Data fitting programming Math 371
-
Upload
rolando-alban -
Category
Documents
-
view
27 -
download
2
description
Transcript of Data fitting programming Math 371
![Page 1: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/1.jpg)
Data fitting programmingMath 371
![Page 2: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/2.jpg)
![Page 3: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/3.jpg)
Can we do better?
.
x
![Page 4: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/4.jpg)
![Page 5: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/5.jpg)
![Page 6: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/6.jpg)
![Page 7: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/7.jpg)
![Page 8: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/8.jpg)
![Page 9: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/9.jpg)
![Page 10: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/10.jpg)
c*x-r
![Page 11: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/11.jpg)
![Page 12: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/12.jpg)
Use these estimated parameters to run the solution of the model
(the initial point is the first data point in the data table)
and compare with data points
![Page 13: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/13.jpg)
![Page 14: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/14.jpg)
![Page 15: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/15.jpg)
I use ode23 here, you can useode45 to obtain the same solution
![Page 16: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/16.jpg)
![Page 17: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/17.jpg)
The solution fits data reasonably well but not very well. Do we have
a better method for parameter estimation and data fitting?
![Page 18: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/18.jpg)
The solution fits data reasonably well but not very well. Do we have
a better method for parameter estimation and data fitting?
YES!
![Page 19: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/19.jpg)
Direct Method
Least-square data fitting
![Page 20: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/20.jpg)
Revisit L-V predator-prey model
Use the least-square method to fit data and estimate parameter values directly
![Page 21: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/21.jpg)
![Page 22: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/22.jpg)
![Page 23: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/23.jpg)
![Page 24: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/24.jpg)
You can use ode45 orother ODE solvers; usehelp files to check theirdifferences
![Page 25: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/25.jpg)
![Page 26: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/26.jpg)
Almost perfect data fitting!
![Page 27: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/27.jpg)
![Page 28: Data fitting programming Math 371](https://reader036.fdocuments.us/reader036/viewer/2022062314/56812d0f550346895d91e92f/html5/thumbnails/28.jpg)
abcr