diff -r 000000000000 -r e8f3b6c55ce7 src/discrete.rs
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/discrete.rs	Fri Nov 28 12:48:17 2025 -0500
@@ -0,0 +1,1143 @@
+//! This module implementes discrete measures.
+
+use super::base::*;
+use super::delta::*;
+use alg_tools::collection::Collection;
+use alg_tools::instance::{ClosedSpace, Decomposition, EitherDecomp, Instance, MyCow, Space};
+use alg_tools::iter::{MapF, Mappable};
+use alg_tools::linops::{Linear, Mapping};
+use alg_tools::loc::Loc;
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use alg_tools::norms::{Norm, Normed};
+use alg_tools::self_ownable;
+use alg_tools::tabledump::TableDump;
+use alg_tools::types::*;
+use nalgebra::DVector;
+use serde::ser::{Serialize, SerializeSeq, Serializer};
+use std::iter::Sum;
+use std::ops::{
+    Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
+};
+
+/// Representation of a discrete measure.
+///
+/// This is the measure $μ = ∑_{k=1}^n α_k δ_{x_k}$, consisting of several
+/// [`DeltaMeasure`], i.e., “spikes” $α_k δ_{x_k}$ with weights $\alpha_k$ in `F` at locations
+/// $x_k$ in `Domain`.
+#[derive(Clone, Debug)]
+pub struct DiscreteMeasure<Domain, F: Num> {
+    pub(super) spikes: Vec<DeltaMeasure<Domain, F>>,
+}
+
+pub type RNDM<const N: usize, F = f64> = DiscreteMeasure<Loc<N, F>, F>;
+
+/// Iterator over the [`DeltaMeasure`] spikes of a [`DiscreteMeasure`].
+pub type SpikeIter<'a, Domain, F> = std::slice::Iter<'a, DeltaMeasure<Domain, F>>;
+
+/// Iterator over mutable [`DeltaMeasure`] spikes of a [`DiscreteMeasure`].
+pub type SpikeIterMut<'a, Domain, F> = std::slice::IterMut<'a, DeltaMeasure<Domain, F>>;
+
+/// Iterator over the locations of the spikes of a [`DiscreteMeasure`].
+pub type LocationIter<'a, Domain, F> =
+    std::iter::Map<SpikeIter<'a, Domain, F>, fn(&'a DeltaMeasure<Domain, F>) -> &'a Domain>;
+
+/// Iterator over the masses of the spikes of a [`DiscreteMeasure`].
+pub type MassIter<'a, Domain, F> =
+    std::iter::Map<SpikeIter<'a, Domain, F>, fn(&'a DeltaMeasure<Domain, F>) -> F>;
+
+/// Iterator over the mutable locations of the spikes of a [`DiscreteMeasure`].
+pub type MassIterMut<'a, Domain, F> = std::iter::Map<
+    SpikeIterMut<'a, Domain, F>,
+    for<'r> fn(&'r mut DeltaMeasure<Domain, F>) -> &'r mut F,
+>;
+
+impl<Domain, F: Num> DiscreteMeasure<Domain, F> {
+    /// Create a new zero measure (empty spike set).
+    pub fn new() -> Self {
+        DiscreteMeasure { spikes: Vec::new() }
+    }
+
+    /// Number of [`DeltaMeasure`] spikes in the measure
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.spikes.len()
+    }
+
+    /// Replace with the zero measure.
+    #[inline]
+    pub fn clear(&mut self) {
+        self.spikes.clear()
+    }
+
+    /// Remove `i`:th spike, not maintaining order.
+    ///
+    /// Panics if indiex is out of bounds.
+    #[inline]
+    pub fn swap_remove(&mut self, i: usize) -> DeltaMeasure<Domain, F> {
+        self.spikes.swap_remove(i)
+    }
+
+    /// Iterate over (references to) the [`DeltaMeasure`] spikes in this measure
+    #[inline]
+    pub fn iter_spikes(&self) -> SpikeIter<'_, Domain, F> {
+        self.spikes.iter()
+    }
+
+    /// Iterate over mutable references to the [`DeltaMeasure`] spikes in this measure
+    #[inline]
+    pub fn iter_spikes_mut(&mut self) -> SpikeIterMut<'_, Domain, F> {
+        self.spikes.iter_mut()
+    }
+
+    /// Iterate over the location of the spikes in this measure
+    #[inline]
+    pub fn iter_locations(&self) -> LocationIter<'_, Domain, F> {
+        self.iter_spikes().map(DeltaMeasure::get_location)
+    }
+
+    /// Iterate over the masses of the spikes in this measure
+    #[inline]
+    pub fn iter_masses(&self) -> MassIter<'_, Domain, F> {
+        self.iter_spikes().map(DeltaMeasure::get_mass)
+    }
+
+    /// Iterate over the masses of the spikes in this measure
+    #[inline]
+    pub fn iter_masses_mut(&mut self) -> MassIterMut<'_, Domain, F> {
+        self.iter_spikes_mut().map(DeltaMeasure::get_mass_mut)
+    }
+
+    /// Update the masses of all the spikes to those produced by an iterator.
