Question on function handles

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Tanmay
Tanmay 2012-6-20
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)
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per isakson
per isakson 2012-6-20
Did you read on "function handle" in the online documentation?

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Tom
Tom 2012-6-20
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.
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Tom
Tom 2012-6-20
Are you suggesting that counting to ten is in some way less rigorous than domains and tuples?
Walter Roberson
Walter Roberson 2012-6-20
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, .... ) ? :-)

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Walter Roberson
Walter Roberson 2012-6-20
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.

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