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【Python】简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）
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【Python】简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）
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Numpy是一個用python實現的科學計算的擴展程序庫，包括：
1、一個強大的N維數組對象Array；
2、比較成熟的（廣播）函數庫；
3、用于整合C/C++和Fortran代碼的工具包；
4、實用的線性代數、傅里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:
$ pip install numpy或
$ conda install numpy本文目錄
基礎
占位符
數組
增加或減少元素
合并數組
分割數組
數組形狀變化
拷貝 /排序
數組操作
其他
數學計算
數學計算
比較
基礎統計
更多
切片和子集
小技巧
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于功能性和速度。
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.array np.array([(1,2,3),(4,5,6)]) 二維數組 https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array np.arange(start,stop,step) 等差數組 https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html 占位符
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 dimensional x = np.array([1,2,3]) # 2 dimensional y = 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])數組屬性
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.html len(array) 數組長度 https://docs.python.org/3.5/library/functions.html#len array.ndim 數組的維度數 https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.html array.size 數組的元素數 https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.html array.dtype 數據類型 https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html array.astype(type) 轉換數組類型 https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.html type(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.html other = array.copy() 創建數組深拷貝 https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html array.sort() 排序一個數組 https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html array.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 order y = 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.html np.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.html np.resize((2,4)) 將數組調整為形狀(2,4) https://docs.scipy.org/doc/numpy/reference/generated/numpy.resize.html np.delete(array,1,axis) 從數組里刪除數據項 https://numpy.org/doc/stable/reference/generated/numpy.delete.html 舉例
import numpy as np # Append items to array a = 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 array print(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.html np.vstack((a,b)) 按照行堆疊數組 https://numpy.org/doc/stable/reference/generated/numpy.vstack.html np.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 np a = np.array([1, 3, 5]) b = np.array([2, 4, 6])# Stack two arrays row-wise print(np.vstack((a,b))) >>> [[1 3 5][2 4 6]]# Stack two arrays column-wise print(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 ~3 a = 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
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.html numpy.flip() 翻轉一維數組中元素的順序 https://docs.scipy.org/doc/stable/reference/generated/numpy.flip.html np.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.html squeeze 從數組的形狀中刪除單維度條目 https://numpy.org/doc/stable/reference/generated/numpy.squeeze.html expand_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.html array = np.transpose(other)
array.T數組轉置 https://numpy.org/doc/stable/reference/generated/numpy.transpose.html inverse = 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.html np.substract(x,y)
x - y減 https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract np.divide(x,y)
x / y除 https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide np.multiply(x,y)
x @ y乘 https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html#numpy.multiply np.sqrt(x) 平方根 https://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt np.sin(x) 元素正弦 https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin np.cos(x) 元素余弦 https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos np.log(x) 元素自然對數 https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html#numpy.log np.dot(x,y) 點積 https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html np.roots([1,0,-4]) 給定多項式系數的根 https://docs.scipy.org/doc/numpy/reference/generated/numpy.roots.html 舉例
# 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 dimension a = 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 == 等于 https://docs.python.org/2/library/stdtypes.html != 不等于 https://docs.python.org/2/library/stdtypes.html < 小于 https://docs.python.org/2/library/stdtypes.html > 大于 https://docs.python.org/2/library/stdtypes.html <= 小于等于 https://docs.python.org/2/library/stdtypes.html >= 大于等于 https://docs.python.org/2/library/stdtypes.html np.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 arrays z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) c = z < 6 print(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) Mean https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean np.median(array) Median https://numpy.org/doc/stable/reference/generated/numpy.median.html#numpy.median array.corrcoef() Correlation Coefficient https://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#numpy.corrcoef np.std(array) Standard Deviation https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html#numpy.std 舉例
# Statistics of an array a = np.array([1, 1, 2, 5, 8, 10, 11, 12])# Standard deviation print(np.std(a)) >>> 4.2938910093294167# Median print(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.html array.min() 數組求最小值 https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.html array.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.html array[i,j] 索引在[i][j]處的二維數組 https://numpy.org/doc/stable/reference/arrays.indexing.html array[i<4] 布爾索引 https://numpy.org/doc/stable/reference/arrays.indexing.html array[0:3] 選擇索引為 0, 1和?2 https://numpy.org/doc/stable/reference/arrays.indexing.html array[0:2,1] 選擇第0,1行，第1列 https://numpy.org/doc/stable/reference/arrays.indexing.html array[:1] 選擇第0行數據項?(與[0:1, :]相同) https://numpy.org/doc/stable/reference/arrays.indexing.html array[1:2, :] 選擇第1行 https://numpy.org/doc/stable/reference/arrays.indexing.html [comment]: <> " array[1,...] 等同于 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 np a1 = 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-arrays a = 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 == 1 other_a = a[b == 1] #Saves every spot in a except at index where b != 1 other_other_a = a[b != 1] import numpy as np x = np.array([4,6,8,1,2,6,9]) y = x > 5 print(x[y]) >>> [6 8 6 9]# Even shorter x = 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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