Replacing Value of Diagonals in (m x m) Matrix With its Column Sum with Memory Efficient Way in C++

Question

I have the following matrix of size m=4

   0.00000   0.09130   0.09130   0.00000
   0.04565   0.00000   0.00000   0.00000
   0.04565   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000

And I want to replace the diagonal of that matrix with (1 - sum of its column). Resulting matrix:

   0.90870   0.09130   0.09130   0.00000
   0.04565   0.90870   0.00000   0.00000
   0.04565   0.00000   0.90870   0.00000
   0.00000   0.00000   0.00000   1.00000

So for example for (1,1) we have

   1 - (0.04565 + 0.04565 + 0.00000) = 0.90870

Now the actual practice the size of m is very large of scale 10^6 to 10^7. So I can't afford to store the initial matrix into a container.

Is there any memory efficient alternative way to do it?

The current is the implementation I have for slurping it into vector of vectors. It cannot handle large m (10^6).

    #include <iostream>
    #include <vector>
    #include <fstream>
    #include <sstream>
    #include <map>
    using namespace std;

      // Initialize Matrix Before Slurping
       vector <vector<double> > Matrix;
        Matrix.resize(nofRow);
        for(size_t i = 0; i < nofRow; ++i)
        {
            Matrix[i].resize(nofCol);
        }



        if (arg_count !=2 ) {
        cerr << "expected one argument" << endl;
        return EXIT_FAILURE;
    }

    string line;
    ifstream myfile (arg_vec[1]);

    // Slurpint it
    int count1=0;
    if (myfile.is_open())
    {   

        while (getline(myfile,line) )
        {
            stringstream ss(line);
            double Value;
            count1++;            

            int count2=0;
            while (ss >> Value) {
                count2++;
                Matrix[count1][count2] = Value;
            }


        }
        myfile.close();
    }
    else { cout << "Unable to open file"; }


     // Summing up Column;
        vector <double> ColSum;
        ColSum.resize(nofCol);
        for(size_t i = 0; i < nofRow; ++i)
        {
            for(size_t j = 0; j < nofCol; ++j)
            {
                //std::cout <<"["<<i<<"]"<<"["<<j<<"] = " <<Matrix[i][j]<<std::endl;
                ColSum[j] += Matrix[i][j];
            }
        }  



        // Printing it
        for(size_t k = 0; k < nofRow; ++k)
        {
            for(size_t l = 0; l < nofCol; ++l)
            {
                  if (k == l ) {
                      double OneMinusSum = 1 - ColSum[k];
                      //if (OneMinusSum < 0) { OneMinusSum = 1; };
                     std::cout << OneMinusSum << "\t";
                  }
                  else {
                      std::cout<< Matrix[k][l] << "\t";
                  }
            }

            std::cout << std::endl;
        }

Answer 1

Create a vector of size m to store the diagonal. Then go through the file and add the ith column of each line to diag[i]. Now go through the file again and output each line, but replace the value of the ith element on the ith line with diag[i]. This way you only need to store a vector of size m in memory.