%% Lesson 5a: Plotting
%
% We are going to go through several plotting schemes, and explore how you
% can customize plotting. We would go through 2D plotting, surface
% plotting, subplot, stem plot and 3D plotting
%
% In this file the `command syntax` style of functions will be used when
% possible, just to get you familiar with the style.
clear; clc; close all;

%% 2D plotting: line graphs
% In general, always annotate your plots appropriately! Use a title,
% axis labels, legends, etc. as necessary. Set appropriate bounds,
% appropriate scaling (e.g., linear vs. logarithmic), and the correct
% type of plot. We'll start simple with line plots.
x = -10:0.1:10;
y = x.^3;
y2 = x.^2;

hold on;    % plotting more than 1 plot on 1 figure rather than overwriting

plot(x, y, 'DisplayName', 'x^3');
plot(x, y2, 'DisplayName', 'x^2');

hold off;

xlabel 'x axis';
ylabel 'y axis';
title 'Example 1';
xlim([-10 10]);
ylim([-10 10]);
% axis([-10 10 -10 10]);
grid on;
legend show;                             % 'DisplayName does this

%% Example 2: Plotting sine and cosine
t = 0:.1:10;
d1 = sin(t);
d2 = cos(t);

figure;

% plot(t, [d1.' d2.']);
% plot(t, d1, t, d2);

hold on;
plot(t, d1);
plot(t, d2);
hold off;

title 'Trig Functions';

% We can use some LaTeX-like symbols like \mu, \beta, \pi, \leq, \infty.
% For full LaTeX support use the `Interpreter: latex` option
xlabel 'time (\mu)s';

ylabel voltage;
legend sin cos;

% Save to file; gcf() is "get current figure"
exportgraphics(gcf(), "sample_plot.png");

%% More plotting options
% Legends, axis ticks (and labels), LaTeX interpreter
figure;

% Options for changing line pattern and color.
% Don't need `hold on`/`hold off` if multiple lines plotted with a single
% `plot` function.
plot(t, d1, 'b-.', t, d2, 'rp');

title 'Trig Functions';
xlabel 'time ($\mu$s)' Interpreter latex
ylabel voltage;
legend('sin', 'cos');
xticks(0:pi/2:10);
xticklabels({'0', '\pi/2', '\pi', '3\pi/2', '2\pi', '5\pi/2', '3\pi'});

% Many other options availible for plotting. Check the documentation or
% search online for options.

%% Subplots
% Subplots exist for stylistic purposes. Let's say you have a signal and
% you want to plot the magnitude and phase of the signal itself. It would
% make more sense if the magnitude and phase plots exist in the same
% figure. There are several examples fo subplot below to explain how it
% works. Note that linear indexing of plots is different from normal linear
% indexing.

figure;
subplot(2,2,1);                   % subplot(# of rows, # of columns, index)
plot(t,d1);
hold on;
plot(t, d2);
title 'Normal plot';

subplot(2, 2, 2);                 % index runs down rows, not columns!
plot(t, d1, 'b-.', t, d2, 'rp');
title 'Customized plot';

%% Stem plots
% stem plots are particularly useful when you are representing digital
% signals, hence it is good (and necessary) to learn them too!
% subplot(2,2,[3 4])                % takes up two slots
subplot(2, 1, 2);
hold on;
stem(t, d1);
stem(t, d2);
hold off;
title 'Stem plots';

sgtitle Subplots;

%% Tiling -- like subplots but newer
figure;
tiledlayout(2, 2);

nexttile;
plot(t, d1);

nexttile;
plot(t, d2);

%% A 3-D parametric function
% A helix curve
t = linspace(0,10*pi);

figure;
plot3(sin(t), cos(t), t);
xlabel sin(t);
ylabel cos(t);
zlabel t;
text(0, 0, 0, 'origin');
grid on;
title Helix;

%% Surface plot
% A shaded look for 2-D functions
%
% $f(x) = x\exp -(x^2+y^2)$
a1 = -2:0.25:2;
b1 = a1;
[A1, B1] = meshgrid(a1);
F = A1.*exp(-A1.^2-B1.^2);

figure;
surf(A1,B1,F);

%% Mesh plot
% A wireframe look for 2-D functions
figure;
mesh(A1,B1,F);