How to multiply multiple matrices with C++

Question

I'm doing a homework assignment which involves multiplying more than 2 matrices.

I thought about multiplying the first 2 matrices then take its result, continue multiplying it with the 3rd matrix, and repeat the same process until I multiply all the matrices together.

A * B * C = (A * B) * C = A * (B * C)

And here is my code so far. All of my matrices are stored in a 3D array of matrix[1][row][column].

// Calculate the result of first 2 matrices
for (int a = 0; a < n7; a++) {
    for (int b = 0; b < n7; b++) {
        for (int l = 0; l < n7; l++) {
            sum += matrix[1][l][b] * matrix[0][a][l];
        }
        resultMatrix[a][b] = sum;
        sum = 0;
    }
}
// Check if k > 2, if yes then continue taking matrix[2] multiply with the result
if (k > 2) {
    // Calculate to a tempResult matrix
    for (int f = 2; f < k; f++) {
        for (int a = 0; a < n7; a++) {
            for (int b = 0; b < n7; b++) {
                for (int l = 0; l < n7; l++) {
                    sum += matrix[f][l][b] * resultMatrix[a][l];
                }
                resultMatrix[a][b] = sum;
                sum = 0;
            }
        }
        // Pass the result to the original resultMatrix
        for (int a = 0; a < n7; a++) {
            for (int b = 0; b < n7; b++) {
                resultMatrix[a][b] = tempResult[a][b];
            }
        }
    }
}

I could not get the same result with an online matrix calculator and some manual input.

Please point out my mistakes, thank you!

Answer 1

Here is one solution.. Although I didn't applied dimension check of the matrices. So if you multiply a (3X4) & (2X4) matrix, it will not warn you. It can be done very easily with very simple steps. It worked for me with

A = 1    2    3    4
    5    6    7    8    [4X4]
    0    1    2    3
    7    8    9    0

B = 2    3    4
    5    6    7         [4X3]
    8    9    0
    3    4    5

c = 1
    2                   [3X1]
    3

D = 1    1   -2   -1    [1X4]

Result = 278   278   556   -278
         718   718  1436   -718 [4X4]
         168   168   336   -168
         678   678  1356   -678

The program:

#include <iostream>
#include <iomanip>

void displaymat(double* p, int r, int c)
{

    for (int i = 0; i < r; i++)
    {
        for (int j = 0; j < c; j++)
        {
            std::cout << std::setw(15) << *(p + i * c + j) << "\t";
        }
        std::cout << std::endl;
    }
    std::cout << "\n\n" << std::endl;
}

void matrix_multiply(double** a, double* b, int* rf, int* cf, int num)
{
    double sum;
    double** interim_result = new double* [num - 1]{nullptr};
    for (int i = 0; i < num - 1; i++)
    {
        interim_result[i] = new double[rf[0] * cf[i + 1]]{ 0 };
    }

    for (int i = 0; i < num - 1; i++)
    {
        for (int j = 0; j < rf[0]; j++)
        {
            for (int k = 0; k < cf[i + 1]; k++)
            {
                sum = 0;
                for (int l = 0; l < cf[i]; l++)
                {
                    if (i == 0)
                    {
                        sum = sum + a[i][cf[i] * j + l] * a[i + 1][cf[i + 1] * l + k];
                    }
                    else
                    {
                        sum = sum + interim_result[i - 1][cf[i] * j + l] * a[i + 1][cf[i + 1] * l + k];
                    }
                }
                interim_result[i][j * cf[i + 1] + k] = sum;
            }
        }
        //displaymat(interim_result[i], rf[0], cf[i + 1]);
    }
    for (int i = 0; i < rf[0] * cf[num - 1]; i++)
    {
        b[i] = interim_result[num - 2][i];
    }
    for (int i = 0; i < num - 1; i++)
    {
        delete[] interim_result[i];
    }
    delete[] interim_result;
}

int main()
{
    int num; // total number of matrices
    char ch = 'a';
    std::cout << "How many matrices/matrix?:";
    std::cin >> num;
    std::cout << std::endl;
    double** mat = new double* [num]; // double pointer for stacks of matrices
    int* r = new int[num]{0}; // to store the rows the matrices
    int* c = new int[num]{0}; // to store the columns of matrices
    for (int n = 0; n < num; n++)
    {
        std::cout << "matrix:" << n + 1 << "\n" << std::endl;
        std::cout << "rows:";
        std::cin >> r[n]; // input
        std::cout << "columns:";
        std::cin >> c[n]; // input
        std::cout << std::endl;
        mat[n] = new double[(r[n] * c[n])]; // for getting elements
        for (int i = 0; i < c[n] * r[n]; i++)
        {
            std::cout << ch << "[" << i / c[n] + 1 << "][" << i % c[n] + 1 << "]:";//ch << "[" << i / c[n] << "]" << "[" << i % c[n] << "]:";
            std::cin >> *(*(mat + n) + i);
        }
        displaymat(mat[n], r[n], c[n]);
        ch++;
    }
    double* result = new double[r[0] * c[num - 1]];
    matrix_multiply(mat, result, r, c, num);
    std::cout << "Result=" << std::endl;
    displaymat(result, r[0], c[num - 1]);
    for (int i = 0; i < num; i++)
    {
        delete[] * (mat + i);
    }
    delete[] mat;
    delete[] result;
    delete[] r;
    delete[] c;
}