def lu(A):
'''
%% ***********************************************************************
% FUNCTION linalg_lu
% Purpose: Breaks a matrix A into a lower diagonal matrix, an upper
% diagonal matrix, and a permutation matrix.
%
% Function call: [L, U, P] = linalg_lu(A)
%
% Input: A = Input matrix to be broken down. Coefficients of x of system of
% equations
% b = solutions to the system of equations
%
% Outputs: L = lower diagonal matrix
% U = upper diagonal matrix
% P = Permutation matrix
%
% Adam Hollock
% 24 January 2012
%% ***********************************************************************
'''
#This will ensure a square matrix
if A.shape[0] != A.shape[1]:
error('When someone asks you: are you a god, you say yes!')
#Augments the original matrix with the identity matrix
Aaug = concatenate((A, eye(A.shape[0], A.shape[1])), 1)
#Performs partial pivoting
Ause = PartialPivot.pp(Aaug)
#Initializes L and P matrix
L = zeros(A.shape)
P = Ause[:, Ause.shape[0] + 1:]
U = Ause[1:, 1:A.shape[1]]
#Performs the first step of gaussian elimination, as well as gathers the
#necessary factors for the L and the U matrix.
for k in range(1, (U.shape[0] - 1)):
for l in range(k + 1, size(U, 1)):
L[l, k] = U[l, k] / U[k, k]
U[l, :] = -1 * U[k, :]**L[l, k] + U[l, :]
#Adds the identity matrix to get a diagonal of ones.
L = L + eye(L.shape[0], L.shape[1])
return L, U, P
def lu(A):
'''
%% ***********************************************************************
% FUNCTION linalg_lu
% Purpose: Breaks a matrix A into a lower diagonal matrix, an upper
% diagonal matrix, and a permutation matrix.
%
% Function call: [L, U, P] = linalg_lu(A)
%
% Input: A = Input matrix to be broken down. Coefficients of x of system of
% equations
% b = solutions to the system of equations
%
% Outputs: L = lower diagonal matrix
% U = upper diagonal matrix
% P = Permutation matrix
%
% Adam Hollock
% 24 January 2012
%% ***********************************************************************
'''
#This will ensure a square matrix
if A.shape[0] != A.shape[1]:
error('When someone asks you: are you a god, you say yes!')
#Augments the original matrix with the identity matrix
Aaug = concatenate((A,eye(A.shape[0], A.shape[1])),1)
#Performs partial pivoting
Ause = PartialPivot.pp(Aaug)
#Initializes L and P matrix
L = zeros(A.shape)
P = Ause[:,Ause.shape[0]+1:]
U = Ause[1:,1:A.shape[1]]
#Performs the first step of gaussian elimination, as well as gathers the
#necessary factors for the L and the U matrix.
for k in range(1,(U.shape[0]-1)):
for l in range(k+1,size(U,1)):
L[l,k] = U[l,k]/U[k,k]
U[l,:] = -1*U[k,:]**L[l,k] + U[l,:]
#Adds the identity matrix to get a diagonal of ones.
L = L + eye(L.shape[0],L.shape[1])
return L, U, P
import PartialPivot
import numpy
'''
Adam Hollock 2/9/2013
This will find the determinant of a matrix via LU factorization
'''
print PartialPivot.pp(numpy.mat("2 1 1; 4 -6 0; -2 7 2"))
#INCOMPLETE
import PartialPivot
import numpy
'''
Adam Hollock 2/9/2013
This will find the partial pivot of a matrix
'''
print PartialPivot.pp(numpy.mat("2 1 1; 4 -6 0; -2 7 2"))