How do I add anonymous functions together?

What I would like to achieve is a for loop with n iterations that lengthens a function after each iteration, but I'm not sure what the syntax is to add two anonyous functions

Sample code:

for n = 1 : iterations

function = function + new_function

end

where 'function' and 'new_function' are anonymous functions

Desired output:

if function = @(x) x.^2

and new_function = @(x) x.^3

function + new_function = x.^2 + x.^3

Answer 1

[Matt J]

Is this possible without converting the anonymous function to a string?

I was hoping for something along these lines:

for n = 0:5

new_func = @(x) (((-1)^n).*((x).^(2*n)))./(factorial(2*n))

final_func = @(x) final_func(x) + new_func(x)

end

After the for loop, I'd like to output to look smiliar to this:

final_func = @(x) (((-1)^0).*((x).^(2*0)))./(factorial(2*0)) + (((-1)^1).*((x).^(2*1)))./(factorial(2*1)) + (((-1)^2).*((x).^(2*2)))./(factorial(2*2));

No, not without string manipulation.

The function generated by your loop will return the correct values (and is equivalent to @Stephen23's answer), but it is grossly inefficient. You could get to a much better implementation of final_func in one line by using vectorization.

n=0:5;

final_func=@(x)  sum( (((-1).^n).*((x).^(2*n)))./(factorial(2*n)) );

[Dylan]

Thanks to @Matt J for help with the solution

Here's my final code

How do I avoid the Warning?

n=0:5;
final_func=@(x)  sum( (((-1).^n).*((x).^(2*n)))./(factorial(2*n)) )

final_func = function_handle with value:
    @(x)sum((((-1).^n).*((x).^(2*n)))./(factorial(2*n)))

fplot(final_func)

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

axis([-pi pi -1 1])

[Matt J]

How do I avoid the Warning?

n=(0:5)';
final_func=@(x)  sum( (((-1).^n).*((x).^(2*n)))./(factorial(2*n)) ,1);
fplot(final_func)
axis([-pi pi -1 1])

Answer 2

[Matt J]

Trying to sum/concatenate anonymous functions is a bad thing to do, in general. Here is one way to accomplish it, however,

fstr=@(z) string( extractAfter(func2str(z),'@(x)') );

func="";
for n = 1 : iterations
    func= func + fstr(new_function);
end

func=str2func( "@(x)"+func )

[Dylan]

Is this possible without converting the anonymous function to a string?

I was hoping for something along these lines:

for n = 0:5

new_func = @(x) (((-1)^n).*((x).^(2*n)))./(factorial(2*n))

final_func = @(x) final_func(x) + new_func(x)

end

After the for loop, I'd like to output to look smiliar to this:

final_func = @(x) (((-1)^0).*((x).^(2*0)))./(factorial(2*0)) + (((-1)^1).*((x).^(2*1)))./(factorial(2*1)) + (((-1)^2).*((x).^(2*2)))./(factorial(2*2));

where for each term, the n value is substituted

In the end, I'd like to plot final_func using fplot

[Stephen23]

" I'd like to output to look smiliar to this: final_func = @(x) (((-1)^0).*((x).^(2*0)))./(factorial(2*0)) + (((-1)^1).*((x).^(2*1)))./(factorial(2*1)) + (((-1)^2).*((x).^(2*2)))./(factorial(2*2));"

Adding functions is a red-herring. You should be using arrays, not adding functions in a loop.