def scale(data_matrix):
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 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 make_scatterplot_matrix():
print("Matrix correlational relations!")
num_points = 100
def random_row():
row = [None, None, None, None]
row[0] = random_normal()
row[1] = -5 * row[0] + random_normal()
row[2] = row[0] + row[1] + 5 * random_normal()
row[3] = 6 if row[2] > -2 else 0
return row
random.seed(0)
data = [random_row()
for _ in range(num_points)]
_, num_columns = shape(data)
fig, ax = plt.subplots(num_columns, num_columns)
for i in range(num_columns):
for j in range(num_columns):
# scatter column_j on the x-axis vs column_i on the y-axis
if i != j: ax[i][j].scatter(get_column(data, j), get_column(data, i))
# unless i == j, in which case show the series name
else: ax[i][j].annotate("series " + str(i), (0.5, 0.5),
xycoords='axes fraction',
ha="center", va="center")
# then hide axis labels except left and bottom charts
if i < num_columns - 1: ax[i][j].xaxis.set_visible(False)
if j > 0: ax[i][j].yaxis.set_visible(False)
# fix the bottom right and top left axis labels, which are wrong because
# their charts only have text in them
ax[-1][-1].set_xlim(ax[0][-1].get_xlim())
ax[0][0].set_ylim(ax[0][1].get_ylim())
plt.show()
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])