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.
EDIT
SOLVED
Solution was to use the long double versions of sin & cos: sinl & cosl.
It is my first post here, so bear with me :).
I come today here to ask for your input on a small problem that I am having with a C application at work. Basically, I am computing an Extended Kalman Filter and one of my formulas (that I store in a variable) has multiple computations of sin and cos, at least 16 in total in the same line. I want to decrease the time it takes for the computation to be done, so the idea is to compute each cos and sin separately, store them in a variable, and then replace the variables back in the formula.
So I did this:
const ComputationType sin_Roll = compute_sin((ComputationType)(Roll));
const ComputationType sin_Pitch = compute_sin((ComputationType)(Pitch));
const ComputationType cos_Pitch = compute_cos((ComputationType)(Pitch));
const ComputationType cos_Roll = compute_cos((ComputationType)(Roll));
Where ComputationType is a macro definition (renaming) of the type Double. I know it looks ugly, a lot of maybe unnecessary castings, but this code is generated in Python and it was specifically designed so....
Also, compute_cos and compute_sin are defined as such:
#define compute_sin(a) sinf(a)
#define compute_cos(a) cosf(a)
My problem is the value I get from the "optimized" formula is different from the value of the original one.
I will post the code of both and I apologise in advance because it is very ugly and hard to follow but the main points where cos and sin have been replaced can be seen. This is my task, to clean it up and optimize it, but I am doing it step by step to make sure I don't introduce a bug.
So, the new value is:
ComputationType newValue = (ComputationType)(((((((ComputationType)-1.0))*(sin_Pitch))+((DT)*((((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(cos_Pitch)*(cos_Roll))+(((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(cos_Pitch)*(sin_Roll)))))*(cos_Pitch)*(cos_Roll))+((((DT)*((((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(cos_Roll)*(sin_Pitch))+(((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(sin_Pitch)*(sin_Roll))))+(cos_Pitch))*(cos_Roll)*(sin_Pitch))+((((ComputationType)-1.0))*(DT)*((((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(cos_Roll))+((((ComputationType)-1.0))*((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(sin_Roll)))*(sin_Roll)));
And the original is:
ComputationType originalValue = (ComputationType)(((((((ComputationType)-1.0))*(compute_sin((ComputationType)(Pitch))))+((DT)*((((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(compute_cos((ComputationType)(Pitch)))*(compute_cos((ComputationType)(Roll))))+(((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(compute_cos((ComputationType)(Pitch)))*(compute_sin((ComputationType)(Roll)))))))*(compute_cos((ComputationType)(Pitch)))*(compute_cos((ComputationType)(Roll))))+((((DT)*((((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(compute_cos((ComputationType)(Roll)))*(compute_sin((ComputationType)(Pitch))))+(((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(compute_sin((ComputationType)(Pitch)))*(compute_sin((ComputationType)(Roll))))))+(compute_cos((ComputationType)(Pitch))))*(compute_cos((ComputationType)(Roll)))*(compute_sin((ComputationType)(Pitch))))+((((ComputationType)-1.0))*(DT)*((((Gz)+((((ComputationType)-1.0))*(Dg_z)))*(compute_cos((ComputationType)(Roll))))+((((ComputationType)-1.0))*((Dg_y)+((((ComputationType)-1.0))*(Gy)))*(compute_sin((ComputationType)(Roll)))))*(compute_sin((ComputationType)(Roll)))));
What I want is to get the same value as in the original formula. To compare them I use memcmp.
Any help is welcome. I kindly thank you in advance :).
EDIT
I will post also the values that I get.
New value : -1.2214615708217025e-005
Original value : -1.2214615708215651e-005
They are similar up to a point, but the application is safety critical and it is necessary to validate the results.
You can not meet your expectation for a couple of reasons.
By altering the code you adjust the machine instructions being used in subtle ways that will impact the final value.
For instance if originally it was using fused multiplies and adds and this is no longer happening it will change the result.
