Plot of the function after integration

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Yuriy Yerin
Yuriy Yerin 2018-10-12
评论： Yuriy Yerin 2018-10-15
Hello. I want to plot a complicated function. Unfortunately at the end I obtain just one point of the function and the empty graph. I'd like to avoid exploitation of the command for to speed up my calculations. Could you explain where is my mistake? Thank you. Below is my code
function z=test_plot
tic
tt=-0.000689609;t=0.242731; muu=0.365908;
[m,NN]=meshgrid(0:100,-3000:1:3000);
y1= @(N,q,k) t*q./k.*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*N.*t-(2*m(1,:)+1)*pi*t))./(-k.^2-2*k.*q-...
q.^2+muu+1i*(2*pi*N.*t-(2*m(1,:)+1)*pi*t)))./(tt*pi+integral(@(a)a.*tanh((a.^2-muu)./(2*t)).*log((2*a.^2+2*a.*q+...
q.^2-2*muu-1i*2*pi*N*t)./(2*a.^2-2*a.*q+q.^2-2*muu-1i*2*pi*N*t))./q-2,0,10000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true));
R1=@(q,k) integral(@(N)y1(N,q,k),3000,10^6,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
R11=@(q,k) integral(@(N)y1(N,q,k),-10^6,-3000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
y2=@(q,k) t*q./k.*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t))./(-k.^2-2*k.*q-...
q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t)))./(tt*pi+integral(@(a)a.*tanh((a.^2-muu)./(2*t)).*log((2*a.^2+2*a.*q+...
q.^2-2*muu-1i*2*pi*NN(:,1).*t)./(2*a.^2-2*a.*q+q.^2-2*muu-1i*2*pi*NN(:,1).*t))./q-2,0,10000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true));
R2=@(q,k) sum(y2(q,k));
S=@(q,k) R1(q,k)+R11(q,k)+R2(q,k)-4*sqrt(2)/pi*(1/1000)/(pi^(3/2)*sqrt(t))*q.^2;
Sigma=@(k) integral(@(q)S(q,k),0.001,7,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
Sum_sigma=@(k) 2*real(sum(Sigma(k)./((1i*(2*m(1,:)+1)*pi*t-k.^2+muu-Sigma(k)).*(1i*(2*m(1,:)+1)*pi*t-k.^2+muu))));
k=0.001:0.05:5.01;
Sum_sigma(k)
plot(k,Sum_sigma(k))
toc
end
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Torsten
Torsten 2018-10-15
I have no experience with parallel computing in MATLAB. But since the calculations for different k-values are independent, it should somehow be possible to parallelize here.
Yuriy Yerin
Yuriy Yerin 2018-10-15
Me too, but anyway thank you again for the help. I will google about that.

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