kleinere Optimierungen

runge_kutta.py

@@ -40,4 +40,84 @@ def rk4_step(ode, t: float, v: np.ndarray, h: float) -> np.ndarray:
     k2 = ode(t + 0.5 * h, v + 0.5 * h * k1)
     k3 = ode(t + 0.5 * h, v + 0.5 * h * k2)
     k4 = ode(t + h, v + h * k3)
-    return v + (h / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4)
+    return v + (h / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4)
+
+def rk4_end(ode, t0: float, v0: np.ndarray, weite: float, schritte: int, fein: bool = False):
+    h = weite / schritte
+    t = float(t0)
+    v = np.array(v0, dtype=float, copy=True)
+
+    for _ in range(schritte):
+        if not fein:
+            v_next = rk4_step(ode, t, v, h)
+        else:
+            v_grob = rk4_step(ode, t, v, h)
+            v_half = rk4_step(ode, t, v, 0.5 * h)
+            v_fein = rk4_step(ode, t + 0.5 * h, v_half, 0.5 * h)
+            v_next = v_fein + (v_fein - v_grob) / 15.0
+
+        t += h
+        v = v_next
+
+    return t, v
+
+# RK4 mit Simpson bzw. Trapez
+def rk4_integral( ode, t0: float, v0: np.ndarray, weite: float, schritte: int, integrand_at, fein: bool = False, simpson: bool = True, ):
+
+    h = weite / schritte
+    habs = abs(h)
+
+    t = float(t0)
+    v = np.array(v0, dtype=float, copy=True)
+
+    if simpson and (schritte % 2 == 0):
+        f0 = float(integrand_at(t, v))
+        odd_sum = 0.0
+        even_sum = 0.0
+        fN = None
+
+        for i in range(1, schritte + 1):
+            if not fein:
+                v_next = rk4_step(ode, t, v, h)
+            else:
+                v_grob = rk4_step(ode, t, v, h)
+                v_half = rk4_step(ode, t, v, 0.5 * h)
+                v_fein = rk4_step(ode, t + 0.5 * h, v_half, 0.5 * h)
+                v_next = v_fein + (v_fein - v_grob) / 15.0
+
+            t += h
+            v = v_next
+
+            fi = float(integrand_at(t, v))
+            if i == schritte:
+                fN = fi
+            elif i % 2 == 1:
+                odd_sum += fi
+            else:
+                even_sum += fi
+
+        S = f0 + fN + 4.0 * odd_sum + 2.0 * even_sum
+        s = (habs / 3.0) * S
+        return t, v, s
+
+    f_prev = float(integrand_at(t, v))
+    acc = 0.0
+
+    for _ in range(schritte):
+        if not fein:
+            v_next = rk4_step(ode, t, v, h)
+        else:
+            v_grob = rk4_step(ode, t, v, h)
+            v_half = rk4_step(ode, t, v, 0.5 * h)
+            v_fein = rk4_step(ode, t + 0.5 * h, v_half, 0.5 * h)
+            v_next = v_fein + (v_fein - v_grob) / 15.0
+
+        t += h
+        v = v_next
+
+        f_cur = float(integrand_at(t, v))
+        acc += 0.5 * (f_prev + f_cur)
+        f_prev = f_cur
+
+    s = habs * acc
+    return t, v, s