You don't mention the target architecture. Some architectures retain more than 64bits in the floating point pipeline. These extra bits get rounded when forced into 64bit memory. Again altering how this works will have minor effects on the final output.
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 currently trying to write a code to solve a non linear system of equations. I am using the functions of the gsl library, more specifically the multiroot_fdf_solver.
My problem is that it currently doesn't want to converge. More specifically, I have the following behavior:
-if my initial conditions are close to the result, the gsl_multiroot_fdf_solver_iterate does not update the parameters at all. I tried to display the results on the different steps, and I have for all the parameters dx = NaN (I think this quite srange), the status of gsl_multiroot_fdf_solver_iterate is "success" and the status of gsl_multiroot_test_residual is "the iteration has not converged yet"
-the parameters are only updated if my initial conditions are really far from the expected result. Obvisously in this case it does not converge to the right values.
I have already checked multiple times the expression of my function and my Jacobian, and they seem good.
I have to precise that my Jacobian (and my system as well) are quite complicated expression with many trigonometric function.
Would you have any idea of what it could be? Is it possible that if the expression of the Jacobian is too complicated, it has troubles to compute it?
Thank you in advance for your answers, I am really stucked at this point.
My project has classes which, unavoidably, contain hundreds upon hundreds of variables that I'm always having to keep straight. For example, I'm always having to keep track of specific kinds of variables for a recurring set of "items" that occur inside of a class, where placing those variables between multiple classes would cause a lot of confusion.
How do I better sort my variables to keep from going crazy, especially when it comes time to save my data?
Am I missing something? Actionscript is an Object Oriented language, so you might have hundreds of variables, but unless you've somehow treated it like a grab bag and dumped it all in one place, everything should be to hand. Without knowing what all you're keeping track of, it's hard to give concrete advice, but here's an example from a current project I'm working on, which is a platform for building pre-employment assessments.
The basic unit is a Question. A Question has a stem, text that can go in the status bar, a collection of answers, and a collection of measures of things we're tracking about what the user does in that particular type of questions.
The measures are, again, their own type of object, and come in two "flavors": one that is used to track a time limit and one that isn't. The measure has a name (so we know where to write back to the database) and a value (which tells us what). Timed ones also have a property for the time limit.
When we need to time the question, we hand that measure to yet another object that counts the time down and a separate object that displays the time (if appropriate for the situation). The answers, known as distractors, have a label and a value that they can impart to the appropriate measure based on the user selection. For example, if a user selects "d", its value, "4" is transferred to the measure that stores the user's selection.
Once the user submits his answer, we loop through all the measures for the question and send those to the database. If those were not treated as a collection (in this case, a Vector), we'd have to know exactly what specific measures are being stored for each question and each question would have a very different structure that we'd have to dig through. So if looping through collections is your issue, I think you should revisit that idea. It saves a lot of code and is FAR more efficient than "var1", "var2", "var3."
If the part you think is unweildy is the type checking you have to do because literally anything could be in there, then Vector could be a good solution for you as long as you're using at least Flash Player 10.
So, in summary:
When you have a lot of related properties, write a Class that keeps all of those related bits and pieces together (like my Question).
When objects have 0-n "things" that are all of the same or very similar, use a collection of some sort, such as an Array or Vector, to allow you to iterate through them as a group and perform the same operation on each (for example, each Question is part of a larger grouping that allows each question to be presented in turn, and each question has a collection of distractors and another of measures.
These two concepts, used together, should help keep your information tidy and organized.
While I'm certain there are numerous ways of keeping arrays straight, I have found a method that works well for me. Best of all, it collapses large amounts of information into a handful of arrays that I can parse to an XML file or other storage method. I call this method my "indexed array system".
There are actually multiple ways to do this: creating a handful of 1-dimensional arrays, or creating 2-dimensional (or higher) array(s). Both work equally well, so choose the one that works best for your code. I'm only going to show the 1-dimensional method here. Those of you who are familiar with arrays can probably figure out how to rewrite this to use higher dimensional arrays.
I use Actionscript 3, but this approach should work with almost any programming or scripting language.
