针对数组元素计算,注意广播原则
在 numpy 中对以上函数进行了运算符的重载,且运算符为元素级。也就是说,它们只用于位置相同的元素之间,所得到的运算结果组成一个新的数组。
以上函数都为通用函数,它对数组中的各个元素逐一操作。
三角函数等很多数学运算符合通用函数的定义,例如,计算平方根的sqrt()
函数、用来取对数的log()
函数和求正弦值的sin()
函数。
【例】运用了linspace来取[0,π/2]的十个值
import numpy as np
x = np.linspace(start=0, stop=np.pi / 2, num=10)
print(x)
# [0. 0.17453293 0.34906585 0.52359878 0.6981317 0.87266463
# 1.04719755 1.22173048 1.3962634 1.57079633]
y = np.sin(x)
print(y)
# [0. 0.17364818 0.34202014 0.5 0.64278761 0.76604444
# 0.8660254 0.93969262 0.98480775 1. ]
z = np.arcsin(y)
print(z)
# [0. 0.17453293 0.34906585 0.52359878 0.6981317 0.87266463
# 1.04719755 1.22173048 1.3962634 1.57079633]
y = np.cos(x)
print(y)
# [1.00000000e+00 9.84807753e-01 9.39692621e-01 8.66025404e-01
# 7.66044443e-01 6.42787610e-01 5.00000000e-01 3.42020143e-01
# 1.73648178e-01 6.12323400e-17]
z = np.arccos(y)
print(z)
# [0. 0.17453293 0.34906585 0.52359878 0.6981317 0.87266463
# 1.04719755 1.22173048 1.3962634 1.57079633]
y = np.tan(x)
print(y)
# [0.00000000e+00 1.76326981e-01 3.63970234e-01 5.77350269e-01
# 8.39099631e-01 1.19175359e+00 1.73205081e+00 2.74747742e+00
# 5.67128182e+00 1.63312394e+16]
z = np.arctan(y)
print(z)
# [0. 0.17453293 0.34906585 0.52359878 0.6981317 0.87266463
# 1.04719755 1.22173048 1.3962634 1.57079633]
对元素进行逐个运算
numpy.sum(a[, axis=None, dtype=None, out=None, …]):沿着给定的轴进行累加
numpy.cumsum:
numpy.cumsum(a, axis=None, dtype=None, out=None):返回沿着给定的轴逐个累加结果
聚合函数 是指对一组值(比如一个数组)进行操作,返回一个单一值作为结果的函数。因而,求数组所有元素之和的函数就是聚合函数。
【例】返回给定轴上的数组元素的累加和。
axis=None就相当于把数组flatten成一维了
import numpy as np
x = np.array([[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25],
[26, 27, 28, 29, 30],
[31, 32, 33, 34, 35]])
y = np.cumsum(x)
print(y)
# [ 11 23 36 50 65 81 98 116 135 155 176 198 221 245 270 296 323 351
# 380 410 441 473 506 540 575]
y = np.cumsum(x, axis=0)
print(y)
# [[ 11 12 13 14 15]
# [ 27 29 31 33 35]
# [ 48 51 54 57 60]
# [ 74 78 82 86 90]
# [105 110 115 120 125]]
y = np.cumsum(x, axis=1)
print(y)
# [[ 11 23 36 50 65]
# [ 16 33 51 70 90]
# [ 21 43 66 90 115]
# [ 26 53 81 110 140]
# [ 31 63 96 130 165]]
numpy.prod(a[, axis=None, dtype=None, out=None, …]) :返回沿轴的累乘
numpy.cumprod(a, axis=None, dtype=None, out=None) :返回沿轴逐个累乘的结果
numpy.diff(a, n=1, axis=-1, prepend=np._NoValue, append=np._NoValue) :计算沿轴的n维离散差值,out[i] = a[i+1] - a[i]
a:输入矩阵
n:可选,代表要执行几次差值
axis:默认是最后一个
【例】沿着指定轴计算第N维的离散差值。
import numpy as np
A = np.arange(2, 14).reshape((3, 4))
A[1, 1] = 8
print(A)
# [[ 2 3 4 5]
# [ 6 8 8 9]
# [10 11 12 13]]
print(np.diff(A))
# [[1 1 1]
# [2 0 1]
# [1 1 1]]
print(np.diff(A, axis=0))
# [[4 5 4 4]
# [4 3 4 4]]
【例】将数组舍入到给定的小数位数。
import numpy as np
x = np.random.rand(3, 3) * 10
print(x)
# [[6.59144457 3.78566113 8.15321227]
# [1.68241475 3.78753332 7.68886328]
# [2.84255822 9.58106727 7.86678037]]
y = np.around(x)
print(y)
