科学计算库¶
1. NumPy¶
##### 1. 数组创建
import numpy as np
print(np.ones(shape=10))
print(np.zeros(shape=10))
print(np.full(shape=10, fill_value=2))
print(np.random.randint(0, 100, size=10))
print(np.random.randn(10)) # 正太分，布平均值0，标准差1
print(np.linspace(1, 99, 50)) # 等差数列
print(np.arange(start=0, stop=10, step=2))
print(np.logspace(1, 10, base=2, num=10)) # 等比数列
print(np.random.randint(0, 100, size=(3, 3))) # 二维数组
2. 数组的保存读取¶
-
保存
import numpy as np x = np.random.randn(5) y = np.arange(0,10,1) #save方法可以存一个 ndarray np.save("x_arr",x) #如果要存多个数组，要是用savez方法 np.savez("some_array.npz",xarr = x,yarr=y) -
读取
import numpy as np np.load('x_arr.npy') # 通过key加载保存的数组数据 np.load('some_array.npz')['yarr'] -
读写csv文件
import numpy as np arr = np.random.randint(0, 10, size=(3, 3)) np.savetxt("arr.csv", arr, delimiter=',') np.loadtxt("arr.csv", delimiter=',', dtype=np.int32) -
数组运算¶
-
加减乘除运算
import numpy as np arr1 = np.random.randint(0, 100, size=10) arr2 = np.random.randint(0, 100, size=10) arr1 - arr2 # 减法 arr1 * arr2 # 乘法 arr1 / arr2 # 除法 arr1**arr2 # 幂运算 -
逻辑运算
import numpy as np arr1 = np.array([1,2,3,4,5,6,7,8,9,10]) arr2 = np.array([1,3,5,6,2,8,2,10,9,4]) arr1 < 10 arr1 >= 10 arr1 == 10 arr1 == arr2 arr1 > arr2 -
*=、+=、-= 操作
import numpy as np arr1 = np.arange(10) arr1 +=10 arr1 -=10 arr1 *=10 # arr1 /=10 不支持运算 -
切片索引¶
import numpy as np
arr = np.array([0,1,2,3,4,5,6,7,8,9])
arr[2] #索引 输出 2
arr[1:4] #切片输出:array([1, 2, 3])
arr1 = np.array([[1,2,3],
[4,5,6],
[7,8,9]])
arr1[0,-1] #索引 等于3
arr1[:2,:2]
#[[1 2]
# [4 5]]
arr1 = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
index = np.ix_([0, 1], [0, 2])
arr1[index]
#[[1 3]
# [4 6]]
-
数据形状改变¶
-
reshape
import numpy as np arr1 = np.random.randint(0, 100, size=(3, 4)) arr2 = arr1.reshape(4, 3) # 形状改变，返回新数组 arr3 = arr1.reshape(-1, 6) # 自动整形，自动计算 -
叠加
import numpy as np arr1 = np.array([[1, 2, 3]]) arr2 = np.array([[4, 5, 6]]) arr3 = np.concatenate([arr1, arr2], axis=0) # 行合并 默认值 arr3 = np.vstack((arr1, arr2)) arr4 = np.concatenate([arr1, arr2], axis=1) # 列合并 arr4 = np.hstack((arr1, arr2)) -
拆分
import numpy as np arr1 = np.random.randint(0, 10, size=(6, 5)) arr2 = np.split(arr1, indices_or_sections=[2, 3], axis=0) # 行的拆分 arr2 = np.hsplit(arr1,indices_or_sections=[2, 3]) # arr3 = np.split(arr1, indices_or_sections=[2, 3], axis=1) # 列的拆分 np.vsplit(arr,indices_or_sections=3) -
转置
import numpy as np arr1 = np.random.randint(0, 10, size=(3, 5)) # shape(3,5) arr2 = arr1.T # shape(5,3) arr3 = np.random.randint(0, 10, size=(3, 4, 5)) # shape(3,4,5) arr4 = np.transpose(arr3, axes=(2, 0, 1)) # shape(5,3,4) -
广播机制¶
import numpy as np
arr1 = np.random.randint(0, 10, size=(3, 5)) # shape(3,5)
arr2 = np.random.randint(0, 10, 5)
arr3 = arr1 + arr2 # 广播
# 打印结果
#[[2 3 5 4 6]
# [8 1 3 1 9]
# [4 0 5 5 2]]
#----------------------
#[2 3 3 1 0]
#----------------------
#[[ 4 6 8 5 6]
# [10 4 6 2 9]
# [ 6 3 8 6 2]]
arr1 = np.random.randint(0, 10, size=(3, 5)) # shape(3,5)
arr2 = np.random.randint(0, 10, 3).reshape(3, 1)
arr3 = arr1 + arr2
# 打印结果
#[[5 0 2 5 5]
# [9 0 8 5 9]
# [5 4 7 1 8]]
#----------------------
#[[9]
# [6]
# [7]]
----------------------
#[[14 9 11 14 14]
# [15 6 14 11 15]
# [12 11 14 8 15]]
2. Pandas¶
-
数据结构¶
- Series(一维数据)
import pandas as pd import numpy as np data = np.arange(2, 10, 1) s1 = pd.Series(data=data) s2 = pd.Series(data=data, index=list('abcdefhi')) s3 = pd.Series(data={'a': 2, 'b': 3, 'c': 4})- DataFrame (二维数据)
import numpy as np import pandas as pd df = pd.DataFrame(data=np.random.randint(0, 100, size=(10, 2)), columns=['column1', 'column2']) -
数据的存储¶
import numpy as np import pandas as pd df = pd.DataFrame(data=np.random.randint(0, 100, size=(10, 2)), columns=['column1', 'column2']) # 保存 df.to_csv('./data.csv', header=True, index=True) # 加载 data = pd.read_csv('./data.csv', header=[0], index_col=0) -
数据清洗¶
# 1、重复数据过滤 df.duplicated() # 判断是否存在重复数据 df.drop_duplicates() # 删除重复数据 # 2、空数据过滤 df.isnull() # 判断是否存在空数据，存在返回True，否则返回False df.dropna(how = 'any') # 删除空数据 df.fillna(value=-1) # 填充空数据 # 3、指定行或者列过滤 del df['color'] # 直接删除某列 d f.drop(labels = ['price'],axis = 1)# 删除指定列 df.drop(labels = [0,1,5],axis = 0) # 删除指定行
3. Matplotlib¶
-
图像绘制
import numpy as np import matplotlib.pyplot as plt # 图形绘制 x = np.linspace(0, 2 * np.pi) # x轴 y = np.sin(x) # y轴 plt.figure(figsize=(9, 6)) # 调整尺寸 plt.plot(x, y) # 绘制线形图 plt.show()
4. 多元线性方程¶
-
正规方程
\(J(θ)=\frac{1}{2}\sum_{i=0}^n(h_{θ(x_i)}-y_i)^2\)
\(J(θ)=\frac{1}{2}\sum_{i=0}^n(h_{θ(x_i)}-y_i)(h_{θ(x_i)}-y_i)\)
\(J(θ)=\frac{1}{2}(hθ-y)^T(hθ-y)\)
\(W = (X^TX)^{-1}X^Ty\)
w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)