+    #[inline]
+    pub fn set_masses<I: Iterator<Item = F>>(&mut self, iter: I) {
+        self.spikes
+            .iter_mut()
+            .zip(iter)
+            .for_each(|(δ, α)| δ.set_mass(α));
+    }
+
+    /// Update the locations of all the spikes to those produced by an iterator.
+    #[inline]
+    pub fn set_locations<'a, I: Iterator<Item = &'a Domain>>(&mut self, iter: I)
+    where
+        Domain: 'static + Clone,
+    {
+        self.spikes
+            .iter_mut()
+            .zip(iter.cloned())
+            .for_each(|(δ, α)| δ.set_location(α));
+    }
+
+    // /// Map the masses of all the spikes using a function and an iterator
+    // #[inline]
+    // pub fn zipmap_masses<
+    //     I : Iterator<Item=F>,
+    //     G : Fn(F, I::Item) -> F
+    // > (&mut self, iter : I, g : G) {
+    //     self.spikes.iter_mut().zip(iter).for_each(|(δ, v)| δ.set_mass(g(δ.get_mass(), v)));
+    // }
+
+    /// Prune all spikes with zero mass.
+    #[inline]
+    pub fn prune(&mut self) {
+        self.prune_by(|δ| δ.α != F::ZERO);
+    }
+
+    /// Prune spikes by the predicate `g`.
+    #[inline]
+    pub fn prune_by<G: FnMut(&DeltaMeasure<Domain, F>) -> bool>(&mut self, g: G) {
+        self.spikes.retain(g);
+    }
+
+    /// Add the spikes produced by `iter` to this measure.
+    #[inline]
+    pub fn extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(&mut self, iter: I) {
+        self.spikes.extend(iter);
+    }
+
+    /// Add a spike to the measure
+    #[inline]
+    pub fn push(&mut self, δ: DeltaMeasure<Domain, F>) {
+        self.spikes.push(δ);
+    }
+
+    /// Iterate over triples of masses and locations of two discrete measures, which are assumed
+    /// to have equal locations of same spike indices.
+    pub fn both_matching<'a>(
+        &'a self,
+        other: &'a DiscreteMeasure<Domain, F>,
+    ) -> impl Iterator<Item = (F, F, &'a Domain)> {
+        let m = self.len().max(other.len());
+        self.iter_spikes()
+            .map(Some)
+            .chain(std::iter::repeat(None))
+            .zip(other.iter_spikes().map(Some).chain(std::iter::repeat(None)))
+            .take(m)
+            .map(|(oδ, orδ)| {
+                match (oδ, orδ) {
+                    (Some(δ), Some(rδ)) => (δ.α, rδ.α, &δ.x), // Assumed δ.x=rδ.x
+                    (Some(δ), None) => (δ.α, F::ZERO, &δ.x),
+                    (None, Some(rδ)) => (F::ZERO, rδ.α, &rδ.x),
+                    (None, None) => panic!("This cannot happen!"),
+                }
+            })
+    }
+
+    /// Subtract `other` from `self`, assuming equal locations of same spike indices
+    pub fn sub_matching(&self, other: &DiscreteMeasure<Domain, F>) -> DiscreteMeasure<Domain, F>
+    where
+        Domain: Clone,
+    {
+        self.both_matching(other)
+            .map(|(α, β, x)| (x.clone(), α - β))
+            .collect()
+    }
+
+    /// Add `other` to `self`, assuming equal locations of same spike indices
+    pub fn add_matching(&self, other: &DiscreteMeasure<Domain, F>) -> DiscreteMeasure<Domain, F>
+    where
+        Domain: Clone,
+    {
+        self.both_matching(other)
+            .map(|(α, β, x)| (x.clone(), α + β))
+            .collect()
+    }
+
+    /// Calculate the Radon-norm distance of `self` to `other`,
+    /// assuming equal locations of same spike indices.