# [[ 7. 4. 8.]
# [ 2. 4. 8.]
# [ 3. 10. 8.]]
y = np.around(x, decimals=2)
print(y)
# [[6.59 3.79 8.15]
# [1.68 3.79 7.69]
# [2.84 9.58 7.87]]
numpy.ceil(x, *args, **kwargs) :向上取整
numpy.floor(x, *args, **kwargs) :向下取整
numpy.clip(a, a_min, a_max, out=None, **kwargs):低于a_min的就赋为min,高于a_max的就赋为max
【例】裁剪(限制)数组中的值。
import numpy as np
x = np.array([[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25],
[26, 27, 28, 29, 30],
[31, 32, 33, 34, 35]])
y = np.clip(x, a_min=20, a_max=30)
print(y)
# [[20 20 20 20 20]
# [20 20 20 20 20]
# [21 22 23 24 25]
# [26 27 28 29 30]
# [30 30 30 30 30]]
numpy.absolute(x, *args, **kwargs)
numpy.abs(x, *args, **kwargs)
【例】
import numpy as np
x = np.arange(-5, 5)
print(x)
# [-5 -4 -3 -2 -1 0 1 2 3 4]
y = np.abs(x)
print(y)
# [5 4 3 2 1 0 1 2 3 4]
y = np.absolute(x)
print(y)
# [5 4 3 2 1 0 1 2 3 4]
numpy.sign(x, *args, **kwargs)
:返回1代表正值、-1代表负值、0
【例】
x = np.arange(-5, 5)
print(x)
#[-5 -4 -3 -2 -1 0 1 2 3 4]
print(np.sign(x))
#[-1 -1 -1 -1 -1 0 1 1 1 1]
numpy.all(a, axis=None, out=None, keepdims=np._NoValue)
:检验是否所有元素都满足(多元素的与)
numpy.any(a, axis=None, out=None, keepdims=np._NoValue)
:检验是否有元素满足(多元素的或)
【例】
import numpy as np
a = np.array([0, 4, 5])
b = np.copy(a)
print(np.all(a == b)) # True
print(np.any(a == b)) # True
b[0] = 1
print(np.all(a == b)) # False
print(np.any(a == b)) # True
print(np.all([1.0, np.nan])) # True
print(np.any([1.0, np.nan])) # True
a = np.eye(3)
print(np.all(a, axis=0)) # [False False False]
print(np.any(a, axis=0)) # [ True True True]
numpy.isnan(x, *args, **kwargs)
:检验是否为nan【例】
a=np.array([1,2,np.nan])
print(np.isnan(a))
#[False False True]
【例】计算非x元素的真值。
import numpy as np
print(np.logical_not(3))
# False
print(np.logical_not([True, False, 0, 1]))
# [False True True False]
x = np.arange(5)
print(np.logical_not(x < 3))
# [False False False True True]
【例】计算x1 AND x2元素的真值。
print(np.logical_and(True, False))
# False
print(np.logical_and([True, False], [True, False]))
# [ True False]
print(np.logical_and(x > 1, x < 4))
# [False False True True False]
【例】逐元素计算x1 OR x2的真值。
print(np.logical_or(True, False))
# True
print(np.logical_or([True, False], [False, False]))
# [ True False]
print(np.logical_or(x < 1, x > 3))
# [ True False False False True]
【例】计算x1 XOR x2的真值,按元素计算。
print(np.logical_xor(True, False))
# True
print(np.logical_xor([True, True, False, False], [True, False, True, False]))
# [False True True False]
print(np.logical_xor(x < 1, x > 3))
# [ True False False False True]
print(np.logical_xor(0, np.eye(2)))
# [[ True False]
# [False True]]
【例】numpy对以上对照函数进行了运算符的重载。
import numpy as np
x = np.array([1, 2, 3, 4, 5, 6, 7, 8])
y = x > 2
print(y)
print(np.greater(x, 2))
# [False False True True True True True True]
y = x >= 2
print(y)
print(np.greater_equal(x, 2))
# [False True True True True True True True]
y = x == 2
print(y)
print(np.equal(x, 2))
# [False True False False False False False False]
y = x != 2
print(y)
print(np.not_equal(x, 2))
# [ True False True True True True True True]
y = x < 2
print(y)
print(np.less(x, 2))
# [ True False False False False False False False]
y = x <= 2
print(y)
