public void UnitMatrixNorms()
{
UnitMatrix I = UnitMatrix.OfDimension(4);
SquareMatrix A = I.ToSquareMatrix();
Assert.IsTrue(I.OneNorm() == A.OneNorm());
Assert.IsTrue(I.InfinityNorm() == A.InfinityNorm());
Assert.IsTrue(I.FrobeniusNorm() == A.FrobeniusNorm());
Assert.IsTrue(I.MaxNorm() == A.MaxNorm());
}
public void SquareMatrixNorms()
{
SquareMatrix Z = new SquareMatrix(3);
Assert.IsTrue(Z.OneNorm() == 0.0);
Assert.IsTrue(Z.InfinityNorm() == 0.0);
Assert.IsTrue(Z.FrobeniusNorm() == 0.0);
Assert.IsTrue(Z.MaxNorm() == 0.0);
SquareMatrix A = CreateSquareRandomMatrix(4);
Assert.IsTrue(A.OneNorm() > 0.0);
Assert.IsTrue(A.InfinityNorm() > 0.0);
Assert.IsTrue(A.FrobeniusNorm() > 0.0);
Assert.IsTrue(A.MaxNorm() > 0.0);
SquareMatrix B = CreateVandermondeMatrix(4);
Assert.IsTrue(B.OneNorm() > 0.0);
Assert.IsTrue(B.InfinityNorm() > 0.0);
Assert.IsTrue(B.FrobeniusNorm() > 0.0);
Assert.IsTrue(B.MaxNorm() > 0.0);
SquareMatrix S = A + B;
Assert.IsTrue(S.OneNorm() <= A.OneNorm() + B.OneNorm());
Assert.IsTrue(S.InfinityNorm() <= A.InfinityNorm() + B.InfinityNorm());
Assert.IsTrue(S.FrobeniusNorm() <= A.FrobeniusNorm() + B.FrobeniusNorm());
Assert.IsTrue(S.MaxNorm() <= A.MaxNorm() + B.MaxNorm());
double t = -1.5;
SquareMatrix M = t * A;
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.OneNorm(), Math.Abs(t) * A.OneNorm()));
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.InfinityNorm(), Math.Abs(t) * A.InfinityNorm()));
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.FrobeniusNorm(), Math.Abs(t) * A.FrobeniusNorm()));
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.MaxNorm(), Math.Abs(t) * A.MaxNorm()));
// Frobenius norm is sub-multiplicative
SquareMatrix P = A * B;
Assert.IsTrue(P.FrobeniusNorm() <= A.FrobeniusNorm() * B.FrobeniusNorm());
}