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

Inherent method that applies α-damping to the outgoing message via
Gaussian::damp_natural. The Factor trait impl delegates with α=1.0,
preserving today's behavior bit-equal. Variable write switched from
`trunc` to `cavity * damped` — algebraically identical when α=1.0
(cavity * new_msg = trunc by construction); reflects partial-update
math when α<1.0.

src/factor/trunc.rs

@@ -33,29 +33,37 @@ impl TruncFactor {
     }
 }
 
-impl Factor for TruncFactor {
-    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+impl TruncFactor {
+    /// 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);
-        // Cavity: marginal divided by our outgoing message.
         let cavity = marginal / self.msg;
 
-        // First-time-only: cache the evidence contribution from the cavity.
         if self.evidence_cached.is_none() {
             self.evidence_cached = Some(cavity_evidence(cavity, self.margin, self.tie));
         }
 
-        // Apply the truncation approximation to the cavity.
         let trunc = approx(cavity, self.margin, self.tie);
-
-        // New outgoing message such that cavity * new_msg = trunc.
         let new_msg = trunc / cavity;
+
+        let damped = self.msg.damp_natural(new_msg, alpha);
         let old_msg = self.msg;
-        self.msg = new_msg;
+        self.msg = damped;
 
-        // Update the marginal: marginal_new = cavity * new_msg = trunc.
-        vars.set(self.diff, trunc);
+        // marginal_new = cavity * stored_msg. With alpha = 1.0 this equals
+        // `trunc` (since cavity * new_msg = trunc by construction); with
+        // alpha < 1.0 it reflects the partially-applied update.
+        vars.set(self.diff, cavity * damped);
 
-        old_msg.delta(new_msg)
+        old_msg.delta(damped)
+    }
+}
+
+impl Factor for TruncFactor {
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        self.propagate_with_alpha(vars, 1.0)
     }
 
     fn log_evidence(&self, _vars: &VarStore) -> f64 {
@@ -127,4 +135,49 @@ mod tests {
         let ev = f.evidence_cached.unwrap();
         assert!(ev > 0.35 && ev < 0.42);
     }
+
+    #[test]
+    fn propagate_with_alpha_one_matches_undamped_propagate() {
+        let mut vars_a = VarStore::new();
+        let diff_a = vars_a.alloc(Gaussian::from_ms(2.0, 3.0));
+        let mut f_a = TruncFactor::new(diff_a, 0.0, false);
+        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(2.0, 3.0));
+        let mut f_b = TruncFactor::new(diff_b, 0.0, false);
+        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(2.0, 3.0));
+        let mut f_full = TruncFactor::new(diff_full, 0.0, false);
+        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(2.0, 3.0));
+        let mut f_half = TruncFactor::new(diff_half, 0.0, false);
+        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);
+    }
 }