NumPy on Clarity

1 Array Creation Routines

Sun, 24 May 2026 00:00:00 +0000

title: "Array creation routines" date: 2026-05-24T13:51:21Z

Array creation routines

Ones and zeros

1import numpy as np

Create a new array of 2*2 integers, without initializing entries.

array([[0, 0],
       [0, 0]])

Let X = np.array([1,2,3], [4,5,6], np.int32). Create a new array with the same shape and type as X.

1X = np.array([[1,2,3], [4,5,6]], np.int32)

array([[1, 2, 3],
       [4, 5, 6]])

Create a 3-D array with ones on the diagonal and zeros elsewhere.

array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])

array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])

Create a new array of 3*2 float numbers, filled with ones.

1 Array Creation Routines Solution

Sun, 24 May 2026 00:00:00 +0000

title: "Array creation routines" date: 2026-05-24T13:51:24Z

Array creation routines

Ones and zeros

1import numpy as np

Create a new array of 2*2 integers, without initializing entries.

1np.empty([2,2], int)

array([[0, 0],
       [0, 0]])

Let X = np.array([1,2,3], [4,5,6], np.int32). Create a new array with the same shape and type as X.

1X = np.array([[1,2,3], [4,5,6]], np.int32)
2np.empty_like(X)

array([[1, 2, 3],
       [4, 5, 6]])

Create a 3-D array with ones on the diagonal and zeros elsewhere.

1np.eye(3)

array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])

1np.identity(3)

array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])

Create a new array of 3*2 float numbers, filled with ones.

1.numpy Beginner

Sun, 24 May 2026 00:00:00 +0000

title: "适合初学者快速入门的Numpy实战全集" date: 2026-05-24T13:49:57Z

适合初学者快速入门的Numpy实战全集

本文由光城同学整理

Numpy是一个用python实现的科学计算的扩展程序库，包括：

1、一个强大的N维数组对象Array；
2、比较成熟的（广播）函数库；
3、用于整合C/C++和Fortran代码的工具包；
4、实用的线性代数、傅里叶变换和随机数生成函数。numpy和稀疏矩阵运算包scipy配合使用更加方便。

NumPy（Numeric Python）提供了许多高级的数值编程工具，如：矩阵数据类型、矢量处理，以及精密的运算库。专为进行严格的数字处理而产生。多为很多大型金融公司使用，以及核心的科学计算组织如：Lawrence Livermore，NASA用其处理一些本来使用C++，Fortran或Matlab等所做的任务。

本文目录

1.Numpy基本操作

1.1 列表转为矩阵

1.2 维度

1.3 行数和列数()

1.4 元素个数

2.Numpy创建array

2.1 一维array创建

2.2 多维array创建

2.3 创建全零数组

2.4 创建全1数据

2.5 创建全空数组

2.6 创建连续数组

2.7 reshape操作

2.8 创建连续型数据

2.9 linspace的reshape操作

3.Numpy基本运算

3.1 一维矩阵运算

3.2 多维矩阵运算

3.3 基本计算

4.Numpy索引与切片

5.Numpy array合并

5.1 数组合并

5.2 数组转置为矩阵

5.3 多个矩阵合并

5.4 合并例子2

6.Numpy array分割

6.1 构造3行4列矩阵

6.2 等量分割

6.3 不等量分割

6.4 其他的分割方式

7.Numpy copy与 =

7.1 =赋值方式会带有关联性

7.2 copy()赋值方式没有关联性

8.广播机制

9.常用函数

1.Numpy基本操作

1.1 列表转为矩阵

1import numpy as np
2array = np.array([
3    [1,3,5],
4    [4,6,9]
5])
6
7print(array)

[[1 3 5]
 [4 6 9]]

1.2 维度

1print('number of dim:', array.ndim)

number of dim: 2

1.3 行数和列数()

1print('shape:',array.shape)

shape: (2, 3)

1.4 元素个数

1print('size:',array.size)

size: 6

2.Numpy创建array

2.1 一维array创建

1import numpy as np
2# 一维array
3a = np.array([2,23,4], dtype=np.int32) # np.int默认为int32
4print(a)
5print(a.dtype)

[ 2 23  4]
int32

2.2 多维array创建

1# 多维array
2a = np.array([[2,3,4],
3              [3,4,5]])
4print(a) # 生成2行3列的矩阵

[[2 3 4]
 [3 4 5]]

