How to speed up the program?

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Henan Fang
Henan Fang 2018-9-28
编辑： Stephen23 2018-9-28
(x,y) is a function generated as the following codes. I need to calculate the integration that "integral2(@(X,Y) arrayfun(@(x,y) Tuu(x,y),X,Y),0.01,pi/2,0,pi/4)". However, the program is too slow to use. How to speed up this program in details? Many thanks! The codes of Tuu(x,y) are as following:
function U=Tuu(x,y)
syms kz d
m = 2;
dd=2.106*(m+1);
vh = 4;
mu = 11;
delta = 8;
HBAR = 1.05457266e-34;
ME = 9.1093897e-31;
ELEC = 1.60217733e-19;
Kh = 2.106;
vKh = [0,0,0;Kh,0,0;-Kh,0,0;0,Kh,0;0,-Kh,0];
kc = sqrt(2.*ME.*ELEC/HBAR^2).*1e-10;
ku = kc.*sqrt(mu+delta);
kd = kc.*sqrt(mu-delta);
a3 = [pi/Kh,pi/Kh,sqrt(2).*pi/Kh];
kuu =[-ku.*sin(x).*cos(y), -ku.*sin(x).*sin(y), kz];
n=0:m;
for p=1:5;
for q=1:5;
tuu(p,q)= (sum((kuu + vKh(p,:)).^2)-ku^2).*(p==q)+ kc^2*vh*sum(exp(i.*n.*sum((vKh(q,:)-vKh(p,:)).*a3)))/(m+1).*(p~=q);
end
end
dtuu=det(tuu);
kz0=vpasolve(dtuu,kz);
kzz=kz0(real(vpa(kz0))>=0&imag(vpa(kz0))>=0);
tuu1=subs(tuu,kz,kzz(1));
tuu2=subs(tuu,kz,kzz(2));
tuu3=subs(tuu,kz,kzz(3));
tuu4=subs(tuu,kz,kzz(4));
tuu5=subs(tuu,kz,kzz(5));
tuu11=double(tuu1);
tuu22=double(tuu2);
tuu33=double(tuu3);
tuu44=double(tuu4);
tuu55=double(tuu5);
nuu1=null(tuu11);
nuu2=null(tuu22);
nuu3=null(tuu33);
nuu4=null(tuu44);
nuu5=null(tuu55);
piuu=[nuu1,nuu2,nuu3,nuu4,nuu5];
pei=[1;0;0;0;0];
A=piuu\pei;
psiuu1=A(1).*nuu1(1)*exp(i*kzz(1)*d)+A(2)*nuu2(1)*exp(i*kzz(2)*d)+A(3)*nuu3(1)*exp(i*kzz(3)*d)+A(4)*nuu4(1)*exp(i*kzz(4)*d)+A(5)*nuu5(1)*exp(i*kzz(5)*d);
psiuu2=A(1).*nuu1(2)*exp(i*kzz(1)*d)+A(2)*nuu2(2)*exp(i*kzz(2)*d)+A(3)*nuu3(2)*exp(i*kzz(3)*d)+A(4)*nuu4(2)*exp(i*kzz(4)*d)+A(5)*nuu5(2)*exp(i*kzz(5)*d);
psiuu3=A(1).*nuu1(3)*exp(i*kzz(1)*d)+A(2)*nuu2(3)*exp(i*kzz(2)*d)+A(3)*nuu3(3)*exp(i*kzz(3)*d)+A(4)*nuu4(3)*exp(i*kzz(4)*d)+A(5)*nuu5(3)*exp(i*kzz(5)*d);
psiuu4=A(1).*nuu1(4)*exp(i*kzz(1)*d)+A(2)*nuu2(4)*exp(i*kzz(2)*d)+A(3)*nuu3(4)*exp(i*kzz(3)*d)+A(4)*nuu4(4)*exp(i*kzz(4)*d)+A(5)*nuu5(4)*exp(i*kzz(5)*d);
psiuu5=A(1).*nuu1(5)*exp(i*kzz(1)*d)+A(2)*nuu2(5)*exp(i*kzz(2)*d)+A(3)*nuu3(5)*exp(i*kzz(3)*d)+A(4)*nuu4(5)*exp(i*kzz(4)*d)+A(5)*nuu5(5)*exp(i*kzz(5)*d);
Tuux=ku.*sin(x).*(imag(conj(psiuu1)*diff(psiuu1,d)+conj(psiuu2)*diff(psiuu2,d)+conj(psiuu3)*diff(psiuu3,d)+conj(psiuu4)*diff(psiuu4,d)+conj(psiuu5)*diff(psiuu5,d)));
U=double(subs(Tuux,d,dd));
end
  3 个评论
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Henan Fang
Henan Fang 2018-9-28
@Stephen Cobeldick Can you tell me, in detail, how to perform numeric calculations instead of symbolic ones in this program?
Stephen23
Stephen23 2018-9-28
编辑：Stephen23 2018-9-28
"Can you tell me, in detail, how to perform numeric calculations instead of symbolic ones in this program?"
Not really, as that function contains no code comments, no help, no links, no references, no examples, no demo, no explanation what it is doing. But it is possible that you could replace symbolic operations with faster numeric operations, if you want a numeric result at the end.
If you ask the author of that function they should be able to describe what the function does, and then you can start to investigate numeric alternatives.

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