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This commit is contained in:
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32.502345269453031,31.70700584656992
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53.426804033275019,68.77759598163891
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61.530358025636438,62.562382297945803
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47.475639634786098,71.546632233567777
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59.813207869512318,87.230925133687393
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55.142188413943821,78.211518270799232
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52.550014442733818,71.300879886850353
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45.419730144973755,55.165677145959123
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58.16847071685779,75.392870425994957
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56.727208057096611,81.43619215887864
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48.955888566093719,60.723602440673965
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44.687196231480904,82.892503731453715
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60.297326851333466,97.379896862166078
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38.816817537445637,56.877213186268506
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66.189816606752601,83.878564664602763
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65.41605174513407,118.59121730252249
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47.48120860786787,57.251819462268969
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41.57564261748702,51.391744079832307
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51.84518690563943,75.380651665312357
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59.370822011089523,74.765564032151374
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57.31000343834809,95.455052922574737
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63.615561251453308,95.229366017555307
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46.737619407976972,79.052406169565586
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50.556760148547767,83.432071421323712
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52.223996085553047,63.358790317497878
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35.567830047746632,41.412885303700563
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42.436476944055642,76.617341280074044
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58.16454011019286,96.769566426108199
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61.89622268029126,77.768482417793024
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33.093831736163963,50.719588912312084
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50.030174340312143,81.536990783015028
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49.239765342753763,72.111832469615663
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48.149858891028863,66.224957888054632
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25.128484647772304,53.454394214850524
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@ -0,0 +1,59 @@
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# https://blog.csdn.net/qq_37236745/article/details/103698507
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import numpy as np
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# compute loss
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def compute_error(b, w, points):
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totalError = 0
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for i in range(len(points)):
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x = points[i, 0]
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y = points[i, 1]
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totalError += (y - (w * x + b)) ** 2
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return totalError / float(len(points)) # average
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# compute gradient
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def step_gradient(b_current, w_current, points, learningRate):
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b_gradient = 0
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w_gradient = 0
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N = float(len(points))
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for i in range(len(points)):
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x = points[i, 0]
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y = points[i, 1]
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b_gradient += 2 * ((w_current * x) + b_current - y)
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w_gradient += 2 * x * ((w_current * x) + b_current - y)
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b_gradient = b_gradient / N
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w_gradient = w_gradient / N
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new_b = b_current - (learningRate * b_gradient)
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new_w = w_current - (learningRate * w_gradient)
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return [new_b, new_w]
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def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations): # num_iteration 迭代次数
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b = starting_b
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w = starting_w
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error = np.zeros(num_iterations)
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for i in range(num_iterations):
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b, w = step_gradient(b, w, np.array(points), learning_rate)
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error[i] = compute_error(b, w, points)
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return [b, w],error
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def run():
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points = np.genfromtxt("data.txt", delimiter=",")
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learning_rate = 0.000001
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initial_b = np.random.random()
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initial_w = np.random.random()
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num_iterations = 1000
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print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
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.format(initial_b, initial_w,
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compute_error(initial_b, initial_w, points)))
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print("Running...")
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[b, w],error = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
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print("After {0} iterations at b = {1}, w = {2}, error = {3}"
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.format(num_iterations, b, w,
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compute_error(b, w, points)))
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import matplotlib.pyplot as plt
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fig, bx = plt.subplots(figsize=(8, 6))
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bx.plot(np.arange(num_iterations), error, 'r')
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bx.set_xlabel('Iterations')
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bx.set_ylabel('Cost')
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bx.set_title('Error vs. Training Epoch')
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plt.show()
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run()
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import numpy as np
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import pandas as pd
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a = np.array([1,2])
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b = a.reshape(1,2)
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# b = np.mat(a)
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c = np.array([[1,2],[1,3],[1,4]])
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# d = c.reshape(3,2)
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d = np.mat(c)
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print(f"a is {a} {a.shape} shape {a.shape[0]}, b is {b} {b.shape} shape {b.shape[0],b.shape[1]}, "
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f"c is {c} {c.shape}, d is {d} {d.shape}")
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# 注意 e = np.mat([[2],[1],[3]]) 是错误的
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# 矩阵与矩阵相乘， 矩阵与数组相乘完全不同
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e = np.array([[2],[1],[3]])
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print(f"c*e is {c*e}\n")
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f = np.mat([[2],[1]])
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print(f" c shape is {c}, and f shape is {f} \n"
