NumPy主要目标是对多维数组进行操作,可以看作是元素(通常指数字)表格,在NumPy中,维度可以称之为轴。
NumPy中数组的类别称之为ndarray
,是array
的别称,不同于Python标准库的array
。
数组维度 即数组轴数,调用格式ndarray_name.ndim
数组形状 即数组的行数n和列数m,调用格式ndarray_name.shape
,输出格式(n,m)
数组内的元素个数 调用格式ndarray_name.size
数组内元素的数据类型 同Python的数据类型,由整数型、浮点数和复数等,调用格式ndarray_name.shape
,输出有int16, int32, float64, complex128
等等
数组内每个元素的字节大小 其值为8的倍数,调用格式ndarray_name.itemsize
数组内元素缓冲区 调用格式ndarray_name.data
实例
import numpy as np
>>> a = np.arange(15).reshape(5,3)
>>> a
array([[ 0, 1, 2],
[ 3, 4, 5],
[ 6, 7, 8],
[ 9, 10, 11],
[12, 13, 14]])
>>> a.ndim
2
>>> a.shape
(5,3)
>>> a.size
15
>>> a.dtype
dtype('int32')
>>> a.itemsize
4
>>> a.data
>>> type(a)
array
创建。import numpy as np
>>> a = np.array([2,3,4])
>>> a
array([2, 3, 4])
>>> a.dtype
dtype('int32')
>>> b = np.array([1.3, 2.4, 3.6])
>>> b.dtype
dtype('float64')
[]
>>> a = np.array(1,2,3,4) #WRONG
>>> a = np.array([1,2,3,4]) #RIGHTS
array
,可将序列转化为二维数组>>> import numpy as np
>>> b = np.array([(1.5,2,3), (4.5,6,7)])
>>> b
array([[1.5, 2. , 3. ],
[4.5, 6. , 7. ]])
>>> c = np.array( [ [1,2,3], [4,5,6] ], dtype=complex) #创建数组的另一种语法形式,将()换乘[],但需space
>>> c
array([[1.+0.j, 2.+0.j, 3.+0.j],
[4.+0.j, 5.+0.j, 6.+0.j]])
以函数reshape(d,n,m)
的形式生成
>>> d = np.arange(24).reshape(2,3,4)
>>> d
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> d = np.arange(24).reshape(4,6)
>>> d
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]])
>>> d.reshape(2,3,4)
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
初始元素不可知,但是数组的大小可知时
zeros
数组元素初始化为0;ones
数组元素初始化为1;empty
数组元素随机生成。创建的数组元素的数据类型默认为float64
,可用dtype
进行设置>>> np.zeros( (2,3) )
array([[0., 0., 0.],
[0., 0., 0.]])
>>> np.ones( (2,4,5), dtype=np.int32 )
array([[[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1]],
[[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1]]])
>>> np.empty( (3,4) )
array([[2.12199579e-314, 6.36598737e-314, 1.06099790e-313,
1.48539705e-313],
[1.90979621e-313, 2.33419537e-313, 2.75859453e-313,
3.18299369e-313],
[3.60739285e-313, 4.03179200e-313, 4.45619116e-313,
4.88059032e-313]])
arange(number_0, number_n, step)
>>> np.arange(0, 2, 0.2)
array([0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2, 1.4, 1.6, 1.8])
linspace(number_0, number_n, nummber_elements)
,而不是按照步长>>> np.linspace(0, 2, 9)
array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ])
>>> from numpy import pi
>>> x = np.linspace(0, 2*pi, 100)
>>> f = np.sin(x)
>>> f
array([ 0.00000000e+00, 6.34239197e-02, 1.26592454e-01, 1.89251244e-01,
2.51147987e-01, 3.12033446e-01, 3.71662456e-01, 4.29794912e-01,
4.86196736e-01, 5.40640817e-01, 5.92907929e-01, 6.42787610e-01,
6.90079011e-01, 7.34591709e-01, 7.76146464e-01, 8.14575952e-01,
8.49725430e-01, 8.81453363e-01, 9.09631995e-01, 9.34147860e-01,
9.54902241e-01, 9.71811568e-01, 9.84807753e-01, 9.93838464e-01,
9.98867339e-01, 9.99874128e-01, 9.96854776e-01, 9.89821442e-01,
9.78802446e-01, 9.63842159e-01, 9.45000819e-01, 9.22354294e-01,
8.95993774e-01, 8.66025404e-01, 8.32569855e-01, 7.95761841e-01,
7.55749574e-01, 7.12694171e-01, 6.66769001e-01, 6.18158986e-01,
5.67059864e-01, 5.13677392e-01, 4.58226522e-01, 4.00930535e-01,
3.42020143e-01, 2.81732557e-01, 2.20310533e-01, 1.58001396e-01,
9.50560433e-02, 3.17279335e-02, -3.17279335e-02, -9.50560433e-02,
-1.58001396e-01, -2.20310533e-01, -2.81732557e-01, -3.42020143e-01,
-4.00930535e-01, -4.58226522e-01, -5.13677392e-01, -5.67059864e-01,
-6.18158986e-01, -6.66769001e-01, -7.12694171e-01, -7.55749574e-01,
-7.95761841e-01, -8.32569855e-01, -8.66025404e-01, -8.95993774e-01,
