def lu(matIn):
'''
%% ***********************************************************************
% FUNCTION linalg_inv_lu
% Purpose: Calculates the inverse of a matrix using LU methods.
% Additionally will check if the matrix is square, and will return the
% pseudoinverse, if not.
%
% Function call: [Ainv] = linalg_inv_lu(A)
%
% Input: A = Input matrix to be inverted
%
% Outputs: Ainv = the inverted matrix
%
% Adam Hollock
% 24 January 2012
%% ***********************************************************************
'''
#This will take the pseudoinverse in case the matrix in question is not
#square.
#Underdetermined case
if (matIn.shape[0] < matIn.shape[1]):
Atest = matIn.T * linalg_inv_lu.lu(matIn * matIn.T)
#Overdetermined case
elif (matIn.shape[0] > matIn.shape[1]):
Atest = linalg_inv_lu.lu(matIn.T * matIn) * matIn.T
else:
Atest = matIn
print Atest
#Calculates the L and U matrices
[L, U, P] = linalg_lu.lu(Atest)
#Finds the inverse of the L and U matrices using the premade RR methods.
Linv = linalg_inv_rr.rr(L)
Uinv = linalg_inv_rr.rr(U)
#Initializes AinvTemp, Ainv and D matrices, as well as a general purpose identity
#matrix.
AinvTemp = zeros(Atest.shape)
D = zeros(Atest.shape)
ident = eye(Atest.shape)
Ainv = zeros(Atest.shape)
for i in arange(1, Atest.shape[1]):
D[:, i] = Linv * ident[:, i]
AinvTemp[:, i] = Uinv * D[:, i]
#This reorganizes the matrix in accordance with the change in P.
for i in range(1, P.shape[0]):
Ainv[:, i] = AinvTemp[:, nonzero(P[:, i] == 1)]
def lu(matIn):
'''
%% ***********************************************************************
% FUNCTION linalg_inv_lu
% Purpose: Calculates the inverse of a matrix using LU methods.
% Additionally will check if the matrix is square, and will return the
% pseudoinverse, if not.
%
% Function call: [Ainv] = linalg_inv_lu(A)
%
% Input: A = Input matrix to be inverted
%
% Outputs: Ainv = the inverted matrix
%
% Adam Hollock
% 24 January 2012
%% ***********************************************************************
'''
#This will take the pseudoinverse in case the matrix in question is not
#square.
#Underdetermined case
if (matIn.shape[0] < matIn.shape[1]):
Atest = matIn.T*linalg_inv_lu.lu(matIn*matIn.T)
#Overdetermined case
elif (matIn.shape[0] > matIn.shape[1]):
Atest = linalg_inv_lu.lu(matIn.T*matIn)*matIn.T
else:
Atest = matIn
print Atest
#Calculates the L and U matrices
[L, U, P] = linalg_lu.lu(Atest)
#Finds the inverse of the L and U matrices using the premade RR methods.
Linv = linalg_inv_rr.rr(L)
Uinv = linalg_inv_rr.rr(U)
#Initializes AinvTemp, Ainv and D matrices, as well as a general purpose identity
#matrix.
AinvTemp = zeros(Atest.shape)
D = zeros(Atest.shape)
ident = eye(Atest.shape)
Ainv = zeros(Atest.shape)
for i in arange(1,Atest.shape[1]):
D[:,i] = Linv*ident[:,i]
AinvTemp[:,i] = Uinv*D[:,i]
#This reorganizes the matrix in accordance with the change in P.
for i in range(1,P.shape[0]):
Ainv[:,i] = AinvTemp[:,nonzero(P[:,i]==1)]
from numpy import *
import linalg_lu
def determ_lu(A):
'''
%% ***********************************************************************
% FUNCTION linalg_determ_lu
% Purpose: Finds the determinant of a matrix via LU factorization
%
% Function call: [DetA] = linalg_determ_lu(A)
%
% Input: A = Input matrix
%
% Outputs: Apiv = Determinant
%
% Adam Hollock
% 24 January 2012
%% ***********************************************************************
'''
if size(A,1) ~= size(A,2):
error('When someone asks you: are you a god, you say yes!');
L, U, P = linalg_lu.lu(A)
DetA = prod(diag(L))*prod(diag(U))