In this example, I'm trying to keep various "properties" of different "activities" straight. In this case, we'll say these properties are Level, High Score, and Play Count. We'll call the activities Pinball, Word Search, Maze, and Memory.
This method involves creating multiple arrays, one for each property, and creating constants that hold the integer "key" used for each activity.
We'll start by creating the constants, as integers. Constants work for this, because we never change them after compile. The value we put into each constant is the index the corresponding data will always be stored at in the arrays.
const pinball:int = 0;
const wordsearch:int = 1;
const maze:int = 2;
const memory:int = 3;
Now, we create the arrays. Remember, arrays start counting from zero. Since we want to be able to modify the values, this should be a regular variable.
Note, I am constructing the array to be the specific length we need, with the default value for the desired data type in each slot. I've used all integers here, but you can use just about any data type you need.
var highscore:Array = [0, 0, 0, 0];
var level:Array = [0, 0, 0, 0];
var playcount:Array = [0, 0, 0, 0];
So, we have a consistent "address" for each property, and we only had to create four constants, and three arrays, instead of 12 variables.
Now we need to create the functions to read and write to the arrays using this system. This is where the real beauty of the system comes in. Be sure this function is written in public scope if you want to read/write the arrays from outside this class.
To create the function that gets data from the arrays, we need two arguments: the name of the activity and the name of the property. We also want to set up this function to return a value of any type.
GOTCHA WARNING: In Actionscript 3, this won't work in static classes or functions, as it relies on the "this" keyword.
public function fetchData(act:String, prop:String):*
{
var r:*;
r = this[prop][this[act]];
return r;
}
That queer bit of code, r = this[prop][this[act]], simply uses the provided strings "act" and "prop" as the names of the constant and array, and sets the resulting value to r. Thus, if you feed the function the parameters ("maze", "highscore"), that code will essentially act like r = highscore[2] (remember, this[act] returns the integer value assigned to it.)
The writing method works essentially the same way, except we need one additional argument, the data to be written. This argument needs to be able to accept any
GOTCHA WARNING: One significant drawback to this system with strict typing languages is that you must remember the data type for the array you're writing to. The compiler cannot catch these type errors, so your program will simply throw a fatal error if it tries to write the wrong value type.
One clever way around this is to create different functions for different data types, so passing the wrong data type in an argument will trigger a compile-time error.
public function writeData(act:String, prop:String, val:*):void
{
this[prop][this[act]] = val;
}
Now, we just have one additional problem. What happens if we pass an activity or property name that doesn't exist? To protect against this, we just need one more function.
This function will validate a provided constant or variable key by attempting to access it, and catching the resulting fatal error, returning false instead. If the key is valid, it will return true.
function validateName(ID:String):Boolean
{
var checkthis:*
var r:Boolean = true;
try
{
checkthis = this[ID];
}
catch (error:ReferenceError)
{
r = false;
}
return r;
}
Now, we just need to adjust our other two functions to take advantage of this. We'll wrap the function's code inside an if statement.
If one of the keys is invalid, the function will do nothing - it will fail silently. To get around this, just put a trace (a.k.a. print) statement or a non-fatal error in the else construct.
public function fetchData(act:String, prop:String):*
{
var r:*;
if(validateName(act) && validateName(prop))
{
r = this[prop][this[act]];
return r;
}
}
public function writeData(act:String, prop:String, val:*):void
{
if(validateName(act) && validateName(prop))
{
this[prop][this[act]] = val;
}
}
Now, to use these functions, you simply need to use one line of code each. For the example, we'll say we have a text object in the GUI that shows the high score, called txtHighScore. I've omitted the necessary typecasting for the sake of the example.
//Get the high score.
txtHighScore.text = fetchData("maze", "highscore");
//Write the new high score.
writeData("maze", "highscore", txtHighScore.text);
I hope ya'll will find this tutorial useful in sorting and managing your variables.
(Afternote: You can probably do something similar with dictionaries or databases, but I prefer the flexibility with this method.)