The document is a C++ program that calculates a random speed using matrix concepts. It initializes a random seed, reads matrix data from a file, and computes the probabilities using log functions to derive values for 'a', 'b', and 'z'. The program outputs the results to a file, indicating whether the calculated speeds meet a certain threshold.

2. Random speed program in CPP
This program is calculating the random speed explicitly and
implementing the concept of matrix.
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;
template<typename T>
void print(T values[], int size) {
cout << "[";
for (int i = 0; i < size; i++) {
if (i > 0) cout << ", ";
cout << values[i];
}
cout << "]" << endl;
}
int main() {
// have to initialize the random seed explictly in C++.
srand(time(NULL));
FILE *input = fopen("TestSensingMatrix.txt", "r");
const int NOS = 30;
const int NOC = 2000;
const int MAX_IT = 10;
int SC[NOS][NOC];
memset(SC, 0, sizeof(SC));
// Generate the SC matrix
int row[2];
while (fscanf(input, "%d,%d", &row[0], &row[1]) == 2) {
// printf("%d,%dn", rows[0], rows[1]);
SC[row[0] - 1][row[1] - 1] = 1;
}
// s
double s[NOS];
memset(s, 0, sizeof(s));
for (int x = 0; x < NOS; x++) {
int cnt = 0;
for (int y = 0; y < NOC; y++) {
if (SC[x][y] == 1) {

3. cnt = cnt + 1;
}
}
s[x] = cnt * 1.0 / NOC;
}
// theta[ai]
double a[NOS];
double b[NOS];
double d = rand() % 12 / 10.0; // randint(0, 11) / 10
double Z[NOC];
memset(a, 0, sizeof(a));
memset(b, 0, sizeof(b));
memset(Z, 0, sizeof(Z));
for (int x = 0; x < NOS; x++) {
a[x] = s[x];
b[x] = 0.5 * s[x];
}
print(a, NOS);
print(b, NOS);
for (int itn = 0; itn < MAX_IT; itn++) { // the outer while
// Compute Z(t, j)
for (int j = 0; j < NOC; j++) {
double A = 0;
double B = 0;
// Compute Z
for (int i = 0; i < NOS; i++) {
A = A + SC[i][j] * log(a[i]) + (1-SC[i][j]) * log(1 -
a[i]);
if (b[i] <= 0) {
cout << "I am dumb and don't know how to use log
functions" << endl;
}
B = B + SC[i][j] * log(b[i]) + (1- SC[i][j]) * log(1-
b[i]);
}
A = exp(A);
B = exp(B);
Z[j] = (A * d) / ((A * d) + (B * (1 - d)));
}
// Compute new theta(t + 1)
for (int i = 0; i < NOS; i++) {
double tempa = 0;
double tempb = 0;
double tempd = 0;
double tempz = 0;

4. double totalz = 0;
int cnt = 0;
for (int j = 0; j < NOC; j++) {
if (SC[i][j] == 1) {
tempz = tempz + Z[j];
cnt = cnt + 1;
}
totalz = totalz + Z[j];
}
a[i] = tempz / totalz;
b[i] = (cnt - tempz) / (NOC - totalz);
if (b[i] < 0) {
cout << i << " is the problem step" << endl;
break;
}
d = totalz / NOC;
}
}
// end of while
cout << d << endl;
print (a, NOS);
print (b, NOS);
FILE *groundtruth = fopen("TestGroundTruth.txt", "r");
int gt[NOC];
memset(gt, 0, sizeof(gt));
while (fscanf(input, "%d,%d", &row[0], &row[1]) == 2) {
// printf("%d,%dn", rows[0], rows[1]);
gt[row[0] - 1] = row[1];
}
int out[NOC];
memset(out, 0, sizeof(out));
FILE *output = fopen("output.txt", "w");
for (int j = 0; j < NOC; j++) {
if (Z[j] >= 0.5) {
out[j] = 1;
}
}
double t[NOS];
memset(t, 0, sizeof(t));
for (int i = 0; i < NOS; i++) {
t[i] = a[i] / (a[i] + b[i]);
cout << t[i] << endl;
}
for (int j = 0; j < NOC; j++) {

5. fprintf(output, "%d, %dn", j+1, out[j]);
}
fclose(input);
}