I am solving a stiff PDE in MATLAB using ode15, and it often freezes depending on the initial conditions. I never actually get an error, it just won't finish even after 10 hours when it should take around 30 seconds to run. I am experimenting with different spatial and time node intervals, but it is hard, because I don't get feedback.
Is there some sort of equivalent to diagnostic for fsolve? stats is not useful because it only displays an output after fsolve is finished.
Check out the documentation on odeset, and specifically the stats option. I think you basically just want to set stats to on and you will get some feedback.
Also, depending on your ODE, you may need a different solver. About half way down the page on this page there is a list of most of the solvers available in MATLAB. Depending on whether your function is stiff or non-stiff, and how accurate you need to get, one of those might work better for you. Sometimes I just code them all in and comment out all but one until I find the one that runs the best for me, but check out the documentation on each if you want to find the "right" one for your application.
Your question is confusing because you refer to both ode15s and fsolve locking up. These are two completely different functions. One does numerical integration and the other solves for roots. Also, fsolve has no option called 'Stats' (see doc fsolve). If you want continuous output from fsolve use:
options = optimist('Display','iter');
[x,fval,exitflag] = fsolve(myfun,x0,options)
This will display the iteration count, number of function evaluations, the function value, and other stuff depending on what algorithm you use (the alorithm can be adjusted via the 'Algorithm' option). Again see doc fsolve for full details.
As far as the 'Stats' option with ode15s goes, it's not going to give you very much information. I doubt that it will you figure out why your system is halting (if it even is ode15s that you have a problem with). What you can try is using an output function via the 'OutputFcn' option of odeset. You can try the simple odeprint first:
options = odeset('OutputFcn',#odeprint)
which will print your state after each integration step. Type edit odeprint to see the code and how you might write your own output function if you need to do more.
Related
I am using Gurobi to run a MIQP (Mixed Integer Quadratic Programming) with linear constraints in Matlab. The solver is very slow and I would like your help to understand whether I can do something about it.
These are the lines which I use to launch the problem
clear model;
clear params;
model.A=[Aineq; Aeq];
model.rhs=[bineq; beq];
model.sense=[repmat('<', size(Aineq,1),1); repmat('=', size(Aeq,1),1)];
model.Q=Q;
model.obj=c;
model.vtype=type;
model.lb=total_lb;
model.ub=total_ub;
params.MIPGap=10^(-1);
result=gurobi(model,params);
This is a screenshot of the output in the Matlab window.
Question 1: It is the first time I am trying to run a MIQP and I would like to have your advice to understand what I can do to improve performance. Let me tell what I have tried so far:
I cheated by imposing params.MIPGap=10^(-1). In this way the phase of node exploration is made shorter. What are the cons of doing this?
I have big-M coefficients and I have tied them to the smallest possible values.
I have tried setting params.ScaleFlag=2; params.ObjScale=2 but it makes things slower
I have changed params.method but it does not seem to help (unless you have some specific recommendation)
I have increase params.Threads but it does not seem to help
Question 2 (minor): Why do I get a negative objective in the root simplex log? How can the objective function be negative?
Without having the full model here, there is not much on advise to give. Tight Big-M formulations are important, but you said, you checked them already. Sometimes splitting them up might help, but this is a complex field.
What might give great benefits for some problems is using the Gurobi parameter tuning tool. So try to export your model and feed the tuning tool with it. It automatically tries different of the hundreds of tuning parameters and might give some nice results.
Regarding the question about negative objectives in the simplex logs, I can think of a couple of possible explanations. First, note that the negative objective values occur in the presence of dual infeasibilities in the dual simplex run. In such a case, I'm not sure exactly what the primal objective values correspond to. Second, if you have a MIQP with products of binaries in the objective, Gurobi may convexify the objective in a way that makes it possible for a negative objective to appear in the reformulated model even when the original model must have a nonnegative objective in any feasible solution.
I am using MATLAB's fitgmdist ("fit a guassian mixture to data", from the Statistics and Machine Learning Toolbox) with some success. Is there a way to make it run in a verbose mode, e.g., tell me what iteration it is on, or show convergence stats during the process, so I know how well it is progressing?
Related, is there a way after the function has run and delivered the gmdistribution object, to determine how many iterations actually ran or how close the convergence came? (It would be useful to know these things so I could better set the options parameters up front.)
Simply put: no and yes.
You can try to access the actual .m-file (e.g. open(fitgmdist)) to copy it and then edit it to your purposes (copy it so you won't overwrite the build-in function), but there is no straight-forward implemented way to obtain the verbosity you want. The name-value pair which comes closest to what you want is display, iter:
iter: Display iterative output to the Command Window for some functions; otherwise display the final output.
I am not quite sure about this part, since I can't run a test, but the final number of iterations should be available in the gmdistribution structure under gmdistribution.NumIterations. The docs state that this is only for objects constructed with fitgmdist.
I am doing parameter estimation in matlab using lsqnonlin function.
In my work, I need to plot a graph to show the error in terms of lsqnonlin iteration. So, I need to know which iteration is running at each point of time in lsqnonlin. Could anybody help me how I can extract the iteration number while lsqnonlin is running?
