def matrix_multiply(A, B):
n1, k1 = shape(A)
n2, k2 = shape(B)
if k1 != n2:
raise ArithmeticError("incompatible shapes!")
return make_matrix(n1, k2, partial(matrix_product_entry, A, B))
def matrix_multiply(A, B):
n1, k1 = shape(A)
n2, k2 = shape(B)
if k1 != n2:
raise ArithmeticError("incompatible shapes!")
return make_matrix(n1, k2, partial(matrix_product_entry, A, B))
def matrix_times_matrix(m1: Matrix, m2: Matrix) -> Matrix:
nr1, nc1 = shape(m1)
nr2, nc2 = shape(m2)
assert nc1 == nr2, "must have (# o f columns in m1) == (# of rows in m2)"
def entry_fn(i: int, j: int) -> float:
"""dot product of i-th row of m1 with the j-th column of m2"""
return sum(m1[i][k]*m2[k][j] for k in range(nc1))
return make_matrix(nr1,nc2, entry_fn)
while True:
result = matrix_times_vector(m, guess) # transform the guess
norm = magnitude(result) # compute the norm
next_guess = [x/norm for x in result] # rescale
if distance(guess, next_guess) < tolerance:
# convergence so return (eigenvector, eigenvalue)
return next_guess, norm
guess = next_guess
return 1 if (i,j) in friend_pairs or (j,i) in friend_pairs else 0
n = len(users)
adjacency_matrix = make_matrix(n,n, entry_fn)
#adjacency_matrix
eigenvector_centrality, _ = find_eigenvector(adjacency_matrix)
(2, 1), (1, 3), (2, 3), (3, 4), (5, 4),
(5, 6), (7, 5), (6, 8), (8, 7), (8, 9)]
from collections import Counter
endorsement_counts = Counter(target for source, target in endorsements)
import tqdm
def page_rank(users: List[User],
endorsements: List[Tuple[int, int]],
def vector_from_matrix(v_as_matrix):
"""returns the n x 1 matrix as a list of values"""
return [row[0] for row in v_as_matrix]
def matrix_operate(A, v):
v_as_matrix = vector_as_matrix(v)
product = matrix_multiply(A, v_as_matrix)
return vector_from_matrix(product)
def find_eigenvector(A, tolerance=0.00001):
guess = [random.random() for _ in A]
while True:
result = matrix_operate(A, guess)
length = magnitude(result)
next_guess = scalar_multiply(1/length, result)
if distance(guess, next_guess) < tolerance:
return next_guess, length # eigenvector, eigenvalue
guess = next_guess
def entry_fn(i, j):
return 1 if (i, j) in friendships or (j, i) in friendships else 0
friendships = [(0,1), (0,2), (1,2), (1,3), (2,3), (3,4), (4,5), (5,6), (5,7), (6,8), (7,8), (8,9)]
n = len(users)
adjacency_matrix = make_matrix(n, n, entry_fn)
eigenvector_centralities, _ = find_eigenvector(adjacency_matrix)