I work on data processing which works with layered data.
The best analogy to my current work is that of network processing. Packets are layered and each layers is processed individually by a specicialized function. The next function to call for a deeper layer is calculated in the current layer. Under some circumstances it can happen that the callstack shows recursive behviour in a way that a previously called function is called again (eg. A()->B()->C()->B()->D()...)
Currently I do that in the following way:
void func_N(void)
{
// get next layer info
switch (next) {
case A:
func_A();
break;
case B:
func_B();
break;
default:
finalize()
}
}
I can guarantee that the call chains do not become arbitrarily long. There is a technical limit, although pretty high. The depth of the callstack is dependent on the data which we can make some assumptions about. I'd need to get some fresh statistics, but a maximum depth of 10 calls would be a good estimate.
I hope you get the idea. Works fine, but the more complex the potential trajectories through the call stack become, the harder this gets to maintain.
However, maintainability is not my primary concern. In this case, performance is. Are there other, faster, better suited programming techniques for this problem?
Related
The N2 diagram for my full problem is below.
The N2 diagram for the coupled portion of the problem is below.
I have a DirectSolver handling the coupling between LLTForces and ImplicitLiftingLine, and an LNBGS solver handling the coupling between LiftingLineGroup and TestCL.
The gist for the problem is here: https://gist.github.com/eufren/31c0e569ed703b2aea3e2ef5360610f7
I have implemented guess_nonlinear() on ImplicitLiftingLine, which should use various outputs from LLTGeometry to give a good initial guess for the vortex strengths based on a linearised form of the governing equations.
def guess_nonlinear(self, inputs, outputs, resids):
freestream_unit_vector = inputs['freestream_unit_vector']
freestream_velocity = inputs['freestream_velocity']
n = inputs['normal_vectors']
A = inputs['surface_areas']
l = inputs['bound_vortices']
ic_tot = inputs['influence_coefficients_total']
v_inf = freestream_velocity
v_inf_vec = v_inf*freestream_unit_vector
lin_numerator = np.pi * v_inf * A * np.sum(n * v_inf_vec, axis=1)
lin_denominator = (np.linalg.norm(np.cross(v_inf_vec, l), axis=1) - np.pi * v_inf * A * np.sum(np.sum(n * ic_tot, axis=2), axis=1))
lin_vtx_str = lin_numerator / lin_denominator
outputs['vortex_strengths'] = lin_vtx_str
However, when the problem is run for the first time, any inputs not explicitly set with p.set_val() are all 1s. This causes guess_nonlinear() to give a bad output and so the system fails to converge:
As far as I can tell, the execution order for the LLT group is correct, and the geometry components should be being executed before the implicit component. I'm confused as to why this doesn't seem to actually be happening when the code is run, and instead these inputs are taking their default values.
What do I need to change to get this to work properly? Additionally, I've found difficulty in getting LNBGS to converge (hence adding guess_nonlinear()) during optimisation - only DirectSolver gets all the way through the optimisation without issues, but it's very slow for large numbers of LLT nodes). How can I improve the linear and nonlinear solver selection, and improve the reliability of the iterative solver?
Note: Thanks for providing a testable example. It made figuring out the answer to your question a lot simpler. Your problem was a bit subtle and I would not have been able to give a good answer without runnable code
Your first question: "Why are all the inputs 1"
"Short" Answer
You have put the nonlinear solver to high in the model hierarchy, which then included a key precurser component that computed your input values. By moving the solver down to a lower level of the model, I was able to ensure that the precurser component (LTTGeometry) ran and had valid outputs before you got to the guess_nonlinear of implicit component.
Here is what you had (Notice the implicit solver included LTTGeometry even though the data cycle does not require that component:
I moved both the nonlinear solver and the linear solver down into the LTTCycle group, which then allows the LTTGeometry component to execute before getting to the nonlinear solver and guess_nonlinear step:
My fix is only partially correct, since there is a secondary cycle from the TestCL component that also needs a solver and does not have one. However, that cycle still does not involve the LTTGeometry group. So the fully correct fix is to restructure you model top run geometry first, and then put the LTTCycle and TestCL groups together so you can run a solver over just them. That was a bit more hacking than I wanted to do on your test problem, but you can see the general idea from the adjusted N2 above.
Long Answer
The guess_nonlinear sequence in OpenMDAO does NOT run the compute method of explicit components or of groups. It follows the execution hierarchy, and calls any guess_nonlinear that it finds. So that means that any explicit components you have in your model will NOT get executed, their outputs will not get updated with computed values, and those computed values will not get passed to the inputs of downstream components.
Things get a little tricky when you have deep model hierarchies. The guess_nonlinear method is called as the first step in the nonlinear solver process. If you have a NonLinearRunOnce solver at the top level, it will follow the compute chain down the line calling compute or solve_nonlinear on each child and doing a data transfer after each one. If one of those children happens to be a group with a nonlinear solver, then that solver will call guess_nonlinear on its children (grandchildren of the top group with the NonLinearRunOnce solver) as the first step. So any outputs that were computed by the siblings of this group will be valid, but none of the outputs from the grandchild level will have been computed yet.
