====================================
Add remaining functions to ulmblas.c                                     [TOC]
====================================

There are still some functions declared in `ulmblas.h` that are currently not
defined in `ulmblas.c`.  These are `dcopy` and `dgemv`.  Furthermore, function
`dlaswp` is neither declared nor defined in `ulmblas.h` and `ulmblas.c`.  This
is supposed to be done now.

Exercise
========

- Add in `ulmblas.c` an implementation for `dgemv`.  You already have
  implemented in Session 11 functions `dgemv_dotf` and `dgemv_axpyf`.  Use
  these two implementations as building blocks as follows:

  - If $A$ is stored row major function `dgemv` calls `dgemv_dotf` and
  - if $A$ is stored col major function `dgemv` calls `dgemv_axpyf`.


Test for gemv
-------------
Use the test program `test_dgemv.c`.  Compile it with

---- SHELL (path=session13, hide) ----------------------------------------------
rm -rf gemv
mkdir gemv
cd gemv
cp /home/numerik/pub/hpc/ss18/ulmblas/*.[hc] .
cp /home/numerik/pub/hpc/ss18/ulmblas/session13b/ulmblas.* .
--------------------------------------------------------------------------------

---- SHELL (path=session13/gemv, hostname=heim) --------------------------------
gcc -Wall -std=c11 -I. -O3 -o test_dgemv test_dgemv.c ulmaux.c ulmblas.c
--------------------------------------------------------------------------------

First, check that your implementation is correct:

---- SHELL (path=session13/gemv, hostname=heim,fold) ---------------------------
./test_dgemv check
--------------------------------------------------------------------------------

Then run benchmarks to see that performance for row and col major cases are
comparable:

- Benchmark for row major case:

  ---- SHELL (path=session13/gemv, hostname=heim) ------------------------------
  ./test_dgemv bench rowmajor
  ------------------------------------------------------------------------------

- Benchmark for col major case:

  ---- SHELL (path=session13/gemv, hostname=heim) ------------------------------
  ./test_dgemv bench colmajor
  ------------------------------------------------------------------------------

Example for solving a system of linear equations
------------------------------------------------
Use the following simple program to solve a system of linear equations:

:import: session13/simple_solve.c