# EIG

### From OpenOpt

**Eigenvalue problems (EIG)**- search for :
- (
**A**has to be square matrix)

- (since v. 0.37) OpenOpt
**example**with arpack solver - (since v. 0.38) OpenOpt
**example**with numpy.linalg.eig solver - (since v. 0.37) FuncDesigner
**EIG**example rendered from SLE - (since v. 0.38) FuncDesigner
**EIG**example for EIG from derivatives of several functions, obtained from Automatic differentiation (Future Plans include handling of fixed variables).

**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 |

- 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