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f"c*f ",c*f)
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# https://www.cnblogs.com/judejie/p/8999832.html
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# 工作年限与收入之间的散点图
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# 导入第三方模块
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import pandas as pd
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import matplotlib.pyplot as plt
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import seaborn as sns
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import numpy as np
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# 导入数据集
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# income = pd.read_csv(r'Salary_Data.csv')
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# 绘制散点图
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# sns.lmplot(x = 'YearsExperience', y = 'Salary', data = income, ci = None)
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# 显示图形
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class GD():
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def __init__(self,data,w,b, lr, nstep):
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self.data = data
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self.w = w
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self.b = b
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self.lr = lr
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self.nstep = nstep
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def loss(self,w,b):
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x,y = self.data[:, 0],self.data[:, 1]
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loss = 0
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for i in range(self.data.shape[0]):
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loss += (w*x[i]+b-y[i])**2
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print(f"loss {loss}")
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return loss/float(self.data.shape[0])
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def grad(self,w,b,x,y):
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x_grad,y_grad = 2*(w*x+b-y)*x,2*(w*x+b-y)
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return x_grad,y_grad
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def step_grad(self,w,b):
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x, y = self.data[:, 0], self.data[:, 1]
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w_gradient = 0
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b_gradient = 0
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for i in range(self.data.shape[0]):
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w_tmp,b_tmp = self.grad(w,b,x[i],y[i])
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w_gradient += w_tmp
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b_gradient += b_tmp
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w_new = w - w_gradient/self.data.shape[0]*self.lr
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b_new = b - b_gradient /self.data.shape[0] * self.lr
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return w_new,b_new
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def gradientDescent(self):
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# history = np.empty( (self.nstep+1, 2) )
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error = np.zeros(self.nstep)
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w,b = self.w,self.b
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for i in range(self.nstep):
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w,b = self.step_grad(w, b)
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error[i]=self.loss(w,b)
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return w,b,error
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w = 12
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b =12
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income = pd.read_csv(r'Salary_Data.csv')
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data = np.array(income.values)
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nstep = 1000
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lr = 0.001
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gd = GD(data,w,b,lr,nstep)
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w,b,error = gd.gradientDescent()
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print("w,b is :",w,b)
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x = data[:,0]
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y = data[:,1]
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plt.scatter(x,y)
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# plt.legend()
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plt.plot(x, w*x+b, 'r')
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plt.show()
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plt.plot(np.arange(nstep), error, 'r')
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plt.show()
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# 回归参数 11768.548124439758 10167.865862562581
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import numpy as np
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import math
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from matplotlib import pyplot as plt
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import torch
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def f(r):
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g = torch.tan(r)+9*torch.tan(3/4*math.pi-r)
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return g
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def drawfig(f):
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x = torch.linspace(1.1/4*math.pi,0.99/2*math.pi,100)
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y = f(x)
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plt.plot(x,y)
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plt.show()
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r = torch.tensor([1.16/4*np.pi], requires_grad=True)
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optimizer = torch.optim.Adam([r], lr=1e-4)
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for step in range(10000):
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pred = f(r)
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optimizer.zero_grad()
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pred.backward()
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optimizer.step()
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if step % 200 == 0:
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print (f'step {step}: r = {r.tolist()}, f(r) = {pred.item()}')
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drawfig(f)
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import math
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import numpy as np
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import matplotlib.pyplot as plt
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def f(r):
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g = np.tan(r)+9*np.tan(3/4*np.pi-r)
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return g
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def drawfig(f):
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x = np.linspace(1.1/4*np.pi,0.99/2*np.pi,100)
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y = f(x)
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# print(y)
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plt.plot(x,y)
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plt.show()
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def grad(r):
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g = 1.0/(np.cos(r)**2) - 9.0/(np.cos(3/4*np.pi-r)**2)
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return g
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def gradientDescent(f,r0, eta, nstep):
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r_history = np.zeros(nstep+1)
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f_history = np.zeros(nstep+1)
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r_history[0] = r0
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f_history[0] = f(r0)
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r = r0
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for i in range(1,nstep+1):
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r = r - eta * grad(r)
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r_history[i] = r
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f_history[i] = f(r)
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print(f"r is :{r} f(r) is {f(r)}")
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return r_history,f_history
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# print(f(1/3*np.pi))
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drawfig(f)
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x,y = gradientDescent(f, 1.12/4*np.pi, 0.0001*np.pi, 10000)
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plt.plot(x,y)
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plt.show()
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