+    pub fn dist_matching(&self, other: &DiscreteMeasure<Domain, F>) -> F
+    where
+        F: Float,
+    {
+        self.both_matching(other)
+            .map(|(α, β, _)| (α - β).abs())
+            .sum()
+    }
+}
+
+impl<Domain, F: Num> IntoIterator for DiscreteMeasure<Domain, F> {
+    type Item = DeltaMeasure<Domain, F>;
+    type IntoIter = std::vec::IntoIter<DeltaMeasure<Domain, F>>;
+
+    #[inline]
+    fn into_iter(self) -> Self::IntoIter {
+        self.spikes.into_iter()
+    }
+}
+
+impl<'a, Domain, F: Num> IntoIterator for &'a DiscreteMeasure<Domain, F> {
+    type Item = &'a DeltaMeasure<Domain, F>;
+    type IntoIter = SpikeIter<'a, Domain, F>;
+
+    #[inline]
+    fn into_iter(self) -> Self::IntoIter {
+        self.spikes.iter()
+    }
+}
+
+impl<Domain, F: Num> Sum<DeltaMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    // Required method
+    fn sum<I>(iter: I) -> Self
+    where
+        I: Iterator<Item = DeltaMeasure<Domain, F>>,
+    {
+        Self::from_iter(iter)
+    }
+}
+
+impl<'a, Domain: Clone, F: Num> Sum<&'a DeltaMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    // Required method
+    fn sum<I>(iter: I) -> Self
+    where
+        I: Iterator<Item = &'a DeltaMeasure<Domain, F>>,
+    {
+        Self::from_iter(iter.cloned())
+    }
+}
+
+impl<Domain, F: Num> Sum<DiscreteMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    // Required method
+    fn sum<I>(iter: I) -> Self
+    where
+        I: Iterator<Item = DiscreteMeasure<Domain, F>>,
+    {
+        Self::from_iter(iter.map(|μ| μ.into_iter()).flatten())
+    }
+}
+
+impl<'a, Domain: Clone, F: Num> Sum<&'a DiscreteMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    // Required method
+    fn sum<I>(iter: I) -> Self
+    where
+        I: Iterator<Item = &'a DiscreteMeasure<Domain, F>>,
+    {
+        Self::from_iter(iter.map(|μ| μ.iter_spikes()).flatten().cloned())
+    }
+}
+
+impl<Domain: Clone, F: Float> DiscreteMeasure<Domain, F> {
+    /// Computes `μ1 ← θ * μ1 - ζ * μ2`, pruning entries where both `μ1` (`self`) and `μ2` have
+    // zero weight. `μ2` will contain a pruned copy of pruned original `μ1` without arithmetic
+    /// performed. **This expects `self` and `μ2` to have matching coordinates in each index**.
+    // `μ2` can be than `self`, but not longer.
+    pub fn pruning_sub(&mut self, θ: F, ζ: F, μ2: &mut Self) {
+        for δ in &self[μ2.len()..] {
+            μ2.push(DeltaMeasure { x: δ.x.clone(), α: F::ZERO });
+        }
+        debug_assert_eq!(self.len(), μ2.len());
+        let mut dest = 0;
+        for i in 0..self.len() {
+            let α = self[i].α;
+            let α_new = θ * α - ζ * μ2[i].α;
+            if dest < i {
+                μ2[dest] = DeltaMeasure { x: self[i].x.clone(), α };
+                self[dest] = DeltaMeasure { x: self[i].x.clone(), α: α_new };
+            } else {
+                μ2[i].α = α;
+                self[i].α = α_new;
+            }
+            dest += 1;
+        }
+        self.spikes.truncate(dest);
+        μ2.spikes.truncate(dest);
+    }
+}
+
+impl<Domain, F: Float> DiscreteMeasure<Domain, F> {
+    /// Prune all spikes with mass absolute value less than the given `tolerance`.
+    #[inline]
+    pub fn prune_approx(&mut self, tolerance: F) {
+        self.spikes.retain(|δ| δ.α.abs() > tolerance);
+    }
+}
+
+impl<Domain, F: Float + ToNalgebraRealField> DiscreteMeasure<Domain, F> {
+    /// Extracts the masses of the spikes as a [`DVector`].
+    pub fn masses_dvector(&self) -> DVector<F::MixedType> {
+        DVector::from_iterator(
+            self.len(),
+            self.iter_masses().map(|α| α.to_nalgebra_mixed()),
+        )
+    }
+
+    /// Sets the masses of the spikes from the values of a [`DVector`].
+    pub fn set_masses_dvector(&mut self, x: &DVector<F::MixedType>) {
+        self.set_masses(x.iter().map(|&α| F::from_nalgebra_mixed(α)));
+    }
+
+    // /// Extracts the masses of the spikes as a [`Vec`].
+    // pub fn masses_vec(&self) -> Vec<F::MixedType> {
+    //     self.iter_masses()
+    //         .map(|α| α.to_nalgebra_mixed())
+    //         .collect()
+    // }
+
+    // /// Sets the masses of the spikes from the values of a [`Vec`].
