How to turn a function handle with 3 inputs (1 variable and 2 parameters) and then assign the inputs parameters and get a function handle with one input? ?

Hello friends!

Consider the following

y=1;z=1;

f=@(x,y,z)x+y+z;

Now, I would like to create another function handle which is only a function of x. You migh suggest the following solution:

g=@(x)f(x,y,z);

but this is not what I want since I need to pass g(x) as input to another function and there I want to reduce the computational time. If I follow this solution whenever I call g, say g(1), it needs f, too plus that it does 3 arithmatics (3 sums) but I would like to have 2 arithmatics since g(x)=x+2.

Any idea?

[Rik]

I don't think this kind of evaluation is possible in Matlab.

I expect this is not what you want to do:

y=1;z=1;
yz=y+z;
g=@(x)x+yz;

[Mohammad Shojaei Arani]

No man. I am a mathematician and know that my question feels very simple but it is not. The point in my question is to reduce the computational time. Of course, for thisproblem I would follow your answer but my f function is super super super big and I need to pre-allocate the parameters in advance to reduce my big function f into a smaller size function g.

[Mohammad Shojaei Arani]

Another way one might anser my question is to use symbolic engine like the following

syms x y z

f=x+y+z;

g=subs(f,{y,z},{1,1});

g=matlabFunction(g);

But, this is computationally very expensive for my super big expressions. So, I seek a solution through function handles without using symbolic toolbox.

[Torsten]

Then start with g and generate f from down to up, not g from up to down.

Men always start with the little things to reach the big ones.

[Mohammad Shojaei Arani]

Haha! I can calculate g, for instance using symbolic toolbox, but that is computationally very expensive. The point is to find g, from f, using techniques of function handles not symbolic toolbox or other expensive ways.

I think it is time for matlab developers to consider this problem : "finding a function handle by another function handle in an appropriate manner". Many times I need this but it is missing in matlab, in my opinion.

[Torsten]

But how do you think it can be possible to define a function handle for g without using the function handle for f if g is deduced from f in some way ? Sounds contradictory to me.

[Mohammad Shojaei Arani]

NO. I did not say that. Of course, we need f in order to build g. But, the point in my question is how to do this in a cheap manner. If you look at my comminication with Rik, I mentioned that the following is a way to answer my question:

syms x y z

f=x+y+z;

g=subs(f,{y,z},{1,1});

g=matlabFunction(g);

But, this is computationally very expensive. In theory, Matlab has the capacity to solve my problem through function handles (not symbolic toolbox). But, it seems that matlab developers did not carefully think about this.

Answer 1

[Steven Lord]

Let's look at the actual time difference between the two approaches.

y=1;
z=1;
f=@(x,y,z)x+y+z;
g=@(x)f(x,y,z);
h = @(x) x+2;
timeit(@() g(42))

ans = 2.8650e-06

timeit(@() h(42))

ans = 7.6423e-08

Is this really the bottleneck in your code?

I realize that this was probably just a simple example to demonstrate what you're trying to do, so can you show the output of timeit called on a more "realistic" f, g, and h functions from your actual application?

[Mohammad Shojaei Arani]

Your calculation of computational time is correct but only for this simple case. Look, my text file expressions have big sizes like 100,000 KB. And, imagine that I need to call the resulting function handle 10^5 times.

[Torsten]

More and more I get the impression that the approach to your problem is not optimal or that MATLAB is not the most-suited tool for your task.

Maybe you could summarize what you are trying to do.

[Matt J]

Yes, what steps did you take that led you to such a monstrous 100MB mathematical expression? It sounds as if you have done nothing at all to vectorize the operations in your equations, like for example if you had rewritten a large matrix/vector operation in terms of their individual scalar components.

I suggest you show us just the first 20 lines of the expression you're trying to evaluate, so we can get a sense of the problem.

Answer 2

[Matt J]

But, this is computationally very expensive for my super big expressions.

What if you use the optimize flag?

g=matlabFunction(f,'File','outfile','Optimize',true)

Answer 3

[Jeff Miller]

Not sure I understand the situation, but this sounds to me like a case where an OO approach could be very helpful. Consider:

classdef myFunc < handle
    
    properties
        ComputedFromYandZ
    end
    
    methods
        
        function obj = myFunc()  % Constructor
            obj.ComputedFromYandZ = 0;
        end
        
        function [] = SetNewYandZ(obj,Y,Z)  % Compute whatever depends on Y and Z
            obj.ComputedFromYandZ = Y + Z;
        end
        
        function  Result = ComputeFromX(obj,X)  % Compute whatever depends on X with Y and Z fixed
            Result = abs( X + obj.ComputedFromYandZ ) ;
            % I included abs() here to make a function for fminsearch to
            % minimize.
        end
        
    end
    
end

You can then use a function handle to a function that depends only on X (after setting Y and Z), something like this:

myF = myFunc;
myF.SetNewYandZ(2,3);
fminsearch(@myF.ComputeFromX,20)
% ans -5

myF.SetNewYandZ(-20,-30);
fminsearch(@myF.ComputeFromX,20)
% ans 50