public static IntSquareMatrix I(int n)
{
IntSquareMatrix identity = new IntSquareMatrix(n);
for (int i = 0; i < n; i++)
{
identity[i, i] = 1;
}
return(identity);
}
public static void Main(string[] args)
{
int[,] a = new int [3, 3] {
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 }
};
IntSquareMatrix matrixA = new IntSquareMatrix(a);
Console.WriteLine(BinaryExponentiation(matrixA, 3));
}
public static IntSquareMatrix BinaryExponentiation(IntSquareMatrix a, int n)
{
if (n == 0)
{
return(IntSquareMatrix.I(a.N));
}
IntSquareMatrix half = BinaryExponentiation(a, n >> 1);
IntSquareMatrix full = half * half;
if ((n & 1) == 1)
{
full *= a;
}
return(full);
}
public static IntSquareMatrix operator*(IntSquareMatrix m1, IntSquareMatrix m2)
{
int n = m1.N;
int m = m2.N;
if (n != m)
{
throw new Exception($"Can not multiply {n}x{n} and {m}x{m} martix");
}
IntSquareMatrix result = new IntSquareMatrix(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
result[i, j] += (m1[i, k] * m2[k, j]);
}
}
}
return(result);
}
public IntSquareMatrix(IntSquareMatrix other) : this(other._a)
{
}