=======================================
Overloaded Operators VS. Function Calls                                  [TOC]
=======================================

There are two aspects:
 - Overloaded operators provide an expressive notation for mathematical
   operations.
 - Function calls have the advantage that you exactly know what is going on
   and how the computation gets done.

In FLENS overloaded operators just provide a convenient notation for BLAS.  But
both are equivalent.  We first show an implementation of the conjugated gradient
method that uses overloaded operators.  Then we show an implementation that
calls the BLAS functions directly.

Using the __previously__ introduced debug mode you can check yourself that
both implementations are doing exactly the same.  It's basically a matter of
taste and background what variant is more favorable for you.


Conjugated Gradient Method with Overloaded Operators
====================================================
The following implementation is almost identical to the pseudo-code of the
algorithm.

  :import: flens/examples/cg.h [downloadable, stripped]


Conjugated Gradient Method with Explicit Function Calls
=======================================================
This is the same algorithm but we call the BLAS functions explicitly:

  :import: flens/examples/cg_blas.h [downloadable, stripped]

Let's check the equivalence of overloaded operation notation and explicit
function calls step-by-step:

  :import: flens/examples/cg_blas.h [brief]


Test Example
============
:import: flens/examples/symatrix-cg.cc [downloadable, stripped]


Compile and Run
===============
Just to check, we use both variants of the cg-method:

 - Using the variant with overloaded operators:

   *--[SHELL]---------------------------------------------------------------*
   |                                                                        |
   |  cd flens/examples                                                     |
   |  g++ -Wall -std=c++11 -I../.. symatrix-cg.cc                           |
   |  ./a.out                                                               |
   |                                                                        |
   *------------------------------------------------------------------------*

 - Using the variant with explicit function calls:

   *--[SHELL]---------------------------------------------------------------*
   |                                                                        |
   |  cd flens/examples                                                     |
   |  g++ -Wall -std=c++11 -DUSE_CG_BLAS -I../.. symatrix-cg.cc             |
   |  ./a.out                                                               |
   |                                                                        |
   *------------------------------------------------------------------------*


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