你已经知道如何创建各种 ndarray，现在将学习 NumPy 使我们如何有效地操纵 ndarray 中的数据。NumPy ndarray 是可变的，意味着 ndarray 中的元素在 ndarray 创建之后可以更改。NumPy ndarray 还可以切片，因此可以通过多种方式拆分 ndarray。例如，我们可以从 ndarray 中获取想要的任何子集。通常，在机器学习中，你需要使用切片拆分数据，例如将数据集拆分为训练集、交叉验证集和测试集。

我们首先将了解如何通过索引访问或修改 ndarray 中的元素。可以在方括号 [ ] 中添加索引来访问元素。在 NumPy 中，你可以使用正索引和负索引访问 ndarray 中的元素。正索引表示从数组的开头访问元素，负索引表示从数组的末尾访问元素。我们来看看如何访问秩为 1 的 ndarray 中的元素：

# We create a rank 1 ndarray that contains integers from 1 to 5x = np.array([1, 2, 3, 4, 5])

# We print x

print()

print('x = ', x)

print()

# Let's access some elements with positive indices

print('This is First Element in x:', x[0])

print('This is Second Element in x:', x[1])

print('This is Fifth (Last) Element in x:', x[4])

print()

# Let's access the same elements with negative indicesprint('This is First Element in x:', x[-5])

print('This is Second Element in x:', x[-4])

print('This is Fifth (Last) Element in x:', x[-1])x = [1 2 3 4 5]This is First Element in x: 1

This is Second Element in x: 2

This is Fifth (Last) Element in x: 5This is First Element in x: 1

This is Second Element in x: 2

This is Fifth (Last) Element in x: 5

注意，要访问 ndarray 中的第一个元素，我们需要使用索引 0，而不是 1。此外注意，可以同时使用正索引和负索引访问同一个元素。正如之前提到的，正索引用于从数组的开头访问元素，负索引用于从数组的末尾访问元素。

现在我们看看如何更改秩为 1 的 ndarray 中的元素。方法是访问要更改的元素，然后使用 = 符号分配新的值：

# We create a rank 1 ndarray that contains integers from 1 to 5x = np.array([1, 2, 3, 4, 5])# We print the original xprint()print('Original:\n x = ', x)print()# We change the fourth element in x from 4 to 20x[3] = 20# We print x after it was modifiedprint('Modified:\n x = ', x)Original: x = [1 2 3 4 5]Modified: x = [ 1 2 3 20 5]

同样，我们可以访问和修改秩为 2 的 ndarray 中的特定元素。要访问秩为 2 的 ndarray 中的元素，我们需要提供两个索引，格式为 [row, column]。我们来看一些示例：

# We create a 3 x 3 rank 2 ndarray that contains integers from 1 to 9X = np.array([[1,2,3],[4,5,6],[7,8,9]])

# We print X

print()

print('X = \n', X)

print()

# Let's access some elements in X

print('This is (0,0) Element in X:', X[0,0])

print('This is (0,1) Element in X:', X[0,1])

print('This is (2,2) Element in X:', X[2,2])X =

[[1 2 3]

[4 5 6]

[7 8 9]]This is (0,0) Element in X: 1

This is (0,1) Element in X: 2

This is (2,2) Element in X: 9

注意，索引 [0, 0] 是指第一行第一列的元素。

可以像针对秩为 1 的 ndarray 一样修改秩为 2 的 ndarray 中的元素。我们来看一个示例：

# We create a 3 x 3 rank 2 ndarray that contains integers from 1 to 9X = np.array([[1,2,3],[4,5,6],[7,8,9]])

# We print the original xprint()print('Original:\n X = \n', X)print()

# We change the (0,0) element in X from 1 to 20X[0,0] = 20# We print X after it was modified

print('Modified:\n X = \n', X)Original:

X =

[[1 2 3]

[4 5 6]

[7 8 9]]Modified:

X =

[[20 2 3]

[ 4 5 6]

[ 7 8 9]]

现在看看如何向 ndarray 中添加元素及删除其中的元素。我们可以使用 np.delete(ndarray, elements, axis) 函数删除元素。此函数会沿着指定的轴从给定 ndarray 中删除给定的元素列表。对于秩为 1 的 ndarray，不需要使用关键字 axis。对于秩为 2 的 ndarray，axis = 0 表示选择行，axis = 1 表示选择列。我们来看一些示例：

# We create a rank 1 ndarray

x = np.array([1, 2, 3, 4, 5])

# We create a rank 2 ndarray

Y = np.array([[1,2,3],[4,5,6],[7,8,9]])

