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

We will implement the following BLAS Level 1 operations:

- Function `dcopy`

  Copying vectors denoted mathematically as $x \to y$.

- Function `daxpy`

  Scaled vector update denoted mathematically as $\alpha x + y \to y$. Hence,
  `axpy` for alpha x plus y.

- Function `ddot`

  Computing the dot product of two vector, i.e. $x^T \cdot y$.

- Function `dscal`

  - If $\alpha \neq 0$ it computed the scaled vector $x \leftarrow \alpha x$.
  - If $\alpha = 0$ it overwrites $x$ with zeros, i.e. $x \leftarrow
    \mathcal{0}$.

  Note that these cases need to be handled separately because in the case
  $\alpha=0$ vector $x$ is allowed to contain *Not-a-Number (NaN)* values.

  If a matrix has NaN entries and $\alpha \neq 0$ the result of scal is
  allowed to be undefined.


Exercise: BLAS Level 1
======================

- The signature of function `dcopy` is given:

  - Add the implementation
  - Fix the function call to match the operation indicated by the preceding
    printf statement

- How function `daxpy` is supposed to be used is given in `main`:

  - Derive a proper declaration for the function and
  - implement the function.

- For function `ddot` we give fewer hints.  Specify a signature that indicates:

  - The function expects two vectors of same length.
  - The vectors are not modified by the function.
  - The function returns the result.

  Then implement the function and use it in `main`.

- For function `dscal` we provide a skeleton:

  - In case $\alpha=1$ the function makes a _quick return_.
  - Implement the cases for

    - $\alpha \neq 1$ and \alpha \neq 0$
    - $\alpha \neq 1$ and \alpha = 0$

  Note that `main` contains a test where NaNs are inserted through function
  `nan` (declared in `math.h`).

:import: session10/matvec_02_ex.c