+    // pub fn set_masses_vec(&mut self, x : &Vec<F::MixedType>) {
+    //     self.set_masses(x.iter().map(|&α| F::from_nalgebra_mixed(α)));
+    // }
+}
+
+// impl<Domain, F :Num> Index<usize> for DiscreteMeasure<Domain, F> {
+//     type Output = DeltaMeasure<Domain, F>;
+//     #[inline]
+//     fn index(&self, i : usize) -> &Self::Output {
+//         self.spikes.index(i)
+//     }
+// }
+
+// impl<Domain, F :Num> IndexMut<usize> for DiscreteMeasure<Domain, F> {
+//     #[inline]
+//     fn index_mut(&mut self, i : usize) -> &mut Self::Output {
+//         self.spikes.index_mut(i)
+//     }
+// }
+
+impl<Domain, F: Num, I: std::slice::SliceIndex<[DeltaMeasure<Domain, F>]>> Index<I>
+    for DiscreteMeasure<Domain, F>
+{
+    type Output = <I as std::slice::SliceIndex<[DeltaMeasure<Domain, F>]>>::Output;
+    #[inline]
+    fn index(&self, i: I) -> &Self::Output {
+        self.spikes.index(i)
+    }
+}
+
+impl<Domain, F: Num, I: std::slice::SliceIndex<[DeltaMeasure<Domain, F>]>> IndexMut<I>
+    for DiscreteMeasure<Domain, F>
+{
+    #[inline]
+    fn index_mut(&mut self, i: I) -> &mut Self::Output {
+        self.spikes.index_mut(i)
+    }
+}
+
+impl<Domain, F: Num, D: Into<DeltaMeasure<Domain, F>>, const K: usize> From<[D; K]>
+    for DiscreteMeasure<Domain, F>
+{
+    #[inline]
+    fn from(list: [D; K]) -> Self {
+        list.into_iter().collect()
+    }
+}
+
+impl<Domain, F: Num> From<Vec<DeltaMeasure<Domain, F>>> for DiscreteMeasure<Domain, F> {
+    #[inline]
+    fn from(spikes: Vec<DeltaMeasure<Domain, F>>) -> Self {
+        DiscreteMeasure { spikes }
+    }
+}
+
+impl<'a, Domain, F: Num, D> From<&'a [D]> for DiscreteMeasure<Domain, F>
+where
+    &'a D: Into<DeltaMeasure<Domain, F>>,
+{
+    #[inline]
+    fn from(list: &'a [D]) -> Self {
+        list.into_iter().map(|d| d.into()).collect()
+    }
+}
+
+impl<Domain, F: Num> From<DeltaMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    #[inline]
+    fn from(δ: DeltaMeasure<Domain, F>) -> Self {
+        DiscreteMeasure { spikes: vec![δ] }
+    }
+}
+
+impl<'a, Domain: Clone, F: Num> From<&'a DeltaMeasure<Domain, F>> for DiscreteMeasure<Domain, F> {
+    #[inline]
+    fn from(δ: &'a DeltaMeasure<Domain, F>) -> Self {
+        DiscreteMeasure { spikes: vec![δ.clone()] }
+    }
+}
+
+impl<Domain, F: Num, D: Into<DeltaMeasure<Domain, F>>> FromIterator<D>
+    for DiscreteMeasure<Domain, F>
+{
+    #[inline]
+    fn from_iter<T>(iter: T) -> Self
+    where
+        T: IntoIterator<Item = D>,
+    {
+        DiscreteMeasure { spikes: iter.into_iter().map(|m| m.into()).collect() }
+    }
+}
+
+impl<'a, F: Num, const N: usize> TableDump<'a> for DiscreteMeasure<Loc<N, F>, F>
+where
+    DeltaMeasure<Loc<N, F>, F>: Serialize + 'a,
+{
+    type Iter = std::slice::Iter<'a, DeltaMeasure<Loc<N, F>, F>>;
+
+    // fn tabledump_headers(&'a self) -> Vec<String> {
+    //     let mut v : Vec<String> = (0..N).map(|i| format!("x{}", i)).collect();
+    //     v.push("weight".into());
+    //     v
+    // }
+
+    fn tabledump_entries(&'a self) -> Self::Iter {
+        // Ensure order matching the headers above
+        self.spikes.iter()
+    }
+}
+
+// Need to manually implement serialisation for DeltaMeasure<Loc<N, F>, F> [`csv`] writer fails on
+// structs with nested arrays as well as with #[serde(flatten)].
+// Then derive no longer works for DiscreteMeasure
+impl<F: Num, const N: usize> Serialize for DiscreteMeasure<Loc<N, F>, F>
+where
+    F: Serialize,
+{
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+    where
+        S: Serializer,
+    {
+        let mut s = serializer.serialize_seq(Some(self.spikes.len()))?;
+        for δ in self.spikes.iter() {
+            s.serialize_element(δ)?;
+        }
+        s.end()
+    }
+}
+
+impl<Domain: PartialEq, F: Float> Measure<F> for DiscreteMeasure<Domain, F> {
+    type Domain = Domain;
+}
+
+impl<Domain: PartialEq, F: Float> Norm<Radon, F> for DiscreteMeasure<Domain, F>
+where
+    DeltaMeasure<Domain, F>: Norm<Radon, F>,
+{
+    #[inline]
+    fn norm(&self, _: Radon) -> F {
+        self.spikes.iter().map(|m| m.norm(Radon)).sum()
+    }
+}
+
+impl<Domain, G, F: Num> Mapping<G> for DiscreteMeasure<Domain, F>
+where
+    Domain: Space,
+    G::Codomain: Sum + Mul<F, Output = G::Codomain>,
+    G: Mapping<Domain, Codomain = F> + Clone + ClosedSpace,
+    for<'b> &'b Domain: Instance<Domain>,
+{
+    type Codomain = G::Codomain;
+
+    #[inline]
+    fn apply<I: Instance<G>>(&self, g: I) -> Self::Codomain {
+        g.eval(|g| self.spikes.iter().map(|m| g.apply(&m.x) * m.α).sum())
+    }
+}
+
+impl<Domain, G, F: Num> Linear<G> for DiscreteMeasure<Domain, F>
+where
+    Domain: Space,
+    G::Codomain: Sum + Mul<F, Output = G::Codomain>,
+    G: Mapping<Domain, Codomain = F> + Clone + ClosedSpace,
+    for<'b> &'b Domain: Instance<Domain>,
+{
+}
+
+/// Helper trait for constructing arithmetic operations for combinations
+/// of [`DiscreteMeasure`] and [`DeltaMeasure`], and their references.
