EIG

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Eigenvalue problems (EIG)
search for \mathbf{ \lambda \in C, x \in C^n}:
\mathbf{A x = \lambda x}
(A has to be square matrix)


EIG solvers connected to OpenOpt:

Solver License Made by Info
arpack BSD Rich Lehoucq, Kristi Maschhoff, Danny Sorensen, Chao Yang Probably most powerful eigenvalue problems solver for nowadays. You should have SciPy installed. Can handle sparse problems (untested in OpenOpt properly yet). There is parallel arpack implementation, but you should check by yourself is your SciPy built (compiled and linked) with serial or parallel one.
numpy_eig BSD G. Strang uses numpy.linalg.eig, that is wrapper around LAPACK routines dgeev and zgeev

ARPACK goals
As you can see in the arpack examples, you should set goal and number of required eigenvalues/vectors, e.g p = EIG(...,goal={'lm':4}). Goal names can be short or full, case-insensitive, with or without spaces inside. Table of available goals:

Short Full
LM largest magnitude
SM smallest magnitude
LR largest real part
SR smallest real part
LI largest imaginary part
SI smallest imaginary part
LA largest amplitude
SA smallest amplitude
BE both ends of the spectrum

Future plans:

  • eigenvalue solvers from NumPy and SciPy (that are mostly LAPACK routines)
  • eigenvalue analysis for general FuncDesigner derivatives obtained from Automatic differentiation, for example, for ODE

See also:

  • Eigenvalues and eigenvectors wikipedia.org entry
Retrieved from "http://openopt.org/EIG"
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