def eqr(A):
'''
%% ***********************************************************************
% FUNCTION eigen_qr
% Purpose: Finds the eigenvalues and eigenvectors of a given matrix using
% the QR method
%
% Function call: [eigVal, eigVect, counter] = eigen_qr(A, guess, eps)
%
% Input: A = Input matrix
%
% Outputs: eigVal - Output array of eigenvalues
% eigVect - Output array of eigenvectors
% counter - Number of iterations it took to solve for the eigenvalues
%
% Adam Hollock
% 5 February 2012
%% ***********************************************************************
'''
#initializes all matrices to be used in the method
e_matrix = eye(A.shape[1])
for i in arange(1, e_matrix.shape[1], 2):
e_matrix[i, :] = e_matrix[i, :] * -1
#Performs the QR factorization method for obtaining an upper triangular
#matrix.
for i in arange(0, A.shape[1]):
#This will make a special case for the first iteration
if i == 0:
#Builds the c vector as needed
c_vector = A[:, i]
else:
#Builds the c vector as needed
c_vector = concatenate((zeros((i, 1)), r_matrixNew[i:, i]))
c_norm = linalg.norm(c_vector, 2)
v = c_vector + c_norm * e_matrix[:, i].reshape(A.shape[0], 1)
house = (eye(A.shape[1]) - multiply((2 / (v.T * v)), (v * v.T)))
#This will make a special case for the first iteration
if i == 0:
#Builds the Householder matrix
q_matrixNew = house
r_matrixNew = house * A
else:
#Builds the Householder matrix
q_matrixOld = q_matrixNew
r_matrixOld = r_matrixNew
q_matrixNew = q_matrixOld * house
r_matrixNew = house * r_matrixOld
A_qr = q_matrixNew * r_matrixNew
eigVal, eigVect = eig_power.epower(A_qr)
return eigVal, eigVect
def eqr(A):
'''
%% ***********************************************************************
% FUNCTION eigen_qr
% Purpose: Finds the eigenvalues and eigenvectors of a given matrix using
% the QR method
%
% Function call: [eigVal, eigVect, counter] = eigen_qr(A, guess, eps)
%
% Input: A = Input matrix
%
% Outputs: eigVal - Output array of eigenvalues
% eigVect - Output array of eigenvectors
% counter - Number of iterations it took to solve for the eigenvalues
%
% Adam Hollock
% 5 February 2012
%% ***********************************************************************
'''
#initializes all matrices to be used in the method
e_matrix = eye(A.shape[1])
for i in arange(1,e_matrix.shape[1],2):
e_matrix[i,:] = e_matrix[i,:]*-1
#Performs the QR factorization method for obtaining an upper triangular
#matrix.
for i in arange(0,A.shape[1]):
#This will make a special case for the first iteration
if i == 0:
#Builds the c vector as needed
c_vector = A[:,i]
else:
#Builds the c vector as needed
c_vector = concatenate((zeros((i,1)),r_matrixNew[i:,i]))
c_norm = linalg.norm(c_vector,2)
v = c_vector+c_norm*e_matrix[:,i].reshape(A.shape[0],1)
house = (eye(A.shape[1]) - multiply((2/(v.T*v)),(v*v.T)))
#This will make a special case for the first iteration
if i == 0:
#Builds the Householder matrix
q_matrixNew = house
r_matrixNew = house*A
else:
#Builds the Householder matrix
q_matrixOld = q_matrixNew
r_matrixOld = r_matrixNew
q_matrixNew = q_matrixOld*house
r_matrixNew = house*r_matrixOld
A_qr = q_matrixNew*r_matrixNew;
eigVal, eigVect = eig_power.epower(A_qr);
return eigVal, eigVect
import eig_power
from numpy import *
'''
Adam Hollock 2/8/2013
Finds the eigenvalues and eigenvectors of a given matrix using the power method
'''
A_2 = mat("3 1 7; 2 9 3; 6 1 4")
eigVal, eigVect = eig_power.epower(A_2)
print eigVal
print eigVect
import eig_power
from numpy import *
'''
Adam Hollock 2/8/2013
Finds the eigenvalues and eigenvectors of a given matrix using the power method
'''
A_2 = mat("3 1 7; 2 9 3; 6 1 4")
eigVal, eigVect = eig_power.epower(A_2)
print eigVal
print eigVect
