diff -r afb3ce40cff6 -r 66b8ac0ebe00 src/sliding_pdps.rs
--- a/src/sliding_pdps.rs	Thu Jul 30 09:27:44 2026 -0500
+++ b/src/sliding_pdps.rs	Fri Jul 31 10:41:47 2026 -0500
@@ -67,9 +67,10 @@
 /// Iteratively solve the pointsource localisation with an additional variable
 /// using sliding primal-dual proximal splitting
 ///
-/// The parametrisation is as for [`crate::forward_pdps::pointsource_forward_pdps_pair`].
+/// The parametrisation is as for [`crate::forward_pdps::pointsource_forward_pdps_pair`],
+/// except an additional domain restriction may be given.
 #[replace_float_literals(F::cast_from(literal))]
-pub fn pointsource_sliding_pdps_pair<
+pub fn pointsource_sliding_pdps_pair_dom<
     F,
     I,
     S,
@@ -95,6 +96,7 @@
     opKz: &KOpZ,
     fnR: &R,
     fnH: &H,
+    domain: Option<&P::Dom>,
 ) -> DynResult<MeasureZ<F, Z, N>>
 where
     F: Float + ToNalgebraRealField,
@@ -236,6 +238,7 @@
             &mut τθ_or_adaptive,
             &v,
             &config.transport,
+            domain,
         );
 
         let mut attempts = 0;
@@ -382,6 +385,144 @@
 /// The implementation uses [`pointsource_sliding_pdps_pair`] with appropriate dummy
 /// variables, operators, and functions.
 #[replace_float_literals(F::cast_from(literal))]
+pub fn pointsource_sliding_fb_pair_dom<F, I, S, Dat, Reg, P, Z, R, Plot, const N: usize>(
+    f: &Dat,
+    reg: &Reg,
+    prox_penalty: &P,
+    config: &SlidingFBConfig<F>,
+    iterator: I,
+    plotter: Plot,
+    (μ0, z): (Option<RNDM<N, F>>, Z),
+    //opKμ : KOpM,
+    fnR: &R,
+    domain: Option<&P::Dom>
+) -> DynResult<MeasureZ<F, Z, N>>
+where
+    F: Float + ToNalgebraRealField,
+    I: AlgIteratorFactory<IterInfo<F>>,
+    Dat: DifferentiableMapping<MeasureZ<F, Z, N>, Codomain = F, DerivativeDomain = Pair<S, Z>>
+        + BoundedCurvature<F>,
+    S: DifferentiableRealMapping<N, F> + ClosedMul<F> + MinMaxMapping<Loc<N, F>, F>,
+    RNDM<N, F>: SpikeMerging<F>,
+    Reg: SlidingRegTerm<Loc<N, F>, F>,
+    P: TransportProxPenalty<Loc<N, F>, S, Reg, F>,
+    for<'a> Pair<&'a P, &'a IdOp<Z>>: StepLengthBoundPair<F, Dat>,
+    Z: ClosedEuclidean<F> + AXPY + Clone,
+    for<'b> &'b Z: Instance<Z>,
+    R: Prox<Z, Codomain = F>,
+    Plot: Plotter<P::ReturnMapping, S, RNDM<N, F>>,
+    // We should not need to explicitly require this:
+    for<'b> &'b Loc<0, F>: Instance<Loc<0, F>>,
+    // Loc<0, F>: StaticEuclidean<Field = F, PrincipalE = Loc<0, F>>
+    //     + Instance<Loc<0, F>>
+    //     + VectorSpace<Field = F>,
+{
+    let opKz: ZeroOp<Z, Loc<0, F>, _, _, F> =
+        ZeroOp::new_dualisable(StaticEuclideanOriginGenerator, z.dual_origin());
+    let fnH = Zero::new();
+    // Convert config. We don't implement From (that could be done with the o2o crate), as σd0
+    // needs to be chosen in a general case; for the problem of this fucntion, anything is valid.
+    let &SlidingFBConfig { τ0, σp0, insertion, transport, guess } = config;
+    let pdps_config = SlidingPDPSConfig { τ0, σp0, insertion, transport, guess, σd0: 0.0 };
+
+    pointsource_sliding_pdps_pair_dom(
+        f,
+        reg,
+        prox_penalty,
+        &pdps_config,
+        iterator,
+        plotter,
+        (μ0, z, Loc([])),
+        &opKz,
+        fnR,
+        &fnH,
+        domain
+    )
+}
+
+
+#[deprecated]
+/// Version of [`pointsource_sliding_pdps_pair`] without domain specification.