-9.22354294e-01, -9.45000819e-01, -9.63842159e-01, -9.78802446e-01,
-9.89821442e-01, -9.96854776e-01, -9.99874128e-01, -9.98867339e-01,
-9.93838464e-01, -9.84807753e-01, -9.71811568e-01, -9.54902241e-01,
-9.34147860e-01, -9.09631995e-01, -8.81453363e-01, -8.49725430e-01,
-8.14575952e-01, -7.76146464e-01, -7.34591709e-01, -6.90079011e-01,
-6.42787610e-01, -5.92907929e-01, -5.40640817e-01, -4.86196736e-01,
-4.29794912e-01, -3.71662456e-01, -3.12033446e-01, -2.51147987e-01,
-1.89251244e-01, -1.26592454e-01, -6.34239197e-02, -2.44929360e-16])
和上述用数组名称直接在命令行打印数组时的区别是,
换成了space
。
>>> y = np.linspace(0, 2*pi, 20).reshape(4,5)
>>> y
array([[0. , 0.33069396, 0.66138793, 0.99208189, 1.32277585],
[1.65346982, 1.98416378, 2.31485774, 2.64555171, 2.97624567],
[3.30693964, 3.6376336 , 3.96832756, 4.29902153, 4.62971549],
[4.96040945, 5.29110342, 5.62179738, 5.95249134, 6.28318531]])
>>> print(y)
[[0. 0.33069396 0.66138793 0.99208189 1.32277585]
[1.65346982 1.98416378 2.31485774 2.64555171 2.97624567]
[3.30693964 3.6376336 3.96832756 4.29902153 4.62971549]
[4.96040945 5.29110342 5.62179738 5.95249134 6.28318531]]
数据类型转换时,浮点型不可转换成整数型,反之相反,且整数型可转化成浮点数,浮点数可转化为复数型。
>>> import numpy as np
a
>>> a = np.array( [20,30,40,50] )
>>> b = np.arange( 4 )
>>> b
array([0, 1, 2, 3])
>>> c= a-b
>>> c
array([20, 29, 38, 47])
>>> b**2
array([0, 1, 4, 9], dtype=int32)
>>> 10*np.sin(a)
array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854])
>>> a<35
array([ True, True, False, False])
>>> a/10
array([2., 3., 4., 5.])
>>> rg = np.random.default_rng(1) # 随机生成数值小于的数
>>> b = rg.random((2,3))
>>> b
array([[0.51182162, 0.9504637 , 0.14415961],
[0.94864945, 0.31183145, 0.42332645]])
>>> b += a
>>> b
array([[3.51182162, 3.9504637 , 3.14415961],
[3.94864945, 3.31183145, 3.42332645]])
>>> a += b
Traceback (most recent call last):
File "", line 1, in
a += b
numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int32') with casting rule 'same_kind'
>>> b = np.arange(12).reshape(3,4)
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> a = rg.random((2,3))
>>> a
array([[0.82770259, 0.40919914, 0.54959369],
[0.02755911, 0.75351311, 0.53814331]])
>>> a.min()
0.027559113243068367
>>> a.max()
0.8277025938204418
>>> b.min(axis=0) # 每行最小值,先行后列
array([0, 1, 2, 3])
>>> b.min(axis=1) # 每列最小值
array([0, 4, 8])
>>> b.min(axis=2)
Traceback (most recent call last):
File "", line 1, in
b.min(axis=2)
File "D:\Program Files\Python38\lib\site-packages\numpy\core\_methods.py", line 34, in _amin
return umr_minimum(a, axis, None, out, keepdims, initial, where)
numpy.AxisError: axis 2 is out of bounds for array of dimension 2
>>>
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> b.sum() # 元素求和
66
>>> b.cumsum() # 累加求和
array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66], dtype=int32)
>>> b.sum(axis=0) # 每列元素求和,与求最小值相反,axis=0对应的是每列求和
array([12, 15, 18, 21])
>>> b.cumsum(axis=1) # 每行累加求和,与求最小值相反,axis=1对应的是每行求和
array([[ 0, 1, 3, 6],
[ 4, 9, 15, 22],
[ 8, 17, 27, 38]], dtype=int32)
>>> A = np.array( [[1,1], [0,1]] )
>>> B = np.array( [[2,0], [3,4]] )
>>> A * B # 矩阵内对应的元素相乘
array([[2, 0],
[0, 4]])
>>> A @ B # 矩阵相乘,左行右列相对应
array([[5, 4],
[3, 4]])
>>> A.dot(B) # 矩阵相乘的另一种形式
array([[5, 4],
[3, 4]])
>>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> np.exp(B)
array([1. , 2.71828183, 7.3890561 ])
>>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> np.sqrt(B)
array([0. , 1. , 1.41421356])
>>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> C = np.array([2., -1., 4.])