2.3 创建全零数组

1a = np.zeros((3,4))
2print(a) # 生成3行4列的全零矩阵

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]]

2.4 创建全1数据

1# 创建全一数据，同时指定数据类型
2a = np.ones((3,4),dtype=np.int)
3print(a)

[[1 1 1 1]
 [1 1 1 1]
 [1 1 1 1]]

2.5 创建全空数组

1# 创建全空数组，其实每个值都是接近于零的数
2a = np.empty((3,4))
3print(a)

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]]

2.6 创建连续数组

1# 创建连续数组
2a = np.arange(10,21,2) # 10-20的数据，步长为2
3print(a)

[10 12 14 16 18 20]

2.7 reshape操作

1# 使用reshape改变上述数据的形状
2b = a.reshape((2,3))
3print(b)

[[10 12 14]
 [16 18 20]]

2.8 创建连续型数据

1# 创建线段型数据
2a = np.linspace(1,10,20) # 开始端1，结束端10，且分割成20个数据，生成线段
3print(a)

[ 1.          1.47368421  1.94736842  2.42105263  2.89473684  3.36842105
  3.84210526  4.31578947  4.78947368  5.26315789  5.73684211  6.21052632
  6.68421053  7.15789474  7.63157895  8.10526316  8.57894737  9.05263158
  9.52631579 10.        ]

2.9 linspace的reshape操作

1# 同时也可以reshape
2b = a.reshape((5,4))
3print(b)

[[ 1.          1.47368421  1.94736842  2.42105263]
 [ 2.89473684  3.36842105  3.84210526  4.31578947]
 [ 4.78947368  5.26315789  5.73684211  6.21052632]
 [ 6.68421053  7.15789474  7.63157895  8.10526316]
 [ 8.57894737  9.05263158  9.52631579 10.        ]]

3.Numpy基本运算

3.1 一维矩阵运算

1import numpy as np
2# 一维矩阵运算
3a = np.array([10,20,30,40])
4b = np.arange(4)
5print(a,b)

[10 20 30 40] [0 1 2 3]

1c = a - b
2print(c)

[10 19 28 37]

1print(a*b) # 若用a.dot(b),则为各维之和

[  0  20  60 120]

1# 在Numpy中，想要求出矩阵中各个元素的乘方需要依赖双星符号 **，以二次方举例，即：
2c = b**2
3print(c)

[0 1 4 9]

1# Numpy中具有很多的数学函数工具
2c = np.sin(a)
3print(c)

[-0.54402111  0.91294525 -0.98803162  0.74511316]

1print(b<2)

[ True  True False False]

1a = np.array([1,1,4,3])
2b = np.arange(4)
3print(a==b)

[False  True False  True]

3.2 多维矩阵运算

1a = np.array([[1,1],[0,1]])
2b = np.arange(4).reshape((2,2))
3print(a)

[[1 1]
 [0 1]]

1print(b)

[[0 1]
 [2 3]]

1# 多维度矩阵乘法
2# 第一种乘法方式:
3c = a.dot(b)
4print(c)

[[2 4]
 [2 3]]

1# 第二种乘法:
2c = np.dot(a,b)
3print(c)

[[2 4]
 [2 3]]

1# 多维矩阵乘法不能直接使用'*'号
2
3a = np.random.random((2,4))
4
5print(np.sum(a))

3.825517216750851

1print(np.min(a))

0.09623355767721398

1print(np.max(a))

0.7420428188342583

1print("a=",a)

a= [[0.48634962 0.74204282 0.09623356 0.69074812]
 [0.60218881 0.52734181 0.41434585 0.26626662]]

如果你需要对行或者列进行查找运算，

10 Random Sampling

Sun, 24 May 2026 00:00:00 +0000

title: "Random Sampling" date: 2026-05-24T13:50:59Z

Random Sampling

1import numpy as np

1np.__version__

'1.11.2'

1__author__ = 'kyubyong. longinglove@nate.com'

Simple random data

Q1. Create an array of shape (3, 2) and populate it with random samples from a uniform distribution over [0, 1).

array([[ 0.13879034,  0.71300174],
       [ 0.08121322,  0.00393554],
       [ 0.02349471,  0.56677474]])

Q2. Create an array of shape (1000, 1000) and populate it with random samples from a standard normal distribution. And verify that the mean and standard deviation is close enough to 0 and 1 repectively.

