Basics

% Welcome to MathLab, a MATLAB-style lab in your browser.
% Run with ⌘/Ctrl + Enter. Type 'help' in the console for all functions.

x = linspace(0, 4*pi, 400);
plot(x, sin(x), 'LineWidth', 2)
hold on
plot(x, cos(x), '--')
plot(x, sin(x) .* exp(-x/6), 'LineWidth', 1.5)
hold off

title('Trigonometry, with a little damping')
xlabel('x'), ylabel('y')
legend('sin x', 'cos x', 'e^(-x/6) · sin x')
grid on

th = linspace(0, 2*pi, 800);
polarplot(th, abs(cos(4*th)), 'LineWidth', 2)
hold on
polarplot(th, 0.5 + 0.4*sin(7*th), '--')
hold off
title('r = |cos 4θ|  and  r = 0.5 + 0.4 sin 7θ')

% The curve where f(x, y) = 0
fimplicit(@(x, y) (x.^2 + y.^2 - 1).^3 - x.^2 .* y.^3, [-1.5 1.5 -1.4 1.6])
title('(x² + y² − 1)³ = x² y³')

rng(4)
subplot(2, 2, 1)
bar([4 7 3 9 5])
title('bar')

subplot(2, 2, 2)
x = randn(1, 300);
scatter(x, x + 0.6*randn(1, 300), 18, x, 'filled')
title('scatter coloured by value')

subplot(2, 2, 3)
imagesc(magic(9))
colorbar
title('imagesc')

subplot(2, 2, 4)
fsurf(@(x, y) cos(x).*sin(y), [-pi pi -pi pi])
title('fsurf')

% Results without a semicolon are printed in the console below.
A = [4 -2 1; -2 4 -2; 1 -2 4]
b = [11; -16; 17];
x = A \ b                     % solve A x = b
check = A*x - b
lambda = eig(A)               % eigenvalues (symmetric A)
d = det(A)

bar(lambda)
title('Eigenvalues of A')

% Temple Fay's butterfly curve, a classic polar parametric plot
s = linspace(0, 12*pi, 4000);
r = exp(cos(s)) - 2*cos(4*s) - sin(s/12).^5;
plot(sin(s).*r, cos(s).*r, 'LineWidth', 1)
axis equal
title('r = e^(cos θ) − 2 cos 4θ − sin⁵(θ/12)')

f  = @(x) x.^3 - 2*x - 5;
df = @(x) 3*x.^2 - 2;
x = linspace(1, 3.2, 300);
plot(x, f(x), 'LineWidth', 2), hold on
yline(0, 'k:')
xn = 3;
for k = 1:4                          % draw each tangent line
  xs = linspace(xn - 0.6, xn + 0.1, 20);
  plot(xs, f(xn) + df(xn)*(xs - xn), '--')
  scatter(xn, f(xn), 40, 'r', 'filled')
  xn = xn - f(xn)/df(xn);
end
hold off
title(sprintf('root ≈ %.6f after 4 steps', xn))

% Figure styles: paper, ieee, ieee-wide, nature, thesis, slides, poster, minimal, grayscale
% (type 'styles' in the console for sizes). The preview shows the exact exported page.
style ieee
rng(4)
x = linspace(0, 10, 40);
y1 = 2 + 0.8*sin(x) + 0.15*randn(size(x));
y2 = 1.2 + 0.5*cos(0.7*x) + 0.15*randn(size(x));
plot(x, y1, 'o-', x, y2, 's--', 'MarkerSize', 4)
xlabel('time (s)'), ylabel('signal (mV)')
legend('channel A', 'channel B')
title('Two recorded channels')

% MATLAB-style tweaks work too:
%   fontsize(9), fontname('Times New Roman'), colororder('tableau')
%   set(gcf, 'Units', 'centimeters', 'Position', [0 0 8.9 6])
exportgraphics(gcf, 'two-channels.pdf', 'Resolution', 600)
exportgraphics(gcf, 'two-channels.svg', 'ContentType', 'vector')