bisekcja

bisekcja/bisekcja.py

@@ -0,0 +1,45 @@
+from math import fabs
+import matplotlib.pyplot as plt
+import numpy as np
+
+def f(x):
+    left_side = 2*np.cos(x + (np.pi/6)) + x**2
+    right_side = 4 * x - 3
+    return left_side - right_side
+
+def oblicz(a,b):
+    x1,x2 = a,b
+    x = 0
+    epsi = 0.01
+
+    while(fabs(f(x)) > epsi):
+        x = (x1 + x2) / 2
+        y = f(x)
+        y1 = f(x1)
+        if y*y1 < 0:
+            x2 = x
+        elif y*y1 > 0:
+            x1 = x
+    return x
+
+a,b = -2,7
+
+print(f"Pierwiastek: {round(oblicz(a,b), 4)}")
+
+x = np.linspace(-15, 15, 1000)
+y = f(x)
+
+plt.figure(figsize=(10, 6))
+plt.plot(x, y, label=r"$f(x) = 2\cos(x + \frac{\pi}{6}) + x^2 - (4x - 3)$", color="blue")
+plt.axhline(0, color="black", linestyle="--", linewidth=0.8)  # Add x-axis
+plt.axvline(0, color="black", linestyle="--", linewidth=0.8)  # Add y-
+
+plt.axvline(a, color="red", linestyle="-", linewidth=2, label="a = {:.2f}".format(a))
+plt.axvline(b, color="green", linestyle="-", linewidth=2, label="b = {:.2f}".format(b))
+
+plt.title("Bisekcja")
+plt.xlabel("x")
+plt.ylabel("f(x)")
+plt.legend()
+plt.grid()
+plt.show()

gaussa/gaussa.py

@@ -0,0 +1,44 @@
+def gaussa(a, b):
+    n = len(b)
+
+    for s in range(n - 1):
+        for i in range(s + 1, n):
+            factor = a[i][s] / a[s][s]
+            for j in range(s, n):
+                a[i][j] -= factor * a[s][j]
+            b[i] -= factor * b[s]
+
+    x = [0] * n
+    for i in range(n - 1, -1, -1):
+        x[i] = (b[i] - sum(a[i][j] * x[j] for j in range(i + 1, n))) / a[i][i]
+
+    return x
+
+
+A = [
+    [4.88, -2.91, 1.34],
+    [1.34, 5.3, -3.31],
+    [2.18, -3.49, 6.7]
+]
+
+B = [7.86, -2.28, 4.47]
+
+solutions = gaussa(A, B)
+
+print("Macierz A:")
+for x in A:
+    for a in x:
+        print(round(a, 2), end="  ")
+    print()
+print()
+
+print("Macierz B:")
+for b in B:
+    print(round(b, 2), end="  ")
+print("\n")
+
+print("Wynik: ")
+i = 1
+for x in solutions:
+    print(f"x{i} = {round(x, 2)}")
+    i += 1

rungego-kutty/rungego-kutty.py

@@ -0,0 +1,33 @@
+import numpy as np
+
+x0 = 1.7
+xk = 2.7
+h = 0.1
+y0 = 5.3
+
+def f(x, y):
+    return x**2 + np.cos(y / np.pi)
+
+def runge_kutta_4(f, x0, y0, h, xk):
+    n = int((xk - x0) / h) + 1
+    x = [x0 + i * h for i in range(n)]
+    y = [0] * n
+    y[0] = y0
+
+    print("Tabela wyników:")
+    print(f"{'i':<5}{'x':<10}{'y':<15}{'k1':<10}{'k2':<10}{'k3':<10}{'k4':<10}{'Δy':<10}")
+
+    for i in range(1, n):
+        k1 = h * f(x[i-1], y[i-1])
+        k2 = h * f(x[i-1] + h/2, y[i-1] + k1/2)
+        k3 = h * f(x[i-1] + h/2, y[i-1] + k2/2)
+        k4 = h * f(x[i-1] + h, y[i-1] + k3)
+        Δy = (k1 + 2*k2 + 2*k3 + k4) / 6
+        y[i] = y[i-1] + Δy
+        print(f"{i-1:<5}{x[i-1]:<10.2f}{y[i-1]:<15.5f}{k1:<10.5f}{k2:<10.5f}{k3:<10.5f}{k4:<10.5f}{Δy:<10.5f}")
+
+    print(f"{n-1:<5}{x[-1]:<10.2f}{y[-1]:<15.5f}")
+
+    return x, y
+
+x, y = runge_kutta_4(f, x0, y0, h, xk)