10 Random Sampling Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Random Sampling" date: 2026-05-24T13:51:01Z

Random Sampling

1import numpy as np

1np.__version__

'1.11.2'

1__author__ = 'kyubyong. longinglove@nate.com'

Simple random data

Q1. Create an array of shape (3, 2) and populate it with random samples from a uniform distribution over [0, 1).

1np.random.rand(3, 2) 
2# Or np.random.random((3,2))

array([[ 0.13879034,  0.71300174],
       [ 0.08121322,  0.00393554],
       [ 0.02349471,  0.56677474]])

100 Numpy Exercises

Sun, 24 May 2026 00:00:00 +0000

title: "Alternative solution, in Python 3.5 and above" date: 2026-05-24T13:50:37Z

100 numpy exercises

This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.

If you find an error or think you've a better way to solve some of them, feel free to open an issue at https://github.com/rougier/numpy-100

100 Numpy Exercises No Solution

Sun, 24 May 2026 00:00:00 +0000

title: "100 numpy exercises" date: 2026-05-24T13:50:39Z

100 numpy exercises

If you find an error or think you've a better way to solve some of them, feel free to open an issue at https://github.com/rougier/numpy-100

100 Numpy Exercises With Hint

Sun, 24 May 2026 00:00:00 +0000

title: "100 numpy exercises with hint" date: 2026-05-24T13:50:42Z

100 numpy exercises with hint

If you find an error or think you've a better way to solve some of them, feel free to open an issue at https://github.com/rougier/numpy-100

11 Set Routines

Sun, 24 May 2026 00:00:00 +0000

title: "Set routines" date: 2026-05-24T13:51:04Z

Set routines

1import numpy as np

1np.__version__

'1.11.2'

1author = 'kyubyong. longinglove@nate.com'

Making proper sets

Q1. Get unique elements and reconstruction indices from x. And reconstruct x.

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

unique elements = [1 2 3 4 6]
reconstruction indices = [0 1 4 3 1 2 1]
reconstructed = [1 2 6 4 2 3 2]

Boolean operations

Q2. Create a boolean array of the same shape as x. If each element of x is present in y, the result will be True, otherwise False.

11 Set Routines Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Set routines" date: 2026-05-24T13:51:07Z

Set routines

1import numpy as np

1np.__version__

'1.11.2'

1author = 'kyubyong. longinglove@nate.com'

Making proper sets

Q1. Get unique elements and reconstruction indices from x. And reconstruct x.

1x = np.array([1, 2, 6, 4, 2, 3, 2])
2out, indices = np.unique(x, return_inverse=True)
3print "unique elements =", out
4print "reconstruction indices =", indices
5print "reconstructed =", out[indices]

unique elements = [1 2 3 4 6]
reconstruction indices = [0 1 4 3 1 2 1]
reconstructed = [1 2 6 4 2 3 2]

Boolean operations

Q2. Create a boolean array of the same shape as x. If each element of x is present in y, the result will be True, otherwise False.

12 Sorting Searching And Counting

Sun, 24 May 2026 00:00:00 +0000

title: "Soring, searching, and counting" date: 2026-05-24T13:51:10Z

Soring, searching, and counting

1import numpy as np

1np.__version__

'1.11.2'

1author = 'kyubyong. longinglove@nate.com'

Sorting

Q1. Sort x along the second axis.

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

[[1 4]
 [1 3]]

Q2. Sort pairs of surnames and first names and return their indices. (first by surname, then by name).

1surnames =    ('Hertz',    'Galilei', 'Hertz')
2first_names = ('Heinrich', 'Galileo', 'Gustav')

[1 2 0]

Q3. Get the indices that would sort x along the second axis.

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

[[0 1]
 [1 0]]

Q4. Create an array such that its fifth element would be the same as the element of sorted x, and it divide other elements by their value.

12 Sorting Searching And Counting Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Soring, searching, and counting" date: 2026-05-24T13:51:13Z

Soring, searching, and counting

1import numpy as np

1np.__version__

'1.11.2'

1author = 'kyubyong. longinglove@nate.com'

Sorting

Q1. Sort x along the second axis.

1x = np.array([[1,4],[3,1]])
2out = np.sort(x, axis=1)
3x.sort(axis=1)
4assert np.array_equal(out, x)
5print out

[[1 4]
 [1 3]]

Q2. Sort pairs of surnames and first names and return their indices. (first by surname, then by name).

