Dear Oshalla,
Just to let you know. I've ported your ingenious code to C++. They are so indispensable! Thanks a million again.

#include <iostream>
#include <vector>
#include <boost/assign/std/vector.hpp>
#include <vector>
#include <stdio.h>
#include <stdlib.h>
using namespace boost::assign;
using namespace std;


int main  ( int arg_count, char *arg_vec[] ) {
    vector <double> realValue;
    realValue +=
       0.994704478,
       0.989459074,
       0.994717023,
       1.000000000,
       1.000000000,
       0.002647761,
       0.005282977,
       0.000882587,
       0.005270463,
       0.000882587,
       0.002635231,
       0.000882587,
       0.002635231;

    vector<int>rowIndex;
    rowIndex +=  1, 2, 3, 4, 5, 1, 3, 1, 2, 1, 2, 1, 2;

    vector<int>colIndex;
    colIndex  +=   1, 2, 3, 4 ,5, 5, 3, 2, 1, 3, 3, 4, 4;

    vector<int>matDim;
    matDim  += 5,5; // M always equal to N
    
    vector <double> theP;
    theP += 0.4, 0.2, 0.2, 0.2, 0.2;
    
  
    vector <double> Result; 
    Result.assign(theP.size(), 0);

     for (int i= 0; i < rowIndex.size(); i++) {
        Result[rowIndex[i]-1] += realValue[i] * theP[colIndex[i]-1];
     }    

    // print it
    for (int k =0; k < Result.size(); k++){
        cout << Result[k] << endl;
    }
    
 
    
    
    return 0;
}
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