Defining anonymous function using an "if" statement

I'm trying to define an anonymous function using an "if" statement. Here is a minimum "not working" example (my code is more convoluted, but this illustrates the issue):

clc;
clear all;

f=@(x)x^2;
g=@(x) x;

if f(x)>=g(x)
    h=@(x) f(x)
else h=@(x) g(x)
end

The point is that I don't want to create an m file and have to recompute both f and g in it (my actual problem would require recomputing many more). So the question is:

1-) Is it possible to create an anonymous function using "if" statements (fixing the code above)?

2-) Is it possible to define function h on a separate m file, without having to recompute f and g inside of it?

Answer 1

[Matt J]

You can also do things like the following

f=@(x)x^2;
g=@(x) x;

h=@(x) fg_mfile(x,f,g);

 function out=fg_mfile(x,f,g)  %put this in mfile

    fval=f(x);
    gval=g(x);

        if fval>=gval
          out=fval;
        else 
          out= gval;
        end
   end

[yang]

you can do like this h=@(x)max(f(x),g(x))

[Matt J]

In this particular example, that is true. More complicated h() might require an mfile to express, however.

Answer 2

[Roger Stafford]

Try this:

   f = @(x) (x.^2>=x).*x.^2+(x.^2<x).*x

[John]

This works for this example that I provided. I could not mimic this idea for the multivariate functions that I'm actually using though.

[Star Strider]

That approach can easily be applied to multivariate functions. See: How do i plot CDF (probability) in Matlab? for an illustration.

[Matt J]

This is a classic technique and Star Strider is right. More generally, you would do

    h = @(x) L(x).*f(x) + (~L(x)).*g(x)

where L(x) is a possibly multivariate indicator function of x (i.e. =1 when f is active and =0 if g is active).

The only thing I'd point out is that it requires L(x) to be computed twice. It also requires that both f and g be computed even though you really only want to compute the one that is active. With a dedicated mfile you can often avoid that.

So, for large calculations, it has its drawbacks in CPU efficiency, but advantages in syntax efficiency.

[John]

I see. I checked the references you provided and now I understand.

[Alec Jacobson]

This style/hack has two (more) "gotchas".

1) Suppose L(x) is true, but g(x) produces nan/inf. Then h(x) = nan rather than f(x).

2) Suppose L(x) is true and g(x) is very expressive to compute or has side-effects (admittedly rare for matlab code), g(x) will still be called. This is very different behavior from:

if L(x)
  return f(x)
else
  return g(x)

I really wish matlab had full-citizen anonymous functions...

Answer 3

[Cristobal Montecino]

I use:

call = @(fun) fun();
cellget = @(cell, index) cell{index};

iff = @(test, truefn, falsefn) call(cellget({falsefn, truefn}, test + 1));

And:

arrayget = @(arr, index) arr(index);

ifv = @(test, trueval, falseval) arrayget([falseval, trueval], test + 1);

%or
cellget = @(cell, index) cell{index};

ifv = @(test, trueval, falseval) cellget({falseval, trueval}, test + 1);

Examples:

iff(true, @() 2, @() this_throw_an_error)
% out: 2

iff(false, @() 2, @() this_throw_an_error)
% out: Undefined function or variable 'this_throw_an_error'.

ifv(true, 2, 3)
% out: 2

ifv(true, 2, this_throw_an_error)
% out: Undefined function or variable 'this_throw_an_error'.

[Oscar Raya i Casanova]

Nice tip. As improvement for the first option:

call = @(fun,par) fun(par{:});
cellget = @(cell, index) cell{index};
iff = @(test, truefn, falsefn, truePar, falsePar) call( ...
    cellget({falsefn, truefn}, test + 1), ... % functions
    cellget({falsePar, truePar}, test + 1) ... % params
);

Examples:

f1 = @(a,b) a + b;
f2 = @(a,b,c) a*b + c;
f3 = @() 7;

iff(true,f1,f2,{1,2},{1,2,3});
% out: 3

iff(false,f1,f2,{1,2},{1,2,3});
% out: 5

iff(false,f1,f3,{1,2},{});
% out: 7

This way you can use functions with different number of parameters.