print(np.less_equal(x, 2))
# [ True True False False False False False False]
【例】两数组比较
import numpy as np
np.random.seed(20200611)
x = np.array([[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25],
[26, 27, 28, 29, 30],
[31, 32, 33, 34, 35]])
y = np.random.randint(10, 40, [5, 5])
print(y)
# [[32 28 31 33 37]
# [23 37 37 30 29]
# [32 24 10 33 15]
# [27 17 10 36 16]
# [25 32 23 39 34]]
z = x > y
print(z)
print(np.greater(x, y))
# [[False False False False False]
# [False False False False False]
# [False False True False True]
# [False True True False True]
# [ True False True False True]]
z = x >= y
print(z)
print(np.greater_equal(x, y))
# [[False False False False False]
# [False False False False False]
# [False False True False True]
# [False True True False True]
# [ True True True False True]]
z = x == y
print(z)
print(np.equal(x, y))
# [[False False False False False]
# [False False False False False]
# [False False False False False]
# [False False False False False]
# [False True False False False]]
z = x != y
print(z)
print(np.not_equal(x, y))
# [[ True True True True True]
# [ True True True True True]
# [ True True True True True]
# [ True True True True True]
# [ True False True True True]]
z = x < y
print(z)
print(np.less(x, y))
# [[ True True True True True]
# [ True True True True True]
# [ True True False True False]
# [ True False False True False]
# [False False False True False]]
z = x <= y
print(z)
print(np.less_equal(x, y))
# [[ True True True True True]
# [ True True True True True]
# [ True True False True False]
# [ True False False True False]
# [False True False True False]]
【例】注意 numpy 的广播规则。
import numpy as np
x = np.array([[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25],
[26, 27, 28, 29, 30],
[31, 32, 33, 34, 35]])
np.random.seed(20200611)
y = np.random.randint(10, 50, 5)
print(y)
# [32 37 30 24 10]
z = x > y
print(z)
print(np.greater(x, y))
# [[False False False False True]
# [False False False False True]
# [False False False False True]
# [False False False True True]
# [False False True True True]]
z = x >= y
print(z)
print(np.greater_equal(x, y))
# [[False False False False True]
# [False False False False True]
# [False False False True True]
# [False False False True True]
# [False False True True True]]
z = x == y
print(z)
print(np.equal(x, y))
# [[False False False False False]
# [False False False False False]
# [False False False True False]
# [False False False False False]
# [False False False False False]]
z = x != y
print(z)
print(np.not_equal(x, y))
# [[ True True True True True]
# [ True True True True True]
# [ True True True False True]
# [ True True True True True]
# [ True True True True True]]
z = x < y
print(z)
print(np.less(x, y))
# [[ True True True True False]
# [ True True True True False]
# [ True True True False False]
# [ True True True False False]
# [ True True False False False]]
z = x <= y
print(z)
print(np.less_equal(x, y))
# [[ True True True True False]
# [ True True True True False]
# [ True True True True False]
# [ True True True False False]
# [ True True False False False]]
参考文献