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])
def scale(data_matrix): """returns the means and standard deviations of each column""" num_rows, num_cols = shape(data_matrix) means = [mean(get_column(data_matrix, j)) for j in range(num_cols)] stdevs = [standard_deviation(get_column(data_matrix, j)) for j in range(num_cols)] return means, stdevs
def rescale(data_matrix): """rescales the input data so that each column has mean 0 and standard deviation 1, leaves columns alone with no deviations""" 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)
