# Re-execute full model after reset: multivariable regression using (x_Q, a, b) and a_p
import numpy as np
import matplotlib.pyplot as plt

# Simulated ECC data
n_samples = 12
k_values = np.array([3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80])
x_Q = np.linspace(0.5, 2.0, n_samples)
y_Q = np.linspace(1.0, 3.0, n_samples)
a_curve = np.linspace(1, 3, n_samples)
b_curve = np.linspace(-1, 2, n_samples)
xy = x_Q + y_Q

# Hecke coefficients from ψ(t)
a_p = np.array([1.0, -1.0, 0.0, 2.0, -2.0, 1.0, -1.0, 3.0, -3.0, 2.0, 0.0, -2.0])
P = len(a_p)

# Build multivariable feature matrix
X_parts = []
for i in range(P):
    for r in range(1, 6):
        X_parts.append(a_p * (xy ** r))
        X_parts.append(a_p * (a_curve ** r))
        X_parts.append(a_p * (b_curve ** r))
X = np.column_stack(X_parts)

# Least squares regression
coeffs, _, _, _ = np.linalg.lstsq(X, k_values, rcond=None)
k_pred = X @ coeffs

# Error metrics
mse = np.mean((k_pred - k_values) ** 2)
max_err = np.max(np.abs(k_pred - k_values))
mean_err = np.mean(np.abs(k_pred - k_values))

# Output
print("\nMultivariable Spectral Regression (k from ψ(t), x_Q, a, b)")
print("=" * 65)
print(f"MSE:             {mse:.6e}")
print(f"Max Error:       {max_err:.6f}")
print(f"Mean Error:      {mean_err:.6f}")
print(f"k (true):        {k_values.tolist()}")
print(f"k (predicted):   {np.round(k_pred, 6).tolist()}")
print(f"First 6 Coeffs:  {np.round(coeffs[:6], 6).tolist()}")

# Visualization
plt.figure(figsize=(8, 5))
plt.plot(k_values, k_values, 'k--', label='Ideal')
plt.plot(k_values, k_pred, 'o-', label='Predicted')
plt.xlabel("True k")
plt.ylabel("Predicted k")
plt.title("Spectral Fit: Multivariable Hecke Model (k ≈ ψ(x,a,b))")
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()


Multivariable Spectral Regression (k from ψ(t), x_Q, a, b)
=================================================================
MSE:             1.142697e-25
Max Error:       0.000000
Mean Error:      0.000000
k (true):        [3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80]
k (predicted):   [3.0, 5.0, 8.0, 12.0, 17.0, 23.0, 30.0, 38.0, 47.0, 57.0, 68.0, 80.0]
First 6 Coeffs:  [0.000527, 0.00011, 0.003505, 0.006097, 0.00205, -0.004563]
2025-05-10 19:10:55.795 Python[37714:21939219] +[IMKClient subclass]: chose IMKClient_Modern
2025-05-10 19:10:55.795 Python[37714:21939219] +[IMKInputSession subclass]: chose IMKInputSession_Modern