Question on function handles

Hi

I am looking at the code for "Learning the Extended Kalman Filter" by by Yi Cao on the File Exchange. In the code , there are a couple of lines that I couldnt get:

f=@(x)[x(2);x(3);0.05*x(1)*(x(2)+x(3))]; h=@(x)x(1);

http://www.mathworks.com/matlabcentral/fileexchange/18189

Can someone explain how handles work here? (in terms of plain math)

[per isakson]

Did you read on "function handle" in the online documentation?

Answer 1

[Tom]

Roughly speaking, f and h are handles to small functions- functions that have been made without having to actually write

function [Out1 Out2...] = FunctionName(In1,In2...)

function handles allow you to run a function using a variable name instead of having to write the name of the function.

For a simpler example:

F=@(x) x(x>5);

F is the function handle, and x(x>5) is the code that it executes if you enter

y=F(1:10)

you will see that it returns the numbers greater than 5.

[Walter Roberson]

The above is correct, but it does not happen to be the mathematical description ;-)

[Tom]

Are you suggesting that counting to ten is in some way less rigorous than domains and tuples?

[Walter Roberson]

It is the "code that it executes" part that is the less rigorous. That and the "run a function". What it *means* to "run a function", in rigorous terms, is surprisingly complex. And what the colon operator does, precisely, when the the increment includes a non-zero fractional part, is a headache.

Did you remember to specify that you are expecting this to be executed on a machine with at least 4 bits? (or 3 bits if using trinary, or 2 bits if using quaternary, .... ) ? :-)

Answer 2

[Walter Roberson]

In terms of plain math:

A function handle is a projection of a subspace of a domain (represented by a tuple) on to a subspace of a range (represented by a tuple). The projection function is arrived at by currying the original function to creating a new function which embeds all elements of the tuple that are to be treated as constants with respect to the projection.

If you prefer, I could rephrase in terms of Denotational Semantics, but I think I packed my reference book for that.

I think you will find the use of function handles rather clearer if you think of them procedurally rather than mathematically, and examine the online MATLAB documentation on function handles.