Not able to plot probability density distribution.

I am trying to plot a probability density fucntion of growth factors of a matrix with respect to LU decomposition ; the growth factor is defined as g_f in my code.

The final plot should look like this for 3 values of m (size of matrix), I tried it for m = 8. But the plot does not appear! It only gives a nlank figure! Can someone suggest me what changes I shall do, thanks a lot for your advice and time!

x = 1:1000:1;
pd = makedist('Normal');
pd = makedist('Weibull','A',5,'B',2);

n = 1000;
gf = zeros(n);

for j = 1:n
    A = (randi([0,1] , 8));
    [L,U] = lu(A);
    g_f(j) = max(U)/max(A);
end

pdf_normal = pdf(pd,g_f);
plot(x,pdf_normal,'LineWidth',2)

[Anshuman]

I tried doing like this: But the plots are not matching!

pd = makedist('Normal');
%pd = makedist('Weibull','A',5,'B',2);

m = 1000;
gf = zeros(m);

for j = 1:m
    A = (randi([1,10] , 8));
    [L,U] = lu(A);
    g_f(j) = max(abs(U))/max(abs(A));
end

pdf_normal = pdf(pd,g_f);
plot(g_f,pdf_normal,'LineWidth',2)

[Torsten]

It's time that you explain in your own words what you are trying to do.

Your code does not help that much.

[KALYAN ACHARJYA]

@Anshuman Pls check again at your level (It's more subjective rather than Matlab)

x = 0:0.1:2;
pd = makedist('Normal');
%pd = makedist('Weibull','A',5,'B',2);
n=length(x);
gf = zeros(n);
m=[8 16 32];
g_f=zeros(1,n);
for i=1:length(m)
    for j = 1:n
        A = (randi([0,1],m(i)));
        [L,U] = lu(A);
        g_f(j) = max(U)/max(A);
    end
    pdf_normal = pdf(pd,g_f);
    plot(x,pdf_normal);
    hold on;
end 
grid on; 

[Anshuman]

Okay, sure! Thanks a lot for the help!

[Anshuman]

But I had to plot this for 1000 such A matrices; and the g_f values will automatically lie in the range [0-10], such that they form a distrbution!

[Anshuman]

And the probability density plot is of g_f.

[Torsten]

You create a distribution

pd = makedist('Normal');

but you don't use it anywhere. What's the sense of it ?

[Anshuman]

pd = makedist('Normal');
%pd = makedist('Weibull','A',5,'B',2);

m=[8 16 32];


for i=1:length(m)

    g_f=zeros(1,1000);

    for j = 1:1000
        A = (randi([0,1],m(i)));
        [L,U] = lu(A);
        g_f(j) = max(U)/max(A);
    end

    pdf_normal = pdf(pd,g_f);
    scatter(g_f,pdf_normal);
    set(gca,'xscale','log')
    set(gca,'yscale','log')
    hold on;

end 

[Anshuman]

I think I don't need that distribution part; the values should automatically create a distribution!

[Anshuman]

I can't understand the y-axis of my origianl plot! What is meant by probability distribution over there!

[Torsten]

Instead of

pdf_normal = pdf(pd,g_f);

try

ksdensity(g_f)

n = 10000;
gf = zeros(n);

for j = 1:n
    A = (randi([0,1] , 8));
    [L,U] = lu(A);
    g_f(j) = max(U(:))/max(A(:));
end

ksdensity(g_f)

[Anshuman]

Thanks

[Anshuman]

I got something like this

m=[8 16 32];


for i=1:length(m)

    g_f=zeros(1,100000);

    for j = 1:100000
        A = (randi([0,1],m(i)));
        [L,U] = lu(A);
        g_f(j) = max(U(:))/max(A(:));
    end

    %pdf_normal = pdf(pd,g_f);
    
    ksdensity(g_f);
    %set(gca,'xscale','log')
    %xlim([0 10])
    %set(gca,'yscale','log')
    hold on;

end 

[Anshuman]

[Torsten]

Since you refuse to explain what you are trying to do, I can only blindly guess - and that's the result.

[Anshuman]

@Torsten, really very sorry! I kind of missed your comment! And thanks a lot for your help and time!

A collection of random matrices has been taken and their growth factor (max(U)/max(A) ; where A = LU) has been plotted as the following: The figure represents the results of LU facotrising 1 million matrices each of dimennsion 8,16 and 32, growth factor has been collected into bins of 0.2 and the resulting data is plotted as a probability density distribution.

Moreover, I am getting somewhat similar plot when increasing the number of matrices from 1000 to 1 millions but not the exact plot! Is it related to the random matrice's entries? I am assuming it to be 0-1.

[Anshuman]

[Torsten]

I don't know from which kind of distribution the matrix entries in the publication are generated. You choose from a discrete distribution with p(A(i,j) = 0) = p(A(i,j) = 1) = 1/2.

[Anshuman]

Yeah, I read the text, they are using it like this: 'A = rand(m(i),m(i))/sqrt(m(i));' Now my current plot after using this looks like the following! Can't understand why it's not matching it exactly! Nevertheless, thanks a lot for your help; I really could not have even came close to plotting this, without the help of you all!

[Torsten]

You also use logarithmic scale for the x-axis. This is not the case in the graphics of the publication.