I have a structure, looking a lot like a graph but I can 'sort' it. Therefore I can have two graphs, that are equivalent, but one is sorted and not the other. My goal is to compute a minimal dominant set (with a custom algorithm that fits my specific problem, so please do not link to other 'efficient' algorithms).
The thing is, I search for dominant sets of size one, then two, etc until I find one. If there isn't a dominant set of size i, using the sorted graph is a lot more efficient. If there is one, using the unsorted graph is much better.
I thought about using threads/multiprocessing, so that both graphs are explored at the same time and once one finds an answer (no solution or a specific solution), the other one stops and we go to the next step or end the algorithm. This didn't work, it just makes the process much slower (even though I would expect it to just double the time required for each step, compared to using the optimal graph without threads/multiprocessing).
I don't know why this didn't work and wonder if there is a better way, that maybe doesn't even required the use of threads/multiprocessing, any clue?
If you don't want an algorithm suggestion, then lazy evaluation seems like the way to go.
Setup the two in a data structure such that with a class_instance.next_step(work_to_do_this_step) where a class instance is a solver for one graph type. You'll need two of them. You can have each graph move one "step" (whatever you define a step to be) forward. By careful selection (possibly dynamically based on how things are going) of what a step is, you can efficiently alternate between how much work/time is being spent on the sorted vs unsorted graph approaches. Of course this is only useful if there is at least a chance that either algorithm may finish before the other.
In theory if you can independently define what those steps are, then you could split up the work to run them in parallel, but it's important that each process/thread is doing roughly the same amount of "work" so they all finish about the same time. Though writing parallel algorithms for these kinds of things can be a bit tricky.
Sounds like you're not doing what you describe. Possibly you're waiting for BOTH to finish somehow? Try doing that, and seeing if the time changes.
Numpy documentation on np.random.permutation suggests all new code use np.random.default_rng() from the Random Generator package. I see in the documentation that the Random Generator package has standardized the generation of a wide variety of random distributions around the BitGenerator vs using Mersenne Twister, which I'm vaguely familiar with.
I see one downside, what used to be a single line of code to do simple permutations:
np.random.permutation(10)
turns into two lines of code now, which feels a little awkward for such a simple task:
rng = np.random.default_rng()
rng.permutation(10)
Why is this new approach an improvement over the previous approach?
And why wouldn't existing methods like np.random.permutation just wrap this new preferred method?
Is there a good reason not to use this new method as a one-liner np.random.default_rng().permutation(10), assuming it's not being called at high volumes?
Is there an argument for switching existing code to this method?
Some context:
Does numpy.random.seed() always give the same random number every time?
NumPy: Decide on new PRNG BitGenerator default
To your questions, in a logical order:
And why wouldn't existing methods like np.random.permutation just wrap this new preferred method?
Probably because of backwards compatibility concerns. Even if the "top-level" API would not be changing, its internals would be significantly enough to be deemed a break in compatability.
Why is this new approach an improvement over the previous approach?
"By default, Generator uses bits provided by PCG64 which has better statistical properties than the legacy MT19937 used in RandomState." (source). The PCG64 docstring provides more technical detail.
Is there a good reason not to use this new method as a one-liner np.random.default_rng().permutation(10), assuming it's not being called at high volumes?
I very much agree that it's a slightly awkward added line of code if it's done at the module-start. I would only point out that the NumPy docs do directly use this form in docstring examples, such as:
n = np.random.default_rng().standard_exponential((3, 8000))
The slight difference would be that one is instantiating a class at module load/import time, whereas in your form it might come later. But that should be a minuscule difference (again, assuming it's only used once or a handful of times). If you look at the default_rng(seed) source, when called with None, it just returns Generator(PCG64(seed)) after a few quick checks on seed.
Is there an argument for switching existing code to this method?
Going to pass on this one since I don't have anywhere near the depth of technical knowledge to give a good comparison of the algorithms, and also because it depends on some other variables such as whether you're concerned about making your downstream code compatibility with older versions of NumPy, where default_rng() simply doesn't exist.
Using dask I have defined a long pipeline of computations; at some point given constraints in apis and version I need to compute some small result (not lazy) and feed it in the lazy operations. My problem is that at this point the whole computation graph will be executed so that I can produce an intermediate results. Is there a way to not loose the work done at this point and have to recompute everything from scratch when in a following step I am storing the final results to disk?
Is using persist supposed to help with that?
Any help will be very appreciated.
