Numpy

Numpy是一種Numerical Python，相較於python sequences, lists, sets, tuples，Numpy廣泛應用在進行數值運算，接下來要簡單介紹Numpy的功能。

Numpy array是一種多維陣列物件，由行列組合而成。

它可以利用Python的list來初始化，意思就是可以將list的element存取到Numpy陣列。

Single-dimensional Numpy Array:

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import numpy as np a=np.array([1,2,3]) print(a)

Output - [1 2 3

Multi-dimensional Array:

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

Output - [[ 1 2 3][4 5 6]]

Python NumPy Array vs. List

通常利用Numpy取代list主要是考慮到以下三種因素：
1.記憶體資源使用率低
2.快速
3.方便

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import numpy as np   import time import sys S= range(1000) print(sys.getsizeof(5)*len(S))   D= np.arange(1000) print(D.size*D.itemsize)

O/P -  14000

4000

上面例子證明list宣告用了14000，然而Numpy只用了4000。
下面例子是證明Numpy處理時間比list快很多。

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import time import sys   SIZE = 1000000   L1= range(SIZE) L2= range(SIZE) A1= np.arange(SIZE) A2=np.arange(SIZE)   start= time.time() result=[(x,y) for x,y in zip(L1,L2)] print((time.time()-start)*1000)   start=time.time() result= A1+A2 print((time.time()-start)*1000)

O/P - 380.9998035430908
49.99995231628418

Python NumPy Operations

ndim:維度 

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

Output - 2

itemsize:byte大小 

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import numpy as np a = np.array([(1,2,3)]) print(a.itemsize)

Output - 4

dtype:資料型態

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import numpy as np a = np.array([(1,2,3)]) print(a.dtype)

Output - int32

size, shape:陣列大小與dimension

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import numpy as np a = np.array([(1,2,3,4,5,6)]) print(a.size) print(a.shape)

Output - 6 (1,6)

reshape:重新配置陣列dimension

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import numpy as np a = np.array([(8,9,10),(11,12,13)]) print(a) a=a.reshape(3,2) print(a)

Output - [[ 8 9 10] [11 12 13]] [[ 8 9] [10 11] [12 13]]

slicing:陣列切割

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import numpy as np a=np.array([(1,2,3,4),(3,4,5,6)]) print(a[0,2])

Output - 3

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import numpy as np a=np.array([(1,2,3,4),(3,4,5,6)]) print(a[0:,2])

Output - [3 5]

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import numpy as np a=np.array([(8,9),(10,11),(12,13)]) print(a[0:2,1])

Output - [9 11]

linspace:等差數列

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import numpy as np a=np.linspace(1,3,10) print(a)

Output - [ 1. 1.22222222 1.44444444 1.66666667 1.88888889 2.11111111 2.33333333 2.55555556 2.77777778 3. ]

max/ min:最大最小值

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import numpy as np   a= np.array([1,2,3]) print(a.min()) print(a.max()) print(a.sum())

Output - 1 3 6

axis:選擇某個維度

1 2	a= np.array([(1,2,3),(3,4,5)]) print(a.sum(axis=0))

Output - [4 6 8]

Square Root & Standard Deviation:平方根與標準差

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import numpy as np a=np.array([(1,2,3),(3,4,5,)]) print(np.sqrt(a)) print(np.std(a))

Output - [[ 1. 1.41421356 1.73205081]
 [ 1.73205081 2. 2.23606798]]
1.29099444874

Elementary arithmetic:基礎四則運算

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import numpy as np x= np.array([(1,2,3),(3,4,5)]) y= np.array([(1,2,3),(3,4,5)]) print(x+y)

Output - [[ 2 4 6] [ 6 8 10]]

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import numpy as np x= np.array([(1,2,3),(3,4,5)]) y= np.array([(1,2,3),(3,4,5)]) print(x-y) print(x*y) print(x/y)

Output - [[0 0 0] [0 0 0]]
[[ 1 4 9] [ 9 16 25]] 
[[ 1. 1. 1.] [ 1. 1. 1.]]

Vertical & Horizontal Stacking

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import numpy as np x= np.array([(1,2,3),(3,4,5)]) y= np.array([(1,2,3),(3,4,5)]) print(np.vstack((x,y))) print(np.hstack((x,y)))

Output - [[1 2 3] [3 4 5] [1 2 3] [3 4 5]]
[[1 2 3 1 2 3] [3 4 5 3 4 5]]

ravel

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import numpy as np x= np.array([(1,2,3),(3,4,5)]) print(x.ravel())

Output - [ 1 2 3 3 4 5]

Python Numpy Special Functions

Exponential Function

1 2	a= np.array([1,2,3]) print(np.exp(a))

Output - [ 2.71828183   7.3890561   20.08553692]

Logarithmic Function

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import numpy as np import matplotlib.pyplot as plt a= np.array([1,2,3]) print(np.log(a))

Output - [ 0.          0.69314718  1.09861229]

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import numpy as np import matplotlib.pyplot as plt a= np.array([1,2,3]) print(np.log10(a))

Output - [ 0.        0.30103      0.47712125]

Matplotlib

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import numpy as np import matplotlib.pyplot as plt x= np.arange(0,3*np.pi,0.1) y=np.sin(x) plt.plot(x,y) plt.show()

Output – 

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import numpy as np import matplotlib.pyplot as plt x= np.arange(0,3*np.pi,0.1) y=np.tan(x) plt.plot(x,y) plt.show()

Output –