Parallel Matrix Multiplication in C++ - parallel-processing

Question

I am trying to implement Parallel Multi-threaded Matrix multiplication in C++. The method i follow involves dividing Arrays into 4 sub-arrays and carry out parallel Multiplication using 4 threads on these 4 sub arrays.
I have written a C++ code but it is throwing error and terminates explicitly. Error :
"terminate called after throwing an instance of std::system_error
what():invalid Argument"
Here is my complete code. I am relatively new to C++ and multi-threading.
#include <iostream>
#include <thread>
#include <mutex>
#include <vector>
#include <algorithm>
#include <string>
#define N 4
using namespace std;
mutex mu;
void stage_1_multiply(int *a,int *b,int *d){
int *xij;
int *yij;
int *zij;
int COLS = N,ROWS = N;
cout<< " thread "<< this_thread::get_id() << " "<<endl;
for(int i = 0;i<(N/2);++i){
for(int j = 0;j < (N/2); j++){
for(int k = 0; k<(N/2);k++){
mu.lock();
xij = a + ((COLS * i) + k);
yij = b + ((COLS * k) + j);
zij = d + ((COLS * i) + j);
*zij += ( (*xij) * (*yij) );
mu.unlock();
}
}
}
}
int main(){
int A[4][4],B[4][4],C[4][4],D_1[4][4],D_2[4][4];
for(int i = 0;i<4;i++){
for(int j = 0;j<4;j++){
A[i][j] = i + 1;
B[i][j] = i + 1;
C[i][j] = 0;
D_1[i][j] = 0;
D_2[i][j] = 0;
}
}
for(int i = 0;i<4;i++){
for(int j = 0;j< 4;j++){
cout << A[i][j] << " ";
}
cout << endl;
}
for(int i = 0;i<4;i++){
for(int j = 0;j< 4;j++){
cout << B[i][j] << " ";
}
cout << endl;
}
vector< thread> threads(8);
int th = 0;
threads[th++] = thread(stage_1_multiply,&A[0][0],&B[0][0],&D_1[0][0]);
threads[th++] = thread(stage_1_multiply,&A[0][2],&B[2][0],&D_2[0][0]);
threads[th++] = thread(stage_1_multiply,&A[2][0],&B[0][2],&D_1[2][2]);
threads[th++] = thread(stage_1_multiply,&A[2][2],&B[2][2],&D_2[2][2]);
for( auto& t : threads){
t.join();
}
threads[th++] = thread(stage_1_multiply,&A[0][0],&B[0][2],&D_1[0][2]);
threads[th++] = thread(stage_1_multiply,&A[0][2],&B[2][2],&D_2[0][2]);
threads[th++] = thread(stage_1_multiply,&A[2][0],&B[0][0],&D_1[2][0]);
threads[th++] = thread(stage_1_multiply,&A[2][2],&B[2][0],&D_2[2][0]);
for( auto& t : threads){
t.join();
}
// code to add The Matrices D_1 and D_2 goes here.
for(int i = 0;i<4;i++){
for(int j = 0;j< 4;j++){
cout << D_1[i][j] << " ";
}
cout << endl;
}
cout << " Main Close "<<endl;
return 0;
}
What am doing wrong? is it anything related to parallel access of shared memory? If so how can i correct it?
PS: This is a homework Assignment.