simpson

Author: FelixGaudin

NumericalIntegration/simpsion_3_8_felix.py

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+from simpson_1_3 import simpson_1_3
+def simpson_3_8(f, n):
+    def simpson_(f, n, a, b):
+        h = (b - a)/n
+        s = 0
+        i = 0
+        xData = []
+        for k in range(n + 1):
+            xData.append(a + k * h)
+        if n % 3:
+            s += simpson_1_3(f, n)(xData[0], xData[1])
+            i = n % 3
+        while i < n - 2 :
+            add = (3*h/8) * (f(xData[i]) + 3 * f(xData[i+1]) + 3*f(xData[i+2]) + f(xData[i+3]))
+            s += add
+            i += 3
+        return s
+    return lambda a, b: simpson_(f, n, a, b)
+
+
+if __name__ == "__main__":
+    def f(x): return 1
+    F = simpson_3_8(f, 200000)
+    print(F(0, 2))
+    def g(x): return x
+    G = simpson_3_8(g, 2000)
+    print(G(0, 3))

NumericalIntegration/simpson_1_3_felix.py

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+#simpson 1/3 - Felix
+from trapezoid import trapezoid
+def simpson_1_3(f, n):
+    def simpson_(f, n, a, b):
+        h = (b - a)/n
+        s = 0
+        i = 0
+        xData = []
+        for k in range(n + 1):
+            xData.append(a + k * h)
+        if n % 2:
+            s += trapezoid(f, n)(xData[0], xData[1])
+            i = 1
+        while i < n - 1:
+            add = (h/3) * (f(xData[i]) + 4 * f(xData[i+1]) + f(xData[i+2]))
+            s += add
+            i += 2
+        return s
+    return lambda a, b: simpson_(f, n, a, b)
+
+
+if __name__ == "__main__":
+    # def f(x): return 1
+    # F = simpson_1_3(f, 100)
+    # print(F(0, 2))
+    def g(x): return x
+    G = simpson_1_3(g, 101)
+    print(G(0, 1.5))
+    print(G(1.5, 3))