NumPy（Numerical Python）是Python的?種開(kāi)源的數(shù)值計(jì)算擴(kuò)展民效。提供多維數(shù)組對(duì)象区岗，各種派?對(duì)象（如掩碼數(shù)組和矩陣），這種?具可?來(lái)存儲(chǔ)和處理?型矩陣眠菇，?Python?身的嵌套列表（nestedlist structure)結(jié)構(gòu)要?效的多（該結(jié)構(gòu)也可以?來(lái)表示矩陣（matrix））边败，?持?量的維度數(shù)組與矩陣運(yùn)算，此外也針對(duì)數(shù)組運(yùn)算提供?量的數(shù)學(xué)函數(shù)庫(kù)琼锋，包括數(shù)學(xué)放闺、邏輯、形狀操作缕坎、排序、選擇篡悟、輸?輸出谜叹、離散傅?葉變換、基本線性代數(shù)搬葬，基本統(tǒng)計(jì)運(yùn)算和隨機(jī)模擬等等荷腊。
- NumPy的功能強(qiáng)?
1.強(qiáng)?的N維數(shù)組
2.成熟的?播功能
3.?于整合C/C++和Fortran代碼的?具包
4.NumPy提供了全?的數(shù)學(xué)功能、隨機(jī)數(shù)?成器和線性代數(shù)功能 - 安裝Python庫(kù)
1.開(kāi)發(fā)工具（類似pycharm急凰，在瀏覽器里而已）：pip install jupyter -i https://pypi.tuna.tsinghua.edu.cn/simple
2.pip install numpy -i https://pypi.tuna.tsinghua.edu.cn/simple - 啟動(dòng)終端
1.Windows----> 快捷鍵：win + R ----->輸?：cmd回?------>命令?出來(lái) Mac ---->啟動(dòng)終端
2.啟動(dòng)jupyter
3.進(jìn)?終端輸?指令:jupyter notebook
4.在哪?啟動(dòng)jupyter女仰，瀏覽器上的?錄就對(duì)應(yīng)那?
5.jupyter擴(kuò)展插件
pip install jupyter_contrib_nbextensions -i https://pypi.tuna.tsinghua.edu.cn/simple
pip install jupyter_nbextensions_configurator -i https://pypi.tuna.tsinghua.edu.cn/simple
jupyter contrib nbextension install --user
jupyter nbextensions_configurator enable --user
設(shè)置：
a.重啟jupyter,菜單欄多了一個(gè)插件（Nbextensions），點(diǎn)擊進(jìn)入，去掉左上角的全選對(duì)勾
b.多勾選：標(biāo)題（Table of Contents）疾忍、代碼提示（Hinterland）乔外、折疊代碼（Codefolding）、折疊標(biāo)題（Collapsible Headings）
已勾選的不用動(dòng)了
數(shù)組創(chuàng)建
import numpy as np
l = [1,3,5,7,9] # 列表
arr = np.array(l) # 將列表轉(zhuǎn)換為NumPy數(shù)組
arr # 數(shù)據(jù)?樣一罩，NumPy數(shù)組的?法杨幼，功能更加強(qiáng)?
