auto_math_trust_regions_and_optimization_4

Snippet from Math-Trust-Regions-and-Optimization.md

def diagnose_negative_rho(g, B, Delta, f, x):
    """Check common causes of negative rho."""
    # Test gradient accuracy
    grad_error = check_gradient(f, x, g)
    print(f"Gradient error: {grad_error:.2e}")
    
    # Test Hessian conditioning
    eigvals = np.linalg.eigvalsh(B)
    cond = eigvals.max() / eigvals.min()
    print(f"Hessian condition number: {cond:.2e}")
    
    # Suggest fixes
    if grad_error > 1e-6:
        print("Fix: Improve gradient computation")
    if cond > 1e8:
        print("Fix: Add regularization: B + lambda*I")
    if Delta > 1.0:
        print("Fix: Reduce initial Delta_0")