creating matrix with probabilities - c++

Question

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