Defining function handles in a for loop

Hello everyone,

I have trying to define a series of function handles that are very similar. They only differ by their constant coefficients. They general idea is that I want to define functions s1 to s5 such that

for i =1:5
    S_i = @(x) z(i)/3.*(p(i+1) -x)^3 
end

where each s takes on their coefficeints from vectors z and p, as shown. But it seems like Matlab does not allow an array of function handles. What should I do?

Thanks a lot guys!

[Stephen23]

https://www.mathworks.com/help/matlab/matlab_prog/creating-a-function-handle.html

"You can create an array of function handles by collecting them into a cell or structure array."

Answer 1

[Walter Roberson]

for i =1:5
  S_i{i} = @(x) z(i)/3.*(p(i+1) -x)^3 
end

[Yancheng Wang]

I tried this but then every cell has the exact same content--an expression in terms of i. It does not get iterated.

[Stephen23]

Lets try it with some random data:

z = rand(1,5);
p = rand(1,6);
for i = 1:5
  S{i} = @(x) z(i)/3.*(p(i+1) -x)^3;
end

Checking:

S{1}(3)

ans = -1.1499

S{2}(3)

ans = -2.1649

S{3}(3)

ans = -3.9047

S{4}(3)

ans = -0.4100

S{5}(3)

ans = -1.1882

They don't look the same to me. Lets check one of them, say the fifth one:

z(5)/3.*(p(5+1) -3)^3

ans = -1.1882

So far everything behaves exactly as expected.

[Yancheng Wang]

This is odd. So in the workspace they appear the same, but somehow they are indeed different as shown by output. If you could do a "whos" command on any cell, you would get exacly the same thing, which is the original expression containing the i. So, in this case, how would I graph these different functions? Matlab would allow me to.

[Steven Lord]

Anonymous functions "remember" certain values in their bodies. You can check this using the functions function (which as its documentation page states should not be used programmatically, just for debugging.)

n = 2;
f = @(x) x.^n

f = function_handle with value:
    @(x)x.^n

metadata = functions(f);
metadata.workspace{1}

ans = struct with fields:
    n: 2

Even if we change n in the workspace, the remembered value in f will not change.

n = 3;
metadata2 = functions(f);
metadata2.workspace{1}

ans = struct with fields:
    n: 2

[Yancheng Wang]

Thank you! I did not know this and it helps!

So, as I defined the functions as above, when I try to graph them, matlab indicates that these are "array inputs" and should be "properly vectorized". Do you know what happened/what I should do to graph these functions?

Thanks again

[Walter Roberson]

  S_i{i} = @(x) z(i)/3.*(p(i+1) -x).^3    %notice .^ instead of ^