Yes, this is the usecase that persist is for. The trick is figuring out where to apply it - this decision is usually influenced by:
The size of your intermediate results. These will be kept in memory until all references to them are deleted (e.g. foo in foo = intermediate.persist()).
The shape of your graph. It's better to persist only components that would need to be recomputed, to minimize the memory impact of the persisted values. You can use .visualize() to look at the graph.
The time it takes to compute the tasks. If the tasks are quick to compute, then it may be more beneficial just to recompute them rather than keep them around in memory.
I have a module to test, module includes a serie of functions / simple classes.
Wondering if there any attempts(ie package) to generate automatically:
1) Generate Python code from initial Python file containing function definition.
2) This code list of call to the functions with random/parametric data as parameters.
It is technically feasible by using inspect and python meta classes,
usually limited to numerical type functions....(numpy array).
Because string (ie url input) would be impossible (only parametrized...).
EDIT: By random, it means obviously "parametric random".
Suppose we have
def f(x1,x2,x3)
For all xi of f
if type(xi) = array1D ->
Do those tests: empty array, zeros array, negative array(random),
positivearray(random), high values, low values, integer array, real
number array, ordered array, equal space array,.....
if type(xi)=int -> test zero, 1, 2,3,4, randomValues, Negative
Do people think such project is possible using inspect and meta class? (limited to numpy/numerical items).
Suppose you have a very large library..., things can be done in background.
You might be thinking of fuzz testing, where a bunch of garbage data is submitted to a function to see if anything makes it behave badly. It sounds like the Hypothesis library will let you generate different test cases based on some parameters.
I spent searching, it seems this kind of project does not really exist (to my knowledge):
Technically, this is a mix of packages (issues):
Hypothese : data generation for input, running the code with crash/error.
(without the invariant part of Hypothese)
Jedi: Static analysis of code/Inference of the type
Type inference is a difficult issue in Python (in general)
implementing type inference
If type is num/array of num:
Boundary exists/ typical usage is clearly defined
If type is string: Inference is pretty difficult without human guessing.
Same for others, Context guessing is important
I am building a script that generates input data [parameters] for another program to calculate. I would like to optimize the resulting data. Previously I have been using the numpy powell optimization. The psuedo code looks something like this.
def value(param):
run_program(param)
#Parse output
return value
scipy.optimize.fmin_powell(value,param)
This works great; however, it is incredibly slow as each iteration of the program can take days to run. What I would like to do is coarse grain parallelize this. So instead of running a single iteration at a time it would run (number of parameters)*2 at a time. For example:
Initial guess: param=[1,2,3,4,5]
#Modify guess by plus minus another matrix that is changeable at each iteration
jump=[1,1,1,1,1]
#Modify each variable plus/minus jump.
for num,a in enumerate(param):
new_param1=param[:]
new_param1[num]=new_param1[num]+jump[num]
run_program(new_param1)
new_param2=param[:]
new_param2[num]=new_param2[num]-jump[num]
run_program(new_param2)
#Wait until all programs are complete -> Parse Output
Output=[[value,param],...]
#Create new guess
#Repeat
Number of variable can range from 3-12 so something such as this could potentially speed up the code from taking a year down to a week. All variables are dependent on each other and I am only looking for local minima from the initial guess. I have started an implementation using hessian matrices; however, that is quite involved. Is there anything out there that either does this, is there a simpler way, or any suggestions to get started?
So the primary question is the following:
Is there an algorithm that takes a starting guess, generates multiple guesses, then uses those multiple guesses to create a new guess, and repeats until a threshold is found. Only analytic derivatives are available. What is a good way of going about this, is there something built already that does this, is there other options?
Thank you for your time.
As a small update I do have this working by calculating simple parabolas through the three points of each dimension and then using the minima as the next guess. This seems to work decently, but is not optimal. I am still looking for additional options.
Current best implementation is parallelizing the inner loop of powell's method.
Thank you everyone for your comments. Unfortunately it looks like there is simply not a concise answer to this particular problem. If I get around to implementing something that does this I will paste it here; however, as the project is not particularly important or the need of results pressing I will likely be content letting it take up a node for awhile.
I had the same problem while I was in the university, we had a fortran algorithm to calculate the efficiency of an engine based on a group of variables. At the time we use modeFRONTIER and if I recall correctly, none of the algorithms were able to generate multiple guesses.
The normal approach would be to have a DOE and there where some algorithms to generate the DOE to best fit your problem. After that we would run the single DOE entries parallely and an algorithm would "watch" the development of the optimizations showing the current best design.