+#[replace_float_literals(F::cast_from(literal))]
+pub fn pointsource_sliding_pdps_pair<
+    F,
+    I,
+    S,
+    Dat,
+    Reg,
+    P,
+    Z,
+    R,
+    Y,
+    Plot,
+    /*KOpM, */ KOpZ,
+    H,
+    const N: usize,
+>(
+    f: &Dat,
+    reg: &Reg,
+    prox_penalty: &P,
+    config: &SlidingPDPSConfig<F>,
+    iterator: I,
+    plotter: Plot,
+    init: (Option<RNDM<N, F>>, Z, Y),
+    //opKμ : KOpM,
+    opKz: &KOpZ,
+    fnR: &R,
+    fnH: &H,
+) -> DynResult<MeasureZ<F, Z, N>>
+where
+    F: Float + ToNalgebraRealField,
+    I: AlgIteratorFactory<IterInfo<F>>,
+    Dat: DifferentiableMapping<MeasureZ<F, Z, N>, Codomain = F, DerivativeDomain = Pair<S, Z>>
+        + BoundedCurvature<F>,
+    S: DifferentiableRealMapping<N, F> + ClosedMul<F> + MinMaxMapping<Loc<N, F>, F>,
+    for<'a> Pair<&'a P, &'a IdOp<Z>>: StepLengthBoundPair<F, Dat>,
+    //Pair<S, Z>: ClosedMul<F>,
+    RNDM<N, F>: SpikeMerging<F>,
+    Reg: SlidingRegTerm<Loc<N, F>, F>,
+    P: TransportProxPenalty<Loc<N, F>, S, Reg, F>,
+    // KOpM : Linear<RNDM<N, F>, Codomain=Y>
+    //     + GEMV<F, RNDM<N, F>>
+    //     + Preadjointable<
+    //         RNDM<N, F>, Y,
+    //         PreadjointCodomain = S,
+    //     >
+    //     + TransportLipschitz<L2Squared, FloatType=F>
+    //     + AdjointProductBoundedBy<RNDM<N, F>, 𝒟, FloatType=F>,
+    // for<'b> KOpM::Preadjoint<'b> : GEMV<F, Y>,
+    // Since Z is Hilbert, we may just as well use adjoints for K_z.
+    KOpZ: BoundedLinear<Z, L2, L2, F, Codomain = Y>
+        + GEMV<F, Z>
+        + SimplyAdjointable<Z, Y, AdjointCodomain = Z>,
+    KOpZ::SimpleAdjoint: GEMV<F, Y>,
+    Y: ClosedEuclidean<F>,
+    for<'b> &'b Y: Instance<Y>,
+    Z: ClosedEuclidean<F> + AXPY,
+    for<'b> &'b Z: Instance<Z>,
+    R: Prox<Z, Codomain = F>,
+    H: Conjugable<Y, F, Codomain = F>,
+    for<'b> H::Conjugate<'b>: Prox<Y>,
+    Plot: Plotter<P::ReturnMapping, S, RNDM<N, F>>,
+{
+    pointsource_sliding_pdps_pair_dom(
+        f,
+        reg,
+        prox_penalty,
+        config,
+        iterator,
+        plotter,
+        init,
+        opKz,
+        fnR,
+        fnH,
+        None,
+    )
+}
+
+#[deprecated]
+/// Version of [`pointsource_sliding_fb_pair_dom`] without domain specification
+#[replace_float_literals(F::cast_from(literal))]
 pub fn pointsource_sliding_fb_pair<F, I, S, Dat, Reg, P, Z, R, Plot, const N: usize>(
     f: &Dat,
     reg: &Reg,
@@ -421,7 +562,7 @@
     let &SlidingFBConfig { τ0, σp0, insertion, transport, guess } = config;
     let pdps_config = SlidingPDPSConfig { τ0, σp0, insertion, transport, guess, σd0: 0.0 };
 
-    pointsource_sliding_pdps_pair(
+    pointsource_sliding_pdps_pair_dom(
         f,
         reg,
         prox_penalty,
@@ -432,5 +573,6 @@
         &opKz,
         fnR,
         &fnH,
+        None
     )
 }