feat(factor): add MarginFactor::propagate_with_alpha for EP damping

Mirrors TruncFactor: inherent damped-propagate method, trait impl
delegates with α=1.0. Existing goldens unchanged because cavity*new_msg
equals the previous marginal write when α=1.0.

src/factor/margin.rs

@@ -32,8 +32,11 @@ impl MarginFactor {
     }
 }
 
-impl Factor for MarginFactor {
-    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+impl MarginFactor {
+    /// Propagate this factor's message, optionally damping the update in
+    /// natural-parameter space. `alpha = 1.0` matches `Factor::propagate`
+    /// exactly; `alpha < 1.0` writes `α·new_msg + (1−α)·old_msg`.
+    pub(crate) fn propagate_with_alpha(&mut self, vars: &mut VarStore, alpha: f64) -> (f64, f64) {
         let marginal = vars.get(self.diff);
         let cavity = marginal / self.msg;
 
@@ -42,12 +45,18 @@ impl Factor for MarginFactor {
         }
 
         let new_msg = Gaussian::from_ms(self.m_obs, self.sigma);
-        let new_marginal = cavity * new_msg;
+        let damped = self.msg.damp_natural(new_msg, alpha);
         let old_msg = self.msg;
-        self.msg = new_msg;
-        vars.set(self.diff, new_marginal);
+        self.msg = damped;
+        vars.set(self.diff, cavity * damped);
 
-        old_msg.delta(new_msg)
+        old_msg.delta(damped)
+    }
+}
+
+impl Factor for MarginFactor {
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        self.propagate_with_alpha(vars, 1.0)
     }
 
     fn log_evidence(&self, _vars: &VarStore) -> f64 {
@@ -120,4 +129,49 @@ mod tests {
         let logz = f.log_evidence(&vars);
         assert!((logz - (-3.062235327364623)).abs() < 1e-10);
     }
+
+    #[test]
+    fn propagate_with_alpha_one_matches_undamped_propagate() {
+        let mut vars_a = VarStore::new();
+        let diff_a = vars_a.alloc(Gaussian::from_ms(0.0, 6.0));
+        let mut f_a = MarginFactor::new(diff_a, 5.0, 1.0);
+        let delta_a = f_a.propagate(&mut vars_a);
+        let result_a = vars_a.get(diff_a);
+
+        let mut vars_b = VarStore::new();
+        let diff_b = vars_b.alloc(Gaussian::from_ms(0.0, 6.0));
+        let mut f_b = MarginFactor::new(diff_b, 5.0, 1.0);
+        let delta_b = f_b.propagate_with_alpha(&mut vars_b, 1.0);
+        let result_b = vars_b.get(diff_b);
+
+        assert_eq!(result_a.pi(), result_b.pi());
+        assert_eq!(result_a.tau(), result_b.tau());
+        assert_eq!(delta_a, delta_b);
+        assert_eq!(f_a.msg.pi(), f_b.msg.pi());
+        assert_eq!(f_a.msg.tau(), f_b.msg.tau());
+    }
+
+    #[test]
+    fn propagate_with_alpha_half_blends_msg_in_natural_params() {
+        // Run undamped to capture (initial_msg, undamped_new_msg).
+        let mut vars_full = VarStore::new();
+        let diff_full = vars_full.alloc(Gaussian::from_ms(0.0, 6.0));
+        let mut f_full = MarginFactor::new(diff_full, 5.0, 1.0);
+        let initial_msg_pi = f_full.msg.pi();
+        let initial_msg_tau = f_full.msg.tau();
+        f_full.propagate(&mut vars_full);
+        let undamped_msg_pi = f_full.msg.pi();
+        let undamped_msg_tau = f_full.msg.tau();
+
+        // Run damped at α = 0.5 from the same initial state.
+        let mut vars_half = VarStore::new();
+        let diff_half = vars_half.alloc(Gaussian::from_ms(0.0, 6.0));
+        let mut f_half = MarginFactor::new(diff_half, 5.0, 1.0);
+        f_half.propagate_with_alpha(&mut vars_half, 0.5);
+
+        let expected_pi = 0.5 * undamped_msg_pi + 0.5 * initial_msg_pi;
+        let expected_tau = 0.5 * undamped_msg_tau + 0.5 * initial_msg_tau;
+        assert!((f_half.msg.pi() - expected_pi).abs() < 1e-12);
+        assert!((f_half.msg.tau() - expected_tau).abs() < 1e-12);
+    }
 }