# 輸出為
# array([1, 3, 5, 7, 9])
import numpy as np
arr1 = np.ones(10) # 輸出為：array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])
arr2 = np.zeros(10) # 輸出為： array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
arr3 = np.full(shape = [2,3],fill_value=2.718)
# 輸出為：
# array([[2.718, 2.718, 2.718],
# [2.718, 2.718, 2.718]])
arr4 = np.arange(start = 0,stop = 20,step = 2)
# 等差數(shù)列 輸出為：array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])
arr5 = np.linspace(start =0,stop = 9,num = 10)
# 等差數(shù)列 輸出為：array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
arr6 = np.random.randint(0,100,size = 10)
# int隨機(jī)數(shù) 輸出為：array([ 4, 8, 79, 62, 34, 35, 2, 65, 47, 18])
arr7 = np.random.randn(5)
# 正態(tài)分布 輸出為：array([ 0.57807872, 0.37922855, 2.37936837, -0.28688769,
0.2882854 ])
arr8 = np.random.random(size = 5)
# float 隨機(jī)數(shù) 輸出為：array([0.59646412, 0.37960586, 0.38077327, 0.76983539,
0.22689201])
數(shù)組的軸數(shù)、維度聂渊、尺寸形狀
import numpy as np
arr = np.random.randint(0,100,size = (3,4,5))
arr.ndim # 輸出 3
import numpy as np
arr = np.random.randint(0,100,size = (3,4,5))
arr.shape # 輸出 (3,4,5)
數(shù)組元素的總數(shù)
import numpy as np
arr = np.random.randint(0,100,size = (3,4,5))
arr.size # 輸出 3*4*5 = 60
索引差购、切?和迭代
arr = np.array([0,1,2,3,4,5,6,7,8,9])
arr[5] #索引 輸出 5
arr[5:8] #切?輸出：array([5, 6, 7])
arr[2::2] # 從索引2開(kāi)始每?jī)蓚€(gè)中取?個(gè) 輸出 array([2, 4, 6, 8])
arr[::3] # 不寫索引默認(rèn)從0開(kāi)始，每3個(gè)中取?個(gè) 輸出為 array([0, 3, 6, 9])
arr[1:7:2] # 從索引1開(kāi)始到索引7結(jié)束汉嗽，左閉右開(kāi)欲逃，每2個(gè)數(shù)中取?個(gè) 輸出 array([1, 3, 5])
arr[::-1] # 倒序 輸出 array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
arr[::-2] # 倒序 每?jī)蓚€(gè)取?個(gè) 輸出 array([9, 7, 5, 3, 1])
arr[5:8]=12 # 切?賦值會(huì)賦值到每個(gè)元素上，與列表操作不同
temp = arr[5:8]
temp[1] = 1024
arr # 輸出：array([ 0, 1, 2, 3, 4, 12, 1024, 12, 8, 9])
arr2d = np.array([[1, 3, 5], [2, 4, 6], [-2, -7, -9], [6, 6, 6]]) # ?維數(shù)組 shape(3,4)
arr2d[0, -1] # 索引 等于arr2d[0][-1] 輸出 5
arr2d[0, 2] # 索引 等于arr2d[0][2] == arr2d[0][-1] 輸出 5
arr2d[:2, -2:] # 切? 第?維和第?維都進(jìn)?切? 等于arr2d[:2][:,1:]
arr2d[:2, 1:] # 切? 1 == -2 ?個(gè)是正序饼暑，另個(gè)?是倒序暖夭，對(duì)應(yīng)相同的位置
# 輸出：
# array([[3, 5],
# [4, 6]])
花式索引
import numpy as np
# ?維
arr1 = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
arr2 = arr1[[1, 3, 3, 5, 7, 7, 7]] # 輸出 array([2, 4, 4, 6, 8, 8, 8])
arr2[-1] = 1024 # 修改值，不影響arr1
# ?維
arr2d = np.array([[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [12, 18, 22, 23, 37],
[123, 55, 17, 88, 103]]) # shape(4,5)
arr2d[[1, 3]] # 獲取第??和第四?撵孤，索引從0開(kāi)始的所以1對(duì)應(yīng)第??
