Plot function given by integral depending on a parameter
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Manuel Ruivo de Oliveira
on 11 Apr 2022
Commented: Manuel Ruivo de Oliveira
on 12 Apr 2022
I have a function given as an integral depending on a parameter, say
.
(Please ignore the fact that this can be integrated exactly.) Here I'm thinking of a as a parameter that can take any real value. Given a fixed value for a, I'd like to plot the function of x given by
.
Here's my best attempt:
f = @(a,t) sin(a.*t); % Define integrand
F_scalar = @(a,x) integral(@(t) f(a,t), 0, x); % Function of interest, except that x must be a scalar here
F = @(a,x) arrayfun(F_scalar, a, x); % Vectorized version of function of interest
fplot(@(x) F(1,x))
This gives me a plot, but with the following warning: "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."
The problem seems to be that arrayfun should accept arguments with the same dimensions, whereas in the last line of code I'm setting but letting MATLAB pass a vector for x. Any ideas?
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Accepted Answer
Torsten
on 11 Apr 2022
Edited: Torsten
on 11 Apr 2022
f = @(a,t) sin(a*t);
F = @(a,x) integral(@(t)f(a,t),0,x);
a = 1;
x = 0:0.1:2*pi;
Result = arrayfun(@(x)F(a,x),x);
plot(x,Result)
3 Comments
Torsten
on 12 Apr 2022
Edited: Torsten
on 12 Apr 2022
To summarize:
a = 1;
x = 0:0.1:2*pi;
f = @(a,t) sin(a*t);
F = @(a,low,high) integral(@(t)f(a,t),low,high);
partial_results = arrayfun(@(low,high)F(a,low,high), x(1:end-1), x(2:end));
initial_value = F(a,0,x(1));
Result = cumsum([initial_value, partial_results]);
plot(x,Result)
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