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 correlation_matrix(data): """returns the num_columns x num_columns matrix whose (i, j)th entry is the correlation between columns i and j of data""" _, num_columns = shape(data) def matrix_entry(i, j): return correlation(get_column(data, i), get_column(data, j)) return make_matrix(num_columns, num_columns, matrix_entry)
def rescale(data_matrix): """rescales the input data so that each column has mean 0 and standard deviation 1 ignores columns with no deviation""" means, stdevs = scale(data_matrix) def rescaled(i, j): if stdevs[j] > 0: return (data_matrix[i][j] - means[j]) / stdevs[j] else: return data_matrix[i][j] num_rows, num_cols = shape(data_matrix) return make_matrix(num_rows, num_cols, rescaled)
def de_mean_matrix(A): """returns the result of subtracting from every value in A the mean value of its column. the resulting matrix has mean 0 in every column""" nr, nc = shape(A) column_means, _ = scale(A) return make_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
while True: result = matrix_operation(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 n = len(users) adjacency_matrix = make_matrix(n, n, entry_fn) eigenvector_centralities, _ = find_eigenvector(adjacency_matrix) """Directed Graphs and PageRank""" for user in users: user["endorses"] = [] # add one list to track outgoing endorsements user["endorsed_by"] = [] # and another to track endorsements for source_id, target_id in endorsements: users[source_id]["endorses"].append(users[target_id]) users[target_id]["endorsed_by"].append(users[source_id]) endorsements_by_id = [(user["id"], len(user["endorsed_by"])) for user in users] sorted(endorsements_by_id,