===== Lab 01 : Introduction / MATLAB =====

Topics:
  * Lab organization, assessment requirements
  * Homework assignment, upload, written report good practice
  * MATLAB introduction
  
==== HW01 Assignment ====

For the homework, HW01  follow the emphasized links to get to the detailed description.

  * **[5 pts]** - [[#(A) MATLAB Introduction]], go through a tutorial, if needed and complete the three tasks specified in the detailed description.
 

Upload your report in PDF format to [[https://cw.felk.cvut.cz/brute/student/course/962|BRUTE]] to the assignment ''L01-Matlab introduction''. Please name the PDF file as ''hw02_<your_fel_id>.pdf''. Zip both the MATLAB code and pdf report in a single file and upload to Brute.

==== MATLAB Introduction ====

Please make yourself familiar with MATLAB commands, use one of the available [[https://www.google.com/search?q=matlab+command+tutorial|tutorials]]. You can also work with Python, consider using the packages [[www.scipy.org|scipy]] and [[https://matplotlib.org|matplotlib]].


**Homework tasks(2.5 points each)**

 Create a 1D signal of the function $y = -3 \cdot x + 1$ over the range [0, 5] with step 0.1. Add uniformly or normally distributed noise within the range [-1, 1] to the signal. Plot the signal as blue circles. Plot also the original line without noise. 
  *  Use //linear least squares// to fit a line to the noisy observations. The MATLAB function is //mldivide//. If we have a system of type $XA = Y $, where $A$ has size $2\times 1 $ contains the line coefficients [slope; intercept] (to be evaluated) and $X$ has size $51\times2$, the with first columns correspond to $x \in [0, 5]$  (51 values) and second column with intercepts 1, $Y$ has size $51\times1$ containing noisy $y$ values. The solution to the fit is $A = X \backslash Y$. Add a plot of the fitted line to the figure, show its coefficients in the title (//sprintf//). The resulting figure will look like the following and you can compare your results with the displayed (they should be similar if not the same)
  {{:courses:zsl:matlab1.jpg}}

  * Plot a 2D surface of some function, for example
    * $z = \frac{\sin(\sqrt(x^2 + y^2))}{\sqrt(x^2 + y^2))}$ for $x, y \in (-15, 15)$.
    * $z = \sin(5*x) + \cos(4*y)$ for $x, y \in (-3, 3)$.
    * function of your own choice

Use appropriate spacing of the grid to get a nicely-looking plot, like in the example below:

{{:courses:zsl:cv1_3dplot.png?600|}}


**Hints**
To add multiple plots to a single figure, use ''hold on''. To then have legend for each of the single plots, get the handle for each(the return values ''ps'' and ''po'') and specify the legend manually, as shown in the following snippet: <code matlab>
figure;
ps = scatter(xc, Y, 'b+');
hold on;
po = plot(xc, A * x, 'b');
legend([ps, po], {'Noisy data','Original'});
</code>