# 輸出 array([[ 2, 4, 6, 8, 10],
# [123, 55, 17, 88, 103]])
arr2d[([1,3],[2,4])] # 相當(dāng)于arr2d[1,2]獲取?個(gè)元素,arr2d[3,4]獲取另?個(gè)元素
# 輸出為 array([ 6, 103])
# 選擇?個(gè)區(qū)域
arr2d[np.ix_([1,3,3,3],[2,4,4])] # 相當(dāng)于 arr2d[[1,3,3,3]][:,[2,4,4]]
arr2d[[1,3,3,3]][:,[2,4,4]]
# ix_()函數(shù)可?于組合不同的向量
# 第?個(gè)列表存的是待提取元素的?標(biāo)迈着，第?個(gè)列表存的是待提取元素的列標(biāo)
# 輸出為
# array([[ 6, 10, 10],
# [ 17, 103, 103],
# [ 17, 103, 103],
# [ 17, 103, 103]])
boolean值索引
names =
np.array(['softpo','Brandon','Will','Michael','Will','Ella','Daniel','softpo','
Will','Brandon'])
cond1 = names == 'Will'
cond1
# 輸出array([False, False, True, False, True, False, False, False, True,
False])
names[cond1] # array(['Will', 'Will', 'Will'], dtype='<U7')
arr = np.random.randint(0,100,size = (10,8)) # 0~100隨機(jī)數(shù)
cond2 = arr > 90
# 找到所有?于90的索引，返回boolean類
形狀操作
數(shù)組變形-從原來(lái)數(shù)組順序取數(shù)拼湊變形后的數(shù)組
import numpy as np
arr1 = np.random.randint(0,10,size = (3,4,5))
arr2 = arr1.reshape(12,5) # 形狀改變邪码，返回新數(shù)組
arr3 = arr1.reshape(-1,5) # ?動(dòng)“整形”裕菠，?動(dòng)計(jì)算
數(shù)組轉(zhuǎn)置-行轉(zhuǎn)列，列轉(zhuǎn)行- 都不會(huì)改變?cè)瓟?shù)組
import numpy as np
arr1 = np.random.randint(0,10,size = (3,5)) # shape(3,5)
arr1.T # shape(5,3) 轉(zhuǎn)置
arr2 = np.random.randint(0,10,size = (3,6,4)) # shape(3,6,4),
np.transpose(arr2,axes=(2,0,1)) # transpose改變數(shù)組維度 shape(4,3,6)
數(shù)組堆疊
import numpy as np
arr1 = np.array([[1,2,3]])
arr2 = np.array([[4,5,6]])
np.concatenate([arr1,arr2],axis = 0)
# 串聯(lián)合并shape(2,3) axis = 0表示第?維串聯(lián) 輸出為
# array([[1, 2, 3],
# [4, 5, 6]])
np.concatenate([arr1,arr2],axis = 1)
# shape(1,6) axis = 1表示第?維串聯(lián) 輸出為：array([[1, 2, 3, 4, 5, 6]])
np.hstack((arr1,arr2)) # ?平?向堆疊 輸出為：array([[1, 2, 3, 4, 5, 6]])
np.vstack((arr1,arr2))
#篩選數(shù)組闭专，保留第5列滿足條件的行
arr_new = arr_old[arr_old[:,4]>=條件,:]
# 豎直?向堆疊奴潘，輸出為：
# array([[1, 2, 3],
# [4, 5, 6]])
split數(shù)組拆分
import numpy as np
arr = np.random.randint(0,10,size = (6,5)) # shape(6,5)
np.split(arr,indices_or_sections=2,axis = 0) # 在第?維（6）平均分成兩份
np.split(arr,indices_or_sections=[2,3],axis = 1) # 在第?維（5）以索引2，3為斷點(diǎn)分割
成3份
np.vsplit(arr,indices_or_sections=3) # 在豎直?向平均分割成3份
np.hsplit(arr,indices_or_sections=[1,4]) # 在?平?向影钉，以索引1画髓，4為斷點(diǎn)分割成3份
?播機(jī)制
當(dāng)兩個(gè)數(shù)組的形狀并不相同的時(shí)候，我們可以通過(guò)擴(kuò)展數(shù)組的?法來(lái)實(shí)現(xiàn)相加平委、相減奈虾、相乘等操作，這
種機(jī)制叫做?播（broadcasting）,行不夠向行上廣播（復(fù)制相同的運(yùn)算）廉赔，列不夠向列上廣播（復(fù)制相同的運(yùn)算）肉微；廣播時(shí)數(shù)組要對(duì)齊
image.png
import numpy as np
arr1 = np.sort(np.array([0,1,2,3]*3)).reshape(4,3) #shape(4,3)
arr2 = np.array([1,2,3]) # shape(3,)
arr3 = arr1 + arr2 # arr2進(jìn)??播復(fù)制4份 shape(4,3)
arr3
image.png
import numpy as np
arr1 = np.sort(np.array([0, 1, 2, 3] * 3)).reshape(4, 3) # shape(4,3)
arr2 = np.array([[1], [2], [3], [4]]) # shape(4,1)
arr3 = arr1 + arr2 # arr2 進(jìn)??播復(fù)制3份 shape(4,3)
arr3
image.png
import numpy as np
arr1 = np.array([0, 1, 2, 3, 4, 5, 6, 7] * 3).reshape(3, 4, 2) # shape(3,4,2)
arr2 = np.array([0, 1, 2, 3, 4, 5, 6, 7]).reshape(4, 2) # shape(4,2)
arr3 = arr1 + arr2 # arr2數(shù)組在0維上復(fù)制3份 shape(3,4,2)
arr3
image.png
通?函數(shù)
通?函數(shù)：元素級(jí)數(shù)字函數(shù)
import numpy as np
arr1 = np.array([1, 4, 8, 9, 16, 25])
np.sqrt(arr1) # 開(kāi)平?
