在C ++中使用2d向量乘法矩阵

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.