==================================
Eigenvalues (Non-Symmetric Matrix)                                      [TOC]
==================================

In this example we compute the eigenvalues $w \in \mathbb{C}$, left eigenvectors
$V_L$ and right eigenvectors $V_R$ of a non-symmetric Matrix $A$.

We use __lapack::ev__ which is the FLENS port of LAPACK's __dgeev__.

:links:  __lapack::ev__  -> file:flens/lapack/ge/ev.h
         __dgeev__       -> file:cxxlapack/netlib/lapack/dgeev.f


Example Code
============
:import: flens/examples/lapack-geev.cc [stripped, downloadable]

Comments on Example Code
========================
:import: flens/examples/lapack-geev.cc

Compile
=======

  *--[SHELL]----------------------------------------------------------------*
  |                                                                         |
  |  cd flens/examples                                                      |
  |  g++ -std=c++11 -Wall -I../.. -o lapack-geev lapack-geev.cc             |
  |                                                                         |
  *-------------------------------------------------------------------------*


Run
===

  *--[SHELL]----------------------------------------------------------------*
  |                                                                         |
  |  cd flens/examples                                                      |
  |  ./lapack-geev                                                          |
  |                                                                         |
  *-------------------------------------------------------------------------*


Using QD (Double-Double and Quad-Double Package)
================================================
The following description is taken from the __QD Library__ page:

  *--[BOX]------------------------------------------------------------------*
  |                                                                         |
  | The __QD Library__ supports both a double-double datatype (approx. 32   |
  | decimal digits) and a quad-double datatype (approx. 64 decimal digits). |
  | The computational library is written in C++. Both C++ and Fortran-90    |
  | high-level language interfaces are provided to permit one to use convert|
  | an existing C++ or Fortran-90 program to use the library with only minor|
  | changes to the source code. In most cases only a few type statements and|
  | (for Fortran-90 programs) read/write statements need to be changed. PSLQ|
  | and numerical quadrature programs are included.                         |
  |                                                                         |
  *-------------------------------------------------------------------------*

:links: __QD Library__ -> http://crd-legacy.lbl.gov/~dhbailey/mpdist/


Modified Example Code
---------------------
:import: flens/examples/qd-lapack-geev.cc [stripped, downloadable]

Comments on Modifications
-------------------------
Only a few modifications were made which will be pointed out in the following:

:import: flens/examples/qd-lapack-geev.cc  [brief]

Compile and Run
---------------

  *--[SHELL]-----------------------------------------------------------------*
  |                                                                          |
  |  cd flens/examples                                                       |
  |  g++ -Wall -std=c++11 -I../.. -I/opt/local/include/ -c qd-lapack-geev.cc |
  |  g++ -o qd-lapack-geev qd-lapack-geev.o /opt/local/lib/libqd.a           |
  |  ./qd-lapack-geev                                                        |
  |                                                                          |
  *--------------------------------------------------------------------------*


Using mpfr::real (C++ Interface for mpfr)
=========================================
The following description is taken from the __mpfr::real__ page:

  *--[BOX]------------------------------------------------------------------*
  |                                                                         |
  | The class __mpfr::real__ is a high-level C++ wrapper for the            |
  | __GNU MPFR library__, _a C library for multiple-precision floating-point|
  | computations with correct rounding_.                                    |
  |                                                                         |
  | The objects of `mpfr::real` can (almost) be used like doubles or other  |
  | fundamental floating-point types, thus avoiding the use of C functions  |
  | to manipulate `MPFR`'s low-level data type directly. In addition to     |
  | all arithmetic and comparison operators available for fundamental       |
  | floating-point types, `mpfr::real` also supports the set of             |
  | mathematical functions for `double` from `math.h/cmath`.  Finally,      |
  | `std::istream operator >>` and `std::ostream operator <<` are           |
  | implemented for `mpfr::reals`. This allows to substitute `double` with  |
  | `mpfr::real` with no further modifications of the code in many cases.   |
  |                                                                         |
  *-------------------------------------------------------------------------*

:links:  __mpfr::real__        ->  http://chschneider.eu/programming/mpfr_real/
         __GNU MPFR library__  ->  http://www.mpfr.org/

Modified Example Code
---------------------
:import: flens/examples/mpfr-real-lapack-geev.cc [stripped, downloadable]

Comments on Modifications
-------------------------
:import: flens/examples/mpfr-real-lapack-geev.cc  [brief]

Compile and Run
---------------

  *--[SHELL]----------------------------------------------------------------*
  |                                                                         |
  |  cd flens/examples                                                      |
  |  g++ -Wall -std=c++11 -I../.. -I/opt/local/include                   +++|
  |       -o mpfr-real-lapack-geev mpfr-real-lapack-geev.cc              +++|
  |       -L /opt/local/lib -lmpfr -lgmp                                    |
  |  ./mpfr-real-lapack-geev                                                |
  |                                                                         |
  *-------------------------------------------------------------------------*

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