C++ - Calculating the inverse of a matrix

Question

I've tried to write a program that should be able to calculate the inverse of a matrix: Here's what I have so far:

#include <iostream>
#include <vector>
#include <math.h>
#include <iomanip>
#include <stdexcept>

double getDeterminant(const std::vector<std::vector<double>> vect) {
    if(vect.size() != vect[0].size()) {
        throw std::runtime_error("Matrix is not quadratic");
    } 
    int dimension = vect.size();

    if(dimension == 0) {
        return 1;
    }

    if(dimension == 1) {
        return vect[0][0];
    }

    //Formula for 2x2-matrix
    if(dimension == 2) {
        return vect[0][0] * vect[1][1] - vect[0][1] * vect[1][0];
    }

    double result = 0;
    int sign = 1;
    for(int i = 0; i < dimension; i++) {

        //Submatrix
        std::vector<std::vector<double>> subVect(dimension - 1, std::vector<double> (dimension - 1));
        for(int m = 1; m < dimension; m++) {
            int z = 0;
            for(int n = 0; n < dimension; n++) {
                if(n != i) {
                    subVect[m-1][z] = vect[m][n];
                    z++;
                }
            }
        }

        //recursive call
        result = result + sign * vect[0][i] * getDeterminant(subVect);
        sign = -sign;
    }

    return result;
}

std::vector<std::vector<double>> getTranspose(const std::vector<std::vector<double>> matrix1) {

    //Transpose-matrix: height = width(matrix), width = height(matrix)
    std::vector<std::vector<double>> solution(matrix1[0].size(), std::vector<double> (matrix1.size()));

    //Filling solution-matrix
    for(size_t i = 0; i < matrix1.size(); i++) {
        for(size_t j = 0; j < matrix1[0].size(); j++) {
            solution[j][i] = matrix1[i][j];
        }
    }
    return solution;
}

std::vector<std::vector<double>> getCofactor(const std::vector<std::vector<double>> vect) {
    if(vect.size() != vect[0].size()) {
        throw std::runtime_error("Matrix is not quadratic");
    } 

    std::vector<std::vector<double>> solution(vect.size(), std::vector<double> (vect.size()));
    std::vector<std::vector<double>> subVect(vect.size() - 1, std::vector<double> (vect.size() - 1));

    for(std::size_t i = 0; i < vect.size(); i++) {
        for(std::size_t j = 0; j < vect[0].size(); j++) {

            int p = 0;
            for(size_t x = 0; x < vect.size(); x++) {
                if(x == i) {
                    continue;
                }
                int q = 0;

                for(size_t y = 0; y < vect.size(); y++) {
                    if(y == j) {
                        continue;
                    }

                    subVect[p][q] = vect[x][y];
                    q++;
                }
                p++;
            }
            solution[i][j] = pow(-1, i + j) * getDeterminant(subVect);
        }
    }
    return solution;
}

std::vector<std::vector<double>> getInverse(const std::vector<std::vector<double>> vect) {
    if(getDeterminant(vect) == 0) {
        throw std::runtime_error("Determinant is 0");
    } 
    double d = 1.0/getDeterminant(vect);
    std::vector<std::vector<double>> solution(vect.size(), std::vector<double> (vect.size()));

    for(size_t i = 0; i < vect.size(); i++) {
        for(size_t j = 0; j < vect.size(); j++) {
            solution[i][j] = vect[i][j] * d; 
        }
    }

    return getTranspose(getCofactor(solution));
}

void printMatrix(const std::vector<std::vector<double>> vect) {
    for(std::size_t i = 0; i < vect.size(); i++) {
        for(std::size_t j = 0; j < vect[0].size(); j++) {
            std::cout << std::setw(8) << vect[i][j] << " ";
        }
        std::cout << "\n";
    }
}

int main() {
    std::vector<std::vector<double>> matrix(3, std::vector<double> (3));
    matrix = {
        {1,2,3},
        {4,5,6},
        {7,8,8}
    };

    printMatrix(getInverse(matrix));
    return 0;
}

The functions for calculating the determinant, the transpose- and the cofactor-matrix work correctly (as far as I can see), but the function for calculating the inverse-matrix doesn't. I searched the internet and found this, which uses the same function for calculating the inverse.

Is this formula incorrect, or do you have any other idea, why it doesnt work?

---

The matrix I am using is

and the inverse of it should be

Answer 1

I know this is an old question but your code does not work when the input matrix's dimension is 1. Here is a workaround that I used:

vector<vector<double>> inverse(const vector<vector<double>> A) {
    double d = 1.0/det(A);
    vector<vector<double>> solution(A.size(), vector<double> (A.size()));

    if(A.size() == 1){
        vector<double> ans = {0};
        ans[0] = 1.0/det(A);
        solution[0] = ans;
        return solution;
    }

    for(size_t i = 0; i < A.size(); i++) {
        for(size_t j = 0; j < A.size(); j++) {
            solution[i][j] = A[i][j] * d; 
        }
    }

    return transpose(cofactor(solution));
}

Answer 2

First of all, thanks for your comments.

The problem was the order of execution. The correct solution is:

std::vector<std::vector<double>> getInverse(const std::vector<std::vector<double>> vect) {
    if(getDeterminant(vect) == 0) {
        throw std::runtime_error("Determinant is 0");
    } 

    double d = 1.0/getDeterminant(vect);
    std::vector<std::vector<double>> solution(vect.size(), std::vector<double> (vect.size()));

    for(size_t i = 0; i < vect.size(); i++) {
        for(size_t j = 0; j < vect.size(); j++) {
            solution[i][j] = vect[i][j]; 
        }
    }

    solution = getTranspose(getCofactor(solution));

    for(size_t i = 0; i < vect.size(); i++) {
        for(size_t j = 0; j < vect.size(); j++) {
            solution[i][j] *= d;
        }
    }

    return solution;
}