try1

R1/TheParabolaMethod.py

@@ -0,0 +1,105 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[25]:
+
+
+from numpy import sign
+from math import cos
+
+
+# In[26]:
+
+
+def f(x):
+    return cos(x)/x**2
+
+def find_convex_triple(x0, a, b, eps, i=1):
+    h = (b-a)/10
+    while (f(x0+h)>f(x0))&(f(x0-h)>f(x0)):
+        h /= 2
+        if (f(x0+h)-f(x0)<=eps)|(f(x0-h)-f(x0)<=eps):
+            return x0
+    if f(x0+h)<=f(x0):
+        x1 = x0 + h
+        x2 = x0 + h*2**(i)
+        f0 = f(x0)
+        while (f0<f(x1))|(f(x2)<f(x1))|(f0+f(x2)-2*f(x1)<=0):
+            i+=1
+            x1 = x0 + h*2**(i-1)
+            x2 = x0 + h*2**(i)
+    else:
+        x1 = x0 - h
+        x2 = x0 - h*2**(i)
+        f0 = f0
+        while (f0<f(x1))|(f(x2)<f(x1))|(f0+f(x2)-2*f(x1)<=0):
+            i+=1
+            x1 = x0 - h*2**(i-1)
+            x2 = x0 - h*2**(i)       
+    return (x0, x1, x2)
+
+def get_top(x1, x2, x3, f1, f2, f3):
+    return (x1+x2)/2 + (f2-f1)*(x3-x2)*(x3-x1)/(2*(f1*(x2-x3)+f2*(x3-x1)+f3*(x1-x2)))
+
+def sort(points):
+    for i in range(3,0,-1):
+        for j in range(i):
+            if points[j][1] > points[j+1][1]:
+                points[j], points[j+1] = points[j+1], points[j]
+    return points
+
+
+# In[27]:
+
+
+def method(x0, eps, a, b, count=1):
+    try:
+        x1, x2, x3 = find_convex_triple(x0, a, b, eps)
+    except:
+        x0 = find_convex_triple(x0, a, b, eps)
+    x4 = get_top(x1, x2, x3, f(x1), f(x2), f(x3))
+    f1 = f(x1)
+    f2 = f(x2)
+    f3 = f(x3)
+    f4 = f(x4)
+    points = sort([(x1, f1), (x2, f2), (x3, f3), (x4, f4)])
+    print(f"Номер итерации: {count}   x1 = {points[0][0]:.4f} f1 = {points[0][1]:.4f}\n\t\t    x2 = {points[1][0]:.4f} f2 = {points[1][1]:.4f}\n\t\t    x3 = {points[2][0]:.4f} f3 = {points[2][1]:.4f}\n\t\t    x4 = {points[3][0]:.4f} f4 = {points[3][1]:.4f}\n")
+    while points[1][1] - points[0][1] >= eps:
+        if sign(points[1][0] - points[0][0]) == sign(points[2][0] - points[0][0]) == -sign(points[3][0] - points[0][0]):
+            count += 1
+            x3 = points[3][0]
+            x2 = points[1][0]
+            x1 = points[0][0]
+            x4 = get_top(x1, x2, x3, f(x1), f(x2), f(x3))
+            f1 = f(x1)
+            f2 = f(x2)
+            f3 = f(x3)
+            f4 = f(x4)
+            points = sort([(x1, f1), (x2, f2), (x3, f3), (x4, f4)])
+            print(f"Номер итерации: {count}   x1 = {x1:.4f} f1 = {f1:.4f}\n\t\t    x2 = {x2:.4f} f2 = {f2:.4f}\n\t\t    x3 = {x3:.4f} f3 = {f3:.4f}\n\t\t    x4 = {x4:.4f} f4 = {f4:.4f}\n")
+        else:
+            count += 1
+            x3 = points[2][0]
+            x2 = points[1][0]
+            x1 = points[0][0]
+            x4 = get_top(x1, x2, x3, f(x1), f(x2), f(x3))
+            f1 = f(x1)
+            f2 = f(x2)
+            f3 = f(x3)
+            f4 = f(x4)
+            points = sort([(x1, f1), (x2, f2), (x3, f3), (x4, f4)])
+            print(f"Номер итерации: {count}   x1 = {x1:.4f} f1 = {f1:.4f}\n\t\t    x2 = {x2:.4f} f2 = {f2:.4f}\n\t\t    x3 = {x3:.4f} f3 = {f3:.4f}\n\t\t    x4 = {x4:.4f} f4 = {f4:.4f}\n")
+    print(f"argmin(f) = {points[0][0]:.4f}")
+
+
+# In[28]:
+
+
+method(9, 0.0001, 7, 11)
+
+
+# In[ ]:
+
+
+
+

R1/ThePolylineMethod.py

@@ -0,0 +1,77 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[196]:
+
+
+import numpy as np
+from math import cos, sin
+
+
+# In[248]:
+
+
+def f(x):
+    return cos(x)/x**2
+
+def df(x):
+    return -sin(x)/x**2 - 2*cos(x)/x**3
+
+def get_R(a, b, h):
+    X = np.arange(a, b+h, h)
+    R = abs(df(X[0]))
+    for i in range(X.size-1):
+        if abs(df(X[i])) >= R:
+            R = df(X[i])
+    return R + h
+
+def x(a, b, R):
+    return (a+b)/2 + (f(a)-f(b))/(2*R)
+
+def m(a, b, R):
+    return R*(a-b)/2 + (f(a)+f(b))/2
+
+
+# In[249]:
+
+
+def Method(a, b, h, eps, get_R, x, m, count=1, q=0, k=0):
+    R = get_R(a, b, h)
+    num = 0
+    digits = eps
+    while digits < 1:
+        digits *= 10
+        num += 1
+    X = np.array([])
+    M = np.array([])
+    x = x(a, b, R)
+    m = m(a, b, R)
+    while f(x) - m >= eps:
+        delta = (f(x)-m)/2/R
+        print(f"Номер итерации: {count}  x = {x:.{num}f}  f(x) = {f(x):.{num}f}  m = {m:.{num}f}  delta = {delta:.{num}f}")
+        X = np.append(X, [x-delta, x+delta])
+        M = np.append(M, [(f(x)+m)/2, (f(x)+m)/2])
+        q = M[0]
+        for i in range(M.size-1):
+            if M[i] <= q:
+                q = M[i]
+                k = i
+        M = np.delete(M, k)
+        x = X[k]
+        X = np.delete(X, k)
+        m = q
+        count += 1
+    print(f"Номер итерации: {count}  x = {x:.{num}f}  f(x) = {f(x):.{num}f}  R = {R:.{num}f}")
+
+
+# In[252]:
+
+
+Method(7, 11, 0.1, 0.0000001, get_R, x, m)
+
+
+# In[ ]:
+
+
+
+