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Curve Fitting in Python (2022)
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- เผยแพร่เมื่อ 16 ส.ค. 2024
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In this video I show how to use the curvefit function in the scipy.optimize library. I also look at practical examples from physics.
Tutorial Playlist:
• The Full Python Tutorial
Code:
github.com/luk...
Discord:
/ discord
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Sometimes one may both know coding and physics but it becomes really exhausting to combine them together; you may not able to know where to start... You are directly attacking to that tricky intersection perfectly and that is exactly what is needed for lots of science students/academics!
I just personally wanted to thank you for such great videos as a PhD student in physics who had worked with paper and pen for years but needed numerical computation eventually. Your videos are awesome and very informing! I hope you keep going.
If you ever try your hand at 3D Graphics Programming and write the underlying core components of the 3D Rendering Engine where you implement a Physics Engine with basic kinematics, collision detection systems, A.I. Path Finding Algorithms, etc. then you get into doing Animations, Particle Effects, Rigid Bodies, Rag Dolls, Liquid or Water Animations, etc... by using advanced shaders for many various lighting, shading, shadow, and other special effects... That's one of the best ways to merge the two fields.
Now, this kind of Physics programming is different from Data Science, Equation Solver type Physics system, but it's a great place to start and most of the topics and transitions would already be covered. A basic 3D Rendering Engine or 3D Game Engine uses mostly linear algebra and trigonometry, but there is still a bit of calculus here and there such as when basic integrals, performing interpolations of various kinds, using runge kutta as well as FFTs all come in handy. Especially FFTs when working with Audio Processing and 3D Sound Environments is another great benefit.
You end up incorporating many mathematical and physics, (maybe even a little bit of chemistry, biology, and environmental systems depending on the context of your Engine and what you are going to build with it) concepts into your Engine that stem across many software engineering and program application development disciplines by using almost every kind of container and associated algorithm there are out there. Other key features would be file management and file parsers, you can end up writing your own scripting or run time interpreted language, if doing multiplayer over networking then multithreading and multiprocessing principles, compression and decompression algorithms, encryption and decryption algorithms come in handy. Then you have many other topics such as batch processing, Storage or Assets Memory Managers, Many Various Shaders with an accompanying Shader Manager, and so much more. This doesn't even include things such as GUIs, HUDs and Font Management...
Now, once you have the Engine Built with all of its core components (and I don't mean using a 3D engine such as Unity or Unreal...) Then the fun begins when you start building your game that is seperate from then engine but requires it as a core underlying library to function properly. Now imagine building a game like Factorio or Minecraft... Both of those games are Turing Complete... or even a 2D with 3D layer slices such as in Oxygen Not Included or a semi-factory but defense tower game like Mindustry which are both Turing Complete... or something similar to those... Then I think you can build just about any kind of software application that you could imagine except maybe an actual robust compiler-debugger-linker suite, or an actual Operating System... Oh they could be done... but they're a challenge. I found it was actually a bit easier to learn how to build a Hardware Emulator in C++ with a focus on the 6502 for the NES... Now that was a fun project as well! So almost anything is possible to build but it does depend on the limitations of your hardware...
This is just a summary of about a 20 year journey of independent studying purely self taught hobbyist and some of the many topics I've learned over the years! There's many other things that I didn't mention as this is starting to become quite long... It's been a great journey. Even watching Ben Eaters 8-Bit Breadboard CPU series was a delight! So much so, that I actually implemented it in Logisim.
That's the scientific channel that we need. Good sound (which is the most important), good picture, Chad-looking science guy (in movies smart people are often nerds with big glasses) and a good explanation - this is really nice! Thank you for video!
Absolutely love this intro to SciPy's 'curve_fit' function! Suggest you to make a video on spline fitting, which is included into SciPy's 'interpolate' module. With splines it is possible to find best fit to a really complex data, including those presented in this tutorial.
Two weeks ago I had a physics assignment involving this method, which was a absolute disaster. This is why I should watch your videos as soon as they show up. Anyway, Thanks for the amazing job!
Nice! Note that (in 19:40) you need to set absolute_sigma=True to get the absolute value errors on the parameters. A good example is using the known formulas to calculate the error on the parameters (A,B) of a strait line fit and compare with the results returning with absolute_sigma=False e absolute_sigma=True.
It's a good comment
Your initial guess was good enough 😂, great tutorial!
