Eigenvalues of a large Matrix

Question

AVM 2020-5-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/534023-eigenvalues-of-a-large-matrix

评论： AVM 2020-5-26

I have to plot the one of the eigenvalues of a large matirx in the following. The matrix is 20*20 dim. Numerically I have to get the eigenvalues and plot that. But the following code is not giving any plot. I have tried to plot it usnig ''For loop'' as normal plot is taking extremely huge time. But using '' for loop'' the plot is empty. Pl somebody help me to solve the long run time case here. Pl see below for my code.

clc;clear
syms x
a=1.0;
b=1.0;
n=20;
I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';
sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];
for x=0.0001:0.1:1.1    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x.*kron(sigx,(crea+anni)); 
    [~,v]=eig(f);
    u=v(1,1);
    plot(x,u,'r')
end

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Answer 1

KSSV 2020-5-26

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/534023-eigenvalues-of-a-large-matrix#answer_439043

编辑：KSSV 2020-5-26

在 MATLAB Online 中打开

clc; clear all ;
clc;clear
a=1.0;
b=1.0;
n=20;
I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';
sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];
figure
hold on
for x=0.0001:0.1:1.1    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x.*kron(sigx,(crea+anni)); 
    [~,v]=eig(f);
    u=v(1,1);
    plot(x,u,'*r')
end

OR

clc; clear all ;
clc;clear
a=1.0;
b=1.0;
n=20;
I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';
sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];
x=0.0001:0.1:1.1 ;
u = zeros(size(x)) ; 
for i = 1:length(x)    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x(i).*kron(sigx,(crea+anni)); 
    [~,v]=eig(f);
    u(i)=v(1,1);    
end
plot(x,u)