Code : loop which repeatedly calls ode45

Problem : slow (er than matlab)

System : Debian Linux (Octave 5.2), Windows (Octave 6.x)

Simulation with a loop and ode 45 inside it executed much slower in Octave (5.2 and 6.x) compared to Matlab. Before optimizing the differential equation I was integrating, I decided to profile the code to see if my differential equation code or the discrete-time-controller code was the bottleneck.

Profiling indicated that most of the execution time is spent inside functions other than the differential equation functions specific to my problem.

**@inputParser_xxxxx and runge_kutta_45_dorpri** are consuming most of the time.

I am simulating a system which has both discrete time sub-system (digital control) and continuous time system (plant being controlled). The fixed-time-step part is implemented by the while loop and the continuous time part is implemented by the ode45.

Is there a way to speed up my simulation ? If the functions at the top of the profile were user written, I could have attempted to convert them to C++ mkoct files.

Below is the code and the profiling result. The code is a minimum working example to illustrate the problem. Even for much more complicated (non linear, time varying) differential equations, I am still getting similar results.

# CODE

```
clc;
clear;
fprintf('example profiled running...\n');
endtime = 1000;
stepsize = 0.5; % the fixed step used by the controller
t = 0;
ii = 1;
% reserve space so that it doesn't slow down the program
tl = zeros(ceil(endtime/stepsize), 1);
yl = zeros(ceil(endtime/stepsize), 2);
ic = [1, 0];
control = 0.1;
profile on;
while(t < endtime)
% run the non linear time varying differential equation
% using a variable time step method.
% example shown here is a linear system.
% but profiling results are the same.
[tt, yy] = ode45(@(t,x)[0,1; -1, control]*x/2, [0, stepsize], ic);
% collect results for plotting later
yl(ii, :) = yy(end, :);
tl(ii) = t + tt(end, :);
ic = yy(end, :);
if(norm(ic) > 5)
% this is where the controller logic would have been written in the real application
control = -0.05;
end
ii = ii+1;
t = t+stepsize;
end
profile off;
profshow;
plot(tl, yl);
fprintf('example profiled ran...\n');
```

## Profiling result

```
# Function Attr Time (s) Time (%) Calls
75 runge_kutta_45_dorpri 14.695 15.45 67522
23 @inputParser/parse 14.132 14.86 11200
73 integrate_adaptive 13.456 14.15 5600
29 @inputParser/add_missing 7.984 8.40 22400
55 @inputParser/is_argname 6.316 6.64 128800
76 feval 4.414 4.64 410732
57 anonymous@:0:0 3.895 4.10 550732
56 @inputParser/validate_arg 3.865 4.06 128800
63 AbsRel_norm 3.263 3.43 84322
35 unique 2.574 2.71 28000
30 setdiff 2.478 2.61 22400
2 ode45 2.419 2.54 5600
24 fieldnames 1.296 1.36 84000
60 odemergeopts 1.146 1.20 5600
62 starting_stepsize 1.064 1.12 5600
5 odeset 1.040 1.09 11200
31 validsetargs 1.032 1.08 22400
27 __fieldnames__ 0.934 0.98 84000
52 binary * 0.827 0.87 1225452
41 sort 0.782 0.82 22400
```

I have posted this question to the GNU mailing list also.