internal void Dgeev(EigensystemJob jobLeft, EigensystemJob jobRight, int orderA,
double[] matrixA, int offsetA, int leadingDimA,
double[] eigvaluesReal, int offsetEigvaluesReal, double[] eigvaluesImaginary, int offsetEigvaluesImaginary,
double[] eigvectorsLeft, int offsetEigvectorsLeft, int leadingDimEigvectorsLeft,
double[] eigvectorsRight, int offsetEigvectorsRight, int leadingDimEigvectorsRight)
{
int info = DefaultInfo;
QueryWorkspaceAndExecute((work, offsetWork, lWork) => Provider.Dgeev(jobLeft.Translate(), jobRight.Translate(),
orderA, ref matrixA, offsetA, leadingDimA,
ref eigvaluesReal, offsetEigvaluesReal, ref eigvaluesImaginary, offsetEigvaluesImaginary,
ref eigvectorsLeft, offsetEigvectorsLeft, leadingDimEigvectorsLeft,
ref eigvectorsRight, offsetEigvectorsRight, leadingDimEigvectorsRight,
ref work, offsetWork, lWork, ref info));
if (info > 0)
{
throw new LapackException($"The QR algorithm failed to compute all the eigenvalues, and no eigenvectors have "
+ $"been computed. Elements {info+1:N} of the eigenvalues arrays (real and imaginary) contain eigenvalues which"
+ "have converged");
}
else if (info < 0)
{
ProcessNegativeInfo(info);
}
}
/// <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));
}
}
internal void Dsyev(EigensystemJob job, StoredTriangle triangle, int orderA, double[] matrixA, int offsetA,
int leadingDimA, double[] eigenvalues, int offsetEigenvalues)
{
int info = DefaultInfo;
QueryWorkspaceAndExecute((work, offsetWork, lWork) => Provider.Dsyev(
job.Translate(), triangle.Translate(), orderA, ref matrixA, offsetA, leadingDimA, ref eigenvalues,
offsetEigenvalues, ref work, offsetWork, lWork, ref info));
if (info > 0)
{
throw new LapackException($"The algorithm failed to converge. There were {info} elements of an intermediate"
+ " tridiagonal form which did not converge to zero");
}
else if (info < 0)
{
ProcessNegativeInfo(info);
}
}
internal static string Translate(this EigensystemJob job) => (job == EigensystemJob.OnlyEigenvalues) ? "N" : "V";