+trait Lift<F: Num, Domain> {
+    type Producer: Iterator<Item = DeltaMeasure<Domain, F>>;
+
+    #[allow(dead_code)]
+    /// Lifts `self` into a [`DiscreteMeasure`].
+    fn lift(self) -> DiscreteMeasure<Domain, F>;
+
+    /// Lifts `self` into a [`DiscreteMeasure`], apply either `f` or `f_mut` whether the type
+    /// this method is implemented for is a reference or or not.
+    fn lift_with(
+        self,
+        f: impl Fn(&DeltaMeasure<Domain, F>) -> DeltaMeasure<Domain, F>,
+        f_mut: impl FnMut(&mut DeltaMeasure<Domain, F>),
+    ) -> DiscreteMeasure<Domain, F>;
+
+    /// Extend `self` into a [`DiscreteMeasure`] with the spikes produced by `iter`.
+    fn lift_extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(
+        self,
+        iter: I,
+    ) -> DiscreteMeasure<Domain, F>;
+
+    /// Returns an iterator for producing copies of the spikes of `self`.
+    fn produce(self) -> Self::Producer;
+}
+
+impl<F: Num, Domain> Lift<F, Domain> for DiscreteMeasure<Domain, F> {
+    type Producer = std::vec::IntoIter<DeltaMeasure<Domain, F>>;
+
+    #[inline]
+    fn lift(self) -> DiscreteMeasure<Domain, F> {
+        self
+    }
+
+    fn lift_with(
+        mut self,
+        _f: impl Fn(&DeltaMeasure<Domain, F>) -> DeltaMeasure<Domain, F>,
+        f_mut: impl FnMut(&mut DeltaMeasure<Domain, F>),
+    ) -> DiscreteMeasure<Domain, F> {
+        self.spikes.iter_mut().for_each(f_mut);
+        self
+    }
+
+    #[inline]
+    fn lift_extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(
+        mut self,
+        iter: I,
+    ) -> DiscreteMeasure<Domain, F> {
+        self.spikes.extend(iter);
+        self
+    }
+
+    #[inline]
+    fn produce(self) -> Self::Producer {
+        self.spikes.into_iter()
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Lift<F, Domain> for &'a DiscreteMeasure<Domain, F> {
+    type Producer = MapF<std::slice::Iter<'a, DeltaMeasure<Domain, F>>, DeltaMeasure<Domain, F>>;
+
+    #[inline]
+    fn lift(self) -> DiscreteMeasure<Domain, F> {
+        self.clone()
+    }
+
+    fn lift_with(
+        self,
+        f: impl Fn(&DeltaMeasure<Domain, F>) -> DeltaMeasure<Domain, F>,
+        _f_mut: impl FnMut(&mut DeltaMeasure<Domain, F>),
+    ) -> DiscreteMeasure<Domain, F> {
+        DiscreteMeasure { spikes: self.spikes.iter().map(f).collect() }
+    }
+
+    #[inline]
+    fn lift_extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(
+        self,
+        iter: I,
+    ) -> DiscreteMeasure<Domain, F> {
+        let mut res = self.clone();
+        res.spikes.extend(iter);
+        res
+    }
+
+    #[inline]
+    fn produce(self) -> Self::Producer {
+        // TODO: maybe not optimal to clone here and would benefit from
+        // a reference version of lift_extend.