Side note: If you don't have a cluster and needs more computing power HTCondor may help you.
Are derivatives of your goal function available? If yes, you can use gradient descent (old, slow but reliable) or conjugate gradient. If not, you can approximate the derivatives using finite differences and still use these methods. I think in general, if using finite difference approximations to the derivatives, you are much better off using conjugate gradients rather than Newton's method.
A more modern method is SPSA which is a stochastic method and doesn't require derivatives. SPSA requires much fewer evaluations of the goal function for the same rate of convergence than the finite difference approximation to conjugate gradients, for somewhat well-behaved problems.
There are two ways of estimating gradients, one easily parallelizable, one not:
around a single point, e.g. (f( x + h directioni ) - f(x)) / h;
this is easily parallelizable up to Ndim
"walking" gradient: walk from x0 in direction e0 to x1,
then from x1 in direction e1 to x2 ...;
this is sequential.
Minimizers that use gradients are highly developed, powerful, converge quadratically (on smooth enough functions).
The user-supplied gradient function
can of course be a parallel-gradient-estimator.
A few minimizers use "walking" gradients, among them Powell's method,
see Numerical Recipes p. 509.
So I'm confused: how do you parallelize its inner loop ?
I'd suggest scipy fmin_tnc
with a parallel-gradient-estimator, maybe using central, not one-sided, differences.
(Fwiw,
this
compares some of the scipy no-derivative optimizers on two 10-d functions; ymmv.)
I think what you want to do is use the threading capabilities built-in python.
Provided you your working function has more or less the same run-time whatever the params, it would be efficient.
Create 8 threads in a pool, run 8 instances of your function, get 8 result, run your optimisation algo to change the params with 8 results, repeat.... profit ?
If I haven't gotten wrong what you are asking, you are trying to minimize your function one parameter at the time.
you can obtain it by creating a set of function of a single argument, where for each function you freeze all the arguments except one.
Then you go on a loop optimizing each variable and updating the partial solution.
This method can speed up by a great deal function of many parameters where the energy landscape is not too complex (the dependency between the parameters is not too strong).
given a function
energy(*args) -> value
you create the guess and the function:
guess = [1,1,1,1]
funcs = [ lambda x,i=i: energy( guess[:i]+[x]+guess[i+1:] ) for i in range(len(guess)) ]
than you put them in a while cycle for the optimization
while convergence_condition:
for func in funcs:
optimize fot func
update the guess
check for convergence
This is a very simple yet effective method of simplify your minimization task. I can't really recall how this method is called, but A close look to the wikipedia entry on minimization should do the trick.
You could do parallel at two parts: 1) parallel the calculation of single iteration or 2) parallel start N initial guessing.
On 2) you need a job controller to control the N initial guess discovery threads.
Please add an extra output on your program: "lower bound" that indicates the output values of current input parameter's decents wont lower than this lower bound.
The initial N guessing thread can compete with each other; if any one thread's lower bound is higher than existing thread's current value, then this thread can be dropped by your job controller.
Parallelizing local optimizers is intrinsically limited: they start from a single initial point and try to work downhill, so later points depend on the values of previous evaluations. Nevertheless there are some avenues where a modest amount of parallelization can be added.
As another answer points out, if you need to evaluate your derivative using a finite-difference method, preferably with an adaptive step size, this may require many function evaluations, but the derivative with respect to each variable may be independent; you could maybe get a speedup by a factor of twice the number of dimensions of your problem. If you've got more processors than you know what to do with, you can use higher-order-accurate gradient formulae that require more (parallel) evaluations.
Some algorithms, at certain stages, use finite differences to estimate the Hessian matrix; this requires about half the square of the number of dimensions of your matrix, and all can be done in parallel.
Some algorithms may also be able to use more parallelism at a modest algorithmic cost. For example, quasi-Newton methods try to build an approximation of the Hessian matrix, often updating this by evaluating a gradient. They then take a step towards the minimum and evaluate a new gradient to update the Hessian. If you've got enough processors so that evaluating a Hessian is as fast as evaluating the function once, you could probably improve these by evaluating the Hessian at every step.
As far as implementations go, I'm afraid you're somewhat out of luck. There are a number of clever and/or well-tested implementations out there, but they're all, as far as I know, single-threaded. Your best bet is to use an algorithm that requires a gradient and compute your own in parallel. It's not that hard to write an adaptive one that runs in parallel and chooses sensible step sizes for its numerical derivatives.