Lanczos Algorithm Puns

Hi everyone! I’m learning about eigenvalue algorithms such as the power method and Lanczos.

I think I understand how it works, starting from a Hermitian matrix H it outputs a tridiagonal matrix T with dimensions n*n where n is the number of iterations.

The sources I have read always stop at this point - but we still don’t have the eigenvalues! My question is, how does having the matrix in tridiagonal form help in computing the eigenvalues? Is there a simple way to obtain them that I’m not seeing?

I'm trying to code up the Lanczos algorithm for eigenvalue approximation at the moment. I've seen on pages like this that the algorithm can't distinguish the eigenvectors if the dimension of the eigenspace is >1, but I don't understand why this makes it actually fail rather than just finish incompletely.

When I run tests the algorithm breaks because it ends up dividing by 0 when trying to find the orthonormal basis. Can anyone direct me to a proof / show my why it fails?

Hey /r/learnprogramming,

I'm beginning a project (condensed matter theory for the curious) that is going to require some programming however I'm not sure which language would best fit my needs, C or python. And unfortunately I don't have any time to experiment with each one to figure out the more suitable language which is why I've come to this subreddit to ask. The project I'm working on will involve the use of matrices, which may become large, and the manipulation of these matrices, as well as the implementation of lanczos algorithms (an iterative algorithm). I'm looking for code that will be efficient and not clumsy when creating and changing the matrices. I worked with MATLAB last year which handled matrices as its main data type but I wasn't a fan of how the language was constructed and used. Can you advise to the more suitable language?

Thanks

This is a PhD thesis for which the digital download is only available on the UC Berkeley campus. The year was 1993.

Also, I'm interested in: Zhuang Wu. The Triple dqds Algorithm for Complex Eigenvalues. 1996.

Suppose I have elevation data represented as a .TIF file. Its 1000x1000 pixels. I want it to be 2000x2000 pixels, but I don't want it to be blocks of 4 pixels with the exact same value as the 1 pixel it was before. I want the new .TIF file to be smoother. Is there a built in function for this?

So far I've mostly used the default scale filter method to scale the x264 video resolution down, for example -vf scale=720:576 but I've noticed that some people often use -vf scale=720:576:flags=name (or -vf scale=720x576:flags=name) where name is the name of the filter.

I've found this: https://legacy.imagemagick.org/Usage/filter/

... and this: https://superuser.com/questions/375718/which-resize-algorithm-to-choose-for-videos/375726#375726

... and this image: https://matplotlib.org/mpl_examples/images_contours_and_fields/interpolation_methods.hires.png

I can imagine that selecting the proper filter can be crucial when scaling the video up but what about scaling it down?

I think the most popular "not default" filter is Lanczos. I've already tried Lanczos and Spline (they were mentioned as "the best ones when scaling down" in my second link) and the first thing that surprised me was nearly no encoding time difference when compared to default method but the only differences in the output file I could notice were the more smooth gradients.

What is "the more proper" syntax: -vf scale=720:576:flags=lanczos or -vf scale=720x576:flags=lanczos?

Are there any best filters to use when scaling down to anamorphic resolutions like 720x576 / 16:9?

What should I look at in the output video to spot most of the main "features" of the used filter?

What is your preferred method to scale the video resolution down and why?

Do your worst!

After messing around with Dlss and FSR in Deathloop, I was reminded that GTX users (pre Turing), don't have access to Dlss, and for them these comparisons are useless. Since RTX users are a small minority, and Nvidia has some upscaling options that work for all GTX users, I decided to see if GTX users are in fact stuck with FSR.

To test this I used AMD's FSR sample utility. The utility creates a very upscale friendly 3d environment that does not compare to modern games with tons of shaders and effects. It shows off FSR in the best light. So, to test against it, I used a 1080p capture card to directly capture Nvidia control panel sharpening + scaling. The control panel option uses Lanczos with 5 taps and CAS (AMD's open source sharpening, which nvidia also uses). Finally, the max output is 85% the resolution, compared to FSR which is 77% at ultra quality.

Below are slider comparisons.

https://imgsli.com/NzcxMTU Native vs Nvidia upscaling with 10% sharpness:

Not a bad comparison, though native is obviously cleaner. The upscale is more blurry, but otherwise most of the detail is retained, which makes sense because 5 taps is used to retain more detail than a faster, less accurate algo.

https://imgsli.com/NzcxMTg FSR vs Upscaling (with 10% sharpness)

Fsr is obviously nicer, though oversharpened, as is its trademark. Also check out the lod differences-ultra quality uses a lower lod than native and upscaling, so it has to be adjusted for upscaling as well.

https://imgsli.com/NzcxMjI Lowered the Lod for Upscaling and boosted the sharpness to 33%. Upscaling is getting better, and the funny thing is that details are starting to be enhanced that don't even exist in the FSR side- 5 taps retains more information than 2, it just needs the same level of sharpness.

https://imgsli.com/NzcxMjM Max lod for upscaling. Upscaling has more details but appears slightly softer. Fsr is missing shadow accuracy but looks "cleaner". While I would probably still pick FSR, it depends on what you value more. Also, sharpness can still be enhanced on upscaling, but at that point you'd start to introduce ringing.

https://imgsli.com/NzcxMjU Deathloop Native vs Upscaling.

Native is better, but how much better? This is using a simple control panel method.

https://imgsli.com/NzcxMjc Deathloop u

It really does, I swear!

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

I'm surprised it hasn't decade.

They’re on standbi

Buenosdillas

Pilot on me!!

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

When I got home, they were still there.

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "

I won't be doing that today!

You take away their little brooms

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

There hasn't been a post all year!

Why

[Removed]

It’s pronounced “Noel.”

After all his first name is No-vac

What, then, is Chinese rap?

Edit:

Notable mentions from the comments:

• Spanish/Swedish/Swiss/Serbian hits

• French/Finnish art

• Country/Canadian rap

• Chinese/Country/Canadian rock

• Turkish/Tunisian/Taiwanese rap

There hasn't been a single post this year!

(Happy 2022 from New Zealand)

Nothing, it just waved