def de_mean_matrix(A):
"""returns the result of subtracting from every value in A
the mean value of its column; resulting matrix has mean 0
in every column"""
nr, nc = algebra.shape(A)
column_means, _ = scale(A)
return algebra.mk_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
def de_mean_matrix(A):
"""returns the result of subtracting from every value in A
the mean value of its column; resulting matrix has mean 0
in every column"""
nr, nc = algebra.shape(A)
column_means, _ = scale(A)
return algebra.mk_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
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 = algebra.shape(data)
def matrix_entry(i, j):
return stats.correlation(algebra.get_column(data, i),
algebra.get_column(data, j))
return algebra.mk_matrix(num_columns, num_columns, matrix_entry)
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 = algebra.shape(data)
def matrix_entry(i, j):
return stats.correlation(algebra.get_column(data, i),
algebra.get_column(data, j))
return algebra.mk_matrix(num_columns, num_columns, matrix_entry)
def rescale(data_matrix):
"""rescales the input data so that each column
has mean 0 and StdDev 1;
leaves alone columns with no deviation"""
means, stddevs = scale(data_matrix)
def rescaled(i, j):
if stddevs[j] > 0:
return (data_matrix[i][j] - means[j]) / stddevs[j]
else:
return data_matrix[i][j]
num_rows, num_cols = algebra.shape(data_matrix)
return algebra.mk_matrix(num_rows, num_cols, rescaled)
def rescale(data_matrix):
"""rescales the input data so that each column
has mean 0 and StdDev 1;
leaves alone columns with no deviation"""
means, stddevs = scale(data_matrix)
def rescaled(i, j):
if stddevs[j] > 0:
return (data_matrix[i][j] - means[j]) / stddevs[j]
else:
return data_matrix[i][j]
num_rows, num_cols = algebra.shape(data_matrix)
return algebra.mk_matrix(num_rows, num_cols, rescaled)