How to save data from a loop as a vector?

Good Morning! I'm new to matlab and I have a question. When I do the loop described in the code below (where I am varying the magnetic field B), only the last data is saved. I would like to construct a vector with all the data of the eigenvalues ​​of the HT matrix, to construct a graph of the magnetic field as a function of the four eigenvalues ​​of Ht. I would like to build four vectors with the data of all the loops of the eigenvalues ​​to build a graph. Anyone who can help me I would be very grateful. Follow the program below.

clear

clc

d0=0.2; %meV delta 0

d1=0.18; %#delta 1

d2=0.05; %#delta 2

%#the electron and hole effective g factor in the z and x directions.

ghx=-0.35 ;

ghz=-2.2;

gex=-0.65;

gez=-0.8;

alpha=0.02; %#meV/T^2 diamagnetic shift coefficient,

ga=0.0 ;

gb=ga ; %# the interaction strength with the exciton state with same polarization.

theta=pi/3 ;

wx=0.01;

wd=wx-d0;

wa=wx+0.5;

wb=wa;

wl=wa;

G0a=0.05; %# is the maximum value of energy of the pulse

G0b=G0a;

tc=30 ; %# the time of the center of the pulse

tal=10 ; %#is the Gaussian rms width

mub=0.0579; %# Bohr magneton

for B=0:0.1:10

bp=mub*B.*sin(theta)*(gez+ghz)*0.5 ; %bp

bm=mub*B.*sin(theta)*(gez-ghz)*0.5; %bm

be=mub*B.*cos(theta)*gex*0.5; %be

bh=mub*B.*cos(theta)*ghx*0.5; %bh

H1=[wx,d1/2,0,0;d1/2,wx,0,0;0,0,wd,d2/2;0,0,d2/2,wd];

H2=[bp+alpha*B.^2,0,be,bh;0,-bp+alpha*B.^2,bh,be;be,bh,-bm+alpha*B.^2,0;bh,be,0,bm+alpha*B.^2];

HT=H1+H2;

[V,D] = eig(HT);

end

Answer 1

[Star Strider]

There are different ways to do this.

This approach simply concatenates them as the third dimension of a (4x4xnumel(B)) array —

d0=0.2;   %meV   delta 0
d1=0.18;      %#delta 1
d2=0.05;     %#delta 2
%#the electron and hole effective g factor in the z and x directions.
ghx=-0.35 ;  
ghz=-2.2;
gex=-0.65;
gez=-0.8;
alpha=0.02;  %#meV/T^2   diamagnetic shift coefficient,
ga=0.0 ;  
gb=ga  ;     %# the interaction strength with the exciton state with same polarization.
theta=pi/3  ;
wx=0.01;
wd=wx-d0;
wa=wx+0.5;
wb=wa;
wl=wa;
G0a=0.05;    %#  is the maximum value of energy of the pulse      
G0b=G0a;
tc=30  ;    %# the time of the center of the pulse
tal=10 ;    %#is the Gaussian rms width
mub=0.0579;  %# Bohr magneton
B=0:0.1:10;
V = NaN(4,4,numel(B));                              % Preallocate
D = V;                                              % Preallocate
for k = 1:numel(B)  
    bp=mub*B(k).*sin(theta)*(gez+ghz)*0.5 ; %bp  
    bm=mub*B(k).*sin(theta)*(gez-ghz)*0.5; %bm
    be=mub*B(k).*cos(theta)*gex*0.5;   %be
    bh=mub*B(k).*cos(theta)*ghx*0.5;   %bh
    H1=[wx,d1/2,0,0;d1/2,wx,0,0;0,0,wd,d2/2;0,0,d2/2,wd];
    H2=[bp+alpha*B(k).^2,0,be,bh;0,-bp+alpha*B(k).^2,bh,be;be,bh,-bm+alpha*B(k).^2,0;bh,be,0,bm+alpha*B(k).^2];
    HT=H1+H2;
    [V(:,:,k),D(:,:,k)] = eig(HT);
end 

Another option would be to store them in cell arrays.

.

[Celso Júnior]

Great! but now how do I get the vector to plot an eigenvalue as a function of the magnetic field? A vector of the type

E1 = [- 0.2150, -0.2156, -0.2134, -0.2043, -0.1868, -0.1608, -0.1264, -0.0843, -0.0350, 0.0210, 0.084, 0.084, 0.085, 0.084, 0.084, 0.084, 0.084, 0.084, 0.084, 0.084, 0.088 1.0597, 1.2167]

For example where B=0:0.5:10 and plot

plot(B,E1)

Thanks in advance for your help!

[Star Strider]

I am not certain what you want.

