I was searching online about how center_box parameter works in sklearn.datasets.make_blobs(). However, I could not find any good answer about it.
How does this parameter affect the sample dataset generation?
From the documentation:
center_box: tuple of float (min, max), default=(-10.0, 10.0)
The bounding box for each cluster center when centers are generated at random.
This means that the parameter center_box is an area of how big a cluster will be.
Related
I am quite new to Julia so I maybe missed the proper documentation.
Is it possible to define a PDESystem in ModelingToolKit with symbolic BCs and Domain for arbitrary geometry?
For instance, if I want to solve the 2D Navier-Stokes equations with a PINN in the following period-hill shape with a curved ground:
How can I defined a no-slip boundary condition on the ground and how can I limit my y-axis to range from y/H = ground(x) to y/H=3 ?
Thanks in advance!
That just doesn't exist right now. The PDESystem parts are still under very active development.
I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct as in this case, the results are matched with the analytical solution. As you know, there is a capability in Comsol called infinite element domain which serves the purpose to the problem mentioned above. In this case, we need to define a limited geometry on which we want to solve the PDE, and also need to draw a small domain acting as the Infinite Element Domain. However, in this case, the results are not correct because they are not matched with the analytical solution. Is there anything that I am missing to correctly use Infinite Element Domain in comsol?
Any help or comment would be appreciated.
Edit:
I edited the post to be more specific.
Please consider the following figure where a fluid with high temperature is being injected into a region with lower temperature:
https://i.stack.imgur.com/BQycC.png
The equation to solve is:
https://i.stack.imgur.com/qrZcK.png
With the following initial and boundary conditions (note that the upper and lower boundary condition is no-flux):
https://i.stack.imgur.com/l7pHo.png
We want to obtain the temperature profile over the length of rw<r<140 m (rw is very small and is equal to 0.005 m here) at different times. One way to model this numerically in Comsol is to draw a rectangle that is 2000 m in the r-direction, and get results only in the span of r [rw,140] m:
https://i.stack.imgur.com/BKCOi.png
The results of this case is fine, because they are well-matched with the analytical solution.
Another way to model this is to replace the above geometry with a bounded one that is [rw, 140] m in the r-direction and then augment it with an Infinite Element domain that is meshed mapped, as follows:
https://i.stack.imgur.com/m9ksm.png
Here, I have set the thickness of Infinite Element to 10 m in the r-direction. However, the results in this case are not matched with the analytical solution (or the above case where Infinite Element domain was not used). Is there anything that I am missing in Comsol? I have also changed some variables with regard to Infinite Element in Comsol such as physical width or distance, but I didn't see any changes in the results.
BTW, here are the results:
https://i.stack.imgur.com/cdaPH.png
I have some features that are zero-centered values and supposed to represent change between a current value and previous value. Generally speaking i believe there should be some symmetry between these values. Ie. there should be roughly the same amount of positive values as negative values and roughly these values should operate on the same scale.
When i try to scale my samples using MaxAbsScaler, i notice that my negative values for this feature get almost completely drowned out by the positive values. And i don't really have any reason to believe my positive values should be that much larger than my negative values.
So what i've noticed is that fundamentally, the magnitude of percentage change values are not symmetrical in scale. For example if i have a value that goes from 50 to 200, that would result in a 300.0% change. If i have a value that goes from 200 to 50 that would result in a -75.0% change. I get there is a reason for this, but in terms of my feature, i don't see a reason why a change of 50 to 100 should be 3x+ more "important" than the same change in value but the opposite direction.
Given this information, i do not believe there would be any reason to want my model to treat a change of 200-50 as a "lesser" change than a change of 50-200. Since i am trying to represent the change of a value over time, i want to abstract this pattern so that my model can "visualize" the change of a value over time that same way a person would.
Right now i am solving this by using this formula
if curr > prev:
return curr / prev - 1
else:
return (prev / curr - 1) * -1
And this does seem to treat changes in value, similarly regardless of the direction. Ie from the example of above 50>200 = 300, 200>50 = -300. Is there a reason why i shouldn't be doing this? Does this accomplish my goal? Has anyone ran into similar dilemmas?
This is a discussion question and it's difficult to know the right answer to it without knowing the physical relevance of your feature. You are calculating a percentage change, and a percent change is dependent on the original value. I am not a big fan of a custom formula only to make percent change symmetric since it adds a layer of complexity when it is unnecessary in my opinion.
If you want change to be symmetric, you can try direct difference or factor change. There's nothing to suggest that difference or factor change are less correct than percent change. So, depending on the physical relevance of your feature, each of the following symmetric measures would be correct ways to measure change -
Difference change -> 50 to 200 yields 150, 200 to 50 yields -150
Factor change with logarithm -> 50 to 200 yields log(4), 200 to 50 yields log(1/4) = -log(4)
You're having trouble because you haven't brought the abstract questions into your paradigm.
"... my model can "visualize" ... same way a person would."
In this paradigm, you need a metric for "same way". There is no such empirical standard. You've dropped both of the simple standards -- relative error and absolute error -- and you posit some inherently "normal" standard that doesn't exist.
Yes, we run into these dilemmas: choosing a success metric. You've chosen a classic example from "How To Lie With Statistics"; depending on the choice of starting and finishing proportions and the error metric, you can "prove" all sorts of things.
