Implement for parameter finding

[kunxianhuang]

An application estimates the parameters of the defined functions on some numerical data. We use maximum likelihood method as an estimation, and finding maximum/minimum is an optimization problem.

First, we have to decide the architecture of this application.
c++ in the bottom
Python API

For the coding side, I have little experiences about programming architecture.

Some objects need to complete as below

• Defined functions:
  • Gaussian function
  • Exponential function
  • Polynomial
  • Chebyshev polynomial
  • Poisson function
  • Crystal ball function: The Crystal ball function is a Gaussian with a tail on the low side (or both side).
  • User defined function: it should be the same with scipy's user defined function
  • Stack up of above functions (or Call "ADD")
• First derivative vector of defined functions
• Hessian matrix of defined functions
• Constrains (parameters bound): for example $0<\mu<20.0$ and $0.5<\sigma<3.0$ for Gaussian function
• Log-likelihood value
• Minimization methods
  • Iterator
  • Stop
  • Linear programming for constrained minimization
• Plots

[yungyuc]

Thanks @kunxianhuang . To get started, we may pick one or two functions and add prototype code. What functions would you like to do first?

[yungyuc]

The issue has been quiet for long time. I am turning this to a discussion conversation. @kunxianhuang, do you have new ideas about this?

[kunxianhuang]

Sorry for quite long. I have some private matters in past half year.
So, we can first start to draw some 1-D plot of data.
Thanks for calling me.

[kunxianhuang]

Wait, I remember that modmesh shows graphical plots. So, I should get familiar with that.
We can start from each class of functions and limits of parameters.

[yungyuc]

@j8xixo12 improved the plotting a lot and we are planning for further revamping of the GUI for releasing. @kunxianhuang, could you please try to build the latest modmesh and play with the Euler solver GUI?