You may be wondering why not just have the guess_nonlinear method call the compute for any explicit components? There is a difficult to balance trade off here. If you assume that all explicit components are very cheap to run, then it might make sense to run the compute methods --- or it might not. A lot depends on the cyclic data structure. If some early component in the group needs guesses from the later one, then running its compute isn't going to help you much at all. Perhaps more importantly though, not all explicit components are cheap to run. You might have a very expensive computation, and calling compute as part of the guess process would be way too costly.
The compromise here, if you need some kind of top level guess process, is that you can implement guess_nonlinear at the group level. It's less common to do, but it gives you total control over what happens. You can call whatever you need to call in whatever sequence.
So the absolute key thing to remember is that the only data you have available to you when a guess_nonlinear is called is any data that was computed before your containing solver was executed. That means any thing that was computed before you got to the model scope of the containing solver (not the scope of the component with the guess_method itself).
Your second question: "How can I speed this up when the number of nodes gets large?"
This one not possible to give a generic answer to at all. I noticed that you have already specified sparse partial derivatives. That is a great start, but if its still not fast enough for you then it means you're reaching the limits of what you can do with a DirectSolver. You note that this solver is the only one that gets you through the optimization without issues, which I will take to mean that ScipyKryloventer link description here and PetscKrylov are not converging the linear system well for you --- at least not by themselves. Thats not surprising, as krylov solvers almost always require some kind of preconditioner... and this is why I can't offer a generic answer. Setting up efficient linear solvers for larger-scale compute is a tricky subject. If you look into the literature, you'll find some good suggestions. You can also study open source implementations like VSPAero for some tips.
effectively, you've reached the limit of what simple linear solvers can offer you. From this point forward, OpenMDAO can help a bit by making it easier to implement some preconditioning, but you'll have to suffer the math side yourself.
My program answers on incoming messages and do some logic based on ID`s and data included in messages.
I have a different function for each ID.
The project is pure C.
To make the code easy to work with I have adjusted all functions to the same style (same return and parameters).
I also want to evade the long switch-case constructions and make code easier to edit later, so I have created the following function:
AnswerStruct IDHandler(Request Message)
{
struct AnswerStruct ANS;
SIDHandler = IDfunctions[Message.ID];
ANS = SIDHandler(Message);
return ANS;
}
AnswerStruct is struct for answer messages.
Request is struct for incoming messages.
IDfunctions is array of pointers to functions which looks like this -
AnswerStruct func1(Request);
AnswerStruct func4(Request);
...
typedef AnswerStruct(*f)(Request);
AnswerStruct (*SIDHandler)(Request);
static f IDfunctions[IDMax] = {0, *func1, 0, 0, *func4, ...};
Function pointers placed in the array cells equal to their id`s, for example:
func1 related to message with ID=1.
func4 related to message with ID=4.
I think, that by using this array I make my life much easier.
I can call function which I need in one step (just go to the IDfunctions[ID]).
Also, adding new functions becomes a two step operation (just add function to the IDfunctions and write logic).
I doubt the efficiency of the selected solution, it seems clunky to me.
The question is - Is this a good architecture?
If no, how can I edit my solution to make it better?
Thanks.
I doubt the efficiency of the selected solution, it seems clunky to
me.
It can be less efficient to call a function via a function pointer than to call it directly by name, because the former denies the compiler any opportunity to optimize the call. But you have to consider whether that actually matters. In a system that dispatches function calls based on messages received from an external source, the I/O involved in receiving the messages is likely to be much more expensive than the indirect function calls, so the difference in call performance is unlikely to be significant.
On the other hand, your approach affords simpler logic and many fewer lines of code, which is a different and potentially more valuable kind of efficiency.
The question is - Is this a good architecture?
The general approach is perfectly good, and I don't see much to complain about in the implementation sketch provided.
Personally, I would declare array IDFunctions to be const (supposing, of course, that you don't intend to replace any of its members after their initialization), but that's a minor safety / performance detail, where again the performance dimension is probably irrelevant.
In an implementation of the Game of Life, I need to handle user events, perform some regular (as in periodic) processing and draw to a 2D canvas. The details are not particularly important. Suffice it to say that I need to keep track of a large(-ish) number of variables. These are things like: a structure representing the state of the system (live cells), pointers to structures provided by the graphics library, current zoom level, coordinates of the origin and I am sure a few others.
