public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Values(1, 2, 5, 10, 50, 100)] int order) { var A = Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1); MatrixHelpers.ForceHermitian(A); var ACopy = A.Clone(); var evd = A.Evd(Symmetricity.Hermitian); var B = Matrix <Complex32> .Build.Random(order, order, 2); var BCopy = B.Clone(); var X = new DenseMatrix(order, order); evd.Solve(B, X); // The solution X row dimension is equal to the column dimension of A Assert.AreEqual(A.ColumnCount, X.RowCount); // The solution X has the same number of columns as B Assert.AreEqual(B.ColumnCount, X.ColumnCount); var BReconstruct = A * X; // Check the reconstruction. AssertHelpers.AlmostEqual(B, BReconstruct, 1); // Make sure A/B didn't change. AssertHelpers.AlmostEqual(ACopy, A, 14); AssertHelpers.AlmostEqual(BCopy, B, 14); }
public void CanSolveForRandomVectorAndSymmetricMatrixWhenResultVectorGiven([Values(1, 2, 5, 10, 50, 100)] int order) { var A = Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1); MatrixHelpers.ForceHermitian(A); var ACopy = A.Clone(); var evd = A.Evd(Symmetricity.Hermitian); var b = Vector <Complex32> .Build.Random(order, 2); var bCopy = b.Clone(); var x = new DenseVector(order); evd.Solve(b, x); var bReconstruct = A * x; // Check the reconstruction. AssertHelpers.AlmostEqual(b, bReconstruct, 2); // Make sure A/B didn't change. AssertHelpers.AlmostEqual(ACopy, A, 14); AssertHelpers.AlmostEqual(bCopy, b, 14); }
public void CanFactorizeRandomSymmetricMatrix([Values(1, 2, 5, 10, 50, 100)] int order) { var A = Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1); MatrixHelpers.ForceHermitian(A); var factorEvd = A.Evd(Symmetricity.Hermitian); var V = factorEvd.EigenVectors; var λ = factorEvd.D; Assert.AreEqual(order, V.RowCount); Assert.AreEqual(order, V.ColumnCount); Assert.AreEqual(order, λ.RowCount); Assert.AreEqual(order, λ.ColumnCount); // Verify A = V*λ*VT var matrix = V * λ * V.ConjugateTranspose(); AssertHelpers.AlmostEqual(matrix, A, 3); AssertHelpers.AlmostEqualRelative(matrix, A, 1); }
public void CanSolveForRandomVectorAndSymmetricMatrix([Values(1, 2, 5, 10, 50, 100)] int order) { var A = new UserDefinedMatrix(Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1).ToArray()); MatrixHelpers.ForceHermitian(A); var ACopy = A.Clone(); var evd = A.Evd(); var b = new UserDefinedVector(Vector <Complex32> .Build.Random(order, 1).ToArray()); var bCopy = b.Clone(); var x = evd.Solve(b); var bReconstruct = A * x; // Check the reconstruction. AssertHelpers.AlmostEqual(b, bReconstruct, 2); // Make sure A/B didn't change. AssertHelpers.AlmostEqual(ACopy, A, 14); AssertHelpers.AlmostEqual(bCopy, b, 14); }