===========================================================
Compute the Inverse of a Symmetric Positive Definite Matrix               [TOC]
===========================================================

In this example we compute the inverse $S^{-1}$ of a symmetric positive
definite matrix $S$.  We first compute the Cholesky factoriation $S=L L^T$.
The inverse $S^{-1}$ then gets computed by __lapack::potri__ which is the
FLENS port of LAPACK's __dpotri__.

:links:  __lapack::potri__  -> file:flens/lapack/po/potri.h
         __dpotri__         -> file:cxxlapack/netlib/lapack/dpotri.f


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


Comments on Example Code
========================
:import: flens/examples/lapack-potri.cc [brief]


Compile
=======

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


Run
===

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


Example with Complex Numbers
============================

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

Comments on Example Code
------------------------
:import: flens/examples/lapack-complex-potri.cc

Compile
-------
Note that an external LAPACK implementation is needed for the complex variant
of `lapack::potrs`

 *--[SHELL]-----------------------------------------------------------------*
 |                                                                          |
 |  cd flens/examples                                                       |
 |  g++ -DUSE_CXXLAPACK -framework vecLib                                +++|
 |      -std=c++11 -Wall -I../.. -o lapack-complex-potri                 +++|
 |      lapack-complex-potri.cc                                             |
 |                                                                          |
 *--------------------------------------------------------------------------*

Run
---

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