簡約而不簡單!值得收藏的 NumPy 小抄表(含主要語法、代碼)

Numpy是一個用python實現的科學計算的擴展程序庫，包括：3、用於整合C/C++和Fortran代碼的工具包；4、實用的線性代數、傅立葉變換和隨機數生成函數。numpy和稀疏矩陣運算包scipy配合使用更加方便。NumPy（Numeric Python）提供了許多高級的數值編程工具，如：矩陣數據類型、矢量處理，以及精密的運算庫。專為進行嚴格的數字處理而產生。多為很多大型金融公司使用，以及核心的科學計算組織如：Lawrence Livermore，NASA用其處理一些本來使用C++，Fortran或Matlab等所做的任務。本文整理了一個Numpy的小抄表，總結了Numpy的常用操作，可以收藏慢慢看。

   安裝Numpy

可以通過 Pip 或者 Anaconda安裝Numpy:

或

   本文目錄

   基礎

NumPy最常用的功能之一就是NumPy數組：列表和NumPy數組的最主要區別在於功能性和速度。

列表提供基本操作，但NumPy添加了FTTs、卷積、快速搜索、基本統計、線性代數、直方圖等。

兩者數據科學最重要的區別是能夠用NumPy數組進行元素級計算。

axis 0 通常指行

axis 1 通常指列

操作描述文檔np.array([1,2,3])一維數組https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.arraynp.array([(1,2,3),(4,5,6)])二維數組https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.arraynp.arange(start,stop,step)等差數組https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html

佔位符

操作

描述

文檔

np.linspace(0,2,9)

數組中添加等差的值

https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html

np.zeros((1,2))

創建全0數組

docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html

np.ones((1,2))

創建全1數組

https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html#numpy.ones

np.random.random((5,5))

創建隨機數的數組

https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random.html

np.empty((2,2))

創建空數組

https://numpy.org/doc/stable/reference/generated/numpy.empty.html

舉例：

import numpy as np
# 1 dimensionalx = np.array([1,2,3])# 2 dimensionaly = np.array([(1,2,3),(4,5,6)])
x = np.arange(3)>>> array([0, 1, 2])
y = np.arange(3.0)>>> array([ 0.,  1.,  2.])
x = np.arange(3,7)>>> array([3, 4, 5, 6])
y = np.arange(3,7,2)>>> array([3, 5])

   數組
數組屬性

語法描述文檔array.shape維度(行,列)https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.htmllen(array)數組長度https://docs.python.org/3.5/library/functions.html#lenarray.ndim數組的維度數https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.htmlarray.size數組的元素數https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.htmlarray.dtype數據類型https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.htmlarray.astype(type)轉換數組類型https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.htmltype(array)顯示數組類型https://numpy.org/doc/stable/user/basics.types.html


拷貝 /排序

操作描述文檔np.copy(array)創建數組拷貝https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.htmlother = array.copy()創建數組深拷貝https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.htmlarray.sort()排序一個數組https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.htmlarray.sort(axis=0)按照指定軸排序一個數組https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html舉例
import numpy as np# Sort sorts in ascending ordery = np.array([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])y.sort()print(y)>>> [ 1  2  3  4  5  6  7  8  9  10]
數組操作例程增加或減少元素操作描述文檔np.append(a,b)增加數據項到數組https://docs.scipy.org/doc/numpy/reference/generated/numpy.append.htmlnp.insert(array, 1, 2, axis)沿著數組0軸或者1軸插入數據項https://docs.scipy.org/doc/numpy/reference/generated/numpy.insert.htmlnp.resize((2,4))將數組調整為形狀(2,4)https://docs.scipy.org/doc/numpy/reference/generated/numpy.resize.htmlnp.delete(array,1,axis)從數組裡刪除數據項https://numpy.org/doc/stable/reference/generated/numpy.delete.html