1surnames =    ('Hertz',    'Galilei', 'Hertz')
2first_names = ('Heinrich', 'Galileo', 'Gustav')
3print np.lexsort((first_names, surnames))

[1 2 0]

Q3. Get the indices that would sort x along the second axis.

13 Statistics

Sun, 24 May 2026 00:00:00 +0000

title: "Statistics" date: 2026-05-24T13:51:15Z

Statistics

1__author__ = "kyubyong. kbpark.linguist@gmail.com"

1import numpy as np

1np.__version__

'1.11.3'

Order statistics

Q1. Return the minimum value of x along the second axis.

1x = np.arange(4).reshape((2, 2))
2print("x=\n", x)

x=
 [[0 1]
 [2 3]]
ans=
 [0 2]

Q2. Return the maximum value of x along the second axis. Reduce the second axis to the dimension with size one.

1x = np.arange(4).reshape((2, 2))
2print("x=\n", x)

x=
 [[0 1]
 [2 3]]
ans=
 [[1]
 [3]]

Q3. Calcuate the difference between the maximum and the minimum of x along the second axis.

13 Statistics Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Statistics" date: 2026-05-24T13:51:18Z

Statistics

1__author__ = "kyubyong. kbpark.linguist@gmail.com"

1import numpy as np

1np.__version__

'1.11.3'

Order statistics

Q1. Return the minimum value of x along the second axis.

1x = np.arange(4).reshape((2, 2))
2print("x=\n", x)
3print("ans=\n", np.amin(x, 1))

x=
 [[0 1]
 [2 3]]
ans=
 [0 2]

Q2. Return the maximum value of x along the second axis. Reduce the second axis to the dimension with size one.

1x = np.arange(4).reshape((2, 2))
2print("x=\n", x)
3print("ans=\n", np.amax(x, 1, keepdims=True))

x=
 [[0 1]
 [2 3]]
ans=
 [[1]
 [3]]

Q3. Calcuate the difference between the maximum and the minimum of x along the second axis.

2 Array Manipulation Routines

Sun, 24 May 2026 00:00:00 +0000

title: "Array manipulation routines" date: 2026-05-24T13:51:27Z

Array manipulation routines

1import numpy as np

1np.__version__

'1.11.2'

Q1. Let x be a ndarray [10, 10, 3] with all elements set to one. Reshape x so that the size of the second dimension equals 150.

[[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.]]

Q2. Let x be array [[1, 2, 3], [4, 5, 6]]. Convert it to [1 4 2 5 3 6].

2 Array Manipulation Routines Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Array manipulation routines" date: 2026-05-24T13:51:30Z

Array manipulation routines

1import numpy as np

1np.__version__

'1.11.2'

Q1. Let x be a ndarray [10, 10, 3] with all elements set to one. Reshape x so that the size of the second dimension equals 150.

1x = np.ones([10, 10, 3])
2out = np.reshape(x, [-1, 150])
3print out
4assert np.allclose(out, np.ones([10, 10, 3]).reshape([-1, 150]))

[[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
   1.  1.  1.  1.  1.  1.]]

Q2. Let x be array [[1, 2, 3], [4, 5, 6]]. Convert it to [1 4 2 5 3 6].

2.numpy

Sun, 24 May 2026 00:00:00 +0000

title: "1.Numpy简易入门" date: 2026-05-24T13:49:59Z

1.Numpy简易入门

1.1 认识NumPy数组对象

Numpy是一个用python实现的科学计算的扩展程序库，包括：

1、一个强大的N维数组对象Array；
2、比较成熟的（广播）函数库；
3、用于整合C/C++和Fortran代码的工具包；
4、实用的线性代数、傅里叶变换和随机数生成函数。numpy和稀疏矩阵运算包scipy配合使用更加方便。

1import numpy as np                     # 导入NumPy工具包

1data = np.arange(12).reshape(3, 4)  # 创建一个3行4列的数组

1data

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

1type(data)

numpy.ndarray

1data.ndim         # 数组维度的个数，输出结果2，表示二维数组

1data.shape        # 数组的维度，输出结果（3，4），表示3行4列

(3, 4)

1data.size         # 数组元素的个数，输出结果12，表示总共有12个元素

1data.dtype # 数组元素的类型，输出结果dtype('int64'),表示元素类型都是int64

dtype('int32')

1.2 创建NumPy数组

1import numpy as np

1data1 = np.array([1, 2, 3])                   # 创建一个一维数组

1data1

array([1, 2, 3])

1data2 = np.array([[1, 2, 3], [4, 5, 6]])   # 创建一个二维数组

1data2

array([[1, 2, 3],
       [4, 5, 6]])

1np.zeros((3, 4))#创建一个全0数组

array([[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]])

1np.ones((3, 4))#创建全一数组

array([[1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.]])