Try this —

d0=0.2;   %meV   delta 0
d1=0.18;      %#delta 1
d2=0.05;     %#delta 2
%#the electron and hole effective g factor in the z and x directions.
ghx=-0.35 ;  
ghz=-2.2;
gex=-0.65;
gez=-0.8;
alpha=0.02;  %#meV/T^2   diamagnetic shift coefficient,
ga=0.0 ;  
gb=ga  ;     %# the interaction strength with the exciton state with same polarization.
theta=pi/3  ;
wx=0.01;
wd=wx-d0;
wa=wx+0.5;
wb=wa;
wl=wa;
G0a=0.05;    %#  is the maximum value of energy of the pulse      
G0b=G0a;
tc=30  ;    %# the time of the center of the pulse
tal=10 ;    %#is the Gaussian rms width
mub=0.0579;  %# Bohr magneton
B=0:0.1:10;
V = NaN(4,4,numel(B));                              % Preallocate
D = V;                                              % Preallocate
for k = 1:numel(B)  
    bp=mub*B(k).*sin(theta)*(gez+ghz)*0.5 ; %bp  
    bm=mub*B(k).*sin(theta)*(gez-ghz)*0.5; %bm
    be=mub*B(k).*cos(theta)*gex*0.5;   %be
    bh=mub*B(k).*cos(theta)*ghx*0.5;   %bh
    H1=[wx,d1/2,0,0;d1/2,wx,0,0;0,0,wd,d2/2;0,0,d2/2,wd];
    H2=[bp+alpha*B(k).^2,0,be,bh;0,-bp+alpha*B(k).^2,bh,be;be,bh,-bm+alpha*B(k).^2,0;bh,be,0,bm+alpha*B(k).^2];
    HT=H1+H2;
    [V(:,:,k),D(:,:,k)] = eig(HT);
end 

for k = 1:size(D,3)
    Dm(:,k) = diag(D(:,:,k));
end

figure
plot(B,Dm)
grid
xlabel('B')
ylabel('\lambda')
legend(compose('D(%d,%d)',repmat(1:4,2,1)'), 'Location','best')

This plots all the eigenvalues as funcitons of ‘B’.

.

[Celso Júnior]

It was exactly what I wanted. I appreciate your help!!!!

[Star Strider]

As always, my pleasure!

[Celso Júnior]

Hi, could I ask one more favor, because I see that you are an expert, with I could make a vector now with the values of the eigenvectors, for example take each all the first columns of the eigenvectors of the l of the loop and build a graph in function of the magnetic field. So

plot(B,V(1,1)^2 , B , V(2,1)^2, B ,V(3,1)^2, B, V(4,1)^2))

and so on up to the fourth eigenvector.

[Star Strider]

Sure!

This plots the columns of each element of ‘V’ —

d0=0.2;   %meV   delta 0
d1=0.18;      %#delta 1
d2=0.05;     %#delta 2
%#the electron and hole effective g factor in the z and x directions.
ghx=-0.35 ;  
ghz=-2.2;
gex=-0.65;
gez=-0.8;
alpha=0.02;  %#meV/T^2   diamagnetic shift coefficient,
ga=0.0 ;  
gb=ga  ;     %# the interaction strength with the exciton state with same polarization.
theta=pi/3  ;
wx=0.01;
wd=wx-d0;
wa=wx+0.5;
wb=wa;
wl=wa;
G0a=0.05;    %#  is the maximum value of energy of the pulse      
G0b=G0a;
tc=30  ;    %# the time of the center of the pulse
tal=10 ;    %#is the Gaussian rms width
mub=0.0579;  %# Bohr magneton
B=0:0.1:10;
V = NaN(4,4,numel(B));                              % Preallocate
D = V;                                              % Preallocate
for k = 1:numel(B)  
    bp=mub*B(k).*sin(theta)*(gez+ghz)*0.5 ; %bp  
    bm=mub*B(k).*sin(theta)*(gez-ghz)*0.5; %bm
    be=mub*B(k).*cos(theta)*gex*0.5;   %be
    bh=mub*B(k).*cos(theta)*ghx*0.5;   %bh
    H1=[wx,d1/2,0,0;d1/2,wx,0,0;0,0,wd,d2/2;0,0,d2/2,wd];
    H2=[bp+alpha*B(k).^2,0,be,bh;0,-bp+alpha*B(k).^2,bh,be;be,bh,-bm+alpha*B(k).^2,0;bh,be,0,bm+alpha*B(k).^2];
    HT=H1+H2;
    [V(:,:,k),D(:,:,k)] = eig(HT);
end 

for k = 1:size(D,2)
    Vm{k} = squeeze(V(:,k,:));
end
Vm

Vm = 1×4 cell array
    {4×101 double}    {4×101 double}    {4×101 double}    {4×101 double}

figure
for k = 1:size(D,2)
    subplot(2,2,k)
    plot(B,Vm{k})
    grid
    xlabel('B')
    ylabel('Right Eigenvector')
    title(sprintf('Column %d',k))
    legend(compose('V(%d,%d)', [1:4;ones(1,4)*k]'), 'Location','best')
end
sgtitle('Eigenvectors')

This plots the each column of ‘V’ for every ‘V’. (It is easiest to use a cell array for this.)

.

[Celso Júnior]

Thanks a lot for the help! Only God to reward you!!!

[Star Strider]

As always, my pleasure!