Matlab Lecture 2

% inline functions

f = @(x) sin(x)-cos(x)+exp(-x)

f(0)

f([0,pi/4,pi/2,3*pi/4,pi])

% m files - scripts

who

timelinsolve

who

% m files - functions

clear

timelinsolvefun(1000)

who

[x1,x2]=timelinsolvefun2(1000);

who

% for loops

for k=1:5

k

end

for k=1:2:10

k

end

mysin(pi)

mysin(linspace(-pi,pi,5))

% while loops

i=1;

while i <= 5

i

i=i+1;

end

x=mynewt(5)

x=mynewt(7)

% if statements

r=randi(100);

if isprime(r)

disp([num2str(r),’ is prime’])

else

disp(’r is not prime’)

factors=factor(r)

end

rand3

% simple plotting

x=linspace(0,2*pi,1000);

plot(x,sin(x),x,cos(x),’r--’,’LineWidth’,2)

help plot

xlabel(’x’)

ylabel(’sin(x) and cos(x)’)

title(’Trig functions’)

legend(’sin(x)’,’cos(x)’,’Location’,’SouthWest’)

shg

figure

fplot(’sin(x)’,[0,2*pi])

fplot(’cos(x)’,[0,2*pi],’k-.’)

hold on

fplot(’sin(x)’,[0,2*pi])

close(1)

close all

f = @(x) sin(x)-cos(x)+exp(-x)

fplot(f,[0,20])

grid

hold on

fplot(’0’,[0,20],’r’)

% Root finding and Optimisation

fzero(f,4)

f(ans)

fzero(f,7)

[x,fval]=fzero(f,10)

[x,fval]=fminbnd(f,4,6)

[x,fval]=fminbnd(f,10,12)

x=fminbnd(@(x)-f(x),0,4)

fmax=f(x)

% file g.m

function y=g(x)

y=sin(x^5)+cos(x^4);

fplot(’g’,[-pi/2,pi/2])

fzero(’g’,1)

[x,gval]=fminbnd(’g’,-pi/2,pi/2)

[x,gval]=fminbnd(’g’,1,1.5)

c=[6 -23 30 -30 24 -7]

roots(c)

% file timelinsolve.m

% this script times how long it takes to solve a linear system

% using backslash and inv

n=1000;

A=randn(n);

b=randn(n,1);

tic, x1=A\b; toc

tic, x2=inv(A)*b; toc

% file timelinsolvefun.m

% this function times how long it takes to solve a linear system

% using backslash and inv, it takes matrix size as an input

function timelinsolvefun(n)

A=randn(n);

b=randn(n,1);

tic, x1=A\b; toc

tic, x2=inv(A)*b; toc

end

% file timelinsolvefun2.m

% this function times how long it takes to solve a linear system

% using backslash and inv, it takes matrix size as an input and outputs the solutions

function [x1,x2]=timelinsolvefun2(n)

A=randn(n);

b=randn(n,1);

tic, x1=A\b; toc

tic, x2=inv(A)*b; toc

end

% file mysin.m

% this function approximates sin(x) using the first 21 terms in the power series

function sinx=mysin(x)

sinx=0*x;

for k=0:20

sinx=sinx+(-1)^k*x.^(2*k+1)/factorial(2*k+1);

end

end

% file mynewt.m

% this function finds a root of sin(x)-cos(x)+exp(-x) using Newton’s method

function x=mynewt()

f=@(x) sin(x)-cos(x)+exp(-x);

fprime=@(x) cos(x)+sin(x)-exp(-x);

x=xguess;

tol=1e-10;

while abs(f(x)) > tol

x=x-f(x)/fprime(x)

end

end

% file rand3.m

% this script generates 3 random numbers and states a fact about them

r=randi(10,1,3)

if (r(1) == r(2) & r(2) == r(3))

disp(’all the integers are the same’)

elseif (r(1) == r(2) | r(1) == r(3))

disp(’r(1) is the same as one of the other integers’)

elseif (r(1) > r(2) && r(1)>r(3))

disp(’r(1) is the biggest of the integers’)

else

disp(’either r(2) or r(3) is the biggest’)

end