1np.empty((5, 2))# 创建全空数组，其实每个值都是接近于零的数

array([[ 6.95312756e-310,  2.12199579e-314],
       [ 2.12199579e-314,  4.94065646e-324],
       [ 0.00000000e+000, -7.06252554e-311],
       [ 0.00000000e+000, -8.12021073e-313],
       [ 1.29923372e-311,  2.07507571e-322]])

1np.arange(1, 20, 5)

array([ 1,  6, 11, 16])

1np.array([1, 2, 3, 4], float)

array([1., 2., 3., 4.])

1np.ones((2, 3), dtype='float64')

array([[1., 1., 1.],
       [1., 1., 1.]])

1.3 ndarry对象的数据类型

1.3.1 查看数据类型

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

1data_one.dtype.name

'int32'

1.3.2 转换数据类型

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

1data.dtype

dtype('int32')

1float_data = data.astype(np.float64) # 数据类型转换为float64

1float_data.dtype

dtype('float64')

1float_data = np.array([1.2, 2.3, 3.5])

1float_data

array([1.2, 2.3, 3.5])

1int_data = float_data.astype(np.int64) # 数据类型转换为int64

1int_data

array([1, 2, 3], dtype=int64)

1str_data = np.array(['1', '2', '3'])

1int_data = str_data.astype(np.int64)

1int_data

array([1, 2, 3], dtype=int64)

1.4 数组运算

1.4.1向量化运算

1import numpy as np

1data1 = np.array([[1, 2, 3], [4, 5, 6]])

1data2 = np.array([[1, 2, 3], [4, 5, 6]])

1data1 + data2        # 数组相加

array([[ 2,  4,  6],
       [ 8, 10, 12]])

1data1 * data2        # 数组相乘

array([[ 1,  4,  9],
       [16, 25, 36]])

1data1 - data2        # 数组相减

array([[0, 0, 0],
       [0, 0, 0]])

1data1 / data2       # 数组相除

array([[1., 1., 1.],
       [1., 1., 1.]])

1.4.2 数组广播

numpy数组间的基础运算是一对一，也就是a.shape==b.shape，但是当两者不一样的时候，就会自动触发广播机制，如下例子：

3 String Operations

Sun, 24 May 2026 00:00:00 +0000

title: "3_String_operations" date: 2026-05-24T13:51:32Z

String operations

1from __future__ import print_function
2import numpy as np

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.11.3'

Q1. Concatenate x1 and x2.

1x1 = np.array(['Hello', 'Say'], dtype=np.str)
2x2 = np.array([' world', ' something'], dtype=np.str)

['Hello world' 'Say something']

Q2. Repeat x three time element-wise.

1x = np.array(['Hello ', 'Say '], dtype=np.str)

['Hello Hello Hello ' 'Say Say Say ']

Q3-1. Capitalize the first letter of x element-wise.
Q3-2. Lowercase x element-wise.
Q3-3. Uppercase x element-wise.
Q3-4. Swapcase x element-wise.
Q3-5. Title-case x element-wise.

3 String Operations Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "compare" date: 2026-05-24T13:51:35Z

String operations

1from __future__ import print_function
2import numpy as np

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.11.3'

Q1. Concatenate x1 and x2.

1x1 = np.array(['Hello', 'Say'], dtype=np.str)
2x2 = np.array([' world', ' something'], dtype=np.str)
3out = np.char.add(x1, x2)
4print(out)

['Hello world' 'Say something']

Q2. Repeat x three time element-wise.

1x = np.array(['Hello ', 'Say '], dtype=np.str)
2out = np.char.multiply(x, 3)
3print(out)

['Hello Hello Hello ' 'Say Say Say ']

Q3-1. Capitalize the first letter of x element-wise.
Q3-2. Lowercase x element-wise.
Q3-3. Uppercase x element-wise.
Q3-4. Swapcase x element-wise.
Q3-5. Title-case x element-wise.

4 Numpy Specific Help Functions

Sun, 24 May 2026 00:00:00 +0000

title: "4_Numpy-specific_help_functions" date: 2026-05-24T13:51:38Z

1import numpy as np

1np.__version__

'1.11.2'

Q1. Search for docstrings of the numpy functions on linear algebra.

