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I am working on converting the matlab function gamfit into objective-c code. Towards the end of gamfit it calls another function called fzero: http://www.mathworks.com/help/techdoc/ref/fzero.html

Even after reading the matlab documentation, I am having trouble understanding how this function operates when x0 is a vector, as it is in my case.

Here is what the matlab documentation says on the subject: "If x0 is a vector of length two, fzero assumes x0 is an interval where the sign of fun(x0(1)) differs from the sign of fun(x0(2)). An error occurs if this is not true. Calling fzero with such an interval guarantees fzero will return a value near a point where fun changes sign."

I was hoping that maybe someone has already implemented this function in C/C++/objective-c to make things easier.

Any help would be appreciated.

exolaris
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  • This is not so easy to do, if I remember correctly fzero solve a polynomial right? – Pepe Mar 08 '12 at 05:27
  • @P.R: fzero looks for a sign change in the given function. – Ken Wayne VanderLinde Mar 08 '12 at 05:38
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    I think you should go and find an existing implementation of `gamfit` or its equivalent somewhere else. These types of algorithms require a lot of care and understanding of the underlying numerical issues. I have taken several numerical analysis courses, but I still would not like to implement this type of stuff in production code. A good place to start would be [here](http://stackoverflow.com/questions/9577541/matlab-gamfit-and-gampdf-functions-written-in-c) – sterin Mar 08 '12 at 05:39
  • @user99279: I have looked everywhere quite extensively for a already implemented gamfit function. I was the one who posted that question you linked me too. The answer the guy gave to that question concerned only gampdf and not gamfit. I am almost done implementing gamfit, just a couple more lines of code and fzero is one of them. – exolaris Mar 08 '12 at 06:00
  • Some implementations in java using bisection, secant and newton's methods: [here](http://www.torkian.info/Site/Research/Entries/2008/2/28_Root-finding_algorithm_Java_Code_%28_Secant%2C_Bisection%2C_Newton_%29.html) – CitizenInsane Mar 08 '12 at 13:26

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GNU Octave is an open-source software similar to MATLAB. It has an implementation of many MATLAB functions. You can find fzero inside -- look for scripts/optimization/fzero.m in the source distribution. Note that Octave is licensed under the GPL, so it might affect your decision.

According to the comments fzero is supposed to be a combination of the Bisection Method with the Secant Method.

Another good place to start would be the Numercial Recipes series of books (pick the most recent C++ version).

sterin
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The GNU Scientific Library implements a number of methods for finding roots of polynomials and other functions. You could probably adapt some of their code, or save yourself time by just calling the necessary functions.

In passing: rather than asking 'how do I implement Matlab function X in Objective-C ?' as you have done a couple of times now, you might make better progress, and get better answers, if you asked 'how do I implement method Y in Objective-C ?'. In some cases, I suspect, you will not require the full generality of Matlab functions to get the functionality that you need so Y may not be all of X.

A slavish line-by-line translation from Matlab's code (even if you have access to it) is unlikely to lead you to good Objective-C code; for example, much of Matlab's code that is available shows little signs of object-orientatedness. A better approach is to understand what the Matlab code does and to implement that in Objective-C.

High Performance Mark
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