/// <summary>
/// Calculates the eigenvalues and optionally the eigenvectors of a symmetric matrix. Does not check if the matrix is
/// symmetric.
/// </summary>
/// <param name="order">The number of rows/columns of the original symmetric matrix.</param>
/// <param name="matrix">
/// The original matrix in full column major format. Will be overwritten.
/// </param>
/// <param name="calcEigenvectors">
/// If true, both eigenvalues and eigenvectors will be computed. Else only eigenvalues will be computed.
/// </param>
/// <returns>An object holding the eigensystem of the matrix.</returns>
public static SymmetricEigensystemFull Create(int order, double[] matrix, bool calcEigenvectors)
{
EigensystemJob job = calcEigenvectors ? EigensystemJob.EigenvaluesAndEigenVectors : EigensystemJob.OnlyEigenvalues;
int leadingDimA = order;
var eigenvalues = new double[order]; // symmetric matrices have as many eigenvalues as their size
LapackEigensystems.Dsyev(job, StoredTriangle.Upper, order, matrix, 0, leadingDimA, eigenvalues, 0);
if (calcEigenvectors)
{
// The original matrix is overwritten by the eigenvectors
var eigenvectors = Matrix.CreateFromArray(matrix, order, order);
return(new SymmetricEigensystemFull(order, Vector.CreateFromArray(eigenvalues), eigenvectors));
}
else
{
return(new SymmetricEigensystemFull(order, Vector.CreateFromArray(eigenvalues), null));
}
}
/// <summary>
/// Calculates the eigenvalues and optionally the left and right eigenvectors of a square matrix. Does not check if the
/// matrix is square.
/// </summary>
/// <param name="order">The number of rows/columns of the original square matrix.</param>
/// <param name="matrix">
/// The original matrix in full column major format. Will be overwritten.
/// </param>
/// <param name="calcLeftEigenvectors">
/// If true, left eigenvectors will be computed, in addition to eigenvalues and possibly right eigenvectors.
/// Else left eigenvectors will not be computed.
/// </param>
/// <param name="calcRightEigenvectors">
/// If true, right eigenvectors will be computed, in addition to eigenvalues and possibly left eigenvectors.
/// Else right eigenvectors will not be computed.
/// </param>
/// <returns>An object holding the eigensystem of the matrix.</returns>
public static NonSymmetricEigensystemFull Create(
int order, double[] matrix, bool calcLeftEigenvectors, bool calcRightEigenvectors)
{
// Prepare LAPACK input
int leadingDimA = order;
// There as many eigenvalues as the order of the matrix, but some the complex eigenvalues come in conjugate pairs.
var eigenvaluesReal = new double[order];
var eigenvaluesImaginary = new double[order];
EigensystemJob jobLeft;
double[] eigenvectorsLeft;
int leadingDimEigenvectorsLeft;
if (calcLeftEigenvectors)
{
jobLeft = EigensystemJob.EigenvaluesAndEigenVectors;
eigenvectorsLeft = new double[order * order];
leadingDimEigenvectorsLeft = order;
}
else
{
jobLeft = EigensystemJob.OnlyEigenvalues;
eigenvectorsLeft = new double[1];
leadingDimEigenvectorsLeft = 1;
}
EigensystemJob jobRight;
double[] eigenvectorsRight;
int leadingDimEigenvectorsRight;
if (calcRightEigenvectors)
{
jobRight = EigensystemJob.EigenvaluesAndEigenVectors;
eigenvectorsRight = new double[order * order];
leadingDimEigenvectorsRight = order;
}
else
{
jobRight = EigensystemJob.OnlyEigenvalues;
eigenvectorsRight = new double[1];
leadingDimEigenvectorsRight = 1;
}
// Call Lapack
LapackEigensystems.Dgeev(jobLeft, jobRight, order, matrix, 0, leadingDimA,
eigenvaluesReal, 0, eigenvaluesImaginary, 0,
eigenvectorsLeft, 0, leadingDimEigenvectorsLeft,
eigenvectorsRight, 0, leadingDimEigenvectorsRight);
// Repack LAPACK output into usable classes
if (!calcLeftEigenvectors)
{
eigenvectorsLeft = null;
}
if (!calcRightEigenvectors)
{
eigenvectorsRight = null;
}
return(new NonSymmetricEigensystemFull(
order, eigenvaluesReal, eigenvaluesImaginary, eigenvectorsLeft, eigenvectorsRight));
}