Search results for 'linear algebra'
-----------------------------------
numpy.linalg.solve
    Solve a linear matrix equation, or system of linear scalar equations.
numpy.poly
    Find the coefficients of a polynomial with the given sequence of roots.
numpy.restoredot
    Restore `dot`, `vdot`, and `innerproduct` to the default non-BLAS
numpy.linalg.eig
    Compute the eigenvalues and right eigenvectors of a square array.
numpy.linalg.cond
    Compute the condition number of a matrix.
numpy.linalg.eigh
    Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix.
numpy.linalg.pinv
    Compute the (Moore-Penrose) pseudo-inverse of a matrix.
numpy.linalg.LinAlgError
    Generic Python-exception-derived object raised by linalg functions.

Q2. Get help information for numpy dot function.

4 Numpy Specific Help Functions Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "4_Numpy-specific_help_functions_Solutions" date: 2026-05-24T13:51:41Z

1import numpy as np

1np.__version__

'1.11.2'

Q1. Search for docstrings of the numpy functions on linear algebra.

1np.lookfor('linear algebra')

Search results for 'linear algebra'
-----------------------------------
numpy.linalg.solve
    Solve a linear matrix equation, or system of linear scalar equations.
numpy.poly
    Find the coefficients of a polynomial with the given sequence of roots.
numpy.restoredot
    Restore `dot`, `vdot`, and `innerproduct` to the default non-BLAS
numpy.linalg.eig
    Compute the eigenvalues and right eigenvectors of a square array.
numpy.linalg.cond
    Compute the condition number of a matrix.
numpy.linalg.eigh
    Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix.
numpy.linalg.pinv
    Compute the (Moore-Penrose) pseudo-inverse of a matrix.
numpy.linalg.LinAlgError
    Generic Python-exception-derived object raised by linalg functions.

Q2. Get help information for numpy dot function.

5 Input And Output

Sun, 24 May 2026 00:00:00 +0000

title: "Input and Output" date: 2026-05-24T13:51:44Z

Input and Output

1from __future__ import print_function
2import numpy as np

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.12.0'

1from datetime import date
2print(date.today())

2017-04-01

NumPy binary files (NPY, NPZ)

Q1. Save x into temp.npy and load it.

1x = np.arange(10)
2...
3
4# Check if there exists the 'temp.npy' file.
5import os
6if os.path.exists('temp.npy'):
7    x2 = ...
8    print(np.array_equal(x, x2))

True

Q2. Save x and y into a single file 'temp.npz' and load it.

1x = np.arange(10)
2y = np.arange(11, 20)
3...
4
5with ... as data:
6    x2 = data['x']
7    y2 = data['y']
8    print(np.array_equal(x, x2))
9    print(np.array_equal(y, y2))

True
True

Text files

Q3. Save x to 'temp.txt' in string format and load it.

5 Input And Output Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Input and Output" date: 2026-05-24T13:51:46Z

Input and Output

1from __future__ import print_function
2import numpy as np

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.12.0'

1from datetime import date
2print(date.today())

2017-04-01

NumPy binary files (NPY, NPZ)

Q1. Save x into temp.npy and load it.

1x = np.arange(10)
2np.save('temp.npy', x) # Actually you can omit the extension. If so, it will be added automatically.
3
4# Check if there exists the 'temp.npy' file.
5import os
6if os.path.exists('temp.npy'):
7    x2 = np.load('temp.npy')
8    print(np.array_equal(x, x2))

True

Q2. Save x and y into a single file 'temp.npz' and load it.

6 Linear Algebra

Sun, 24 May 2026 00:00:00 +0000

title: "Linear algebra" date: 2026-05-24T13:51:49Z

Linear algebra

1import numpy as np

1np.__version__

'1.11.2'

Matrix and vector products

Q1. Predict the results of the following code.

1x = [1,2]
2y = [[4, 1], [2, 2]]
3#print np.dot(x, y)
4#print np.dot(y, x)
5#print np.matmul(x, y)
6#print np.inner(x, y)
7#print np.inner(y, x)

Q2. Predict the results of the following code.

1x = [[1, 0], [0, 1]]
2y = [[4, 1], [2, 2], [1, 1]]
3#print np.dot(y, x)
4#print np.matmul(y, x)

Q3. Predict the results of the following code.

