smartnormalized

Normalizes a function to "unity".

Description

Derives number of dimensions ( variables ) of given function then
normalizes it "unity".

Clarification: unity has different meanings in each dimensions e.g. for
one variable function the output function has a unit area between the
curve and x-axis in the interval that user defines, for two variables
function the output function has a unit volume between the surface and xy
plane in the intervals that user defines and so on.
Example:
 A = inline ( ' tan ( x ) + ( i * x ) + sin ( y ) + i * ( y ^ 2 ) + i * cos ( z ) + ( z ^ 2 ) ' ) ;
 B = smartnormalized ( A , [0 0 0.01] , [pi/4 pi/4 pi/4] , 'sym' )
 B =
    (2928464171262539/4503599627370496-1072148456816461/1125899906842624*i)*(tan(x)+i*x+sin(y)+i*y^2+i*cos(z)+z^2)

• Required Products: Symbolic Math Toolbox
• MATLAB release: MATLAB 7.2 (R2006a)

[John D'Errico]

I'm pleased to see real progress in this author's work. Its not what I'd describe as perfect, but I can't always say that about my own codes either.

As I read through this code, I see error checks on the variables to help the user. I see an H1 line. There is good help (more on this later.) Use of the symbolic toolbox is documented. The internal comments are well done.

A couple of somewhat minor points - the help is spread throughout the code. So for help on the 5 argument version of this code, you must look down inside the code. You don't see that part using help. You must edit the code.

Next, I don't see why it is necessary to use dblquad or triplequad to do the integration for the 2-d or 3-d cases. They are adaptive numerical tools, as such are quite CPU intensive, especially for the 3-d case.

Finally, I'm not entirely sure about the use of the phrase "area normalization", even though I myself suggested it as an alternative. As applied to a possibly complex function, "area" seems not entirely appropriate to me, but a better word escapes me at the moment.

So as a whole, while not perfect, this is a good effort by the author. I hope & expect to see continued improvement from this author.