Do vector fields mapping R^2 to R^2 have to be coded in separate function files, or can I define anonymous functions for them directly in the script file?

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Noob 2020-9-22

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评论： Noob 2020-9-22

Hi,

I've been writing functions from R^2 to R^2, i.e. F( f_1(x,y), f_2(x,y) )= (z_1, z_2), in separate function files, and then calling F in a script file. Could I instead write the two component functions f_1 and f_2 as anonymous functions directly in the script file? I read something on the Mathworks documentation that an anonymous function can only have one "executable" statement, but I'm not sure what that means.

Thanks,

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Answer 1

Ameer Hamza 2020-9-22

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在 MATLAB Online 中打开

Can MATLAB anonymous function return two outputs?

Yes, for example

>> f = @(x) deal(x, x^2);
>> [a, b] = f(2)
a =
     2
b =
     4

But then you will always need to call it with two output arguments. The following will not work

>> a = f(3)
Error using deal (line 37)
The number of outputs should match the number of inputs.

So it is better to write a function in seperate file to handle such cases.

"anonymous function can only have one "executable" statement"

It means that you cannot do something like the following in an anonymous function

f = @(x) y=1, x+y; % not allowed
f = @(x) if x=1, y=2, end; % not allowed

"if the function file name is "nonlinear_equations", then in the script file, I store a variable f = @nonlinear_equations, and then use f instead."

Yes, you can directly use nonlinear_equations instead of f; there will be no difference. However, it is not entirely useless. For example, instead of nonlinear_equations, you need to use some other function. In the current code, you will only need to change the line: f = @new_function; however, in the other case, you will need to change it everywhere.

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Steven Lord 2020-9-22

在 MATLAB Online 中打开

Not quite. If you want two functions:

f_1 = @(x) cos(x(1)) + x(2);
f_2 = @(x) sin(x(2)) + x(1)^2;

and want to have one function to evaluate them all (and in the darkness bind them ;) you need to have that one function evaluate them.

F = @(x) [f_1(x), f_2(x)];
F([1, 2])

Compare with the following, which returns a cell array each element of which contains a function handle.

G = @(x) {f_1, f_2};
G([1, 2])

If your functions are more complicated than can "fit" in an anonymous function consider writing a function file.

function [value, fcnHandles] = F(x)
value = [f_1(x), f_2(x)];
fcnHandles = {@f_1, @f_2};
end
function y = f_1(x)
% Do stuff to compute f_1
end
function y = f_2(x)
% Do stuff to compute f_2
end

This assumes you may need to call f_1 and f_2 outside F. Even though f_1 and f_2 are local functions inside F.m (and so normally out of scope outside of F.m) they can be called via their function handles that were created when they were in scope.

[value, fh] = F([1, 2]);
f_1 = fh{1};
v1 = f_1([1, 2]); % v1 should be equal to value(1)

If you don't need to call f_1 and f_2 outside F, you can eliminate the fcnHandles output.

Steven Lord 2020-9-22

That's an example demonstrating that what I wrote works. F([1, 2]) should return a two element vector, the first element of which is f_1([1, 2]) and the second is f_2([1, 2]).

Noob 2020-9-22