Multiplying matrices c++ - c++

Question

I want to make a program capable of rising the 2x2 matrix to k power. I know how to make one that is going to square it but once i want to reach higher powers i struggle to save the results I have and use it in the next equation. a,b,c,d are the numbers in the matrix, n is the amount of matrix I will want to do in one time, k is the power i want the matrix to be taken to and m is modulo which I want to use on the numbers. I know there is a method of making this fairly simply but I am unable to figure out a good way to use my results from the equation done before in the next equation.
#include <iostream>
using namespace std;
int mnoz(int a, int b, int c,int d,int m){
int a2 = (a*a + c*b) % m;
int b2 = (a*b + b*d) % m;
int c2 = (c*a + d*c) % m;
int d2 = (c*b + d*d) % m;
return a2, b2, c2, d2;
}
int main()
{
int a, b, c, d, k, m, n;
int e, f, g, h;
int e2, f2, g2, h2;
cin >> n;
// a^k = (a^2)^k/2
for (int i = 0; i<n; i++){
cin >> a >> b >> c >> d >> k >> m;
if (k == 1){
cout << a << " " << b << " " << c << " " << d << endl;
}
else if (k == 2){
e = (a*a + c*b) % m;
f = (a*b + b*d) % m;
g = (c*a + d*c) % m;
h = (c*b + d*d) % m;
cout << e << " " << f << " " << g << " " << h << endl;
}
else{
if (k % 2 == 0){
e = (a*a + c*b) % m;
f = (a*b + b*d) % m;
g = (c*a + d*c) % m;
h = (c*b + d*d) % m;
int z = (k/2)-1;
for (int j = 0; j < z; j++){
int e2 = e;
int f2 = f;
int g2 = g;
int h2 = h;
mnoz(e2, f2, g2, h2, m);
}
cout << e << " " << f << " " << g << " " << h << endl;
}
}
}
system("pause");
return 0;
}

Answer 1

To minimize the number of multiplications, you can use a recursive method.
To give an analogy with real numbers, say you want to compute a^n.
Check whether n is even or odd.
If even, compute b = a^(n/2). Then the final result is b*b.
If odd, compute b = a^((n-1)/2. Then the final result is b*b*a.
Since you are talking matrices instead of numbers, you need to be able multiply any two matrices. You can create a class/struct for the matrix and add an operator*() function.
Here's some sample code.
#include <iostream>
struct Matrix
{
Matrix(double pa, double pb, double pc, double pd) : a(pa), b(pb), c(pc), d(pd) {}
Matrix operator*(Matrix const& rhs) const
{
double an = this->a*rhs.a + this->b*rhs.c;
double bn = this->a*rhs.b + this->b*rhs.d;
double cn = this->c*rhs.a + this->d*rhs.c;
double dn = this->c*rhs.b + this->d*rhs.d;
return Matrix(an, bn, cn, dn);
}
Matrix square() const
{
return (*this)*(*this);
}
double a;
double b;
double c;
double d;
};
Matrix matrixPower(Matrix const& m, int k)
{
if ( k == 1 )
{
return m;
}
Matrix out = matrixPower(m, k/2).square();
if ( k%2 == 1 )
{
return out*m;
}
else
{
return out;
}
}
std::ostream& operator<<(std::ostream& out, Matrix const& m)
{
out << "[ " << m.a << " " << m.b << " ]\n";
out << "[ " << m.c << " " << m.d << " ]\n";
}
int main()
{
Matrix m(0.4, 0.7, 0.7, 0.4);
std::cout << matrixPower(m, 5) << std::endl;
std::cout << matrixPower(m, 10) << std::endl;
std::cout << matrixPower(m, 15) << std::endl;
};
The output:
[ 0.80404 0.80647 ]
[ 0.80647 0.80404 ]
[ 1.29687 1.29687 ]
[ 1.29687 1.29687 ]
[ 2.08862 2.08862 ]
[ 2.08862 2.08862 ]