public void MatrixPeriodTest()
{
// Period 1 (idempotent) matrix
SquareMatrix A = new SquareMatrix(new double[, ] {
{ 1.0, 1.0 },
{ 0.0, 0.0 }
});
SquareMatrix A2 = A.Power(2);
Assert.IsTrue(TestUtilities.IsNearlyEqual(A2, A));
// Period 2 (self-inverse) matrix
SquareMatrix B = new SquareMatrix(2);
B[0, 0] = 0.0; B[0, 1] = 1.0;
B[1, 0] = 1.0; B[1, 1] = 0.0;
SquareMatrix B3 = B.Power(3);
Assert.IsTrue(TestUtilities.IsNearlyEqual(B3, B));
// Period 3 matrix
// Use the cyclic permutation matrix of order 3
SquareMatrix C = new SquareMatrix(3);
C[0, 1] = 1.0; C[1, 2] = 1.0; C[2, 0] = 1.0;
SquareMatrix C4 = C.Power(4);
Assert.IsTrue(TestUtilities.IsNearlyEqual(C4, C));
}
public void MatrixPowerSpecialCases()
{
SquareMatrix A = CreateSquareRandomMatrix(3);
// Zero power is identity
SquareMatrix A0 = A.Power(0);
// One power is self
SquareMatrix A1 = A.Power(1);
Assert.IsTrue(A == A1);
// Two powers same as multiplying by self
SquareMatrix A2 = A.Power(2);
Assert.IsTrue(TestUtilities.IsNearlyEqual(A2, A * A));
}