1x = np.array([[1, 4], [5, 6]])
2y = np.array([[4, 1], [2, 2]])
3#print np.vdot(x, y)
4#print np.vdot(y, x)
5#print np.dot(x.flatten(), y.flatten())
6#print np.inner(x.flatten(), y.flatten())
7#print (x*y).sum()

Q4. Predict the results of the following code.

6 Linear Algebra Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Linear algebra" date: 2026-05-24T13:51:52Z

Linear algebra

1import numpy as np

1np.__version__

'1.11.2'

Matrix and vector products

Q1. Predict the results of the following code.

1x = [1,2]
2y = [[4, 1], [2, 2]]
3print np.dot(x, y)
4print np.dot(y, x)
5print np.matmul(x, y)
6print np.inner(x, y)
7print np.inner(y, x)

[8 5]
[6 6]
[8 5]
[6 6]
[6 6]

Q2. Predict the results of the following code.

1x = [[1, 0], [0, 1]]
2y = [[4, 1], [2, 2], [1, 1]]
3print np.dot(y, x)
4print np.matmul(y, x)

[[4 1]
 [2 2]
 [1 1]]
[[4 1]
 [2 2]
 [1 1]]

Q3. Predict the results of the following code.

7 Discrete Fourier Transform

Sun, 24 May 2026 00:00:00 +0000

title: "cf." date: 2026-05-24T13:51:55Z

1from __future__ import print_function
2import numpy as np
3import matplotlib.pyplot as plt
4%matplotlib inline

1from datetime import date
2date.today()

datetime.date(2017, 11, 2)

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.13.1'

Complex Numbers

Q1. Return the angle of a in radian.

1a = 1+1j
2output = ...
3print(output)

0.785398163397

Q2. Return the real part and imaginary part of a.

1a = np.array([1+2j, 3+4j, 5+6j])
2real = ...
3imag = ...
4print("real part=", real)
5print("imaginary part=", imag)

real part= [ 1.  3.  5.]
imaginary part= [ 2.  4.  6.]

Q3. Replace the real part of a with 9, the imaginary part with [5, 7, 9].

7 Discrete Fourier Transform Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "cf." date: 2026-05-24T13:51:58Z

1from __future__ import print_function
2import numpy as np
3import matplotlib.pyplot as plt
4%matplotlib inline

1from datetime import date
2date.today()

datetime.date(2017, 11, 2)

1author = "kyubyong. https://github.com/Kyubyong/numpy_exercises"

1np.__version__

'1.13.1'

Complex Numbers

Q1. Return the angle of a in radian.

1a = 1+1j
2output = np.angle(a, deg=False)
3print(output)

0.785398163397

Q2. Return the real part and imaginary part of a.

1a = np.array([1+2j, 3+4j, 5+6j])
2real = a.real
3imag = a.imag
4print("real part=", real)
5print("imaginary part=", imag)

real part= [ 1.  3.  5.]
imaginary part= [ 2.  4.  6.]

Q3. Replace the real part of a with 9, the imaginary part with [5, 7, 9].

8 Logic Functions

Sun, 24 May 2026 00:00:00 +0000

title: "Logic functions" date: 2026-05-24T13:52:01Z

Logic functions

1import numpy as np

1np.__version__

'1.11.2'

Truth value testing

Q1. Let x be an arbitrary array. Return True if none of the elements of x is zero. Remind that 0 evaluates to False in python.

1x = np.array([1,2,3])
2#
3
4x = np.array([1,0,3])
5#

True
False

Q2. Let x be an arbitrary array. Return True if any of the elements of x is non-zero.

1x = np.array([1,0,0])
2#
3
4x = np.array([0,0,0])
5#

True
False

Array contents

Q3. Predict the result of the following code.

8 Logic Functions Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Logic functions" date: 2026-05-24T13:52:03Z

Logic functions

1import numpy as np

1np.__version__

'1.11.2'

Truth value testing

Q1. Let x be an arbitrary array. Return True if none of the elements of x is zero. Remind that 0 evaluates to False in python.

1x = np.array([1,2,3])
2print np.all(x)
3
4x = np.array([1,0,3])
5print np.all(x)

True
False

Q2. Let x be an arbitrary array. Return True if any of the elements of x is non-zero.

1x = np.array([1,0,0])
2print np.any(x)
3
4x = np.array([0,0,0])
5print np.any(x)

True
False

Array contents

Q3. Predict the result of the following code.