+        self.spikes.iter().mapF(Clone::clone)
+    }
+}
+
+impl<F: Num, Domain> Lift<F, Domain> for DeltaMeasure<Domain, F> {
+    type Producer = std::iter::Once<DeltaMeasure<Domain, F>>;
+
+    #[inline]
+    fn lift(self) -> DiscreteMeasure<Domain, F> {
+        DiscreteMeasure { spikes: vec![self] }
+    }
+
+    #[inline]
+    fn lift_with(
+        mut self,
+        _f: impl Fn(&DeltaMeasure<Domain, F>) -> DeltaMeasure<Domain, F>,
+        mut f_mut: impl FnMut(&mut DeltaMeasure<Domain, F>),
+    ) -> DiscreteMeasure<Domain, F> {
+        f_mut(&mut self);
+        DiscreteMeasure { spikes: vec![self] }
+    }
+
+    #[inline]
+    fn lift_extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(
+        self,
+        iter: I,
+    ) -> DiscreteMeasure<Domain, F> {
+        let mut spikes = vec![self];
+        spikes.extend(iter);
+        DiscreteMeasure { spikes: spikes }
+    }
+
+    #[inline]
+    fn produce(self) -> Self::Producer {
+        std::iter::once(self)
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Lift<F, Domain> for &'a DeltaMeasure<Domain, F> {
+    type Producer = std::iter::Once<DeltaMeasure<Domain, F>>;
+
+    #[inline]
+    fn lift(self) -> DiscreteMeasure<Domain, F> {
+        DiscreteMeasure { spikes: vec![self.clone()] }
+    }
+
+    #[inline]
+    fn lift_with(
+        self,
+        f: impl Fn(&DeltaMeasure<Domain, F>) -> DeltaMeasure<Domain, F>,
+        _f_mut: impl FnMut(&mut DeltaMeasure<Domain, F>),
+    ) -> DiscreteMeasure<Domain, F> {
+        DiscreteMeasure { spikes: vec![f(self)] }
+    }
+
+    #[inline]
+    fn lift_extend<I: Iterator<Item = DeltaMeasure<Domain, F>>>(
+        self,
+        iter: I,
+    ) -> DiscreteMeasure<Domain, F> {
+        let mut spikes = vec![self.clone()];
+        spikes.extend(iter);
+        DiscreteMeasure { spikes: spikes }
+    }
+
+    #[inline]
+    fn produce(self) -> Self::Producer {
+        std::iter::once(self.clone())
+    }
+}
+
+macro_rules! make_discrete_addsub_assign {
+    ($rhs:ty) => {
+        // Discrete += (&)Discrete
+        impl<'a, F: Num, Domain: Clone> AddAssign<$rhs> for DiscreteMeasure<Domain, F> {
+            fn add_assign(&mut self, other: $rhs) {
+                self.spikes.extend(other.produce());
+            }
+        }
+
+        impl<'a, F: Num + Neg<Output = F>, Domain: Clone> SubAssign<$rhs>
+            for DiscreteMeasure<Domain, F>
+        {
+            fn sub_assign(&mut self, other: $rhs) {
+                self.spikes.extend(other.produce().map(|δ| -δ));
+            }
+        }
+    };
+}
+
+make_discrete_addsub_assign!(DiscreteMeasure<Domain, F>);
+make_discrete_addsub_assign!(&'a DiscreteMeasure<Domain, F>);
+make_discrete_addsub_assign!(DeltaMeasure<Domain, F>);
+make_discrete_addsub_assign!(&'a DeltaMeasure<Domain, F>);
+
+macro_rules! make_discrete_addsub {
+    ($lhs:ty, $rhs:ty, $alt_order:expr) => {
+        impl<'a, 'b, F: Num, Domain: Clone> Add<$rhs> for $lhs {
+            type Output = DiscreteMeasure<Domain, F>;
+            fn add(self, other: $rhs) -> DiscreteMeasure<Domain, F> {
+                if !$alt_order {
+                    self.lift_extend(other.produce())
+                } else {
+                    other.lift_extend(self.produce())
+                }
+            }
+        }
+
+        impl<'a, 'b, F: Num + Neg<Output = F>, Domain: Clone> Sub<$rhs> for $lhs {
+            type Output = DiscreteMeasure<Domain, F>;
+            fn sub(self, other: $rhs) -> DiscreteMeasure<Domain, F> {
+                self.lift_extend(other.produce().map(|δ| -δ))
+            }
+        }
+    };
+}
+
+make_discrete_addsub!(DiscreteMeasure<Domain, F>,     DiscreteMeasure<Domain, F>,     false);
+make_discrete_addsub!(DiscreteMeasure<Domain, F>,     &'b DiscreteMeasure<Domain, F>, false);
+make_discrete_addsub!(&'a DiscreteMeasure<Domain, F>, DiscreteMeasure<Domain, F>,     true);
+make_discrete_addsub!(
+    &'a DiscreteMeasure<Domain, F>,
+    &'b DiscreteMeasure<Domain, F>,
+    false
+);
+make_discrete_addsub!(DeltaMeasure<Domain, F>,        DiscreteMeasure<Domain, F>,     false);
+make_discrete_addsub!(DeltaMeasure<Domain, F>,        &'b DiscreteMeasure<Domain, F>, false);
+make_discrete_addsub!(&'a DeltaMeasure<Domain, F>,    DiscreteMeasure<Domain, F>,     true);
+make_discrete_addsub!(
+    &'a DeltaMeasure<Domain, F>,
+    &'b DiscreteMeasure<Domain, F>,
+    false
+);
+make_discrete_addsub!(DiscreteMeasure<Domain, F>,     DeltaMeasure<Domain, F>,        false);
+make_discrete_addsub!(DiscreteMeasure<Domain, F>,     &'b DeltaMeasure<Domain, F>,    false);
+make_discrete_addsub!(&'a DiscreteMeasure<Domain, F>, DeltaMeasure<Domain, F>,        false);
+make_discrete_addsub!(
