http://matrixprogramming.com/2011/03/linear-solve-in-python-numpy-and-scipy
This is a great tutorial on Linear Solver approaches in Python. In particular, I like the reference to the Cholesky Decomposition. For those that aren't familiar, Cholesky Decomposition only works on symmetric positive definite matrices. This is pretty common in the Statistics world, since those are the properties of a well defined Covariance Matrix.
When I write up my code, I'll make sure to write up a cool tutorial on how to do the Cholesky Decomposition in Python for inverting a Covariance Matrix. I promise!
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