new

梯度下降/梯度下降解决面积问题 tensor.py

@@ -0,0 +1,25 @@
+import  numpy as np
+import math
+from    matplotlib import pyplot as plt
+import  torch
+
+def f(r):
+    g = 9*torch.tan(r)+9*torch.tan(3/4*math.pi-r)
+    return g
+def drawfig(f):
+
+    x = torch.linspace(1.1/4*math.pi,0.99/2*math.pi,100)
+    y = f(x)
+    plt.plot(x,y)
+    plt.show()
+
+r = torch.tensor([1.16/4*np.pi], requires_grad=True)
+optimizer = torch.optim.Adam([r], lr=1e-4)
+for step in range(10000):
+    pred = f(r)  #1 向前
+    optimizer.zero_grad() #归0
+    pred.backward()  #向后
+    optimizer.step()  #下一步
+    if step % 200 == 0:
+        print (f'step {step}: r = {r.tolist()}, f(r) = {pred.item()}')
+drawfig(f)

梯度下降/梯度下降解决面积问题.py

@@ -0,0 +1,39 @@
+import math
+import numpy as np
+import matplotlib.pyplot as plt
+
+def f(r):
+    g = 9*np.tan(r)+9*np.tan(3/4*np.pi-r)
+    return g
+
+def drawfig(f):
+
+    x = np.linspace(1.01/4*np.pi,0.99/2*np.pi,100)
+    y = f(x)
+    # print(y)
+    plt.plot(x,y)
+    plt.show()
+
+def grad(r):
+    g = 9.0/(np.cos(r)**2) - 9.0/(np.cos(3/4*np.pi-r)**2)
+    return g
+
+def gradientDescent(f,r0, eta, nstep):
+    r_history = np.zeros(nstep+1)
+    f_history = np.zeros(nstep+1)
+    r_history[0] = r0
+    f_history[0] = f(r0)
+    r = r0
+    for i in range(1,nstep+1):
+        r = r - eta * grad(r)
+        r_history[i] = r
+        f_history[i] = f(r)
+        print(f"r is :{r}   f(r) is {f(r)}")
+    return r_history,f_history
+# print(f(1/3*np.pi))
+drawfig(f)
+x,y = gradientDescent(f, 1.22/4*np.pi, 0.0001*np.pi, 10000)
+plt.plot(x,y)
+plt.show()
+
+