How to code sparse diagonal matrix of increasing dimensions

I need to code a growing matrix via for loop and evaluate the time fo some computations, but when i plot the time implied related to the computation it doesn't respect the intervals in which i want to calculate it. Please help!

I'd be very grateful!

clc
clear all
close all

for n= 500:50:1000
   e = ones(n,1);
   A = spdiags([-2*e 0*e 6*e 0*e -2*e],-2:2,n,n);
   for i = 1:n
      bi(i) = -(i+1)^2;
      b = bi';
   end

   tic;
   L1 = chol(A,'lower');
   y1 = L1\b;
   x1 = L1'\y1;

   toc;
   t1(n) = toc;
   A2 = full(A);

   tic;
   L2 = chol(A2,'lower');
   y2 = L2\b;
   x2 = L2'\y2;
   toc;

   t2(n) = toc;
end

abs_plot = linspace(500,1000,1000);

plot(abs_plot,t1,'ro','markerfacecolor','r')
hold on
plot(abs_plot,t2,'bo','markerfacecolor','b')
axis tight

[Jan]

I do not understand this sentene: " it doesn't respect the intervals in which i want to calculate it"

Answer 1

[Jan]

Maybe this is not, what you want:

for n = 500:50:1000
    tic
    t1(n) = toc;
end

Setting t(500) in the 1st step ist not useful. Better:

nList = 500:50:1000
for k = 1:numel(nList)
    n = nList(k);
    
    tic
    ...
    t1(k) = toc;   % Not t(n)
end

Or the full code without the time wasting "brute clearing header":

function YourFcn  % Smarter than "clear all"

nList = 500:50:1000;
for k = 1:numel(nList)
   n = nList(k);
   e = ones(n,1);
   A = spdiags([-2*e 0*e 6*e 0*e -2*e],-2:2,n,n);
   b = -(2:n+1).' .^ 2;  % Vectorized instead of a for loop

   tic;
   L1 = chol(A,'lower');
   y1 = L1 \ b;
   x1 = L1' \ y1;
   t1(k) = toc;

   A2 = full(A);

   tic;
   L2 = chol(A2,'lower');
   y2 = L2 \ b;
   x2 = L2' \ y2;
   t2(k) = toc;
end

plot(nList, t1, 'ro', 'markerfacecolor', 'r')
hold on
plot(nList, t2, 'bo', 'markerfacecolor', 'b')
axis tight
end

[Leone Dragone]

Thank you very much! This was really helpful, thanks a lot!!