import numpy as np
import cvxpy as cp

# Construct the problem
N = 1000 # Population size
S = 10 # Number of infected individuals
M = 100 # Number of tests
K = 10 # Number of splits of each sample

# Define x0
ind0 = np.random.choice(N,S,0) # index subset 
x0 = np.zeros(N) 
x0[ind0] = np.random.rand(S)

# Define A
A = np.zeros((M,N))
for i in np.arange(N):
    ind = np.random.choice(M,K,0)
    A[ind,i] = 1

y = A @ x0