex i.
*/
double *extreme_vertices(const double *ineqs, const size_t nrows,
const size_t ncols, float lower_bound,
float upper_bound, /*OUT*/ size_t * output_size)
{
/* Preconditions */
assert(ineqs != NULL);
assert(ncols == 3);
assert(output_size != NULL);
/* Check for approx equal lower and upper bound */
if (abs(lower_bound - upper_bound) < EPS)
return NULL;
assert(lower_bound <= upper_bound);
/*
* Initialize library
* TODO: Do we want to do this on every call?
*/
dd_set_global_constants();
dd_ErrorType err;
dd_MatrixPtr generators;
dd_MatrixPtr m =
init_ineq_doubles(ineqs, nrows, ncols, lower_bound, upper_bound);
dd_SetFamilyPtr incidence;
/* Outputs */
dd_PolyhedraPtr poly = dd_DDMatrix2Poly(m, &err);
if (err != dd_NoError) {
return NULL;
}
/* Get generators */
generators = dd_CopyGenerators(poly);
/* Get incidence */
incidence = dd_CopyIncidence(poly);
double *result =
list_extreme_vertices(generators, incidence, nrows, m->rowsize - 1,
output_size);
dd_FreeMatrix(m);
dd_FreeMatrix(generators);
dd_FreePolyhedra(poly);
dd_FreeSetFamily(incidence);
dd_free_global_constants();
return result;
}
void
file_ine(int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])
/* Ine file input, V output, similar to extreme */
{
dd_PolyhedraPtr poly;
dd_MatrixPtr M;
dd_ErrorType err;
char *inputfile;
FILE *reading=NULL;
dd_MatrixPtr A, G;
dd_SetFamilyPtr GI,GA;
int buflen, status;
dd_set_global_constants(); /* First, this must be called. */
if (nrhs == 1 && nlhs <=2 && mxIsChar(prhs[0])) {
/* dd_SetInputFile(&reading,inputfile, &err); */
buflen = mxGetN(prhs[0]) + 1;
inputfile= mxCalloc(buflen, sizeof(char));
status = mxGetString(prhs[0], inputfile, buflen);
if ( (reading = fopen(inputfile,"r") )== NULL) {
mxErrMsgTxt("Input file not found\n");
return;
}
printf(" Input file opened. \n");
M=dd_PolyFile2Matrix(reading, &err);
if (err==dd_NoError) {
poly=dd_DDMatrix2Poly(M, &err); /* compute the second representation */
if (err!=dd_NoError) {
dd_WriteErrorMessages(stdout,err);
mxErrMsgTxt("CDD internal error\n");
return;
}
A=dd_CopyInequalities(poly);
G=dd_CopyGenerators(poly);
GI=dd_CopyInputIncidence(poly);
GA=dd_CopyAdjacency(poly);
plhs[0] = FT_set_V_MatrixPtr(G);
plhs[1] = ZH_set_Vlist(GI,GA);
dd_FreePolyhedra(poly);
dd_FreeMatrix(M);
return;
}
}
else {
mexErrMsgTxt("file-ine expects an file input");
}
return;
}
dd_MatrixPtr dd_BlockElimination(dd_MatrixPtr M, dd_colset delset, dd_ErrorType *error)
/* Eliminate the variables (columns) delset by
the Block Elimination with dd_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.
*/
{
dd_MatrixPtr Mdual=NULL, Mproj=NULL, Gdual=NULL;
dd_rowrange i,h,m,mproj,mdual,linsize;
dd_colrange j,k,d,dproj,ddual,delsize;
dd_colindex delindex;
mytype temp,prod;
dd_PolyhedraPtr dualpoly;
dd_ErrorType err=dd_NoError;
dd_boolean localdebug=dd_FALSE;
*error=dd_NoError;
m= M->rowsize;
d= M->colsize;
delindex=(long*)calloc(d+1,sizeof(long));
dd_init(temp);
dd_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) dd_WriteMatrix(stdout, M);
linsize=set_card(M->linset);
ddual=m+1;
mdual=delsize + m - linsize; /* #equalitions + dimension of z1 */
/* setup the dual matrix */
Mdual=dd_CreateMatrix(mdual, ddual);
Mdual->representation=dd_Inequality;
for (i = 1; i <= delsize; i++){
set_addelem(Mdual->linset,i); /* equality */
for (j = 1; j <= m; j++) {
dd_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++;
dd_set(Mdual->matrix[delsize+k-1][i], dd_one);
}
}
/* 2. Compute the generators of the dual system. */
dualpoly=dd_DDMatrix2Poly(Mdual, &err);
Gdual=dd_CopyGenerators(dualpoly);
/* 3. Take the linear combination of the original system with each generator. */
dproj=d-delsize;
mproj=Gdual->rowsize;
Mproj=dd_CreateMatrix(mproj, dproj);
Mproj->representation=dd_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 */
dd_set(prod, dd_purezero);
for (h = 1; h <= m; h++){
dd_mul(temp,M->matrix[h-1][j-1],Gdual->matrix[i-1][h]);
dd_add(prod,prod,temp);
}
dd_set(Mproj->matrix[i-1][k-1],prod);
}
}
}
if (localdebug) printf("Size of the projection system: %ld x %ld\n", mproj, dproj);
dd_FreePolyhedra(dualpoly);
free(delindex);
dd_clear(temp);
dd_clear(prod);
dd_FreeMatrix(Mdual);
dd_FreeMatrix(Gdual);
return Mproj;
}
