Indices = list(range(n)) # allow flexible row referencing ***įor fd in range(n): # fd stands for focus diagonalįor j in range(n): # Use j to indicate column looping. The programming ( extra lines outputting documentation of steps have been deleted) is in the block below. py files of each notebook if you don’t use Jupyter. There are other Jupyter notebooks in the GitHub repository that I believe you will want to look at and try out. One creates the text for the mathematical layouts shown above using LibreOffice math coding. There are complementary.
The code in python employing these methods is shown in a Jupyter notebook called SystemOfEquationsStepByStep.ipynb in the repo. Please appreciate that I completely contrived the numbers, so that we’d come up with an X of all 1’s.
Ĭonsider a typical system of equations, such as: AX=B,\hspaceYES!Ī \cdot B_M should be B and it is! Therefore, B_M morphed into X. Linear Algebra Backgroundįirst, let’s review the linear algebra that illustrates a system of equations. Consider AX=B, where we need to solve for X. However, just working through the post and making sure you understand the steps thoroughly is also a great thing to do. Remember too, try to develop the code on your own with as little help from the post as possible, and use the post to compare to your math and approach.
However, near the end of the post, there is a section that shows how to solve for X in a system of equations using numpy / scipy. Also, we know that numpy or scipy or sklearn modules could be used, but we want to see how to solve for X in a system of equations without using any of them, because this post, like most posts on this site, is about understanding the principles from math to complete code. We’ll use python again, and even though the code is similar, it is a bit different. So there’s a separate GitHub repository for this project. This post covers solving a system of equations from math to complete code, and it’s VERY closely related to the matrix inversion post. There are times that we’d want an inverse matrix of a system for repeated uses of solving for X, but most of the time we simply need a single solution of X for a system of equations, and there is a method that allows us to solve directly for X where we don’t need to know the inverse of the system matrix. Published by Thom Ives on DecemDecember 3, 2018įind the complimentary System Of Equations project on GitHubĬheck out Integrated Machine Learning & AI coming soon to YouTube.
Solving a System of Equations in Pure Python without Numpy or Scipy