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)

Not able to plot probability density distribution.

Anshuman 2022-10-29

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 2022-10-30

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 2022-10-30

在 MATLAB Online 中打开

@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 2022-10-30

Okay, sure! Thanks a lot for the help!

Anshuman 2022-10-30

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 2022-10-30

And the probability density plot is of g_f.

Torsten 2022-10-30

在 MATLAB Online 中打开

You create a distribution

pd = makedist('Normal');

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

Anshuman 2022-10-30

在 MATLAB Online 中打开

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 2022-10-30

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

Anshuman 2022-10-30

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

Torsten 2022-10-30

编辑：Torsten 2022-10-30

在 MATLAB Online 中打开

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 2022-10-30

Thanks

Anshuman 2022-10-30

编辑：Torsten 2022-10-30

在 MATLAB Online 中打开

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 2022-10-30

Torsten 2022-10-30

编辑：Torsten 2022-10-30

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

Anshuman 2022-10-30

@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 2022-10-30

Torsten 2022-10-30

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 2022-10-30

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 2022-10-30

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

Not able to plot probability density distribution.

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