init commit

MonteCarlo_python.py

@@ -0,0 +1,85 @@
+import random
+import time
+
+from scipy.integrate import quad
+
+
+class Point:
+    x: float
+    y: float
+
+    def __init__(self, point: (float, float)):
+        self.x, self.y = point
+
+
+class LinearBounds:
+    lower: float
+    higher: float
+
+    def __init__(self, lower: float, higher: float):
+        self.lower = lower
+        self.higher = higher
+
+    def length(self) -> float:
+        return self.higher - self.lower
+
+    def get_random_value(self) -> float:
+        return random.uniform(self.lower, self.higher)
+
+
+class Bounds:
+    x: LinearBounds
+    y: LinearBounds
+
+    def __init__(self, x: LinearBounds, y: LinearBounds):
+        self.x = x
+        self.y = y
+
+    def area(self) -> float:
+        return self.x.length() * self.y.length()
+
+    def get_random_point(self) -> Point:
+        return Point((self.x.get_random_value(), self.y.get_random_value()))
+
+
+def function(x: float) -> float:
+    return x**4-4*x**3+18*x**2-12*x-69
+
+
+def getIsInside(p: Point) -> bool:
+    y_0: float = function(p.x)
+    if abs(y_0) > abs(p.y) and y_0*p.y >= 0:
+        return True
+
+    return False
+
+
+def getRealIntegral(bounds: LinearBounds) -> float:
+    return quad(function, bounds.lower, bounds.higher)[0]
+
+
+def main():
+    startTime = time.time()
+    pointsInside: int = 0
+    samples: int = 1000000
+    bounds = Bounds(LinearBounds(0, 20), LinearBounds(-100, 150000))
+
+    for i in range(samples):
+        toTestPoint = bounds.get_random_point()
+        if getIsInside(toTestPoint):
+            pointsInside += 1
+
+    integral = (pointsInside / samples) * bounds.area()
+    print(f"The approximated Integral of the function is: {integral:.2f}")
+
+    real_value: float = getRealIntegral(bounds.x)
+    print(f"The real Integral of the function is: {real_value:.2f}")
+
+    error: float = abs(real_value-integral)
+    print(f"That's an error of {error:.2f} or {(error/real_value)*100:.5f}% ")
+
+    print(f"And the whole thing took {time.time()-startTime:.5f} Seconds for {samples} samples")
+
+
+if __name__ == "__main__":
+    main()