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          【Python】簡約而不簡單|值得收藏的Numpy小抄表(含主要語法、代碼)

          共 10583字,需瀏覽 22分鐘

           ·

          2021-08-15 11:58

          Numpy是一個用python實現(xiàn)的科學(xué)計算的擴展程序庫,包括:

          • 1、一個強大的N維數(shù)組對象Array;

          • 2、比較成熟的(廣播)函數(shù)庫;

          • 3、用于整合C/C++和Fortran代碼的工具包;

          • 4、實用的線性代數(shù)、傅里葉變換和隨機數(shù)生成函數(shù)。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(shù)值編程工具,如:矩陣數(shù)據(jù)類型、矢量處理,以及精密的運算庫。專為進行嚴格的數(shù)字處理而產(chǎn)生。多為很多大型金融公司使用,以及核心的科學(xué)計算組織如:Lawrence Livermore,NASA用其處理一些本來使用C++,F(xiàn)ortran或Matlab等所做的任務(wù)。

          本文整理了一個Numpy的小抄表,總結(jié)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

          $ conda install numpy

          本文目錄

          1. 基礎(chǔ)
            • 占位符
          2. 數(shù)組
            • 增加或減少元素
            • 合并數(shù)組
            • 分割數(shù)組
            • 數(shù)組形狀變化

            • 拷貝 /排序

            • 數(shù)組操作
            • 其他
          3. 數(shù)學(xué)計算
            • 數(shù)學(xué)計算
            • 比較
            • 基礎(chǔ)統(tǒng)計
            • 更多
          4. 切片和子集
          5. 小技巧

          基礎(chǔ)

          NumPy最常用的功能之一就是NumPy數(shù)組:列表和NumPy數(shù)組的最主要區(qū)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(tǒng)計、線性代數(shù)、直方圖等。

          兩者數(shù)據(jù)科學(xué)最重要的區(qū)別是能夠用NumPy數(shù)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(shù)組https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array
          np.array([(1,2,3),(4,5,6)])二維數(shù)組https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array
          np.arange(start,stop,step)等差數(shù)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(shù)組中添加等差的值https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html
          np.zeros((1,2))創(chuàng)建全0數(shù)組docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html
          np.ones((1,2))創(chuàng)建全1數(shù)組https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html#numpy.ones
          np.random.random((5,5))創(chuàng)建隨機數(shù)的數(shù)組https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random.html
          np.empty((2,2))創(chuàng)建空數(shù)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(shù)組屬性

          數(shù)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(shù)組長度https://docs.python.org/3.5/library/functions.html#len
          array.ndim數(shù)組的維度數(shù)https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.html
          array.size數(shù)組的元素數(shù)https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.html
          array.dtype數(shù)據(jù)類型https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html
          array.astype(type)轉(zhuǎn)換數(shù)組類型https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.html
          type(array)顯示數(shù)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(chuàng)建數(shù)組拷貝https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html
          other = array.copy()創(chuàng)建數(shù)組深拷貝https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html
          array.sort()排序一個數(shù)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(shù)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(shù)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(shù)據(jù)項到數(shù)組https://docs.scipy.org/doc/numpy/reference/generated/numpy.append.html
          np.insert(array, 1, 2, axis)沿著數(shù)組0軸或者1軸插入數(shù)據(jù)項https://docs.scipy.org/doc/numpy/reference/generated/numpy.insert.html
          np.resize((2,4))將數(shù)組調(diào)整為形狀(2,4)https://docs.scipy.org/doc/numpy/reference/generated/numpy.resize.html
          np.delete(array,1,axis)從數(shù)組里刪除數(shù)據(jù)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(shù)組

          操作描述文檔
          np.concatenate((a,b),axis=0)連接2個數(shù)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(shù)組https://numpy.org/doc/stable/reference/generated/numpy.vstack.html
          np.hstack((a,b))按照列堆疊數(shù)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(shù)組

          操作描述文檔
          numpy.split()分割數(shù)組
          https://docs.scipy.org/doc/numpy/reference/generated/numpy.split.html
          np.array_split(array, 3)將數(shù)組拆分為大?。◣缀酰┫嗤淖訑?shù)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(shù)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(shù)組形狀變化

          操作
          操作描述文檔
          other = ndarray.flatten()平鋪一個二維數(shù)組到一維數(shù)組https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html
          numpy.flip()翻轉(zhuǎn)一維數(shù)組中元素的順序https://docs.scipy.org/doc/stable/reference/generated/numpy.flip.html
          np.ndarray[::-1]翻轉(zhuǎn)一維數(shù)組中元素的順序
          reshape改變數(shù)組的維數(shù)https://docs.scipy.org/doc/stable/reference/generated/numpy.reshape.html
          squeeze從數(shù)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(shù)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(shù)組到1維數(shù)組https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html
          array = np.transpose(other)
          array.T
          數(shù)組轉(zhuǎn)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(shù)學(xué)計算

          操作

          操作描述文檔
          np.add(x,y)
          x + y
          https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.html
          np.substract(x,y)
          x - y
          https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract
          np.divide(x,y)
          x / y
          https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide
          np.multiply(x,y)
          x @ y
          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(shù)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(shù)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 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(shù)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(tǒng)計

          操作描述文檔
          np.mean(array)Meanhttps://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean
          np.median(array)Medianhttps://numpy.org/doc/stable/reference/generated/numpy.median.html#numpy.median
          array.corrcoef()Correlation Coefficienthttps://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#numpy.corrcoef
          np.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(shù)組求和https://numpy.org/doc/stable/reference/generated/numpy.sum.html
          array.min()數(shù)組求最小值https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.html
          array.max(axis=0)數(shù)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(shù)組https://numpy.org/doc/stable/reference/arrays.indexing.html
          array[i,j]索引在[i][j]處的二維數(shù)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 2https://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(shù)據(jù)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(zhuǎn)數(shù)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


          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

          往期精彩回顧




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