How to compose a function n-times and want value for a particular value of n?

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Sayantan Panja
Sayantan Panja 2020-9-30
评论： Ameer Hamza 2020-10-1
Suppose f(x)=x^2+1. Composition of two f, I mean f(f(x)), Similarly composition of 3 f is f(f(f(x))). n-th composition of f is denoted by f^n(x).
What is the general command to evaluate f^10(2) ?

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采纳的回答

Bruno Luong
Bruno Luong 2020-9-30
f = @(x) x.^2-x;
n = 10;
x = 1/pi;
y = x;
for k=1:n
y = f(y)
end
% y is f^10(x)

更多回答（1 个）

Ameer Hamza
Ameer Hamza 2020-9-30
编辑：Ameer Hamza 2020-9-30
Use recursion
f = @(x) x.^2 + 1;
n = 2;
fn = nRecursion(f, n);
function f = nRecursion(f, n)
if n == 1
f = @(x) f(f(x));
return
else
f = nRecursion(f, n-1);
end
end
f, and fn are function handles.
Example
>> f(f(5))
ans =
677
>> fn(5)
ans =
677
>> f(f(10))
ans =
10202
>> fn(10)
ans =
10202
  2 个评论
Ameer Hamza
Ameer Hamza 2020-10-1
No, Run it inside a script. It will not work directly on the command line.
You can also do it like this. Create a file named nRecursion.m in MATLAB path and paste the following code in it
function f = nRecursion(f, n)
if n == 1
f = @(x) f(f(x));
return
else
f = nRecursion(f, n-1);
end
end
and then run
f = @(x) x.^2 + 1;
n = 2;
fn = nRecursion(f, n);
in command window.

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