Guide

Toolboxes

Beyond the core language, MathLab includes the everyday parts of several MATLAB toolboxes, with the same function names. Each section links to its functions in the reference and its examples in the gallery.

Optimisation

linprog and intlinprog (simplex, branch and bound), quadprog (active set), fmincon (constraints of every kind), fminunc, lsqcurvefit, lsqnonlin and optimoptions. → functions · examples

% minimise cost subject to constraints: linprog, quadprog, fmincon, lsqcurvefit
f = @(x) (x(1) - 2)^2 + (x(2) - 1)^2;
[x, fval] = fmincon(f, [0; 0], [1 2], 2, [], [], [0; 0], [])   % stay below the line x1 + 2 x2 = 2
[X, Y] = meshgrid(linspace(-0.5, 2.5, 80));
contour(X, Y, (X - 2).^2 + (Y - 1).^2, 15), hold on
plot([0 2], [1 0], 'k', 'LineWidth', 1.5), plot(x(1), x(2), 'rp', 'MarkerSize', 12), hold off
axis equal, title('fmincon: the best point on the boundary')

Control systems

Transfer functions you can add, multiply and feed back (s = tf('s')), step, impulse, lsim, stepinfo, bode, margin, nyquist, rlocus, pzmap, pid and pidtune. → functions · examples

s = tf('s');
G = 1 / (s^3 + 3*s^2 + 3*s + 1);       % three lags
C = pidtune(G, 'PID');                  % a tuned PID controller
step(G, feedback(C*G, 1), 15)
legend('open loop', 'with PID control')

Symbolic maths

syms x and ordinary operators build exact expressions: diff, int (definite and indefinite), solve, subs, simplify, expand, factor, limit, taylor, jacobian, vpa, matlabFunction and latex — handy for papers and for LabTeX. Exact for polynomials, the elementary functions and the usual integration techniques; numbers where no closed form is found. → functions · examples

syms x
f = exp(-x)*sin(2*x)
F = int(f, x, 0, Inf)                 % exact: 2/5
d = diff(f, x)
fplot(f, [0 6]), hold on, fplot(d, [0 6], '--'), hold off
legend('f', "f'"), title(['f''(x) = ' char(d)])

Econometrics and statistics

fitlm (coefficient table with standard errors, t statistics, p-values, R², F test), predict, regress; arima and garch models with estimate, forecast, infer and simulate; autocorr, parcorr, lbqtest, adftest; and the t, F and χ² distributions. → functions · examples

rng(4)
y = simulate(arima('AR', 0.8, 'Constant', 0.5, 'Variance', 1), 200);
EstMdl = estimate(arima(1, 0, 0), y)     % coefficient table in the console
[yF, mse] = forecast(EstMdl, 20, y);
plot(1:200, y, 201:220, yF, 'r', 'LineWidth', 1.5)
title(sprintf('AR(1) estimated: %.2f (true 0.8)', EstMdl.AR))

Mapping

worldmap (world, continents, countries or a globe), geoplot, geoscatter, geobubble, distance — and countrymap to colour countries by data such as World Bank indicators. Country outlines come from Natural Earth (public domain) and are served with this site. → functions · examples

worldmap('Europe')
countrymap({'NLD', 'BEL', 'LUX', 'DEU', 'FRA', 'ESP', 'PRT', 'ITA'}, [1 2 3 4 5 6 7 8])
geoscatter([52.37 50.85 49.61], [4.90 4.35 6.13], 60, 'r')
title('Benelux and neighbours')

Image processing, signals, finance

Covered in their own sections: images (filters, edges, histograms, morphology, regions), signal processing (FFT, filters, windows, spectra) and finance (cash flows, loans, bonds, Black–Scholes, portfolios).

I = testimage('shapes');
subplot(1, 2, 1), imshow(I)
subplot(1, 2, 2), imshow(edge(rgb2gray(I), 'canny'))