The kind of detailed explanation i needed! The examples nailed it! Thanks a lot :)
Great video. Especially focusing and repeating multiple times that our goal is the parameters and not just having a good fit! Parameters = Context = Reason why we're doing the fit
This is exactly the tutorial I needed given I had to perform many counting experiments . I wish I had found this channel sooner before going insane over tutorials that made zero sense to me.
Great video, just a little correction, as the physicist in me is happy to show himself every now and then: It's actually Lennard-Jones potential, sometimes also called Van der Waals potentials (dipole-dipole potential) big brother. I don't think there's a thing called Leonard-Weibeck potential reguarding atomic repulsion, but if there is and it's related to the LJ potential, let me know!
Oh I might have misspoke! Thank you for this correction 😂
Thanks a lot! This was a really thorough explanation which gave me everything I need to plot my data in a nice way :) Keep it up!
dude your videos rock, i love the no-nonsense type of attitude when tackling things, cheers! (;
Wow! You explain very clearly! I was fighting with my code since I did not understand how to work with curve_fit and you fell out of the sky! Thank you so much!
This is excellent content. Clearly explained a problem I've been having trouble grasping for months. Thanks!
Hi, first off EXCELLENT VIDEO THANK YOU SO MUCH
Just for those who need this video, there are a couple of clarifications (sorry if you made them and I didnt notice), but its popt, pcov = scipy.optimize.curve_fit
not just curve_fit () . Unless you made a shortcut beforehand
Other than that , thank you again so much help !
Super helpful and so nicely explained! Thank you so much for making this video! The multiple examples helped me a lot and in fact covered what I was as looking for!
Thank you! Your tutorials are very clear and useful!
Your Videos are really helping me. Thanks a lot.
Thank you for making this video I particularly liked that you gave more than one example.
superb video with respect to physics and maths! Best application based explanation. Period. Please I request you to post such concepts with such physics based applications visualisation. I just feel blessed. Thanks a lot. tons
Like 25 years ago i wrote code to fit multiple gauss function to some spectrum comming from Cherenkov radiation emitted from cristals. Those days everythibg had to be done in C/C++. I use the "Numerical recipies in C" book and lib and the Marquard Levenberg algorithm. Took 3 weeks to progam that (including some GUI and other stuff). Today with Scipy maybe one or two days... Some stuff actually get's better.
Brilliant explanation of the covariance!
Was expecting a good description of what's going on with the curve-fitting functions, albeit with boring data. But actually I found exactly what I was looking for. Trying to get the photopeaks and their resolutions in a similar spectroscopy. Also the walking through cell-by-cell helps for digestion. Used to begrudingly use python, but after a semester I much more prefer it over finicky excel sheets.
Thank you so much for making such videos. Specifically in physics. It is of so much help. Please keep doing such videos.
This is super clear!
awesome video as always. Learned a lot - especially the cov-Matrix was super helpful
One note: It is the Lennard-Jones potential, not the Leonard Weibeck potential
i found your videos about 10 minutes ago and mate, what an amazing content, you remind me of keith galli, he is awesome too
You give quality out there. Respect man.
I learnt a lot from thus vedio, thanks bro👍
Your videos are sweet! I found you earlier today and have already learned a ton. Thanks!
Dude! this video is so useful! Great explanation and great material!
Thank you now I understood how the errors behave!
Amazing! Thank you. This has been perfect help with plotting an exponential curve to my data.
you gained a subscriber sir thanks
Excellent video. Very clear unpacking of the logic. Thank you! I've subbed.
great videos! continue your greatwork bro! supporting from philippines here.
perfect please do more in physcis and more intuitive
This is great! Glad to find your channel
This is so very helpful...thank you
Thank you for the content,
I would like to see a video on hysteresis curvefitting with multiple conditions
Thank you very much for such beautiful tutorials.
Can you show fitting hysteresis models
Please, make a numba tutorial :)
Your videos are awsome
Great video! Thank you!
Great video, thank you. Hope to see you @ UBC some day :)
Very good ,very Useful very : )
Great video ! I just finished a lab report last Saturday, this would been useful jajaja. I would like you to make a video about animations in python tool
Same. I wish I had found this tutorial a couple of weeks ago for my lab reports. But better late than never.
Very helpful video...👍👍👍
Thanks for explaining this so well!! Super helpful!!
excellent explanation, very detailed
Please consider doing some stuff on Bayesian inference using Markov Chains, maybe using the PyMC library?
Very helpful content. The error(as obtained from experiment) is sometimes not symmetric about the mean y position. Is it possible to encode that into curve_fit function?
