feat: made explicit gradient function for 2d and 3d case, might be better to...

feat: made explicit gradient function for 2d and 3d case, might be better to create a N dimensional case but icba honestly

derive_and_min-max.py

 from rf_methods import rec_bisection, rec_regula_falsi, iter_bisection, \
     iter_regula_falsi
 from Dual_Numbers import Dual_Number
+from typing import Callable
 import numpy as np
 
 
@@ -46,41 +47,39 @@ import numpy as np
 #     return h(Dual_Number(x, 1))
 
 
-def P(x: Dual_Number, y: Dual_Number) -> float:
+def A(x: Dual_Number, y: Dual_Number) -> float:
     return (3 * (x * x) * y + 2 * x * (y * y) - x * y + 2 * x - 1).d
 
 
-def delPdelx(x: float, y: float) -> float:
-    return P(Dual_Number(x, 1), y)
-
-
-def delPdely(x: float, y: float) -> float:
-    return P(x, Dual_Number(y, 1))
+def B(x: Dual_Number, y: Dual_Number, z: Dual_Number) -> float:
+    return (x * y * z + x * x + y * y).d
 
 
-def Z(x: Dual_Number, y: Dual_Number, z: Dual_Number) -> float:
-    return (x * y * z + x * x + y * y).d
+def C(x: Dual_Number, y: Dual_Number, z: Dual_Number) -> float:
+    return (x * Dual_Number.exp(y * y + z * z)).d
 
 
-def delZdelx(x: float, y: float, z: float) -> float:
-    return Z(Dual_Number(x, 1), y, z)
+def D(x: Dual_Number, y: Dual_Number) -> float:
+    return (Dual_Number.sin(x) * Dual_Number.cos(y) + Dual_Number.sin(y) * Dual_Number.cos(x)).d
 
 
-def delZdely(x: float, y: float, z: float) -> float:
-    return Z(x, Dual_Number(y, 1), z)
+def grad2D(x: float, y: float, func: Callable[[Dual_Number, Dual_Number], float]) -> tuple[float, float]:
+    return (func(Dual_Number(x, 1), y), func(x, Dual_Number(y, 1)))
 
 
-def delZdelz(x: float, y: float, z: float) -> float:
-    return Z(x, y, Dual_Number(z, 1))
+def grad3D(x: float, y: float, z: float, func: Callable[[Dual_Number, Dual_Number, Dual_Number], float]) -> tuple[float, float, float]:
+    return (func(Dual_Number(x, 1), y, z), func(x, Dual_Number(y, 1), z), func(x, y, Dual_Number(z, 1)))
 
 
 if __name__ == "__main__":
-    print(delPdelx(1, 1))
-    print(delPdely(1, 1))
-    print()
-    print(delZdelx(0, 1, -1))
-    print(delZdely(0, 1, -1))
-    print(delZdelz(0, 1, -1))
+    print(f"3x²y + 2xy² − xy + 2x − 1, P = (1, 1)\t∇ = {grad2D(1, 1, A)}")
+    print(f"xyz + x² + y², P = (0, 1, -1)\t∇ = {grad3D(0, 1, -1, B)}")
+    print(f"xe^(y² + z²), P = (1, 1, 1)\t∇ = {grad3D(1, 1, 1, C)}")
+    print(
+        f"sin(x)cos(y) + sin(y)cos(x), P(π / 4, π / 4)\t∇ = {grad2D(np.pi / 4, np.pi / 4, D)}")
+    # print(delZdelx(0, 1, -1))
+    # print(delZdely(0, 1, -1))
+    # print(delZdelz(0, 1, -1))
     # Example for f(x)
     # start = -6
     # stop = -1