===============
Applying Pivots                                                         [TOC]
===============

In general the LU factorization requires pivoting.  The pivot vector

---- LATEX ---------------------------------------------------------------------
p = (p_0, \dots, p_k)
--------------------------------------------------------------------------------

represents a $k \times k$ permutation matrix $P$ such that

---- LATEX ---------------------------------------------------------------------
P A = L U
--------------------------------------------------------------------------------

In this exercise you are supposed to implement a function `dlaswp` to apply $P$
and $P^{-1}$ to a matrix $A$:

- perform the operation $B \leftarrow P A$ or
- the operation $B \leftarrow P^{-1}A$.

Furthermore the function should be implemented such that only a sub-range of $p$
is used.  This depends on two integer bounds $k_0$ and $k_1$:

- if $k_0 < k_1$ it applies the permutation represented by
  $p_{k_0},\dots,p_{k_1}$ and
- otherwise the permutation represented by $p_{k_1},\dots,p_{k_0}$.

Algorithm
=========
The function receives a matrix $A$ with $n$ columns, a pivot vector $p$ and
the two indices $k_0$ and $k_1$.  The number of rows in $A$ and the length of
$p$ are not explicitly specified.

The function implements the following algorithm:

- for $k = k_0, \dots, k_1$
    - if $k \neq p_k$
        - interchange in $A$ rows with index $k$ and $p_k$

Skeleton for simple Example
===========================
:import: session13/simple_dlaswp_ex.c [fold]

Exercise
========

- Make yourself familiar with the structure of the program.  Compile and run it:

  - For testing the *col major case* compile it with

    ---- SHELL(path=session13) -------------------------------------------------
    gcc -Wall -std=c11 -o simple_dlaswp_ex simple_dlaswp_ex.c
    ----------------------------------------------------------------------------

  - For testing the *row major case* compile it with

    ---- SHELL(path=session13) -------------------------------------------------
    gcc -Wall -std=c11 -o simple_dlaswp_ex -DCOLMAJOR=0 simple_dlaswp_ex.c
    ----------------------------------------------------------------------------

- What should the program print once function `dlaswp` is implemented?
- Implement function `dlaswp` and test it.