Why does my script takes longer time to execute than expected?

Hi, I tried to run my matlab script. In the attached file: MBBA5CBPAA_Result.m, I tried to run only the second section:Active dissipation. The computation is supposed to take 11 hours 36 minutes but is still running even after 12 hours. Please is there any way to speed up the running time. The Non_linear1_differentu_MBBA_func1.m and dissipative_elastic_energy_MBBA_fun.m are subroutines (functions), while the MBBA5CBPAA_Result.m is where the run the code.

Your assistance is highly appreciated. Thank you.

[Walter Roberson]

What leads you to expect that the code should take 11 hours 36 minutes?

[University Glasgow]

Hi Walter,

I did a rough calculation. For 11 by 11 array it took 1.32 minutes and I increased the mesh size to 250 by 250, which i think should be approx. 11.32 hours.

[Torsten]

Oh, how nice it would be if the solution of linear systems would scale linearily with the number of equations ...

But it scales cubic, thus expected time roughly (250^2/11^2)^3 * 1,5 [min] = 393 years (at least for full Jacobians).

[Walter Roberson]

11 x 11 appears to be length(u) by length(xi) . Your last commented-out u and xi are 11 elements each, suggesting that those are what you calculated with. Your current u and xi are 251 elements each (not 250); perhaps you had an off-by one in making that remark.

On the other hand there is an N inside of dissipative_elastic_energy_MBBA_func and that N is exactly 250, so the amount of work done is proporational to length(u) by length(xi) by N .

Did you possibly increase N ?

[Walter Roberson]

You are running an ode for tspan = 0:20000 for each combination of u and xi. Although it is possible to combine independent ode into a single ode45 call, it is often not advised to do so as the points at which ode45() needs to internally refine the system might be at different locations for the different odes so it can be inefficient and a source of numeric roundoff problems to combine independent odes.

Your ode45 with 20001 is probably taking the bulk of your computation time.

The Non_linear1_differentu_MBBA_func1 is already designed to run through combinations of u and xi, so you could reduce the calling overhead by calling it once over the full xi and u, instead of calling it once for each individual combination of xi and u. I doubt that will make significant difference, though.

[University Glasgow]

Thank you so much Walter for your expalanation. Is actually making sense now. I did not increase N. Please how do I call over Non_linear1_differentu_MBBA_func1 once for the full xi and u?

[Torsten]

I saw from your code that the number of equations is 2*11 and 2*250, not 11^2 and 250^2.

Thus the expected computation time is

(500/22)^3 * 1.5 [min] = 12.22 [days]

[University Glasgow]

Okay, thank you Torsten.

[Torsten]

It would be interesting to know if the theoretical estimate is not that bad. So if you get computation time for different grid resolutions, post them here if possible.

[Walter Roberson]

@Torsten

I do not understand why you say "2*11" and "2*250" rather than 11^2 and 250^2 ?

dissipative_elastic_energy_MBBA_func has

for iu=1:length(u)
     for  ixi=1:length(xi)

so operations are being done proporational to the product of the lengths of u and xi -- each of which used to be length 11

          % xi = -0.2:0.04:0.2;
          % u = 0:0.2:2;

but are now 251

         xi = -0.2:0.0016:0.2;
         u =  0:0.008:2;

[Walter Roberson]

@University Glasgow

Your current code in dissipative_elastic_energy_MBBA_func has

for iu=1:length(u)
     for  ixi=1:length(xi)
         [nt,tspan,THETA, V, z, t]= Non_linear1_differentu_MBBA_func1(u(iu), xi(ixi), d, N);

so you are passing in individual u and individual xi values to Non_linear1_differentu_MBBA_func1

But that function has

Xix = xi;
Ui = u;
for Xidx = 1:length(Xix)
    xi = Xix(Xidx);  
    for Uidx = 1:length(Ui)
        u = Ui(Uidx);

so that function is already looping over each xi and u value. You do not need to pass in individual u and xi pairs into Non_linear1_differentu_MBBA_func1 -- you could call

[all_nt, tspan, all_THETA, all_V, all_z, all_t] = Non_linear1_differentu_MBBA_func1(u, xi, d, N);

0r something similar to that, knowing that Non_linear1_differentu_MBBA_func1 is already designed to return data for all of the u xi combinations. You would have to look more carefully at the output values for Non_linear1_differentu_MBBA_func1 to see how it puts the values together.

Perhaps you would want to still loop over individual u elements but process all of the xi elements at the same time.

I would expect that the overhead of calling Non_linear1_differentu_MBBA_func1 length(u) by length(xi) times instead of just once would be only a small portion of the cost of the code. It looks to me as if your major cost is the ode45 call with the timespan that is 20001 elements. It is not obvious to me why you are asking for so many output times.

[University Glasgow]

I tried to restructure my code by calling my function: dissipative_elastic_energy_MBBA_func in a for loop. For 11 by 11 mesh, I got 1.06 [min]. I tried for 51 by 51 mesh, I got 26.7 [min].

[Walter Roberson]

1.06 * 60 / (11*11)

ans = 0.5256

26.7 * 60 / (51*51)

ans = 0.6159

so it is a little slower per iteration as you increase the mesh size, but not greatly so. 20%-ish ?

[University Glasgow]

Okay, thank you.