# We print x

print()

print('Original x = ', x)

# We delete the first and last element of x

x = np.delete(x, [0,4])

# We print x with the first and last element deleted

print()

print('Modified x = ', x)

# We print Y

print()

print('Original Y = \n', Y)

# We delete the first row of y

w = np.delete(Y, 0, axis=0)

# We delete the first and last column of y

v = np.delete(Y, [0,2], axis=1)

# We print w

print()

print('w = \n', w)

# We print v

print()

print('v = \n', v)Original x = [1 2 3 4 5]Modified x = [2 3 4]Original Y =

[[1 2 3]

[4 5 6]

[7 8 9]]w =

[[4 5 6]

[7 8 9]]v =

[[2]

[5]

[8]]

现在我们来看看如何向 ndarray 中附加值。我们可以使用 np.append(ndarray, elements, axis) 函数向 ndarray 中附加值。该函数会将给定的元素列表沿着指定的轴附加到 ndarray 中。我们来看一些示例：

# We create a rank 1 ndarray

x = np.array([1, 2, 3, 4, 5])

# We create a rank 2 ndarray

Y = np.array([[1,2,3],[4,5,6]])

# We print xprint()print('Original x = ', x)

# We append the integer 6 to x

x = np.append(x, 6)

# We print xprint()print('x = ', x)

# We append the integer 7 and 8 to x

x = np.append(x, [7,8])

# We print xprint()print('x = ', x)

# We print Yprint()print('Original Y = \n', Y)

# We append a new row containing 7,8,9 to y

v = np.append(Y, [[7,8,9]], axis=0)

# We append a new column containing 9 and 10 to y

q = np.append(Y,[[9],[10]], axis=1)

# We print vprint()print('v = \n', v)

# We print qprint()print('q = \n', q)Original x = [1 2 3 4 5]x = [1 2 3 4 5 6]x = [1 2 3 4 5 6 7 8]Original Y =

[[1 2 3]

[4 5 6]]v =

[[1 2 3]

[4 5 6]

[7 8 9]]q =

[[ 1 2 3 9]

[ 4 5 6 10]]

注意，当我们将行或列附加到秩为 2 的 ndarray 中时，行或列的形状必须正确，以与秩为 2 的 ndarray 的形状相符。

现在我们来看看如何向 ndarray 中插入值。我们可以使用 np.insert(ndarray, index, elements, axis) 函数向 ndarray 中插入值。此函数会将给定的元素列表沿着指定的轴插入到 ndarray 中，并放在给定的索引前面。我们来看一些示例：

# We create a rank 1 ndarray

x = np.array([1, 2, 5, 6, 7])

# We create a rank 2 ndarray

Y = np.array([[1,2,3],[7,8,9]])

# We print x

print()

print('Original x = ', x)

# We insert the integer 3 and 4 between 2 and 5 in x.

x = np.insert(x,2,[3,4])

# We print x with the inserted elements

print()

print('x = ', x)

# We print Y

print()

print('Original Y = \n', Y)

# We insert a row between the first and last row of y

w = np.insert(Y,1,[4,5,6],axis=0)

# We insert a column full of 5s between the first and second column of y

v = np.insert(Y,1,5, axis=1)

# We print w

print()

print('w = \n', w)

# We print v

print()

print('v = \n', v)Original x = [1 2 5 6 7]x = [1 2 3 4 5 6 7]Original Y =

[[1 2 3]

[7 8 9]]w =

[[1 2 3]

[4 5 6]

[7 8 9]]v =

[[1 5 2 3]

[7 5 8 9]]

NumPy 还允许我们将 ndarray 上下堆叠起来，或者左右堆叠。可以使用 np.vstack() 函数进行垂直堆叠，或使用 np.hstack() 函数进行水平堆叠。请务必注意，为了堆叠 ndarray，ndarray 的形状必须相符。我们来看一些示例：

# We create a rank 1 ndarrayx = np.array([1,2])# We create a rank 2 ndarrayY = np.array([[3,4],[5,6]])# We print xprint()print('x = ', x)# We print Yprint()print('Y = \n', Y)# We stack x on top of Yz = np.vstack((x,Y))# We stack x on the right of Y. We need to reshape x in order to stack it on the right of Y.w = np.hstack((Y,x.reshape(2,1)))# We print zprint()print('z = \n', z)# We print wprint()print('w = \n', w)x = [1 2]Y =

[[3 4]

[5 6]]z =

[[1 2]

[3 4]

[5 6]]w =

[[3 4 1]

[5 6 2]]