舉例
import numpy as np# Append items to arraya = np.array([(1, 2, 3),(4, 5, 6)])b = np.append(a, [(7, 8, 9)])print(b)>>> [1 2 3 4 5 6 7 8 9]
# Remove index 2 from previous arrayprint(np.delete(b, 2))>>> [1 2 4 5 6 7 8 9]
組合數組操作描述文檔np.concatenate((a,b),axis=0)連接2個數組，添加到末尾https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.htmlnp.vstack((a,b))按照行堆疊數組https://numpy.org/doc/stable/reference/generated/numpy.vstack.htmlnp.hstack((a,b))按照列堆疊數組docs.scipy.org/doc/numpy/reference/generated/numpy.hstack.html#numpy.hstack舉例
import numpy as npa = np.array([1, 3, 5])b = np.array([2, 4, 6])
# Stack two arrays row-wiseprint(np.vstack((a,b)))>>> [[1 3 5]     [2 4 6]]
# Stack two arrays column-wiseprint(np.hstack((a,b)))>>> [1 3 5 2 4 6]
分割數組

操作
描述
文檔
numpy.split()
分割數組
https://docs.scipy.org/doc/numpy/reference/generated/numpy.split.html
np.array_split(array, 3)
將數組拆分為大小（幾乎）相同的子數組
https://docs.scipy.org/doc/numpy/reference/generated/numpy.array_split.html#numpy.array_split
numpy.hsplit(array, 3)
在第3個索引處水平拆分數組
https://numpy.org/doc/stable/reference/generated/numpy.hsplit.html#numpy.hsplit
舉例
# Split array into groups of ~3a = np.array([1, 2, 3, 4, 5, 6, 7, 8])print(np.array_split(a, 3))>>> [array([1, 2, 3]), array([4, 5, 6]), array([7, 8])]
數組形狀變化操作描述文檔other = ndarray.flatten()平鋪一個二維數組到一維數組https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.htmlnumpy.flip()翻轉一維數組中元素的順序https://docs.scipy.org/doc/stable/reference/generated/numpy.flip.htmlnp.ndarray[::-1]翻轉一維數組中元素的順序
reshape改變數組的維數https://docs.scipy.org/doc/stable/reference/generated/numpy.reshape.htmlsqueeze從數組的形狀中刪除單維度條目https://numpy.org/doc/stable/reference/generated/numpy.squeeze.htmlexpand_dims擴展數組維度
https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.expand_dims.html其他操作描述文檔other = ndarray.flatten()平鋪2維數組到1維數組https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.htmlarray = np.transpose(other)
array.T數組轉置https://numpy.org/doc/stable/reference/generated/numpy.transpose.htmlinverse = np.linalg.inv(matrix)求矩陣的逆矩陣https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html

舉例
# Find inverse of a given matrix>>> np.linalg.inv([[3,1],[2,4]])array([[ 0.4, -0.1],       [-0.2,  0.3]])
   數學計算操作操作描述文檔np.add(x,y)
x + y加https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.htmlnp.substract(x,y)
x - y減https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtractnp.divide(x,y)
x / y除https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.dividenp.multiply(x,y)
x * y乘https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html#numpy.multiplynp.sqrt(x)平方根https://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrtnp.sin(x)元素正弦https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sinnp.cos(x)元素餘弦https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cosnp.log(x)元素自然對數https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html#numpy.lognp.dot(x,y)點積https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.htmlnp.roots([1,0,-4])給定多項式係數的根https://docs.scipy.org/doc/numpy/reference/generated/numpy.roots.html