Thanks,
You want to pass it an options parameter setting 'display' to either 'iter' or 'iter-detailed'
http://www.mathworks.com/help/optim/ug/lsqnonlin.html#f265106
Never used it myself, but looking at the help of lsqnonlin, it seems that there is an option to set a custom output function, which gets called during every iteration of the solver. Looking at the specification, it seems that the values optimValues.iteration and optimValues.fval get passed into the function, which is probably the things you are interested in.
You should thus define your own function with the right signature, and depending on your wishes, this function prints it on the command line, makes a plot, saves the intermediate results in a vector, etc. Finally, you need to pass this function as a function handle to the solver: lsqnonlin(..., 'OutputFcn', #your_outputfun).
The simple way to do this would be:
Start with a low number of (maximum) iterations
Get the result
Increase the number of iterations
Get the result
If the maximum iterations is used Go to step 3
This is what I would recommend in most cases when performance is not a big issue.
However, if you cannot afford to do it like this, try edit lsqnonlin and go digging untill you find the point where the number of iterations is found. Then change the function to make sure you store the results you need at that point. (don't forget to change it back afterwards).
The good news is that all relevant files seem to be editable, the bad news is that it is not so clear where you can find the current number of iterations. A quick search led me to fminbnd, but I did not manage to confirm that this is actually used by lsqnonlin.
I have a problem with ode45. I've defined a function and trying to solve it by ode, but when i run it, it takes so long. I tried to display the "t" input in my function and it showed time step was 10^-8 ! [I do not get any error from ode45]
So i put a breakpoint at the end of my function, and after I Step once, it goes to sym.m file and calls Function delet(h)
function dxr=Dynfun(t,x)
...
dxr=[A;B]
after Step it goes to
function delete(h)
if builtin('numel',h)==1 && inmem('-isloaded','mupadmex') && builtin('numel',h.s)==1 && ~isa(h.s,'maplesym')
mupadmex(h.s,1);
end
end
and that's what makes it too long, because it goes in a loop in there.
what's the problem?! Thanks
Sounds like it's a "stiff" problem to me. I would recommend using a solver that is designed for stiff problems. I would also recommend trying a fixed step solver at a small step size ~ 0.001 and see what the output looks like. If you are breaking in sym.m, sounds like you've some some symbolic logic going on in there. Is there a way you could take your symbolic expression and convert it to a matlab script?
As indicated by macduff, your problem could be stiff. Try ode15s (which is designed for stiff problems) and see if the stepsize still decreases to unacceptably low values.
If that is indeed the case, then your problem might contain a singularity for the initial values you give it. If your problem has dimensions lower than 3, you can define a small event function to get insight into the values at each step, and plot them to see if there is indeed something problematic going on.
Then -- do you really need symbolic math? The philosophy behind that is that it's easier to read for humans, which makes it terrible to deal with for computers :) If you can transform it into something non-symbolic, please do -- this will noticeably increase performance.
Also, more a word of advice, delete is also Matlab builtin function. It is generally a bad idea to name your functions after Matlab buitins -- it's confusing, and can cause a lot of overhead while Matlab is deciding which one to use.
I used Matlab-fminsearch for a negativ max likelihood model for a binomial distributed function. I don't get any error notice, but the parameter which I want to estimate, take always the start value. Apparently, there is a mistake. I know that I ask a totally general question. But is it possible that anybody had the same mistake and know how to deal with it?
Thanks a lot,
#woodchips, thank you a lot. Step by step, I've tried to do what you advised me. First of all, I actually maximized (-log(likelihood)) and this is not the problem. I think I found out the problem but I still have some questions, if I don't bother you. I have a model(param) to maximize in paramstart=p1. This model is built for (-log(likelihood(F))) and my F is a vectorized function like F(t,Z,X,T,param,m2,m3,k,l). I have a data like (tdata,kdata,ldata),X,T are grids and Z is a function on this grid and (m1,m2,m3) are given parameters.When I want to see the value of F(tdata,Z,X,T,m1,m2,m3,kdata,ldata), I get a good output. But I think fminsearch accept that F(tdata,Z,X,T,p,m2,m3,kdata,ldata) like a constant and thatswhy I always have as estimated parameter the start value. I will be happy, if you have any advise to tweak that.
You have some options you can try to tweak. I'd start with algorithm.
When the function value practically doesn't change around your startpoint it's also problematic. Maybe switching to log-likelyhood helps.
I always use fminunc or fmincon. They allow also providing the Hessian (typically better than "estimated") or 'typical values' so the algorithm doesn't spend time in unfeasible regions.
It is virtually always true that you should NEVER maximize a likelihood function, but ALWAYS maximize the log of that function. Floating point issues will almost always corrupt the problem otherwise. That your optimization starts and stops at the same point is a good indicator this is the problem.
You may well need to dig a little deeper than the above, but even so, this next test is the test I recommend that all users of optimization tools do for every one of their problems, BEFORE they throw a function into an optimizer. Evaluate your objective for several points in the vicinity. Does it yield significantly different values? If not, then look to see why not. Are you creating a non-smooth objective to optimize, or a zero objective? I.e., zero to within the supplied tolerances?
If it does yield different values but still not converge, then make sure you know how to call the optimizer correctly. Yeah, right, like nobody has ever made this mistake before. This is actually a very common cause of failure of optimizers.
If it does yield good values that vary, and you ARE calling the optimizer correctly, then think if there are regions into which the optimizer is trying to diverge that yield garbage results. Is the objective generating complex or imaginary results?