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
[[1,2],[3,4]]
. You must have some subtler bug in there. You need to go through it step-by-step and see where the incorrect numbers start appearing for the first time.std::vector<std::vector<double>>
for a matrix, you should probably check every inner vector is the same size as the outer.if(std::any_of(vect.begin(), vect.end(),[size = vect.size()](auto & inner){ return inner.size() != size; })) { throw ... }
It will also remove the undefined behaviour of thedimension == 0
case.