Simple matrix exponentiation in c++

So I was asked to define a matrix as:

typedef vector<double> vec;
typedef vector<vec> matrix;

and based on that write some functions like scalar multiplication, addition, etc. Everything but exponentiation works pretty well and I have no clue what could be causing problems in this one function. First of all I defined multiplication as:

void multip(const matrix& A, const matrix& B, matrix& result){
    int n = A.size();
    for (int i = 0; i<n; i++){
        for (int j = 0; j<n; j++){
            for (int k = 0; k< n; k++){
                result[i][j] += A[i][k] * B[k][j];
            }
        }
    }
}

and based on that I wanted to make a recursive (this is a must) exponentiation function as follows:

void expo(matrix& M, unsigned n){
    if (n>0){
        n--;
        multip(M, expo(M, n), M);}
    else{return;}
}

This does not work, returning [Error] Invalid use of void expression. I understood why this wouldn't work, but I have no clue how to get around that. Could somebody help me with that problem?

Solution

The main problem is that multip changes its 3rd argument, so it cannot be the same as the 1st, as in call multip(M, expo(M, n), M); in your code.

If you use function return values for returning values, as you should, it becomes straightforward.

Fixes and a working example:

#include <iostream>
#include <vector>

using namespace std;

typedef vector<double> vec;
typedef vector<vec> matrix;

matrix multip(const matrix& A, const matrix& B) {
    size_t n = A.size();
    matrix result(n, vec(n));
    for (size_t i = 0; i < n; ++i) {
        for (size_t j = 0; j < n; ++j) {
            for (size_t k = 0; k < n; ++k) {
                result[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    return result;
}

matrix expo(matrix const& M, unsigned n) {
    if(n < 1)
        throw;
    if(n == 1)
        return M;
    return multip(M, expo(M, n - 1));
}

void print(matrix const& M) {
    size_t n = M.size();
    for(size_t i = 0; i < n; ++i) {
        for(size_t j = 0; j < n; ++j)
            cout << M[i][j] << ' ';
        cout << '\n';
    }
}

int main() {
    matrix m(2, vec(2));
    m[0][0] = 2;
    m[1][1] = 2;
    print(m);
    cout << '\n';

    m = expo(m, 3);
    print(m);
    cout << '\n';
}

Outputs: