Exemple #1
0
        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);

            SquareMatrix A = CreateSquareRandomMatrix(4);

            Assert.IsTrue(A.OneNorm() > 0.0);
            Assert.IsTrue(A.InfinityNorm() > 0.0);
            Assert.IsTrue(A.FrobeniusNorm() > 0.0);

            SquareMatrix B = CreateVandermondeMatrix(4);

            Assert.IsTrue(B.OneNorm() > 0.0);
            Assert.IsTrue(B.InfinityNorm() > 0.0);
            Assert.IsTrue(B.FrobeniusNorm() > 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());

            SquareMatrix P = A * B;

            Assert.IsTrue(P.FrobeniusNorm() <= A.FrobeniusNorm() * B.FrobeniusNorm());
            // Frobenium norm is sub-multiplicative
        }
Exemple #2
0
        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());
        }