def matrix_multiply(A, B):
n1, k1 = shape(A)
n2, k2 = shape(B)
if k1 != n2:
raise ArithmeticError("incompatible shapes!")
return make_matrix(n1, k2, partial(matrix_product_entry, A, B))
def matrix_multiply(A, B):
n1, k1 = shape(A)
n2, k2 = shape(B)
if k1 != n2:
raise ArithmeticError("incompatible shapes!")
return make_matrix(n1, k2, partial(matrix_product_entry, A, B))
def correlation_matrix(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 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 scale(data_matrix):
"""returns the mean and standard deviation 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 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 print_distances(data_matrix):
num_rows, num_cols = shape(data_matrix)
print("Distances:")
for i in range(num_rows):
for i_next in range(num_rows):
if i_next > i:
d = distance(data_matrix[i], data_matrix[i_next])
print(i, "to", i_next, d)
def scale(data_matrix):
"""returns the mean and standard deviation 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 correlation_matrix(data):
#i列とj列のデータ間の相関を(i, j)の値とすると、列数×列数の行列を返す
_, num_colums = shape(data)
def matrix_entry(i, j):
return correlation(get_column(data, i), get_column(data, j))
return make_matrix(num_colums, num_colums, 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 = 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 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):
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 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 make_scatterplot_matrix():
# first, generate some random data
#初始化点数量
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)
#生成上方函数的矩阵
data = [random_row()
for _ in range(num_points)]
# then plot it
_, num_columns = shape(data)
#创建子图
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
#i,j不相等则绘制散点图
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
#隐藏部分坐标轴
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
#固化左上右下图像
ax[-1][-1].set_xlim(ax[0][-1].get_xlim())
ax[0][0].set_ylim(ax[0][1].get_ylim())
plt.show()
def rescale(data_matrix):
#各列が平均0、標準偏差1となるように入力データのスケールを修正する
#標準偏差が0の列は表示しない
maens, stdevs = scal(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_colums = shape(data_matrix)
return make_matrix(num_rows, num_colums, rescaled)
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"""
#得到矩阵的行数列数
_, num_columns = shape(data)
#得到两个维度的相关性
def matrix_entry(i, j):
#得到相关系数（第i列和第j列）
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
leaves alone 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 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():
# first, generate some random data
num_points = 100
def random_row():
row = [None for _ in range(6)]
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
row[4] = row[0] + row[1] + -1 * random_normal()
row[5] = 3 if row[2] < -2 else 0
return row
random.seed(0)
data = [random_row()
for _ in range(num_points)]
# then plot it
_, 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 visual_approach():
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 columm_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))
# unlesss i == j, in which case show the series name
else:
ax[i][j].annotate("series {}".format(i), (0.5, 0.5),
xycoords='axes fraction',
ha="center", va="center")
# then hide dxis 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 except left and bottom charts
ax[-1][-1].set_xlim(ax[0][-1].get_xlim())
ax[1][1].set_xlim(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])
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 de_mean_matrix(A):
nr, nc = shape(A)
column_means, _ = scale(A)
return make_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
def correlation_matrix(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)
C = la.sum_of_squares(A)
print("A^2's summary = ", C)
C = la.magnitude(A)
print("A's magnitude = ", C)
C = la.distance(A, B)
print("A's distance = ", C)
print()
print("*** matrix ......")
M = [[1, 2, 3], [5, 6, 7], [3, 6, 9]]
print("M = ", M)
shape = la.shape(M)
print("M's shape = ", shape)
row_1 = la.get_row(M, 1)
print("M[1,:] = ", row_1)
col_1 = la.get_column(M, 1)
print("M[:1] = ", col_1)
I = la.make_matrix(5, 5, la.is_diagonal)
print("identity matrix = ", I)
print("\n\n")
print("*** Test Module <stats> ***")
A = [1, 3, 5, 7, 9, 2, 3, 4, 4, 4, 6, 8, 10, 13, 15, 17]
random.seed(0)
data = [random_row() for _ in range(num_points)]
def correlation_matrix(data):
#i列とj列のデータ間の相関を(i, j)の値とすると、列数×列数の行列を返す
_, num_colums = shape(data)
def matrix_entry(i, j):
return correlation(get_column(data, i), get_column(data, j))
return make_matrix(num_colums, num_colums, matrix_entry)
_, num_colums = shape(data)
fig, ax = plt.subplots(num_colums, num_colums)
for i in range(num_colums):
for j in range(num_colums):
#X軸のcolumns_j、Y軸のcolumns_iの位置に散布図を描画する
if i != j:
ax[i][j].scatter(get_column(data, j), get_column(data, i))
#i == jであれば列名を表示する
else:
ax[i][j].annotate("series " + str(i), (0.5, 0.5),
xycoords='axes fraction',
ha="center",
va='center')
def de_mean_matrix(A):
#Aのすべての値と各列の平均との差を返す。
#結果の行列は各列の平均が0となる
nr, nc = shape(A)
column_means, _ = scale(A)
return make_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
def de_mean_matrix(A):
nr, nc = shape(A)
column_means, _ = scale(A)
return make_matrix(nr, nc, lambda i, j: A[i][j] - column_means[j])
