Initial Refactoring of yoshi_otter and Test Implementation

yoshi_otter/algebra/integral/double.py

@@ -0,0 +1,79 @@
+from typing import Callable
+
+
+class Double:
+
+    def __init__(self, function: Callable[[float, float], float]):
+        self.f = function
+
+    def riemann(self, a: float, b: float, c: float, d: float,
+                n: int = 10 ** 4, m: int = None) -> float:
+
+        if m is None:
+            m = n
+
+        dx = (b - a) / n
+        dy = (d - c) / m
+        kappa = a
+        psi = c
+        theta = 0
+
+        while (psi + dy) < d:
+
+            while (kappa + dx) < b:
+                theta = theta + self.f(kappa, psi)
+                kappa = kappa + dx
+
+            psi = psi + dy
+            kappa = a
+
+        return theta * dx * dy
+
+    def simpson(self, a: float, b: float, c: float, d: float,
+                n: int = 10 ** 4, m: int = None) -> float:
+
+        if m is None:
+            m = n
+
+        dx = (b - a) / n
+        dy = (d - c) / m
+
+        def x(i):
+            return a + i * dx
+
+        def y(i):
+            return c + i * dy
+
+        def g(i):
+
+            sigma = 0
+            upsilon = 0
+
+            zeta = 1
+            csi = 1
+
+            while zeta <= (m / 2):
+                sigma += self.f(x(i), y(2 * zeta - 1))
+                zeta += 1
+
+            while csi <= ((m / 2) - 1):
+                upsilon += self.f(x(i), y(2 * csi))
+                csi += 1
+
+            return (dy / 3) * (self.f(x(i), y(0)) + self.f(x(i), y(m)) + 4 * sigma + 2 * upsilon)
+
+        eta = 0
+        theta = 0
+
+        psi = 1
+        kappa = 1
+
+        while psi <= (n / 2):
+            eta += g(2 * psi - 1)
+            psi += 1
+
+        while kappa <= ((n / 2) - 1):
+            theta += g(2 * kappa)
+            kappa += 1
+
+        return (dx / 3) * (g(0) + g(n) + 4 * eta + 2 * theta)