How to calculate number of function evaluation used?

Hi guys, can some one help me to solve my problem?

i've be facing difficulty to find the number of function evaluation. let's say that i have f(x)=x^3+x^2-2 with initial value of x(0)=1.5

i want to calculate x(n+1)=x(n)-(f(x(n)/fprime(x(n))) until n=5

thus, i want to calculate how many time of f(x(n)) have been use until n=5. but if the first iteration has use f(x(1)) then the second iteration also use f(x(1)), it is considered as we only use f(x(1)) one time only.

can someone help me

[KSSV]

What is fprime ?

[Jan]

The obvious answer is, that f(x) is called n=5 times.

Answer 1

[Steven Lord]

If you're using release R2017a or later you could use memoizedFunction. Once you've used memoizedFunction to solve the problem, call stats on it to determine how many times and with which inputs it was called.

[Jan]

@Stephen: How is the number of calls obtained?

s = stats(mf);
calls = s.Cache.TotalHits + s.Cache.TotalMisses

?

[Steven Lord]

Yes, that's how I would do it. The first time you call the function with a new set of inputs, that increments TotalMisses. Each subsequent time you call the function with inputs that are already in the cache, that increments TotalHits.

[Tamas Kis]

Found a way to do this using a handle class: https://www.mathworks.com/matlabcentral/fileexchange/122422-counted-function-countedfunction. In an example I included it is about 5 times faster than using a memoized function.

If you have a function handle f, you can simply do

[f,count] = count_function_calls(f)

and keep using f in the same way as before. When you want to know the number of function calls, you just use

count()

Answer 2

[Torsten]

When n=5, f and fprime have been called 5 times each, namely to evaluate f(x1),f(x2),...,f(x5), fprime(x1),fprime(x2),...,fprime(x5).

Best wishes

Torsten.

[NUR ZAFIRAH MOHD SIDEK]

do you know how to write the coding?

[Jan]

@NUR ZAFIRAH MOHD SIDEK: Accepting an answer means, that the problem is solved.

[Torsten]

f=@(x)x^3+x^2-2;
fprime=@(x)3*x^2+2*x;
x=4;
for n=1:5
  x=x-f(x)/fprime(x);
end

Best wishes

Torsten.

[NUR ZAFIRAH MOHD SIDEK]

@Jan Simon: ops..sorry..because this is my first time.

Answer 3

[Jan]

function fx = f(x)
persistent Count
if isempty(Count)
  Count = 0;
end
if nargin == 0  % Reply counter and reset it
  fx    = Count;
  Count = 0;
  return;
end

fx    = x^3+x^2-2;
Count = Count + 1;
end

Now:

f();
x = f(1) + f(2) + f(3);
Count = f()

[NUR ZAFIRAH MOHD SIDEK]

and is it the same process if i want to find more than one function at the same time?

[Jan]

I do not understand you question. This example shows how to insert and request a counter ina function. Of course you can do exactly the same with other functions also.