/// <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>
public static MatrixDefiniteness ComputeDefiniteness(this Matrix matrix)
{
Double[] eigenValues = QRDecomposition.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);
}
}
/// <summary>
/// Computes the eigenvalues of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The array containing the eigenvalues of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Double[] ComputeEigenvalues(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix", "The matrix is null.");
}
Double[] eigenValues = new Double[matrix.NumberOfRows];
QRDecomposition decomposition = new QRDecomposition(matrix);
decomposition.Compute(10);
for (int i = 0; i < matrix.NumberOfRows; ++i)
{
eigenValues[i] = decomposition.QR[i, i];
}
return(eigenValues);
}
/// <summary>
/// Computes the eigenvectors of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The array containing the eigenvectors of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Vector[] ComputeEigenvectors(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix", "The matrix is null.");
}
Vector[] eigenVectors = new Vector[matrix.NumberOfRows];
QRDecomposition decomposition = new QRDecomposition(matrix);
decomposition.Compute(2);
for (int i = 0; i < matrix.NumberOfRows; ++i)
{
eigenVectors[i] = new Vector(matrix.NumberOfColumns);
for (int j = 0; j < matrix.NumberOfColumns; ++j)
{
eigenVectors[i][j] = decomposition.Q[i, j];
}
}
return(eigenVectors);
}
/// <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(QRDecomposition.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(QRDecomposition.ComputeEigenvalues(matrix));
}