How do I implement a Matlab function, findtbracket.m, that, when a random function is inputed, the file will find the initial interval of the function?

The assignment asks us to implement a Matlab file, findtracket.m, of the form

function [a,b]=findbracket(f,X0)
% f: function handle f(x) to find a zero for
% x0: starting point/center of interval containing zero

to try to find an initial interval [a,b] containing the input x_0 and bracketing the zero of f(x)

Also, the function should begin with a=b=x_0 and a step size del=2^(-k) choosen so that

fl(x_0-del)<fl(x_0-del/2)=x_0

While sgn f(a)=sgn f(b), decrease a by del, increase b by del, evaluate f(a) and f(b) and double del.

This is what I have so far (I am a Matlab newbie):

function [a,b]=find bracket(f,x0)
a=x0;
b=x0;

while 1
    a=a-dx;
    if f(a)*f(b)<0,break; 
    b=b+del;
    if f(a)*f(b)<0, break;
end

[Walter Roberson]

The PNG image asks for "findbracket" not "findtracket".

You are not showing us how you invoke the code. And for sure you will need del and/or dx to be defined to use your code.

Answer 1

[John BG]

Mónica

prueba lo siguiente:

x0=4.333  
a=x0
b=x0
k=1
f=@(x) sin(x)

k3=1
while ~(floor(x0-2^(-k3-1))==floor(x0))
k3=k3+1
end

k4=1
while ~(floor(x0-2^-k4)==floor(x0))
k4=k4+1
end

k=max(k3,k4)

d=2^-k

while (sign(f(a))==sign(f(b)))
  a=a-d
  b=b+d
  d=2*d
end

da

a =   2.583333000000000
b =   6.083333000000000

me parece que el enunciado que has adjuntado, implementado tal y como se lee, se cuelga para ciertos valores de x0, por ejemplo, tanto

k2=1
while ~(floor(x0-2^(-k2-1))==x0 && floor(x0-2^-k2)<x0) 
  k2=k2+1
end

como

k2=1
while ~(floor(x0-2^(-k2-1))==floor(x0) && floor(x0-2^-k2)<floor(x0))  
  k2=k2+1
end

se cuelgan para x0=4.9

por lo que quizás sea posible modificar el enunciado así:

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Atentamente

John

[e-mail]

[Monica Medina]

Ah, gracias John. Voy a intentarlo.

Answer 2

[Walter Roberson]

It is not acceptable to have a space in the name of a function. "findbracket" not "find bracket".

Your code does not initialize dx or del. It appears to me from the PNG that dx and del should be the same value.