def upper_triangle(mat_a_vec_b):
m_row, n_col = matrix.shape(mat_a_vec_b)
for i_pivot in range(m_row - 1):
pivot = float(mat_a_vec_b[i_pivot][i_pivot])
for j_row in range(i_pivot + 1, m_row):
ratio = -(mat_a_vec_b[j_row][i_pivot] / pivot)
matrix.row_mul_add(mat_a_vec_b, j_row, i_pivot, ratio, i_pivot)
def de_mean_matrix(A):
# вернуть результат вычесления из каждого значения
# в А среднього значения столбца
# Результирующия матрица имеет нулевое среднее в кождом столбце
nr, nc = mat.shape(A)
colomn_means, _ = scale(A)
return mat.make_matrix(nr, nc, lambda i, j: A[i][j] - colomn_means[j])
def gauss_elimination(mat_a, b):
"""
1차 다원 연립 방정식 Ax = b에서 x를 구함
A : 계수행렬
b : 상수벡터
:param mat_a:
:param b:
:return:
"""
m_row, n_col = matrix.shape(mat_a)
mat_a_vec_b = matrix.alloc_mat(m_row, n_col + 1)
for i in range(m_row):
for j in range(n_col):
mat_a_vec_b[i][j] = mat_a[i][j]
mat_a_vec_b[i][-1] = b[i]
upper_triangle(mat_a_vec_b)
x = back_substitution(mat_a_vec_b)
del mat_a_vec_b[:]
del mat_a_vec_b
return x
def de_mean_matrix(A):
"""returns the result of subtracting from everty value in A the
mean value of its column, the resulting matri has mean 0 in every column"""
nr, nc = matrix.shape(A)
column_means, __ = scale(A)
return matrix.make_mtr(nr, nc, lambda i, j: A[i][j] -
column_means[j])
def scale(data_matrix):
# вернуть среднии и стандартные отклонения для каждого столпца
num_rows, num_cols = mat.shape(data_matrix)
mean = [mat.mean(get_column(data_matrix, j)) for j in range(num_rows)]
stdevs = [
standart_deviation(get_column(data_matrix, j)) for j in range(num_cols)
]
return means, stdevs
def scale(data_matrix):
"""returns the means and std dev of each col"""
num_rows, num_cols = matrix.shape(data_matrix)
means = [stats.mean(matrix.get_col(j,data_matrix)) for j in
range(num_cols)]
stdevs = [stats.stdev(matrix.get_col(j, data_matrix)) for j in
range(num_cols)]
return means, stdevs
def generate_mat_ai(mat_a):
m_row, n_col = matrix.shape(mat_a)
mat_ai = matrix.alloc_mat(m_row, n_col + m_row)
for i_pivot in range(m_row):
for j_col in range(n_col):
mat_ai[i_pivot][j_col] = mat_a[i_pivot][j_col]
mat_ai[i_pivot][n_col + i_pivot] = 1.0
return mat_ai
def correlation_matrix(data):
# возвращает матрицу num_colums * num_colums где запись
# в ячейке (i , j ) - это корреляция между столбцами i и j данных
_, num_colums = mat.shape(data)
# pfgbcm d vfnhbwt
def matrix_entry(i, j):
return ind.correlation(mat.get_collumn(data, i),
mat.get_collumn(data, j))
return mat.make_matrix(num_colums, num_colums, matrix_entry)
def rescale(data_matrix):
"""rescales the input data_raw so that each column has mean 0 and
stdev1"""
means, stdevs = scale(data_matrix)
def rescaled(i,j):
if stdevs[j]>0:
return (data_matrix[i][j] - means[j])/stdevs[j]
else:
data_matrix[i][j]
num_rows, num_cols = matrix.shape(data_matrix)
return matrix.make_mtr(num_rows, num_cols, rescaled)
def rescale(data):
"""
rescales the input data so that each column has mean 0 and standard deviation 1
leaves alone columns with no deviation
"""
means, stdevs = scale(data)
def rescaled(i, j):
if stdevs[j] > 0:
return (data[i][j] - means[j]) / stdevs[j]
else:
return data[i][j]
num_rows, num_cols = shape(data)
return make_matrix(num_rows, num_cols, rescaled)
def gauss_elimination(mat_a, b):
m_row, n_col = matrix.shape(mat_a)
mat_a_vec_b = matrix.alloc_mat(m_row, n_col + 1)
for i in range(m_row):
for j in range(n_col):
mat_a_vec_b[i][j] = mat_a[i][j]
mat_a_vec_b[i][-1] = b[i]
upper_triangle(mat_a_vec_b)
x = back_substitution(mat_a_vec_b)
del mat_a_vec_b[:]
del mat_a_vec_b
return x
def scale(data):
num_rows, num_cols = shape(data)
means = [mean(get_column(data, j)) for j in range(num_cols)]
stdevs = [standard_deviation(get_column(data, j)) for j in range(num_cols)]
return means, stdevs
import matrix matrix = matrix.Matrix() shape = [[0,0,0,0,0,0,0,0], [0,1,1,0,0,1,1,0], [1,0,0,1,1,0,0,1], [1,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,1], [0,1,0,0,0,0,1,0], [0,0,1,0,0,1,0,0], [0,0,0,1,1,0,0,0]] matrix.shape(shape)
