creating matrix with probabilities

Question

Hi all, I want to generate a matrix of NxN to test some code that I have where each row contains floats as the elements and has to add up to 1 (i.e. a row with a set of probabilities).

Where it gets tricky is that I want to make sure that randomly some of the elements should be 0 (in fact most of the elements should be 0 except for some random ones to be the probabilities). I need the probabilities to be 1/m where m is the number of elements that are not 0 within a single row. I tried to think of ways to output this, but essentially I would need this stored in a C++ array. So even if I output to a file I would still have the issue of not having it in array as I need it. At the end of it all I need that array because I want to generate a Market Matrix file. I found an implementation in C++ to take an array and convert it to the market matrix file, so this is what I am basing my findings on. My input for the rest of the code takes in this market matrix file so I need that to be the primary form of output. The language does not matter, I just want to generate the file at the end (I found a way mmwrite and mmread in python as well)

Please help, I am stuck and not really sure how to implement this.

Answer 1

import random

N = 10

matrix = []

for j in range(N):
        t = [int(random.random()<0.6)  for i in range(N)]
        ones = t.count(1)
        row = [float(x)/ones for x in t] if ones else t
        matrix.append(row)

for r in matrix:
        print r

Answer 2

By C++ array, do you mean a C array or a STL vector<vector< > >? The latter would be cleaner, but here's an example using C arrays:

#include <stdlib.h>
#include <stdio.h>

float* makeProbabilityMatrix(int N, float zeroProbability)
{
   float* matrix = (float*)malloc(N*N*sizeof(float));

   for (int ii = 0; ii < N; ii++)
   {
      int m = 0;
      for (int jj = 0; jj < N; jj++)
      {
         int val = (rand() / (RAND_MAX*1.0) < zeroProbability) ? 0 : 1;
         matrix[ii*N+jj] = val;
         m += val;
      }
      for (int jj = 0; jj < N; jj++)
      {
         matrix[ii*N+jj] /= m;
      }
   }

   return matrix;
}

int main() 
{
   srand(234);
   int N = 10;

   float* matrix = makeProbabilityMatrix(N, 0.70);

   for (int ii = 0; ii < N; ii++)
   {      
      for (int jj = 0; jj < N; jj++)
      {
         printf("%.2f ", matrix[ii*N+jj]);
      }
      printf("\n");
   }

   free(matrix);

   return 0;
};

Output:

0.00 0.20 0.20 0.00 0.00 0.00 0.00 0.20 0.20 0.20 
0.25 0.00 0.00 0.00 0.00 0.25 0.00 0.25 0.25 0.00 
0.00 0.33 0.33 0.33 0.00 0.00 0.00 0.00 0.00 0.00 
0.00 0.00 0.00 0.00 0.00 0.50 0.00 0.00 0.50 0.00 
0.25 0.25 0.00 0.00 0.00 0.00 0.25 0.00 0.25 0.00 
0.00 0.25 0.00 0.00 0.00 0.25 0.25 0.00 0.25 0.00 
0.00 0.00 0.33 0.00 0.33 0.00 0.00 0.00 0.33 0.00 
0.00 0.20 0.20 0.20 0.20 0.00 0.00 0.20 0.00 0.00 
0.20 0.00 0.20 0.00 0.00 0.00 0.00 0.20 0.20 0.20 
0.00 0.00 0.00 0.00 0.00 0.50 0.00 0.50 0.00 0.00