subspace | Reactive Dapp Development with auto | Reactive Programming library

I have the following empty ggplot in R, lets call that plot as (***)

I wanted to take a quick look at the following distribution function and noticed that something is very wrong with the way I'm trying to do that. When applying the function to x_range, all values end up being 0. I am very confused about this and struggle to understand why that would be the case. Am I using numpy wrong in this situation? At least that is the only explanation I have, but I have not been able to find any sort of explanation for why I am seeing these results.

Below is my code.

I have a strange bug in this naive code for Gram-schmidt orthogonalization I wrote for numpy (v1.21.2).

I have a set of vectors which are pairwise perpendicular. Then I would like to generate a new vector which should be perpendicular to all the vectors in the given set and it should be chosen at random. Basically, if d is the dimensionality of the problem and m is the number of given vectors, then the set of vectors that are perpendicular to those spans a (d-m)-dimensional subspace. I would like to randomly sample a vector from this subspace.

I can use np.linalg.lstsq in order to find a vector that is perpendicular to all the others, but the result won't be random:

Hey I am working with Flutter, My AndroidManifest.xml looks like this. Not able to get merged manifest in android studio. Can you help me in finding out where am I missing exported=" true", Playstore is not allowing me to update the app?

I tried to update all the dependencies in pubspec.yaml but nothing helped. Checking each library for the manifest file is time-consuming. How can I detect which library manifest file needs to be changed?

I am working on principal component analysis (PCA) in Python. For comprehension reasons, I want to implement it myself. For that, I create random data based on a given covariance matrix, so that I can play with different values and how the principal component behave. So this script is just for understanding and clarifying the PCA.

My understanding is, that the principal components (which are the eigenvectors of the covariance matrix) are always orthogonal to each other. This is what the following picture of Wikipedia also says:

The description of the Image from Wikipedia (Source):

PCA of the multivariate Gaussian distribution centered at ( 1 , 3 ) with a standard deviation of 3 in roughly the ( 0.878 , 0.478 ) direction and of 1 in the orthogonal direction. The vectors shown are unit eigenvectors of the (symmetric, positive-semidefinite) covariance matrix scaled by the square root of the corresponding eigenvalue. Just as in the one-dimensional case, the square root is taken because the standard deviation is more readily visualized than the variance.

So I would expect that for my case, if I plot the eigenvectors that I've derived from my random data, are also orthogonal with each other. But this is not the case. Their direction always differs by approx. 60 degrees, and not 90 degress as I would expect. This also happens if I use the PCA from the sklearn library. See the image below, where red are the eigenvectors of the sklearn PCA and green are the eigenvectors from my own code.

My Python script:

For a project, I need to be able to sample random points uniformly from linear subspaces (ie. lines and hyperplanes) within a certain radius. Since these are linear subspaces, they must go through the origin. This should work for any dimension n from which we draw our subspaces for in Rn.

I want my range of values to be from -0.5 to 0.5 (ie, all the points should fall within a hypercube whose center is at the origin and length is 1). I have tried to do the following to generate random subspaces and then points from those subspaces but I don't think it's exactly correct (I think I'm missing some form of normalization for the points):

Some background story!
I have been working with git to contribute to an open source package, and I am somewhat novice in this area. I know some basic stuff. Furthermore, I also read that if merge conflict happens, we can go through the file and the markers can help us to find the block of codes that have conflict with each other in two versions of the same file.

Recently, I confronted a merge conflict for the first time, and it is on Jupyter notebook file (.ipynb). However, the markers of merge conflict make the notebook unreadable by Jupyter. So, I tried JSON editor and VS CODE and Notepad++. Although I can now see the file, it is really messy because it not only has all metadata of Jupyter notebook but also it shows conflict even for the number of execution. In addition, if there is a figure as an output of a cell in the notebook, it is converted to a lot of characters and scrolling down and go through them is headache.

After searching google and stackoverflow and discuss the issue with the owner of the project, we decided to take another approach. But, it doesn't work. (I explained it below, but first I need to provide further info. Please bear with me)

According to the history of the commits, I should be the one who created such conflicts locally by probably changing the same file on the PARENT branch as nobody changes it in the upstream (in the originAL repo)

Therefore, please let me first briefly walk you through the branches and some changes I did on files.

• After forking and cloning, I created a branch branch-A
• I changed the notebook 'notebook-file`
• I did Pull Request (PR)
• I created a sub-branch of A, lets call it sub-branch-of-A
• After switching to sub-branch, I changed two .py files and then also change that notebook-file
• merge sub-branch-of-A into branch-A

Inside my branch-A, I did: git push origin branch-A but I got non-fast-forward error. Which means a divergence happened. Right? So, I did git pull origin branch-A to resolve it, but I get merge conflict for the notebook-file.

Alternative Solution

So, I was told that I can copy the file to somewhere outside my local git repo, then do git checkout notebook-file to get the file in the parent node where divergence happened. Right? Then, if I do git pull ... there should be no problem (then I can include the changes of that copied file)

BUT...

I, again, got the merge conflict error. I went crazy and tried several things and still nothing.

I attached the git log below. The branch I am talking about is Snippets_Tutorial, And its sub-branch is Snippets_Regime. If I remember correctly, I used git checkout -b Snippets_Regime Snippets_Tutorial to create that sub-branch. As I mentioned earlier, I switched to the sub-branch Snippets_Regime and did some changes to somefile.py files and the notebook-file. Then, I merge it into Snippets_Tutorial.

I have a piece of numpy code that I know works. I know this because I have tested it in my generic case successfully. However, I arrived at the solution after two hours of back and forth referencing the docs and trial and error. I can't grasp how I would know to do this intuitively.

The setup: