jonasgreim / choleskydecompositionexistencecheck

Cholesky decomposition existence check

About The Project

I wrote this Fortran code for a friend´s university project. It is clearly not the best Fortran code out there, but the code works with every quadratic matrices. You can test whether there is a Cholesky decomposition or not. I am uploading this project because if someone gets a similar task in the following semesters, this code could help. Also, I have not found a standard solution for this problem via Google.

Usually you don't comment every line of code, but it was requested that way. I leave the comments like this because I think it helps a lot if you don't understand Fortran well.

Installation

• Install at least Fortran 90
• Go to the root folder of the project
• Compile (Windows)

 gfortran code.f90

• Execute (Windows)

  a.exe

How to use it

• Change this variable to the length of your quadratic matrix (Line 3)

  integer , parameter:: columnRowLength = 4

• Put your matrix formatted in .txt or .csv in the root folder of the project and change it to your file name (line 15)

  open(10,file='CholeskyPossible.txt')

  For test purposes you can use the matrices: CholeskyNotPossible.txt, CholeskyPossible.txt & 5x5Matrix.txt (with the last one you have to change the variable to 5)
• Compile and run/execute the project
• The results are now printed out in your command line

How it works

If the matrix is quadratic, symmetric and positiv definit => then there is a Cholesky decomposition.

Quadratic:

• square matrices are required (there is no test that sort out non-square matrices!)

Test symmetry:

• compare the matrix to its own transposition

Test positiv definit:

• via Laplace expansion:
  • If Laplace expansion is greater than 0 then the matrix is semi postiv definit
  • And if Laplace expansion is is greater than 0 and the matrix is symmetric then the matrix is postiv definit

License

Distributed under the MIT License. See LICENSE for more information.