/// <summary>
///Computes all the eigenvalues and eigenvectors of
/// a real symmetric band matrix A.
/// </summary>
/// <param name="A">The real symmetric band matrix A.</param>
/// <param name="EigenVects">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricBandMatrix A, out Matrix EigenVects)
{
if (this._dsbev == null) this._dsbev = new DSBEV();
this.CheckDimensions(A);
Matrix SymmetricBand = A.GetSymmetricBandPackedMatrix();
double[] SymmetricBandData = SymmetricBand.Data;
EigenVects = new Matrix(A.RowCount, A.ColumnCount);
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[3 * A.RowCount - 2];
_dsbev.Run("V", "U", A.RowCount, A.UpperBandWidth, ref SymmetricBandData, 0, SymmetricBand.RowCount, ref EigenValsData, 0, ref EigenVectsData, 0, A.RowCount, ref Work, 0, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
private void lapackeigsys(int numevals, int num, double[] a,
bool packed, bool upper,
double[] lowevals, double[] lowevecs)
{
// The inputs
char jobz = 'V'; // Compute eigenvalues and eigenvectors
char range = 'I'; // the IL-th through IU-th eigenvalues will be found.
char uplo = (upper ? 'U' : 'L');
// If not packed, then it makes no difference if up or down.
int n = num; // The order of the matrix A. N >= 0.
int lda = num; // The leading dimension of the array A.
// This is not needed for packed, since packed is really a vector, so no LDA
double vl = 0.0; // Not referenced if RANGE = 'A' or 'I'.
double vu = 0.0; // Not referenced if RANGE = 'A' or 'I'.
int il = 1; // lowest eigenvalue thru the
int iu = numevals; // numevals eigenvalues are found.
/* indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; */
char slamchchar = 'S';
double abstol = 2 * Double.Epsilon; // 2 * slamch_(&slamchchar);
/* The absolute error tolerance for the eigenvalues.
ABSTOL + EPS * max( |a|,|b| ) ,
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero. */
int ldz = num; // The leading dimension of the array
int lwork = 8 * num; // The length of the arr WORK. LWORK >= max(1,8*N).
// This is not needed for packed, since it assumes LWORK = 8*N
// now the outputs
int m;
/* Output: The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
double[] w = new double[num]; // malloc(sizeof(double)*num);
/* (output) On normal exit, the first M elements contain the selected
eigenvalues in ascending order. However, we must allocate extra space?*/
// double *z = new double[num*numevals];
// This is what we use lowevecs for. Not so for W, since that has
// num elements, not numevals. We have to copy over those values.
/* (output) If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i). */
double[] work = new double[lwork];
// On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
int[] iwork = new int[5 * num]; // dimension (5*N)
int[] ifail = new int[num];
/* If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge. */
int info = 0;
/* = 0: successful exit
< 0: if INFO = -i, i-th argument had illegal value
> 0: if INFO = i, i eigenvectors failed to converge
Their indices are stored in array IFAIL. */
// Compute! -- LAPACK driver routine (version 2.0) -- September 30, 1994
if (packed)
{
DotNumerics.LinearAlgebra.CSLapack.DSBEV dsbev_ = new DotNumerics.LinearAlgebra.CSLapack.DSBEV();
dspevx_(jobz, range, uplo, n,
a, /*-*/ vl, vu, il, iu, abstol, m, w,
lowevecs, ldz, work, /*---*/ iwork, ifail, info);
// dspevx_.Run(jobz, "",
}
else
dsyevx_(jobz, range, uplo, n,
a, lda, vl, vu, il, iu, abstol, m, w,
lowevecs, ldz, work, lwork, iwork, ifail, info);
// Done!
if (info != 0)
{
string err = "Errors in lapackeigsys with " + (packed ? "sspevx_" : "ssyevx_") + "!!! info: " + info + "\n";
if (info < 0)
{
err += "The " + info + "'th argument had an illegal value!\n";
}
else
{
err += info + " eigenvectors failed to converge! They were:\n";
for (int i = 0; i < num; i++)
{
if (ifail[i] != 0)
{
err += "Index number:" + ifail[i] + "\n";
}
}
}
throw new InvalidOperationException(err);
}
// We didn't use lowevals as the input for the routine
// since it expects num elements in lowevals, instead of numevals.
for (int i = 0; i < numevals; i++) lowevals[i] = w[i];
}