Matlab cheat sheet
Numbers and variables
Multiple instructions can go in a .m file (script).
a = 5e7 %means 5·107
b = 2; %semicolons suppress output
c = 3.5+2i %complex numbers
a=b*c
format(’long’) %displays more digits
a = 2*sqrt(pi) + exp(1)
help(’length’) %shows docs
Flow control
if a == 5 && b <= 6
y = true
else
y = false
end
|| is ‘or’; ~is ‘not’; a ~= b is ‘not equal’
while x < 10
x=x+1
end
for x = 1:10
disp(x)
end
for x = 10:-1:1 %loop backwards
disp(x)
end
v = [2, 3, 5, 7, 11];
for x = v %RHS can be any vector
fprintf(’%d is prime\n’, x)
end
Functions
One function per file (usually), named as the function + .m
function y = sum_two_numbers(a, b)
% the first comment is a docstring
y=a+b;%value of y at end of evaluation returned
function [x, y] = returns_multiple_values(a, b)
x = a + b;
y = a - b;
f = @(a, b) a + b; %lambda expression
f(1, 2)
some_function(@f) %to pass a function as an argument
Vectors and matrices
M=[123;456]
M = [M N; P Q] %concatenate matrices with same syntax
M = zeros(2, 3) %2x3 zero matrix
M = zeros(4) %square 4x4
M = ones(2, 3)
rand(2, 3) %uniform random in [0, 1]
randn(2, 3) %normal distribution N(0, 1)
size(M), length(v), sum(v), max(v)
2:5 %range [2, 3, 4, 5]
1:2:10 %range [1, 3, 5, 7, 9]
5:-1:1 %range [5, 4, 3, 2, 1]
Indexes start with 1 (boo).
v(1), M(1:5, 1:2), v(2:end), M(end:-1:1, end:-1:1)
Writing out of range resizes the matrix (wtf?!):
M(7, 9) = 2.5 %now M is at least 7x9, padded with zeros
v+w,v.*w,v./w,v.^w%elementwise
sin(v), abs(M), sqrt(v) %elementwise
Linear algebra
A*B%linear algebra row-by-column product
det(A), inv(A) %usually avoided in numerics
A\b%same as inv(A)*b, but more efficient
rowvector / A %same as rowvector * inv(A)
eig(A)
norm(v, 1), norm(v, inf), norm(M, ’fro’)
norm(v) %same as norm(v, 2)
M’ %transpose conjugate
Matrix decompositions
[P, L, U] = lu(A)
[Q, R] = qr(A)
[Q, T] = schur(A)
[V, D] = eig(A) %eigvecs=columns of V, eigvals=diag(D)
[U, S, V] = svd(A)
[Q, R] = qr(A, 0), [U, S, V] = svd(A, 0) %economy-sized
Sparse matrices
M = sparse(7, 9) %7x9 all zeros
M(2,3) = 5 %work like dense matrices in most cases
nnz(M) %number of nonzeros
[V, D] = eigs(A, 10) %top 10 eigenvalues
[U, S, V] = svds(A, 10) %singular values
spy(A) %plot sparsity pattern
Plots
plot(x, y) %line joining (x(1),y(1)) -- (x(2),y(2)) -- ...
plot(x1, y1, x2, y2) %multiple plots
hold(’on’), hold(’off’) %keeps previous plot
semilogx(x, y), semilogy(x, y), loglog(x, y) %log scales
plot(x, y, ’rx’) %set plot options
Colors: ymcrgbwk, markers: o+*.xsd, styles: - -- : -.
Debugging
To toggle breakpoints: click on the left of a line in the IDE.
The debugger has prompt K>>.
dbstop if error %starts debugger on error
dbquit %quits debugger
Optimization toolbox
linprog(c, A, b, Aeq, beq, lb, ub)
%solve the linear optimization problem
%min c’*x
%A*x <= b
%Aeq*x = beq
%lb <= x <= ub
quadprog(Q, c, A, b, Aeq, beq, lb, ub)
%solve the quadratic optimization problem
%min 0.5*x’*Q*x + c’*x
%A*x <= b
%Aeq*x = beq
%lb <= x <= ub
fminunc(’f’,x0,options)
%solve the unconstrained optimization problem
%min f(x)
%x in domain(f)
%with starting point x0 and possible options
Keyboard issues
To set the Italian keyboard on Linux: setxkbmap it (undo
with setxkbmap us).
To set MATLAB keyboard shortcuts to the Windows default
(e.g. copy with CTRL+C): Preferences (top-right in the
ribbon)→Matlab→Keyboard→Shortcuts→Active set→
Windows default set.