You definitely making a good thing, killing a Matlab!
Thank you so much !! You've been a really big help.
OH GOD!!, thank you very much!!!!!
How to come up with the equation for curve fit method? Suppose the data doesn't follow a specific distribution which can be determined by seeing the scatter plot.
How to come up with the equation for curve fit? Suppose the scatter plot is not showing a particular distribution.
Thanks for the great tutorial. Since in real life we have only the data, how can we find the best non-linear model function that fits to our data?
Good job!
The heatmap of the covariance is brilliant, I'm definitely going to experiment with that. You mentioned the importance of the diagonal, but what do the other values in the covariance matrix mean?
That’s how one parameter affects another if at all.
Have you done any videos on FFTs or any Runge Kutta methods?
These videos are really great
I'd like to ask you a question about the standardisation: why didn't you just multiply the ordinates by 10^(-21), in order to have numbers in the order of mangitude of 1?
I had a question, what if the function had constants in its definition that were an array that take certain values at specific points of xdata?
Really great video!
Thanks a lot for this nice explanation! I wonder what you use to fix one or some of the fitted parameters using the Scipy curve fitting function?
Simply WOW!
Great video!
In the given case that you want to work multiple samples, and perform simultaneous fits. Is that possible? It is something I use often in XPS.
Same question here. I have tried clustering without luck.
Say I have a histogram plot with bars. I would like to do a skew norm fit to it. How do I proceed with this? can anyone help? like what initial data should I have
Perfect
great vid
pretty nice explanation, thanks! would it give some sense to use R or Scilab to achieve this, would it be more efficient?
Amazing
Is there a way to do R^2?
Hello Mr. P Solver,
First of all a great video on optimization. I have a question regarding the optimization and identification of values in a given curve. Since I am completely new to this, I am not much aware of reverse engineering. I have an experimental Time-Temperature curve of a heat transfer system and based on it I need to identify the convective heat transfer coefficient. Is it possible to make it? if yes could you please give me an example. Thanks in advance.
With Regards,
Preshit
For the Gaussian fit again. If I add a +c factor at the end in the gauss_f definition, will the plot work if I expand popt with c_opt so that the measurement points are taken into account which do not look "parabolic"?
Sir, can u make video on Heisenberg spin chain and correlation between spins.
where is the csv file ? @13:47
Hmmm i was expecting something more clicking this video. When you have object returned by the fit method it has method called plot. It shows data with fitted model as well as plots the residuals.
could you please show how to add bound to parameter?
Hello, Thanks a lot for yours tutorials! They help me a lot. I have a question. How to use curve_fit (or how to cope with the problem) if I have a system of ODEs. How to use it as a model for curve_Fit function?
👍💯
thank you..
good video. How would I estimate the data based on those parameters?
I am getting the following error. I tried multiple methods like using numpy.asarray, np.array...... Is there any other solution?
setting an array element with a sequence. The requested array has an inhomogeneous shape after 1 dimensions. The detected shape was (5,) + inhomogeneous part.
Can you tell something about fitting multiple gaussians in a signal?
how to get that sample data, if i need
Can we solve a multi-variable function through curve-fitting , for example - y = f(x1,x2,x3,x4)?
My values in y axis are all less than 1. So taking the sq root considering Poison statistics of photons gives very high error. What should I do ? Should i take some kind of scaling factor?
Thanks 👏👏
Great video as always!
May I ask you to recommend some good books to dive further into this stuff? Maybe the ones you learned from, if any? It would be great!
Keep doing these great videos, sir!
ye im also wondering how did he reach all that knowledge
@@jay89boy Same here, he might and actually should do a short video about giving some advices on how to dig deeper into the topic, especially book recommendations. He is a great guy and I think he will read this and respond in one way or another.
What is that algorith? I mean that is working in the background.
Hello Mr. P solver, is there a way to solve for a complex function- meaning that the function that I have defrined returns complex(both real and imaginary parts) simultaneously, I tried doing it this with Scipy.optimize.curve_fit() but does not help If you have any idea pls share, thanks :)
Hey could you do a tutorial for a CFD simulation in python?
you left out a 2 in the gaussian formula
but when i plug in 2 it gives wrong answer. i tried it on my dataset. without it it gives right answer. why?
This isn't at all related to the video content, but I have the same exact scar on my forehead
Your style annoys me but the content is good
this scipy shit hard to understand man.
Great content. Just some feedback, I feel it would be less distracting if you didn’t show yourself talking while showing content on screen.