How can i vectorize this for loop? please help.

2017 3 18
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回答已采纳
更新时间：2017 3 21
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t = 0:dt:T;
x = xl:dx:xr;
u = zeros(xn+1,tn+1);
for j = 1:tn;
tm = j*dt;
if j == 1;
for i = 2:xn;
T1 = ((gamma(2-bta))/((gamma(j-1+2))*(gamma(1-bta-j+1))))*(u(i+1,1)-2*u(i,1)+u(i-1,1));
T2 = (2.5*(tm.^1.5)+(gamma(3.5)/gamma(3.5-bta))*(tm.^(2.5-bta)))*sin(x(i));
u(i,j+1)=u(i,j)+mu.*T1+dt.*(T2);
end
end
end

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Jan
Jan 2017-3-18
编辑：Jan 2017-3-18

1 个投票

Start with moving all repeated but constant expressions outside the loops:
t = 0:dt:T;
x = xl:dx:xr;
u = zeros(xn+1,tn+1);
c1 = gamma(2-bta);
c4 = gamma(3.5) / gamma(3.5-bta);
for j = 1:tn;
tm = j*dt;
c5 = tm.^(2.5-bta);
c6 = tm.^1.5;
c7 = 2.5*c6 + c4*c5;
if j == 1 % ??? Why do you use a loop over j, if only j==1 is considered?
c2 = gamma(j-1+2);
c3 = gamma(1-bta-j+1);
c8 = (c1 / (c2*c3));
for i = 2:xn
T1 = c8 * (u(i+1,1) - 2*u(i,1) + u(i-1,1));
T2 = c7 * sin(x(i));
u(i,j+1) = u(i,j) + mu.*T1+dt.*T2;
end
end
end
Now the innerloop can be vectorized by moving the index from the for loop insice the calculations: Instead of the block "for i... end"
T1 = c8 .* (u(3:xn+1,1) - 2 * u(2:xn,1) + u(1:xn-1,1));
T2 = c7 .* sin(x(2:xn));
u(2:xn,j+1) = u(2:xn,j) + mu .* T1 + dt .* T2;
I cannot test the code, because some variables are missing.

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Priya Khot
Priya Khot 2017-3-19
Thank you so much for the reply. actually i further have "else" condition for that if now m concentrating on that vectorization part.
here, mu = 0.787 and bta = 0.476
t = 0:dt:T;
x = xl:dx:xr;
u = zeros(xn+1,tn+1);
for j = 1:tn;
tm = j*dt;
if j == 1;
for i = 2:xn;
T1 = ((gamma(2-bta))/((gamma(j-1+2))*(gamma(1-bta-j+1))))*(u(i+1,1)-2*u(i,1)+u(i-1,1));
T2 = (2.5*(tm.^1.5)+(gamma(3.5)/gamma(3.5-bta))*(tm.^(2.5-bta)))*sin(x(i));
u(i,j+1)=u(i,j)+mu.*T1+dt.*(T2);
end
else
for i = 2:xn;
for k = 1:j;
T1 = ((gamma(2-bta))/((gamma(j-k+2))*(gamma(1-bta-j+k))))*(u(i+1,k)-2*u(i,k)+u(i-1,k));
end
T2=(2.5*(tm.^1.5)+(gamma(3.5)/gamma(3.5-bta))*(tm.^(2.5-bta)))*sin(x(i));
u(i,j+1)=u(i,j)+mu.*T1+dt*(T2);
end
end
end
now i want to vectorize the "for... loops" after "else". please guide me. Thank you.
Jan
Jan 2017-3-21
This solution suffers again from the repeated calculations of the expensive gamma function for the same constant values. It does not seem that you understand the idea of my suggested code.
The above code overwrites "T1" in the "for k" loop repeatedly. This is not useful, because you can replace the loop by "k=j".

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