9 Mathematical Functions

Sun, 24 May 2026 00:00:00 +0000

title: "Mathematical functions" date: 2026-05-24T13:52:06Z

Mathematical functions

1import numpy as np

1np.__version__

'1.11.2'

1__author__ = "kyubyong. kbpark.linguist@gmail.com. https://github.com/kyubyong"

Trigonometric functions

Q1. Calculate sine, cosine, and tangent of x, element-wise.

1x = np.array([0., 1., 30, 90])

sine: [ 0.          0.84147098 -0.98803162  0.89399666]
cosine: [ 1.          0.54030231  0.15425145 -0.44807362]
tangent: [ 0.          1.55740772 -6.4053312  -1.99520041]

Q2. Calculate inverse sine, inverse cosine, and inverse tangent of x, element-wise.

1x = np.array([-1., 0, 1.])

inverse sine: [ 1.57079633  0.          1.57079633]
inverse cosine: [ 0.          1.57079633  0.        ]
inverse tangent: [ 0.78539816  0.          0.78539816]

Q3. Convert angles from radians to degrees.

9 Mathematical Functions Solutions

Sun, 24 May 2026 00:00:00 +0000

title: "Mathematical functions" date: 2026-05-24T13:52:09Z

Mathematical functions

1import numpy as np

1np.__version__

'1.11.2'

1__author__ = "kyubyong. kbpark.linguist@gmail.com. https://github.com/kyubyong"

Trigonometric functions

Q1. Calculate sine, cosine, and tangent of x, element-wise.

1x = np.array([0., 1., 30, 90])
2print "sine:", np.sin(x)
3print "cosine:", np.cos(x)
4print "tangent:", np.tan(x)

sine: [ 0.          0.84147098 -0.98803162  0.89399666]
cosine: [ 1.          0.54030231  0.15425145 -0.44807362]
tangent: [ 0.          1.55740772 -6.4053312  -1.99520041]

Q2. Calculate inverse sine, inverse cosine, and inverse tangent of x, element-wise.

1x = np.array([-1., 0, 1.])
2print "inverse sine:", np.arcsin(x2)
3print "inverse cosine:", np.arccos(x2)
4print "inverse tangent:", np.arctan(x2)

inverse sine: [ 1.57079633  0.          1.57079633]
inverse cosine: [ 0.          1.57079633  0.        ]
inverse tangent: [ 0.78539816  0.          0.78539816]

Q3. Convert angles from radians to degrees.

03.01 Numpy 简介

Tue, 05 May 2026 00:00:00 +0000

Numpy科学计算库简介

03.03 Numpy 数组及其索引

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的创建和索引操作

03.04 数组类型

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的数据类型介绍

03.05 数组方法

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的计算方法

03.06 数组排序

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的排序方法

03.07 数组形状

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的形状操作

03.08 对角线

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的对角线提取

03.09 数组与字符串的转换

Tue, 05 May 2026 00:00:00 +0000

Numpy数组与字符串之间的转换

03.10 数组属性方法总结

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的属性和方法汇总

03.11 生成数组的函数

Tue, 05 May 2026 00:00:00 +0000

Numpy中用于生成数组的函数

03.12 矩阵

Tue, 05 May 2026 00:00:00 +0000

Numpy矩阵对象的使用

03.13 一般函数

Tue, 05 May 2026 00:00:00 +0000

Numpy中的通用函数

03.14 向量化函数

Tue, 05 May 2026 00:00:00 +0000

Numpy向量化函数的创建和使用

03.15 二元运算

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的二元运算

03.16 ufunc 对象

Tue, 05 May 2026 00:00:00 +0000

Numpy通用函数对象

03.17 choose 函数实现条件筛选

Tue, 05 May 2026 00:00:00 +0000

Numpy choose函数实现条件筛选

03.18 数组广播机制

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的广播机制

03.19 数组读写

Tue, 05 May 2026 00:00:00 +0000

Numpy数组的读取和写入

03.20 结构化数组

Tue, 05 May 2026 00:00:00 +0000

Numpy结构化数组的使用

03.21 记录数组

Tue, 05 May 2026 00:00:00 +0000

Numpy记录数组的使用

03.22 内存映射

Tue, 05 May 2026 00:00:00 +0000

Numpy内存映射的使用

03.23 从 Matlab 到 Numpy

Tue, 05 May 2026 00:00:00 +0000

从Matlab迁移到Numpy的指南