/// <summary>
/// Computes the eigenvectors of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="numberOfIterations">The number of iterations.</param>
/// <returns>The collection containing the eigenvectors of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="ArgumentOutOfRangeException">The number of iterations is less than 1.</exception>
public static Vector[] ComputeEigenvectors(Matrix matrix, Int32 numberOfIterations)
{
QRAlgorithm algorithm = new QRAlgorithm(matrix);
algorithm.Compute(numberOfIterations);
return(algorithm.Eigenvectors);
}
/// <summary>
/// Computes the eigenvectors of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The collection containing the eigenvectors of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Vector[] ComputeEigenvectors(Matrix matrix)
{
QRAlgorithm algorithm = new QRAlgorithm(matrix);
algorithm.Compute();
return(algorithm.Eigenvectors);
}
/// <summary>
/// Computes the eigenvalues of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="numberOfIterations">The number of iterations.</param>
/// <returns>The collection containing the eigenvalues of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="ArgumentOutOfRangeException">The number of iterations is less than 1.</exception>
public static Double[] ComputeEigenvalues(Matrix matrix, Int32 numberOfIterations)
{
QRAlgorithm algorithm = new QRAlgorithm(matrix);
algorithm.Compute(numberOfIterations);
return(algorithm.Eigenvalues);
}
/// <summary>
/// Computes the eigenvalues of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The collection containing the eigenvalues of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Double[] ComputeEigenvalues(Matrix matrix)
{
QRAlgorithm algorithm = new QRAlgorithm(matrix);
algorithm.Compute();
return(algorithm.Eigenvalues);
}
/// <summary>
/// Computes the eigenvectors of the matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The eigenvectors of the matrix.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Vector[] Eigenvectors(this Matrix matrix)
{
return(QRAlgorithm.ComputeEigenvectors(matrix));
}
/// <summary>
/// Computes the eigenvalues of the matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The eigenvalues of the matrix.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Double[] Eigenvalues(this Matrix matrix)
{
return(QRAlgorithm.ComputeEigenvalues(matrix));
}
/// <summary>
/// Computes the definiteness of the matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The definiteness of the matrix.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">
/// The matrix is empty.
/// or
/// The matrix is not symmetric.
/// </exception>
public static MatrixDefiniteness Definiteness(this Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException(nameof(matrix));
}
if (matrix.NumberOfRows == 0 && matrix.NumberOfColumns == 0)
{
throw new ArgumentException(NumericsMessages.MatrixIsEmpty, nameof(matrix));
}
if (!IsSymmetric(matrix))
{
throw new ArgumentException(NumericsMessages.MatrixIsNotSymmetric, nameof(matrix));
}
if (matrix.All(value => value == 0))
{
return(MatrixDefiniteness.PositiveSemidefinite);
}
Double[] eigenvalues = QRAlgorithm.ComputeEigenvalues(matrix);
Int32 posValues = 0;
Int32 negValues = 0;
Int32 zeroValues = 0;
for (Int32 index = 0; index < eigenvalues.Length; ++index)
{
if (eigenvalues[index] > 0)
{
posValues++;
}
else if (eigenvalues[index] < 0)
{
negValues++;
}
else
{
zeroValues++;
}
}
if (posValues > 0 && negValues == 0 && zeroValues == 0)
{
return(MatrixDefiniteness.PositiveDefinite);
}
else if (negValues > 0 && posValues == 0 && zeroValues == 0)
{
return(MatrixDefiniteness.NegativeDefinite);
}
else if (posValues > 0 && zeroValues > 0 && negValues == 0)
{
return(MatrixDefiniteness.PositiveSemidefinite);
}
else if (negValues > 0 && zeroValues > 0 && posValues == 0)
{
return(MatrixDefiniteness.NegativeSemiDefinite);
}
else
{
return(MatrixDefiniteness.Indefinite);
}
}
