How to vectorize integral?

h=0.1;

t1=0:h:2*pi;

alpha=0.3;

f=@(x) sin(x);

for i=2:length(t1)

      t=t1(i);
      k=1/gamma(1-alpha);
      w=@(s) (t-s).^(-alpha).*cos(s);
      p(i)=integral(w,0,t);
  end

[TheStranger]

Hello Sameer. Sorry for the offtop, but have you tested, whether a vectorized version is faster than just looping? I tried "integral" function with "ArrayValued=1" and it turned out that it is 20% slower than just looping over the parameter, for example.

Answer 1

[Walter Roberson]

alpha=0.3;
syms s t
w = int((t-s).^(-alpha).*cos(s), s, 0, t);

h=0.1;
t1=0:h:2*pi;
p = double(subs(w, t, t1));

[Sameer Chikane]

Thanks a lot. It worked!!!

Answer 2

[Andrei Bobrov]

h=0.1;
t1=0:h:2*pi;
p = arrayfun(@(t)integral(@(s)(t-s).^-alpha.*cos(s),0,t),t1)

[Sameer Chikane]

Thank you!!!