double summation in matlab

Question

Samuel Suakye 2020-4-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/519518-double-summation-in-matlab

编辑： darova 2020-4-21

Plotting j_z/j_o against beta_1 = {0,...,10}; and beta_2 = 1, This is what I have done (check the code below) using symsum but for days now it is still running and want to find out whether there are different methods to that. Thanks in advance ;

clc;
b = 0.142e-9; gammao = 3.0; m = 101;
hbar = 1; e = -1; 
K = 8.617e-16; T = 287.5;
a = ((3*b)/(2*hbar)); Pz = ((2*pi*hbar)/(3*b));
beta2 = 1; beta1 = linspace(0,10, 30); % However many you want.
Wcnzz = sqrt(3);
jo = ((8*e*Wcnzz*gammao)/(3*hbar*m*b));
%%
syms q s 
B1 = q.*beta1; B2 = q.*beta2; v = ((pi.*s)./m); h = (a.*Pz);
z = (2.*(pi.^2).*s.*sqrt(3).*(a./(2*pi)));
Eqszz = (a./(2*pi)).*((1+(4.*cos(h).*cos(v))+(4.*((cos(v)).^2))).^0.5);
Fqszz = ((a.^2).*m)./((z.*((1+(4.*cos(h).*cos(v))+(4.*((cos(v)).^2))).^0.5))./(K.*T));
J1 = besselj(0,B1); J2 = besselj(0,B2);
J = q.*Fqszz.*Eqszz.*J1.*J2;
X = symsum(J,s,1,m);
jz = symsum(X,q,1,inf);
j = jz./jo; 
fplot(beta1, j, 'r-', 'LineWidth', 2 );
drawnow;
grid on;
fontSize = 20;
xlabel('\beta_1', 'FontSize', fontSize)
ylabel('j_z/j_o', 'FontSize', fontSize)
hold on
%%
b = 0.142e-9; gammao = 3.0; m = 101;
hbar = 1; e = -1; 
K = 8.617e-16; T = 287.5;
a = ((3*b)/(2*hbar)); Pz = ((2*pi*hbar)/(3*b));
beta2 = 1; beta1 = linspace(0,10, 30); % However many you want.
Wcnac = 1; t = sqrt(3); n = 1e-9;
jo = ((8*e*Wcnac*gammao)/(3*hbar*m*b));
%%
syms q s 
B1 = q.*beta1; B2 = q.*beta2; u = ((a.*Pz)./t); g = ((pi.*s.*t)./n);
y = (2.*(pi.^2).*s.*t);
Eqsac = ((1+(4.*cos(g).*cos(u))+(4.*((cos(u)).^2))).^0.5);
Fqsac = ((a.^2).*n)./((y.*((1+(4.*cos(g).*cos(u))+(4.*((cos(u)).^2))).^0.5))./(K.*T));
J1 = besselj(0,B1); J2 = besselj(0,B2);
J = q.*Fqsac.*Eqsac.*J1.*J2;
X1 = symsum(J,s,1,m);
jz = symsum(X1,q,1,inf);
j = jz./jo;
fplot(beta1, j, 'b-', 'LineWidth', 2);
drawnow;
grid on; 
fontSize = 20;
xlabel('\beta_1', 'FontSize', fontSize)
ylabel('j_z/j_o', 'FontSize', fontSize)
title('j_x/j_o vs.  \beta_1', 'FontSize', fontSize)
legend('zigzig CNs','armchair CNs','Location','Best');
% Maximize the figure window.
hFig.WindowState = 'maximized';

3 个评论
显示 1更早的评论隐藏 1更早的评论

Samuel Suakye 2020-4-21

编辑：Samuel Suakye 2020-4-21

not a mistake.

darova 2020-4-21

It's strangle because it can be simplified

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Answer 1

darova 2020-4-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/519518-double-summation-in-matlab#answer_427317

在 MATLAB Online 中打开

Here is numerical approach

clc,clear
% alignComments
b      = 0.142e-9;
gammao = 3.0;
m      = 101;
hbar   = 1;
e      = -1;
K      = 8.617e-16;
T      = 287.5;
a      = 3*b/(2*hbar);
Pz     = 2*pi*hbar/(3*b);
beta2  = 1;
beta1  = linspace(0,10, 100); % However many you want.
Wcnzz  = sqrt(3);
jo     = 8*e*Wcnzz*gammao/(3*hbar*m*b);
[q,s] = meshgrid(1:0.1:3,1:m);  % 1:0.1:3 span for 'q'
cps   = cos(pi.*s./m);
cap   = cos(a.*Pz);
Eqszz = a/2/pi*sqrt(1 + 4*cap.*cps + 4*cps.^2);
Fqszz = a^2*m*K*T ./ (2*pi^2*s.*sqrt(3).*Eqszz);
for i = 1:length(beta1)
    B1 = q.*beta1(i);
    B2 = q.*beta2;    
    J1 = besselj(0,q.*B1);
    J2 = besselj(0,q.*B2);    
    tmp = q.*Fqszz.*Eqszz.*J1.*J2;
    J(i) = sum(tmp(:));
end
plot(beta1,J)