Dear PPL developers,

I forward the message that I sent to Roberto. Since he is traveling, maybe some of you can help us...

Thanks a lot

Best Regards

Ezio

On Thu, May 3, 2012 at 4:42 PM, Ezio Bartocci ezio.bartocci@gmail.com wrote:

Dear Roberto,

I have another question. This time in English so that also Radu and Gregory can read. I have the following points, describing a polytope:

1                  0.005             0.007883 0.9967750    0.004769   0.007988 1                  0.000250     0.007883 0.9967750         1.900e-05     0.007988 1                 0.005000      0.004225 0.9967750   0.004769    0.004331 1                 0.000250      0.004225 0.9967750   1.900e-05   0.004331 1                 0.0050000     0.007883 0.4194590         0.0047690     0.007988 1                 0.0002500     0.007883 0.4194590         1.9000e-05    0.007988 1                 0.0050000     0.004225 0.4194590   0.0047690   0.004331 1                 0.0002500     0.004225 0.4194590  1.90000e-05  0.004331

From this points stored in a matrix P with rows_P = 16 and cols_P = 3.

I call this function that I developed to generate a C_Polyhedron (or Polytope), that uses

add_generator

as you suggested and assign  to P the result that is private member of the class ppl_wrap

ppl_wrap::ppl_wrap (double * Points, int rows_P, int cols_P):rows_P(rows_P), cols_P(cols_P) {

int debug = 1;        int i, j, k;

// Convert the standard double representation to a much    // accurate representation    vector<mpf_class> *P1_row = double2mpzclass(Points, &rows_P, &cols_P);    vector<vector<mpf_class> > *P1 = vec2mat(P1_row, &rows_P, &cols_P);    vector<mpf_class> single_point;

list<Variable> VarList;        list<Variable>::iterator it;    Linear_Expression lin_exp[rows_P];    if (debug)        cout << "Cols num: " << cols_P << "\n";

for(i=0; i< cols_P; i++)                            // create a list of n_col_C "Variable" objects                VarList.push_back(Variable(i));

C_Polyhedron ph (cols_P, EMPTY);

if (debug)        cout << "Rows num: " << rows_P << "\n";    for (j = 0; j < rows_P; j++)    {        if (debug)            cout << " j = " << j << "\n";        single_point.clear();

/*Create linear expression for expressing the point*/                if (debug)            cout << " k = ";        for (k = 0; k < cols_P; k++){                   // pick the needed row of matrix C                        if (debug)                    cout << "(" << k << ") " << (*P1)[k][j] << " ";                        single_point.push_back((*P1)[k][j]);

}        if (debug)            cout << ";\n";

int m;        for ( it=VarList.begin() ; it != VarList.end(); it++ )  // creates linear expression "lin_exp_temp" by using the iterator of the Variable-List        {                m = it->id();                if (debug)                    cout << " m = " << m <<"\n";                lin_exp[j]+=single_point[m]*(*it);        }

ph.add_generator(point(lin_exp[j]));    }    P = ph; }

After obtaining a polytope I need to have the following representation to store the polytope back in matlab C * x <= d.

Now as I wrote in a previous email I saw that with:

Constraint_System ConSys_P; ConSys_P = P.constraints();

we can actually obtain the representation: C * x >= d

but if I print the constraints:

ConSys_P.print();

-A + C >= 0, -C >= -1, A >= 0, B >= 0, -B >= -1

This does not seem to match with the points and it seems an over approximation. I would expected constraints more tight constraints.

Why is like that ?

Thanks,

Best

Ezio

-- Dr. Ezio Bartocci, Assistant Professor Dependable Systems Group Department of Computer Engineering Faculty of informatics TU Wien, Vienna University of Technology, Austria Treitlstraße   3, 1040 Vienna, Austria E-Mail:     ezio.bartocci@tuwien.ac.at Phone:     +43 (1) 58801 - 18210 Webiste: http://www.eziobartocci.com