===========================
Some BLAS Level 1 functions                                             [TOC]
===========================

BLAS Level 1 functions operate on vectors.  In practical cases these
vectors are often rows or columns of a matrix.  Hence, it is important
to recall that in memory the vector elements are separated from each
other by a constant increment that can be larger than one.

Skeleton for the exercises
==========================

You can use the following skeleton to solve the exercises below step by step:

:import: session03/blas1_example.c

---- SHELL (path=session03) ---------------------------
gcc -Wall -std=c99 -o blas1_example blas1_example.c
./blas1_example
-------------------------------------------------------


Exercise: One-Norm of a vector `dnrm1`
======================================

Write a function `dnrm1` that computes and returns

---- LATEX -------------------------------------------------
\alpha = \| x \|_1
       = \left\| \left(\begin{array}{c}
                  x_1 \\ \vdots \\ x_n
                  \end{array}\right)
        \right\|_1
       = |x_1| + \dots + |x_n|
------------------------------------------------------------

Adjust the previous test program such that it computes the one-norm

- of the second row (i.e. row with index one),
- the third column (i.e. column with index two),
- the diagonal.


Exercise: Swap vectors `dswap`
==============================

Write a function `dswap` that swaps (i.e. exchanges) the elements of
two vectors.

Extend the test program, such that it

- swaps the second and third row,
- swaps the second and third column.

Exercise: Adding a scaled vector `daxpy`
========================================

The so called axpy-operation (alpha x plus y) computes

---- LATEX -------------------------------------------------
y \leftarrow \alpha x + y
------------------------------------------------------------

Implement a function `daxpy` for this operation.  Test it by

- adding 3 times the second column to the third column,
- subtracting 2.5 times the second row from the 4th row.


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