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.
- Install at least Fortran 90
- Go to the root folder of the project
- Compile (Windows)
gfortran code.f90- Execute (Windows)
a.exe- 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)
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)
open(10,file='CholeskyPossible.txt') - Compile and run/execute the project
- The results are now printed out in your command line
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
Distributed under the MIT License. See LICENSE for more information.