In the main function, there is a game loop like this:
// Setup stuff
while (!finished) {
while (get_event(&e) != 0) {
if (e.type == KEYBOARD_EVENT) {
switch (e.key.keysym) {
case q:
case x:
// More branching and nesting follows
The maximum level of nesting at the moment is 5. It quickly becomes unmanageable and difficult to read, especially on a small screen. The solution then is to split this up into multiple functions. Something like:
while (!finished {
while (get_event(&e) !=0) {
handle_event(state, origin_x, origin_y, &canvas, e...) //More parameters
This is the crux of the question. The subroutine must necessarily have access to the state (represented by the origin, the canvas, the live cells etc.) in order to function. Passing them all explicitly is error prone (which order does the subroutine expect them in) and can also be difficult to read. Aside from that, having functions with potentially 10+ arguments strikes me as a symptom of other design flaws. However the alternatives that I can think of, don't seem any better.
To summarise:
Accept deep nesting in the game loop.
Define functions with very many arguments.
Collate (somewhat) related arguments into structs - This really only hides the problem, especially since the arguments are only loosely related.
Define variables that represent the application state with file scope (static int origin_x; for example). If it weren't for the fact that it has been drummed into me that global variable are usually a terrible idea, this would be my preferred option. But if I want to display two views of the same instance of the Game of Life in the future, then the file scope no longer looks so appealing.
The question also applies in slightly more general terms I suppose: How do you pass state around a complicated program safely and in a readable way?
EDIT:
My motivations here are not speed or efficiency or performance or anything like this. If the code takes 20% longer to run as a result of the choice made here that's just fine. I'm primarily interested in what is less likely to confuse me and cause the least headache in 6 months time.
I would consider the canvas as one variable, containing a large 2D array...
consider static allocation
bool canvas[ROWS][COLS];
or dynamic
bool *canvas = malloc(N*M*sizeof(int));
In both cases you can refer to the cell at position i,j as canvas[i][j]
though for dynamic allocation, do not forget to free(canvas) at the end. You can then use a nested loop to update your state.
Search for allocating/handling a 2d array in C and examples or tutorials... Possibly check something like this or similar? Possibly this? https://www.geeksforgeeks.org/nested-loops-in-c-with-examples/
Also consider this Fastest way to zero out a 2d array in C?
I am using MATLAB to build a code that does automatic tuning of the three PID controller gains. The way I am thinking of it, is to minimize the error (the difference between the desired state and the obtained one) of my system, for that, I coded a function that accepts the PID gains as input parameters and returns the calculated error, namely:
errors_vector = closedLoopSimulation(pidGains)
Since I have three set points (input commands), then the dimension of the output errors_vector is 3*N, where N is the number of time samples I have (1000 in my case). So that is the function I want to minimize, and for doing so, I tried using fminunc command, namely:
pidGains_ini = [2.4 0.1 0.4];
func = #closedLoopSimulation;
[pid, fval] = fminunc(func, pidGains_ini)
However, when I run the last piece of code, I get this error:
User supplied objective function must return a scalar value.
which is clearly due to the fact that that errors_vector is a 3*1000 array and not a scalar.
My questions would be, from the programming point of view, is there a way that I can make fminunc minimize functions that return arrays?
On the other hand, and from the Control Theory point of view, is there another way which I can optimize the PID gains automatically?
I hope I made myself clear enough.
Thanks
Minimizing a vector is not very well defined (there is something called multi-objective or multi-criteria optimization but that is somewhat specialized). "Normal" optimization methods can only minimize (or maximize) scalar objectives. I suspect in your case you could form such an objective by taking the sum of the squared errors and minimize that. To be complete: this is standard operating procedure and is often called "least squares".
I work in safety critical application development. Recently as a code reviewer I complained against coding style shown below, but couldn't make a strong case against it. So what would be a good argument against such Variable redundancy/duplication, I am looking for cases where this might lead to problems or test cases which might fail, rather than just coding style.
//global data
// global data
int Block1Var;
int Block2Var;
...
//Block1
{
...
Block1Var = someCondition; // someCondition is an logical expression
...
}
//Block2
{
...
Block2Var = Block1Var; // Block2Var is an unconditional copy of Block1Var
...
}
I think a little more context would be helpful perhaps.
You could argue that the value of Block1Var is not guaranteed to stay the
same across concurrent access/modification. This is only valid if Block1Var
ever changes (ie is not only read). I don't know if you are concerned with
multi-threaded applications or not.
Readability is an important issue as well. Future code maintainers
don't want to have to trace around a bunch of trivial assignments.
Depends on what's done with those variables later, but one argument is that it's not future-proof. If, in the future, you change the code such that it changes the value of Block1Var, but Block2Var is used instead (without the additional change) later on, then this will result in erroneous behavior.
If the shown function context reaches a certain length (I'm assuming a lot of detail has been discarded to create the minimal reproducible example for this question), a good next step could be to create a new (sub-)function out of Block 2. This subfunction then should be started assigning Block1Var (-> actual parameter) to Block2Var (-> formal parameter). If there were no other coupling to the rest of the function, one could cut the rest of Block 2 and drop it as a function definition, and would only have to replace the assignment by the subfunction call.
My answer is fairly speculative, but I have seen many cases where this strategy helped me to mark useful points to split a complex function later during the development. Of course, this interpretation only applies to an intermediate stage of development and not to code that is stated to be "ready for release".