Generalised Eigenvalue Problems

Generalised Eigenvalue Problems

ojAlgo v47.3 was released 2019-08-08. The main new features are:

  • New, long overdue, functionality to help control multithreading
  • Support for (some) Generalised Eigenvalue Problems
  • A bunch of minor changes and improvements. To get a complete list of what’s changed check out the changelog.

Generalised Eigenvalue Problems

ojAlgo now has built-in direct support for (some) generalised eigenvalue problems

$A z = \lambda B z$
$A B z = \lambda z$
$B A z = \lambda z$

where both A and B are symmetric/hermitian and B is positive definite. Each of these problems can be reduced to a standard symmetric eigenvalue problem, using a Cholesky factorisation of B. ojAlgo now handles this for you.

Example Code

Console Output

class GeneralisedEigenvalueProblem
ojAlgo
2019-08-07


Generalised Eigenproblem [A][V] = [B][V][D]
[A]
 1.604074 0.006127 0.133308 0.250127 0.259224
 0.006127 1.010143 0.002238   0.0042 0.004353
 0.133308 0.002238 1.220681 0.091377   0.0947
 0.250127   0.0042 0.091377 1.414067 0.177687
 0.259224 0.004353   0.0947 0.177687 1.429126
[B]
 1.412855 0.107653 0.393856  0.33646 0.313754
 0.107653 1.260753 0.248753 0.212503 0.198162
 0.393856 0.248753 1.953979 0.777454 0.724987
  0.33646 0.212503 0.777454 1.814959 0.619337
 0.313754 0.198162 0.724987 0.619337 1.759961
Eigenvectors - [V]
 -0.666868  0.341593 -0.447915 -0.083526 -0.024999
  0.091459 -0.030955  0.045101 -0.879487  0.195642
  0.509203  0.331432 -0.346537  0.186981  0.408749
 -0.227578 -0.755407 -0.104048  0.109849  0.251976
 -0.266076  0.262438  0.717441  0.100321  0.222165
Eigenvalues - [D]
 1.263856        0        0        0        0
        0 1.075374        0        0        0
        0        0 1.052367        0        0
        0        0        0 0.863366        0
        0        0        0        0 0.452183
Left - [A][V]
 -1.127161  0.471016 -0.604457 -0.060962  0.136204
  0.087327 -0.030464  0.044724 -0.887602  0.200414
  0.486888  0.405867 -0.424187  0.234679  0.540121
 -0.488978 -0.905967 -0.163164  0.165659  0.427706
 -0.544943  0.360632  0.858094  0.155118  0.395354
Right - [B][V][D]
 -1.127161  0.471016 -0.604457 -0.060962  0.136204
  0.087327 -0.030464  0.044724 -0.887602  0.200414
  0.486888  0.405867 -0.424187  0.234679  0.540121
 -0.488978 -0.905967 -0.163164  0.165659  0.427706
 -0.544943  0.360632  0.858094  0.155118  0.395354

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