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This library provide fast linear algebra implementations for Scalar and Block Tridiagonal Matrices.

They are:

• lu decomposition(O(np^3))
• ul decomposition(O(np^3))
• ldu decomposition(O(np^3))
• udl decomposition(O(np^3))
• fast inversion(O(xp^3))

Here, n is the matrix dimension with respect to blocks, and p the block size, N = n*p the true matrix idmension, and x <= n is the number of matrix element you want to get.

The programming language is Python, with underlying fortran support.

###Purpose: Tridiagonal Matrix, especially Block Tridiagonal Hermitian Matrices are frequently used data structure in physics.

It can be intepreted as a Hamiltonian of a chain Model and layered structures.

It's trivial implementation is the recursive Green's function method to get the surface Green's function, solve the Landauer formula to get the conductance.

This package provide an elementwise view of Green's function for a general tridiagonal matrix, in the language of matrix theory.

###To use

1. Install numpy/scipy
2. Download this repository, import and use it, e.g.

import trid,linalg                  #import this library
from numpy.linalg import inv        #numpy inversion method
import time
n,p=100,10
tm=trid.get_trid(n,p,herm=True)     #construct a random block (np x np) hermitian tridiagonal matrix with block size p.
tma=tm.toarray()                    #parse this tridiagonal matrix to a numpy array.
t0=time.time()
isys=linalg.get_inv_system(tm)      #get the inversion generator.
inv00=isys.get_item(0,0)            #the the first element of the inverse matrix.
t1=time.time()
invtm=inv(tma)                      #the traditional method without optimization.
t2=time.time()
print 'Difference -> %s, Elapse %s(this), %s(numpy).'%(invtm[:p,:p]-inv00,t1-t0,t2-t1)

###To run tests/sample python tests.py python sample.py

###Contact the author: Leo Email: cacate0129@gmail.com

Welcome to improve it!