>>> np.add(B, C)
array([2., 0., 6.])
>>> a = np.arange(10)**3
>>> a
array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729], dtype=int32)
>>> a[3]
27
>>> a[3:5]
array([27, 64], dtype=int32)
>>> a[:6:2] = 10
>>> a
array([ 10, 1, 10, 27, 10, 125, 216, 343, 512, 729], dtype=int32)
>>> a[ : :-1] # 倒序索引
array([729, 512, 343, 216, 125, 10, 27, 10, 1, 10], dtype=int32)
>>> for i in a:
print(i**(1/2.))
3.1622776601683795
1.0
3.1622776601683795
5.196152422706632
3.1622776601683795
11.180339887498949
14.696938456699069
18.520259177452132
22.627416997969522
27.0
多维数组每个轴可以有一个索引,以二位数组(矩阵)为例,ndarray_name[ , ]
,逗号前面是行(第一轴)的索引,逗号后面是列(地轴)的索引。这些索引以元组的形式给出,中间用逗号分隔
>>> def f(x,y):
return 10*x + y
>>> b = np.fromfunction(f,(5,4),dtype=int)
>>> b
array([[ 0, 1, 2, 3],
[10, 11, 12, 13],
[20, 21, 22, 23],
[30, 31, 32, 33],
[40, 41, 42, 43]])
>>> b[1,3]
13
>>> b[0:5, 1] # 每行第2个数值
array([ 1, 11, 21, 31, 41])
>>> b[ : , 1] # 同上
array([ 1, 11, 21, 31, 41])
>>> b[0:2, : ]
array([[ 0, 1, 2, 3],
[10, 11, 12, 13]])
当提供的索引少于轴的数量时,缺失的索引被认为是完整的切片
# 二维数组(矩阵)
>>> b
array([[ 0, 1, 2, 3],
[10, 11, 12, 13],
[20, 21, 22, 23],
[30, 31, 32, 33],
[40, 41, 42, 43]])
>>> b[-1]
array([40, 41, 42, 43])
>>> b[1]
array([10, 11, 12, 13])
# 三维数组,索引时可以用.来代替:和,
>>> c = np.arange(24).reshape(2,3,4)
>>> c
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> c.shape
(2, 3, 4)
>>> c[1,...]
array([[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]])
>>> c[1,:,:]
array([[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]])
>>> c[...,2]
array([[ 2, 6, 10],
[14, 18, 22]])
>>> c[:,:,2]
array([[ 2, 6, 10],
[14, 18, 22]])
遍历多维数组是在第一个轴基础上完成的,如果想对数组中的每个元素执行操作,可以使用flat
属性,它是数组中所有元素的遍历
>>> import numpy as np
>>> b = np.arange(12).reshape(3,4)
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> for row in b:
print(row)
[0 1 2 3]
[4 5 6 7]
[ 8 9 10 11]
>>> for element in b.flat:
print(element)
0
1
2
3
4
5
6
7
8
9
10
11
>>> c = np.arange(24).reshape(2,3,4)
>>> c
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> for row in c:
print(row)
[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
[[12 13 14 15]
[16 17 18 19]
[20 21 22 23]]
>>> for element in c.flat:
print(element)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
NumPy数组基本知识