def user_venue_scores(usr_location_matrix):
M = usr_location_matrix.as_matrix()
user_hub__initial_score = usr_location_matrix.sum(axis=1).values
user_hub_score = power_method.power_method(np.dot(M, M.T), user_hub__initial_score, 10)
venue_auth_initial_score = usr_location_matrix.sum(axis=0).values
venue_hub_score = power_method.power_method(np.dot(M.T, M), venue_auth_initial_score, 10)
return user_hub_score, venue_hub_score
def testPowerMethod(self):
# expected value
eigenvalue = 2 + math.sqrt(13)
# tolerance
e = 0.00005
MAX_ITERATIONS = 20
result = power_method.power_method(self.A, [1,1], e, MAX_ITERATIONS)
self.assertTrue(result)
self.assertTrue(abs(result['value'] - eigenvalue) <= e)
self.assertTrue(result['iterations'] < MAX_ITERATIONS)
def rayleigh_method(matrix, sigma=None, eps=10 ** -6, steps=10 ** 5):
if sigma is None:
_, sigma = power_method(matrix, steps=10)
vector = np.random.rand(matrix.shape[0])
k = 0
while k < steps:
next_vect = scipy.linalg.inv(matrix - sigma * np.identity(matrix.shape[0])) @ vector
next_vect = norm(next_vect)
sigma = (next_vect.T @ matrix @ next_vect) / (next_vect.T @ next_vect)
if np.linalg.norm(abs(vector - next_vect)) < eps:
break
vector = next_vect
k += 1
return vector, sigma
def inv_pow_method(matrix, sigma=None, eps=10**-9, steps=10**9):
if sigma is None:
_, sigma = power_method(matrix, steps=10)
vector = np.random.rand(matrix.shape[0])
vector = norm(vector)
k = 0
A = (matrix - sigma * np.identity(matrix.shape[0]))
lu_piv = lu_factor(A)
while k < steps:
next_vect = lu_solve(lu_piv, vector)
next_vect = norm(next_vect)
if np.linalg.norm(abs(next_vect) - abs(vector)) < eps:
break
vector = next_vect
k += 1
sigma = vector.T @ matrix @ vector
return norm(vector), sigma
from power_method import power_method
def inv_pow_method(matrix, sigma=None, eps=10**-9, steps=10**9):
if sigma is None:
_, sigma = power_method(matrix, steps=10)
vector = np.random.rand(matrix.shape[0])
vector = norm(vector)
k = 0
A = (matrix - sigma * np.identity(matrix.shape[0]))
lu_piv = lu_factor(A)
while k < steps:
next_vect = lu_solve(lu_piv, vector)
next_vect = norm(next_vect)
if np.linalg.norm(abs(next_vect) - abs(vector)) < eps:
break
vector = next_vect
k += 1
sigma = vector.T @ matrix @ vector
return norm(vector), sigma
if __name__ == '__main__':
matrix = rand_sym_matrix(100)
_, sigma = power_method(matrix, steps=10)
vector, dominant = inv_pow_method(matrix, sigma)
print(vector)
print(dominant)
lib_vector, lib_dominant = lib_solution(matrix)
check_correct(vector, dominant, lib_vector, lib_dominant)
from DecomposicaoLU import pivot_matrix import DecomposicaoCholesky from power_method import power_method from power_method import power_method_inverse from power_method import power_method_shifted from QRdecomposition import QRdecomposition from QRdecomposition import QReigenvalues import numpy as np import os import scipy.linalg #A = np.asarray([[6.0, 3, 4, 8], [3, 6, 5,1], [4, 5, 10, 7], [8, 1, 7, 25]]) #A = np.asarray([ [7.0, 3, -1, 2], [3, 8, 1, -4], [9, 9, 4, -1], [2, 10, -1, 6] ]) #A = np.asarray([ [7.0, 3, -1, 2], [3, 8, 1, -4], [-1, 1, 4, -1]]) #A = np.asarray([ [7.0, 3, -1, 2, 5], [3, 8, 1, -4,6], [-1,8, 1, 4, -1]]) #A = np.asarray([[4.0, 1, -1], [3, 2, -3], [1, 3, 0]]) A = np.asarray([[6.0, 3, 4, 8], [3, 6, 5, 1], [4, 5, 10, 7], [8, 1, 7, 25]]) #A = np.asarray([[0,1.0],[-2,-3]]) L,U,P = LU(A) C,Ct = DecomposicaoCholesky.cholesky(A) eigenvectormax,maxeigenvalue = power_method(A) #eigenvalues = power_method_shifted(A) eigenvectormin,mineigenvalue = power_method_inverse(A) Q,R = QRdecomposition(A) eigenvaluesA = QReigenvalues(A)