+    &'a DiscreteMeasure<Domain, F>,
+    &'b DeltaMeasure<Domain, F>,
+    false
+);
+make_discrete_addsub!(DeltaMeasure<Domain, F>,        DeltaMeasure<Domain, F>,        false);
+make_discrete_addsub!(DeltaMeasure<Domain, F>,        &'b DeltaMeasure<Domain, F>,    false);
+make_discrete_addsub!(&'a DeltaMeasure<Domain, F>,    DeltaMeasure<Domain, F>,        false);
+make_discrete_addsub!(
+    &'a DeltaMeasure<Domain, F>,
+    &'b DeltaMeasure<Domain, F>,
+    false
+);
+
+macro_rules! make_discrete_scalarop_rhs {
+    ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
+        make_discrete_scalarop_rhs!(@assign DiscreteMeasure<Domain, F>, F, $trait_assign, $fn_assign);
+        make_discrete_scalarop_rhs!(@assign DiscreteMeasure<Domain, F>, &'a F, $trait_assign, $fn_assign);
+        make_discrete_scalarop_rhs!(@new DiscreteMeasure<Domain, F>, F, $trait, $fn, $fn_assign);
+        make_discrete_scalarop_rhs!(@new DiscreteMeasure<Domain, F>, &'a F, $trait, $fn, $fn_assign);
+        make_discrete_scalarop_rhs!(@new &'b DiscreteMeasure<Domain, F>, F, $trait, $fn, $fn_assign);
+        make_discrete_scalarop_rhs!(@new &'b DiscreteMeasure<Domain, F>, &'a F, $trait, $fn, $fn_assign);
+    };
+
+    (@assign $lhs:ty, $rhs:ty, $trait_assign:ident, $fn_assign:ident) => {
+        impl<'a, 'b, F : Num, Domain> $trait_assign<$rhs> for $lhs {
+            fn $fn_assign(&mut self, b : $rhs) {
+                self.spikes.iter_mut().for_each(|δ| δ.$fn_assign(b));
+            }
+        }
+    };
+    (@new $lhs:ty, $rhs:ty, $trait:ident, $fn:ident, $fn_assign:ident) => {
+        impl<'a, 'b, F : Num, Domain : Clone> $trait<$rhs> for $lhs {
+            type Output = DiscreteMeasure<Domain, F>;
+            fn $fn(self, b : $rhs) -> Self::Output {
+                self.lift_with(|δ| δ.$fn(b), |δ| δ.$fn_assign(b))
+            }
+        }
+    };
+}
+
+make_discrete_scalarop_rhs!(Mul, mul, MulAssign, mul_assign);
+make_discrete_scalarop_rhs!(Div, div, DivAssign, div_assign);
+
+macro_rules! make_discrete_unary {
+    ($trait:ident, $fn:ident, $type:ty) => {
+        impl<'a, F: Num + Neg<Output = F>, Domain: Clone> Neg for $type {
+            type Output = DiscreteMeasure<Domain, F>;
+            fn $fn(self) -> Self::Output {
+                self.lift_with(|δ| δ.$fn(), |δ| δ.α = δ.α.$fn())
+            }
+        }
+    };
+}
+
+make_discrete_unary!(Neg, neg, DiscreteMeasure<Domain, F>);
+make_discrete_unary!(Neg, neg, &'a DiscreteMeasure<Domain, F>);
+
+// impl<F : Num, Domain> Neg for DiscreteMeasure<Domain, F> {
+//     type Output = Self;
+//     fn $fn(mut self, b : F) -> Self {
+//         self.lift().spikes.iter_mut().for_each(|δ| δ.neg(b));
+//         self
+//     }
+// }
+
+macro_rules! make_discrete_scalarop_lhs {
+    ($trait:ident, $fn:ident; $($f:ident)+) => { $(
+        impl<Domain> $trait<DiscreteMeasure<Domain, $f>> for $f {
+            type Output = DiscreteMeasure<Domain, $f>;
+            fn $fn(self, mut v : DiscreteMeasure<Domain, $f>) -> Self::Output {
+                v.spikes.iter_mut().for_each(|δ| δ.α = self.$fn(δ.α));
+                v
+            }
+        }
+
+        impl<'a, Domain : Copy> $trait<&'a DiscreteMeasure<Domain, $f>> for $f {
+            type Output = DiscreteMeasure<Domain, $f>;
+            fn $fn(self, v : &'a DiscreteMeasure<Domain, $f>) -> Self::Output {
+                DiscreteMeasure{
+                    spikes : v.spikes.iter().map(|δ| self.$fn(δ)).collect()
+                }
+            }
+        }
+
+        impl<'b, Domain> $trait<DiscreteMeasure<Domain, $f>> for &'b $f {
+            type Output = DiscreteMeasure<Domain, $f>;
+            fn $fn(self, mut v : DiscreteMeasure<Domain, $f>) -> Self::Output {
+                v.spikes.iter_mut().for_each(|δ| δ.α = self.$fn(δ.α));
+                v
+            }
+        }
+
+        impl<'a, 'b, Domain : Copy> $trait<&'a DiscreteMeasure<Domain, $f>> for &'b $f {
+            type Output = DiscreteMeasure<Domain, $f>;
+            fn $fn(self, v : &'a DiscreteMeasure<Domain, $f>) -> Self::Output {
+                DiscreteMeasure{
+                    spikes : v.spikes.iter().map(|δ| self.$fn(δ)).collect()
+                }
+            }
+        }
+    )+ }
+}
+
+make_discrete_scalarop_lhs!(Mul, mul; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize);
+make_discrete_scalarop_lhs!(Div, div; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize);
+
+impl<F: Num, Domain> Collection for DiscreteMeasure<Domain, F> {
+    type Element = DeltaMeasure<Domain, F>;
+    type RefsIter<'a>
+        = std::slice::Iter<'a, Self::Element>
+    where
+        Self: 'a;
+
+    #[inline]
+    fn iter_refs(&self) -> Self::RefsIter<'_> {
+        self.iter_spikes()
