[英]C++ - Calculating the inverse of a matrix
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:我试图编写一个应该能够计算矩阵逆的程序:这是我到目前为止所拥有的:
#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.计算行列式、转置矩阵和辅因子矩阵的函数正常工作(据我所知),但计算逆矩阵的函数却没有。 I searched the internet and found this , which uses the same function for calculating the inverse.我在互联网上搜索并找到了this ,它使用相同的函数来计算逆。
Is this formula incorrect, or do you have any other idea, why it doesnt work?这个公式是否不正确,或者您有任何其他想法,为什么它不起作用?
The matrix I am using is我使用的矩阵是
and the inverse of it should be它的倒数应该是
First of all, thanks for your comments.首先,感谢您的评论。
The problem was the order of execution.问题是执行顺序。 The correct solution is:正确的解决办法是:
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;
}
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:我知道这是一个老问题,但是当输入矩阵的维度为 1 时,您的代码不起作用。这是我使用的解决方法:
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));
}
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