# If a 1d array is added to a 2d array (or the other way), NumPy# chooses the array with smaller dimension and adds it to the one# with bigger dimensiona = np.array([1, 2, 3])b = np.array([(1, 2, 3), (4, 5, 6)])print(np.add(a, b))>>> [[2 4 6]     [5 7 9]]
# Example of np.roots# Consider a polynomial function (x-1)^2 = x^2 - 2*x + 1# Whose roots are 1,1>>> np.roots([1,-2,1])array([1., 1.])# Similarly x^2 - 4 = 0 has roots as x=±2>>> np.roots([1,0,-4])array([-2.,  2.])
比較操作描述文檔==等於https://docs.python.org/2/library/stdtypes.html!=不等於
https://docs.python.org/2/library/stdtypes.html<小於https://docs.python.org/2/library/stdtypes.html>大於https://docs.python.org/2/library/stdtypes.html<=小於等於https://docs.python.org/2/library/stdtypes.html>=大於等於https://docs.python.org/2/library/stdtypes.htmlnp.array_equal(x,y)數組比較https://numpy.org/doc/stable/reference/generated/numpy.array_equal.html舉例：
# Using comparison operators will create boolean NumPy arraysz = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])c = z < 6print(c)>>> [ True  True  True  True  True False False False False False]
基本的統計操作描述文檔np.mean(array)Meanhttps://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.meannp.median(array)Medianhttps://numpy.org/doc/stable/reference/generated/numpy.median.html#numpy.medianarray.corrcoef()Correlation Coefficienthttps://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#numpy.corrcoefnp.std(array)Standard Deviationhttps://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html#numpy.std


舉例
# Statistics of an arraya = np.array([1, 1, 2, 5, 8, 10, 11, 12])
# Standard deviationprint(np.std(a))>>> 4.2938910093294167
# Medianprint(np.median(a))>>> 6.5
更多操作描述文檔array.sum()數組求和https://numpy.org/doc/stable/reference/generated/numpy.sum.htmlarray.min()數組求最小值https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.htmlarray.max(axis=0)數組求最大值（沿著0軸）
array.cumsum(axis=0)指定軸求累計和https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html

   切片和子集

操作描述文檔array[i]索引i處的一維數組https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[i,j]索引在[i][j]處的二維數組https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[i<4]布爾索引https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[0:3]選擇索引為 0, 1和 2https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[0:2,1]選擇第0,1行，第1列https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[:1]選擇第0行數據項 (與[0:1, :]相同)https://numpy.org/doc/stable/reference/arrays.indexing.htmlarray[1:2, :]選擇第1行https://numpy.org/doc/stable/reference/arrays.indexing.html[comment]: <> "array[1,...]等同於 array[1,:,:]array[ : :-1]反轉數組同上


舉例
b = np.array([(1, 2, 3), (4, 5, 6)])
# The index *before* the comma refers to *rows*,# the index *after* the comma refers to *columns*print(b[0:1, 2])>>> [3]
print(b[:len(b), 2])>>> [3 6]
print(b[0, :])>>> [1 2 3]
print(b[0, 2:])>>> [3]
print(b[:, 0])>>> [1 4]
c = np.array([(1, 2, 3), (4, 5, 6)])d = c[1:2, 0:2]print(d)>>> [[4 5]]

切片舉例

import numpy as npa1 = np.arange(0, 6)a2 = np.arange(10, 16)a3 = np.arange(20, 26)a4 = np.arange(30, 36)a5 = np.arange(40, 46)a6 = np.arange(50, 56)a = np.vstack((a1, a2, a3, a4, a5, a6))

生成矩陣和切片圖示



   小技巧

例子將會越來越多的，歡迎大家提交。
布爾索引 
# Index trick when working with two np-arraysa = np.array([1,2,3,6,1,4,1])b = np.array([5,6,7,8,3,1,2])
# Only saves a at index where b == 1other_a = a[b == 1]#Saves every spot in a except at index where b != 1other_other_a = a[b != 1]
import numpy as npx = np.array([4,6,8,1,2,6,9])y = x > 5print(x[y])>>> [6 8 6 9]
# Even shorterx = np.array([1, 2, 3, 4, 4, 35, 212, 5, 5, 6])print(x[x < 5])>>> [1 2 3 4 4]

【參考】
https://github.com/juliangaal/python-cheat-sheet
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