def make_scatterplot_matrix():
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_cols = shape(data)
fig, ax = plt.subplots(num_cols, num_cols)
for i in range(num_cols):
for j in range(num_cols):
if i != j: ax[i][j].scatter(get_col(data, j), get_col(data, i))
else:
ax[i][j].annotate("Series " + str(i), (.5, .5),
xycoords='axes fraction',
ha="center",
va="center")
if i < num_cols - 1: ax[i][j].xaxis.set_visible(False)
if j > 0: ax[i][j].yaxis.set_visible(False)
ax[-1][-1].set_xlim(ax[0][-1].get_xlim())
ax[0][0].set_ylim(ax[0][1].get_ylim())
def correlation_matrix(data):
_, num_columns = shape(data)
def matrix_entry(i, j):
return correlation(get_col(data, i), get_col(data, j))
return make_matrix(num_columns, num_columns, matrix_entry)
def rescale(data_matrix):
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):
num_rows, num_cols = shape(A)
columns_means, _ = scale(A)
return make_matrix(num_rows, num_cols,
lambda i, j: A[i][j] - columns_means[j])
def scale(data_matrix):
num_rows, num_cols = shape(data_matrix)
means = [mean(get_col(data_matrix, j)) for j in range(num_cols)]
stdevs = [std_dev(get_col(data_matrix, j)) for j in range(num_cols)]
return means, stdevs