"Arrays have incompatible sizes for this operation" with for loop in integral2

I am going to find a fixed point for some intergal represented function.

(this is just an example, I do not know if the fixed point exists or not) by the iteration:

My code is like that:

input  = @(y,s) y;

N_it=10;
output=cell(1, N_it);
output{1}=input;
density = @(z,t,s) exp( -(z.^2)./(2.*(s-t)) ) ./ (sqrt(2*pi).*sqrt(s-t));

for i=1:N_it
input=output{i};
integral = @(y,t) integral2( @(z,s) input(z,s).*density(z-y,t,s),0,100,@(t)t,T,'RelTol',0,'AbsTol',1e-5);
n_output=@(y,t)integral(y,t);
output{i+1}=n_output;
end

For N_it =1, I can get the answer, there is no error. For N_it>1, when I find the value of n_output(1,1), there is an error "Arrays have incompatible sizes for this operation." and then a very long list indicating my problematic lines.

Answer 1

[VBBV]

input  = @(y,s) y;

N_it=10;
output=cell(1, N_it);
output{1}=input;
density = @(z,t,s) exp( -(z.^2)./(2.*(s-t))  ./ (sqrt(2*pi).*sqrt(s-t)));

for i=1:N_it
input=output{i};
integral = @(y,t) integral2( @(z,s) input(z,s).*density(z-y,t,s),0,100,@(t)t,T,'RelTol',0,'AbsTol',1e-5);
n_output=@(y,t)integral(y,t);
output{i+1}=n_output;
end
output(1,1)

ans = 1×1 cell array
    {@(y,s)y}

[VBBV]

the parenthesis is used incorrectly when writing the formula in this line

density = @(z,t,s) exp( -(z.^2)./(2.*(s-t))  ./ (sqrt(2*pi).*sqrt(s-t)));
                    %->                                                 <--

[ho man]

Thank you for the comment. But I am so sorry that I can not see any mistake there. May be if we look at a simplest case

density =@(z,t,s) sin(z.*(s-t));

this still gives the same error. For N_it =1, I can get the answer, there is no error. For N_it>1, there is an error.

[Torsten]

Did you think about how many integrations it will need to evaluate output{10}(2,4), e.g. ? This single value will take days - if it finishes at all. Not to speak of the complete function output{10}.

[VBBV]

@ho man, When N_it >1 the code works without error if you include the parenthesis according to the expressions you have The outputs shown are when N_it = 10

[ho man]

@VBBV I still get the same error if I replace the exp by the sine in the comment when N_it >1.

@Torsten Do you have any suggestion to tackle this?

[VBBV]

@ho man I dont get error though. can you share your code when you replace exp with sin function as shown in your comment ? btw try with ArrayValued as true argument in the integral2 function. Change the tolerance range and check

input  = @(y,s) y;

N_it=10;
output=cell(1, N_it);
output{1}=input;
density = @(z,t,s) sin(z.*(s-t));

for i=1:N_it
input=output{i};
integral = @(y,t) integral2( @(z,s) input(z,s).*density(z-y,t,s),0,100,@(t)t,T,'RelTol',0,'AbsTol',1e-5, ...
    'ArrayValued',1); % use array valued argument 
n_output=@(y,t)integral(y,t);
output{i+1}=n_output;
end
output(1,1)

ans = 1×1 cell array
    {@(y,s)y}

[ho man]

Yes, your code is correct. Thank you so much. My code is the same as yours but the last line "output(1,1)" is replaced by "n_output(1,1)". What is the mistake here?

[ho man]

@VBBV I finally see the extra ) in the exp function in the very beginnin code, thank you.