+    }
+}
+
+impl<Domain: Clone, F: Num> Space for DiscreteMeasure<Domain, F> {
+    type Principal = Self;
+
+    type Decomp = MeasureDecomp;
+}
+
+pub type SpikeSlice<'b, Domain, F> = &'b [DeltaMeasure<Domain, F>];
+
+pub type EitherSlice<'b, Domain, F> =
+    EitherDecomp<Vec<DeltaMeasure<Domain, F>>, SpikeSlice<'b, Domain, F>>;
+
+impl<F: Num, Domain: Clone> Decomposition<DiscreteMeasure<Domain, F>> for MeasureDecomp {
+    type Decomposition<'b>
+        = EitherSlice<'b, Domain, F>
+    where
+        DiscreteMeasure<Domain, F>: 'b;
+    type Reference<'b>
+        = SpikeSlice<'b, Domain, F>
+    where
+        DiscreteMeasure<Domain, F>: 'b;
+
+    /// Left the lightweight reference type into a full decomposition type.
+    fn lift<'b>(r: Self::Reference<'b>) -> Self::Decomposition<'b> {
+        EitherDecomp::Borrowed(r)
+    }
+}
+
+impl<F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for DiscreteMeasure<Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(self.spikes.as_slice())
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self)
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        self
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Owned(self.spikes)
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for &'a DiscreteMeasure<Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(self.spikes.as_slice())
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Borrowed(self)
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        self.clone()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Borrowed(self.spikes.as_slice())
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for EitherSlice<'a, Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        match self {
+            EitherDecomp::Owned(v) => f(v.as_slice()),
+            EitherDecomp::Borrowed(s) => f(s),
+        }
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        match self {
+            EitherDecomp::Owned(v) => v.into(),
+            EitherDecomp::Borrowed(s) => s.into(),
+        }
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        self
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for &'a EitherSlice<'a, Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        match self {
+            EitherDecomp::Owned(v) => f(v.as_slice()),
+            EitherDecomp::Borrowed(s) => f(s),
+        }
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        match self {
+            EitherDecomp::Owned(v) => v.as_slice(),
+            EitherDecomp::Borrowed(s) => s,
+        }
+        .into()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        match self {
+            EitherDecomp::Owned(v) => EitherDecomp::Borrowed(v.as_slice()),
+            EitherDecomp::Borrowed(s) => EitherDecomp::Borrowed(s),
+        }
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for SpikeSlice<'a, Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(self)
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        self.into()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Borrowed(self)
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for &'a SpikeSlice<'a, Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(*self)
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        (*self).into()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Borrowed(*self)
+    }
+}
+
+impl<F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for DeltaMeasure<Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(std::slice::from_ref(self))
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        self.into()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Owned(vec![self])
+    }
+}
+
+impl<'a, F: Num, Domain: Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
+    for &'a DeltaMeasure<Domain, F>
+{
+    fn eval_ref<'b, R>(&'b self, f: impl FnOnce(SpikeSlice<'b, Domain, F>) -> R) -> R
+    where
+        DiscreteMeasure<Domain, F>: 'b,
+        Self: 'b,
+    {
+        f(std::slice::from_ref(*self))
+    }
+
+    fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>>
+    where
+        Self: 'b,
+    {
+        MyCow::Owned(self.own())
+    }
+
+    fn own(self) -> DiscreteMeasure<Domain, F> {
+        self.into()
+    }
+
+    fn decompose<'b>(self) -> EitherSlice<'b, Domain, F>
+    where
+        Self: 'b,
+    {
+        EitherDecomp::Borrowed(std::slice::from_ref(self))
+    }
+}
+
+impl<F, Domain> Normed<F> for DiscreteMeasure<Domain, F>
+where
+    F: Float,
+    Domain: Clone + PartialEq,
+    DeltaMeasure<Domain, F>: Norm<Radon, F>,
+{
+    type NormExp = Radon;
+
+    fn norm_exponent(&self) -> Radon {
+        Radon
+    }
+}
+
+self_ownable!(DiscreteMeasure<Domain, F> where Domain: Clone, F: Num);