Update app.py

app.py

@@ -62,8 +62,27 @@ def missing_for(action: str, hud: dict):
     return miss
 
 # ---------- Model ----------
-def Y_logistic(X, L, k, x0):
-    return float(L) / (1.0 + np.exp(-float(k) * (X - float(x0))))
+import numpy as np
+import matplotlib.pyplot as plt
+
+def Y_logistic_zero(X, L, k, x0):
+    """
+    Logistic-like yield function that forces Y(0) = 0.
+    L = maximum yield (asymptote)
+    k = slope parameter
+    x0 = inflection point (fertilizer where curve steepens)
+    """
+    return L * (1 - np.exp(-k * X)) / (1 + np.exp(-k * (X - x0)))
+
+# Example
+X = np.linspace(0, 150, 200)
+Y = Y_logistic_zero(X, L=1200, k=0.06, x0=60)
+
+plt.plot(X, Y)
+plt.xlabel("Fertilizer (lbs)")
+plt.ylabel("Yield")
+plt.title("Shifted logistic yield (Y(0)=0)")
+plt.show()
 
 def MPP_logistic(X, L, k, x0):
     e = np.exp(-float(k) * (X - float(x0)))