Plot function given by integral depending on a parameter

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Manuel Ruivo de Oliveira
评论： Manuel Ruivo de Oliveira 2022-4-12
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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Torsten
Torsten 2022-4-11
编辑：Torsten 2022-4-11
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)
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Torsten
Torsten 2022-4-12
编辑：Torsten 2022-4-12
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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