Manual Gauss Jordan in Python.

What if we didn't do back substitution on Gauss Naif method but eliminate the rest instead? Nah, we get the Gauss Jordan here.

The idea is after we do operation to make the  lower-triangle have zero value,  we continue the operation until all the component in the upper-triangle have zero value too, and the diagonal have value of one.

Basically, the matrix becomes identity matrix. This way, we didn't need subtitution at all since all variables already has the exact value on the right side, :)

Manual Gauss Naif Elimination using Python

How about some manual matrix using manual Gauss just like always, but in Python? Okay, here it is.

I use tuple, I think it's just the same as array for this purpose.

I created matrix a with random value.  It's like linear equation system; three unknown variables with three equation. The purpose of this code is to find x1, x2 and x3.

Oh, in this case, its x0, x1 and x2, :)

That's Not Fair!

Maybe that's something come to our mind when we read this code. Yeah, that's forward dfference. It's designed to get the difference value using the point we calculate and the next one. That means the value will "lopsided" by nature, :)

Searching Multiple Roots Numerically.

This Python code only works with function that crossing x-axis.

The idea is we started from x=0 and walking to the positive direction and evaluating f(x) as we walk.

If there's change of the sign of f(x) from + to -, or vice versa, there must be a root in that area.

We began to surround it to find the-x that correspond to f(x)=0. That x value is the root.

After the root is found, we began to walk along x-axis again until found any sign change of f(x), or until x limit set on code.

Manual Gauss Elimination on 3x3 Matrices in Delphi

I use this code in order to find its pattern.

Yes, there is many Gauss code out there. I plan to write it on next post about it. The dynamic Gauss Elimination code that could be implemented to any size of matrices.

But for now, let just settle on this.

https://youtu.be/csiFpdsrzzQ

Tadaa...

Again, :)

Lagrange Polynomial Interpolation on Python.

It's a whole a lot easier than Newton's divided differences interpolation polynomial, because there is no divided difference part that need a recursive function.