Multiplying Matrices using 2d Vectors in C++ - c++

Question

I'm trying to design a program that creates a matrix using vectors of vectors of integers, and then multiplyies it with another matrix. I know how to multiply matrices on paper, but when I try to implement it in my program, I'm not getting it to work. I know that both matrices are entered correctly and are passed correctly as I have the the output of those functions so that I can debug. The program works incorrectly when I try to multiply them. The answer and the number of elements are not right. I know I'm missing something but can't figure out what.
Matrix Matrix::operator*(Matrix m){
vector<int> mRow = m.getRow(0);
vector<int> mCol = m.getCol(0);
vector<int> newElem;
int product = 0;
//adds the contents of the 2nd matrix to the 2d vector
vector< vector<int> > m2(mRow.size(), vector<int>(mCol.size()));
for (int i = 0; i < mRow.size(); i++){
mRow.clear();
mRow = m.getRow(i);
for (int j = 0; j < mCol.size(); j++){
m2[j][i] = mRow[j];
}
}
//Multiplies the matrices using the 2d matrix**THIS IS WHERE IT GOES WRONG**
for (int i = 0; i < row; i++){
for (int j = 0; j < column; j++){
product += matrix[i][j]*m2[j][i];
}
newElem.insert(newElem.begin()+i,product);
product = 0;
}
//displays the products so that i can see if its working
for (int i = 0; i < newElem.size(); i++){
cout << " "<<newElem[i]<<endl;
}
//adds the new product vector to a new Matrix object and returns it
Matrix newM(row, mCol.size());
vector<int> temp;
for (int i = 0; i < row; i++){
for (int j = 0; j < mCol.size(); j++){
temp.insert(temp.begin()+j, newElem[0]);
newElem.erase(newElem.begin());
}
newM.setRow(temp,i);
temp.clear();
}
return newM;
}
Although I don't know whether this helps, I'm using this site as a reference for multiplying 2 matrices together.

Answer 1

Your matrix representation has nothing to do with your mistake. You need to have more nested iterations. Think of a result matrix and iterate through that to calculate it's every element. In a pseudocode:
for i in result column
for j in result row
res[i, j] = multiply(m1, m2, i, j)
where multiply function is the nested loop, something like this:
multiply(m1, m2, i, j)
{
val = 0;
for k in row
val += m1[i, k] * m2[k, j]
return val
}
Here is an implementation of the outer loops. Mind you, there are no error checking in the code.
vector<vector<int> > ml;
vector<vector<int> > mr;
// fill in ml and mr
...
// result matrix
vector<vector<int> > res;
// allocate the result matrix
res.resize(ml.size());
for( it = res.begin(); it != res.end(); ++it)
it->resize(ml[0].size());
// loop through the result matrix and fill it in
for( int i = 0; i < res.size(); ++i)
for( int j = 0; j < res[0].size(); ++j)
res[i][j] = multiply(ml, mr, i, j);
Leaving a proper implementation of multiply() function to you.