Multivariate Root Finding in Python

2024/4/15 1:15:26

Using excel solver, it is easy to find a solution (optimum value for x and y )for this equation:

(x*14.80461) + (y * -4.9233) + (10*0.4803) ≈ 0

However, I can't figure out how to do this in Python. The existing scipy optimize library function like fsolve() or leastsq() seems to work with only one variable.... (I might just not know how to use them)...

Any suggestions?

Thanks!

Answer
>>> def f(x):
...     return x[0]*14.80461 + x[1]*(-4.9233) + x[2]*(10*0.4803) 
>>> def vf(x):
...    return [f(x), 0, 0]
>> xx = fsolve(vf, x0=[0,0,1])
>>> 
>>> f(xx)
8.8817841970012523e-16

Since the solution is not unique, different initial values for an unknown lead to different (valid) solutions.

EDIT: Why this works. Well, it's a dirty hack. It's just that fsolve and its relatives deal with systems of equations. What I did here, I defined a system of three equations (f(x) returns a three-element list) for three variables (x has three elements). Now fsolve uses a Newton-type algorithm to converge to a solution.

Clearly, the system is underdefined: you can specify arbitrary values of two variables, say, x[1] and x[2] and find x[0] to satisfy the only non-trivial equation you have. You can see this explicitly by specifying a couple of initial guesses for x0 and see different outputs, all of which satisfy f(x)=0 up to a certain tolerance.

https://en.xdnf.cn/q/72988.html

Related Q&A

Python print not working when embedded into MPI program

I have an Python 3 interpreter embedded into an C++ MPI application. This application loads a script and passes it to the interpreter.When I execute the program on 1 process without the MPI launcher (s…

Detecting USB Device Insertion on Windows 10 using python

I cant get the following code for Detecting USB Device Insertion to work on my Windows 10 (64 bit) computer with Python 3.7.import win32serviceutil import win32service import win32event import servicem…

I get NotImplementedError when trying to do a prepared statement with mysql python connector

I want to use prepared statements to insert data into a MySQL DB (version 5.7) using python, but I keep getting a NotImplementedError. Im following the documentation here: https://dev.mysql.com/doc/con…

parsing transcript .srt files into readable text

I have a video transcript SRT file with lines in conventional SRT format. Heres an example:1 00:00:00,710 --> 00:00:03,220 Lorem ipsum dolor sit amet consectetur, adipisicing elit.2 00:00:03,220 --…

Sphinx Public API documentation

I have a large number of python file and I would like to generate public API documentation for my project. All the functions that are part of the api I have decorated with a decorator. for example:@api…

Debugging a scripting language like ruby

I am basically from the world of C language programming, now delving into the world of scripting languages like Ruby and Python.I am wondering how to do debugging. At present the steps I follow is, I c…

Running unittest Test Cases and Robot Framework Test Cases Together

Our group is evaluating Robot Test Framework for our QA group, not just for BDD, but also to possibly cover a lot of our regular functionality testing needs. It certainly is a compelling project.To wha…

numpy.ndarray enumeration over a proper subset of the dimensions?

(In this post, let np be shorthand for numpy.)Suppose a is a (n + k)‑dimensional np.ndarray object, for some integers n > 1 and k > 1. (IOW, n + k > 3 is the value of a.ndim). I w…

How can I work with a GLib.Array in Python?

I am writing a plugin for Rhythmbox, wherein a signal raised is passing in an object of type GArray. The documentation for GLib Arrays shows me a few methods I am interested in, but am unable to acces…

Categorical dtype changes after using melt

In answering this question, I found that after using melt on a pandas dataframe, a column that was previously an ordered Categorical dtype becomes an object. Is this intended behaviour?Note: not looki…