================================================================
Solving a Symmetric Positive Definite System of Linear Equations          [TOC]
================================================================

In this example we solve a system of linear equations $Sx = b$ were the
coefficient matrix is symmetric and positiv definite.  We first compute the
Cholesky factorization $S = L L^T$ with __lapack::potrf__ which is the FLENS
port of LAPACK's __dpotrf__.  We then solve $Lu=b$ and then $L^T x = u$ using
__lapack::potrs__ which is the port of __dpotrs__.

:links:  __lapack::potrf__ -> file:flens/lapack/po/potrf.h
         __lapack::potrs__ -> file:flens/lapack/po/potrs.h
         __dpotrf__        -> file:cxxlapack/netlib/lapack/dpotrf.f
         __dpotrs__        -> file:cxxlapack/netlib/lapack/dpotrs.f

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


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


Compile
=======

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


Run
===

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


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

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

Comments on Example Code
------------------------
:import: flens/examples/lapack-complex-potrs.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-potrs                 +++|
 |      lapack-complex-potrs.cc                                             |
 |                                                                          |
 *--------------------------------------------------------------------------*

Run
---

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