np.square(arr1) # 平?
np.clip(arr1, 2, 16) # 輸出 array([ 2, 4, 8, 9, 16, 16])，將arr1限制在2,16之間蜡塌，超出范圍的都置為對(duì)應(yīng)邊界的值
x = np.array([1, 5, 2, 9, 3, 6, 8])
y = np.array([2, 4, 3, 7, 1, 9, 0])
np.maximum(x, y) # 返回兩個(gè)數(shù)組中的?較?的值array([2, 5, 3, 9, 3, 9, 8])
arr2 = np.random.randint(0, 10, size=(5, 5))
np.inner(arr2[0], arr2) # 返回?維數(shù)組向量?jī)?nèi)積 array([15, 6, 4, 14, 6])
where函數(shù)
import numpy as np
arr1 = np.array([1, 3, 5, 7, 9])
arr2 = np.array([2, 4, 6, 8, 10])
cond = np.array([True, False, True, True, False])
np.where(cond, arr1, arr2) # True選擇arr1碉纳，F(xiàn)alse選擇arr2的值
# 輸出 array([ 1, 4, 5, 7, 10])
arr3 = np.random.randint(0, 30, size=20)
np.where(arr3 < 15, arr3, -15) # ?于15還是?身的值，?于15設(shè)置成-15
排序?法
import numpy as np
arr = np.array([9, 3, 11, 6, 17, 5, 4, 15, 1])
arr.sort() # 直接改變?cè)瓟?shù)組
np.sort(arr) # 返回深拷?排序結(jié)果
arr = np.array([9, 3, 11, 6, 17, 5, 4, 15, 1])
arr.argsort() # 返回從?到?排序索引 array([8, 1, 6, 5, 3, 0, 2, 7, 4])
集合運(yùn)算函數(shù)
A = np.array([2,4,6,8])
B = np.array([3,4,5,6])
np.intersect1d(A,B) # 交集 array([4, 6])
np.union1d(A,B) # 并集 array([2, 3, 4, 5, 6, 8])
np.setdiff1d(A,B) #差集馏艾，A中有劳曹，B中沒(méi)有 array([2, 8])
數(shù)學(xué)和統(tǒng)計(jì)函數(shù)
import numpy as np
arr1 = np.array([1,7,2,19,23,0,88,11,6,11])
arr1.min() # 計(jì)算最?值 0
arr1.argmax() # 計(jì)算最?值的索引 返回 6
np.argwhere(arr1 > 20) # 返回?于20的元素的索引
np.cumsum(arr1) # 計(jì)算累加和
arr2 = np.random.randint(0,10,size = (4,5))
arr2.mean(axis = 0) # 計(jì)算列的平均值
arr2.mean(axis = 1) # 計(jì)算?的平均值
np.cov(arr2,rowvar=True) # 協(xié)?差矩陣
np.corrcoef(arr2,rowvar=True) # 相關(guān)性系數(shù)
線性代數(shù)
#矩陣的乘積
A = np.array([[4,2,3],
[1,3,1]]) # shape(2,3)
B = np.array([[2,7],
[-5,-7],
[9,3]]) # shape(3,2)
np.dot(A,B) # 矩陣運(yùn)算 A的最后?維和B的第?維必須?致
A @ B # 符號(hào) @ 表示矩陣乘積運(yùn)算
# 計(jì)算矩陣的逆
from numpy.linalg import inv, det, eig, qr, svd
A = np.array([[1, 2, 3],
[2, 3, 4],
[4, 5, 8]]) # shape(3,3)
inv(t) # 逆矩陣
det(t) # 計(jì)算矩陣?列式