This brings us to your central question:
Does this accomplish my goal?
We don't know. First of all, you haven't given us your actual goal. Rather, you've given us an indefinite description and a single example of two data points. Second, you're asking the wrong entity. Make your changes, run the model on your data set, and examine the properties of the resulting predictions. Do those properties satisfy your desired end result?
For instance, given your posted data points, (200, 50) and (50, 200), how would other examples fit in, such as (1, 4), (1000, 10), etc.? If you're simply training on the proportion of change over the full range of values involved in that transaction, your proposal is just what you need: use the higher value as the basis. Since you didn't post any representative data, we have no idea what sort of distribution you have.
I tried to follow this tutorial on using ELKI with pre-computed distances for clustering.
http://elki.dbs.ifi.lmu.de/wiki/HowTo/PrecomputedDistances
I used the following set of command line options:
-dbc.filter FixedDBIDsFilter -dbc.startid 0 -algorithm clustering.OPTICS
-algorithm.distancefunction external.FileBasedDoubleDistanceFunction
-distance.matrix /path/to/matrix -optics.minpts 5 -resulthandler ResultWriter
ELkI fails with a configuration error saying db.in file is needed to make the computation.
The following configuration errors prevented execution:
No value given for parameter "dbc.in":
Expected: The name of the input file to be parsed.
No value given for parameter "parser.distancefunction":
Expected: Distance function used for parsing values.
My question is what is db.in file? Why should I provide it in addition to the distance matrix file since the pair-wise distance matrix file completely specifies all the information about the point cloud. (also I don't have access to any other information other than the pair-wise distance information).
What should I do about db.in? Should I override it, or specify some dummy information etc. Kindly help me understand.
thank you.
This is documented in the ELKI HowTos:
http://elki.dbs.ifi.lmu.de/wiki/HowTo/PrecomputedDistances
Using without primary data
-dbc DBIDRangeDatabaseConnection -idgen.count 100
However, there is a bug (patch is on the howto page, and will be in the next release) so you right now can't fully use this; as a workaround you can use a text file that enumerates the objects.
The reason for this is that ELKI is designed to work on multi-relational data. It's not just processing matrixes. But some algorithms may e.g. need a geographic representation of an object, some measurements for this object, and a label for evaluation. That is three relations.
What the DBIDRange data source essentially does is create a single "fake" relation that is just the DBIDs 0 to 99. On algorithms that don't need actual data, but only distances (e.g. LOF or DBSCAN or OPTICS), it is sufficient to have object IDs and a distance matrix.
I want to get the properly rendered projection result from a Stage3D framework that presents something of a 'gray box' interface via its API. It is gray rather than black because I can see this critical snippet of source code:
matrix3D.copyFrom (renderable.getRenderSceneTransform (camera));
matrix3D.append (viewProjection);
The projection rendering technique that perfectly suits my needs comes from a helpful tutorial that works directly with AGAL rather than any particular framework. Its comparable rendering logic snippet looks like this:
cube.mat.copyToMatrix3D (drawMatrix);
drawMatrix.prepend (worldToClip);
So, I believe the correct, general summary of what is going on here is that both pieces of code are setting up the proper combined matrix to be sent to the Vertex Shader where that matrix will be a parameter to the m44 AGAL operation. The general description is that the combined matrix will take us from Object Local Space through Camera View Space to Screen or Clipping Space.
My problem can be summarized as arising from my ignorance of proper matrix operations. I believe my failed attempt to merge the two environments arises precisely because the semantics of prepending one matrix to another is not, and is never intended to be, equivalent to appending that matrix to the other. My request, then, can be summarized in this way. Because I have no control over the calling sequence that the framework will issue, e.g., I must live with an append operation, I can only try to fix things on the side where I prepare the matrix which is to be appended. That code is not black-boxed, but it is too complex for me to know how to change it so that it would meet the interface requirements posed by the framework.
Is there some sequence of inversions, transformations or other manuevers which would let me modify a viewProjection matrix that was designed to be prepended, so that it will turn out right when it is, instead, appended to the Object's World Space coordinates?
I am providing an answer more out of desperation than sure understanding, and still hope I will receive a better answer from those more knowledgeable. From Dunn and Parberry's "3D Math Primer" I learned that "transposing the product of two matrices is the same as taking the product of their transposes in reverse order."
Without being able to understand how to enter text involving superscripts, I am not sure if I can reduce my approach to a helpful mathematical formulation, so I will invent a syntax using functional notation. The equivalency noted by Dunn and Parberry would be something like:
AB = transpose (B) x transpose (A)
That comes close to solving my problem, which problem, to restate, is really just a problem arising out of the fact that I cannot control the behavior of the internal matrix operations in the framework package. I can, however, perform appropriate matrix operations on either side of the workflow from local object coordinates to those required by the GPU Vertex Shader.
I have not completed the test of my solution, which requires the final step to be taken in the AGAL shader, but I have been able to confirm in AS3 that the last 'un-transform' does yield exactly the same combined raw data as the example from the author of the camera with the desired lens properties whose implementation involves prepending rather than appending.
BA = transpose (transpose (A) x transpose (B))
I have also not yet tested to see if these extra calculations are so processing intensive as to reduce my application frame rate beyond what is acceptable, but am pleased at least to be able to confirm that the computations yield the same result.