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);
}