src/measures/discrete.rs

//! This module implementes discrete measures.

use std::ops::{
    Div,Mul,DivAssign,MulAssign,Neg,
    Add,Sub,AddAssign,SubAssign,
    Index,IndexMut,
};
use std::iter::Sum;
use serde::ser::{Serializer, Serialize, SerializeSeq};
use nalgebra::DVector;

use alg_tools::norms::Norm;
use alg_tools::tabledump::TableDump;
use alg_tools::linops::{Mapping, Linear};
use alg_tools::iter::{MapF,Mappable};
use alg_tools::nalgebra_support::ToNalgebraRealField;
use alg_tools::collection::Collection;
use alg_tools::instance::{Instance, Decomposition, MyCow, EitherDecomp, Space};

use crate::types::*;
use super::base::*;
use super::delta::*;

/// 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<F, const N : usize> = DiscreteMeasure<Loc<F, N>, 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<F, N>,F>
where DeltaMeasure<Loc<F, N>, F> : Serialize + 'a {
    type Iter = std::slice::Iter<'a, DeltaMeasure<Loc<F, N>, 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<F, N>, 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<F, N>, 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<F, Radon> for DiscreteMeasure<Domain, F>
where DeltaMeasure<Domain, F> : Norm<F, Radon> {
    #[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 + Space,
    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 + Space,
    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 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 decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Owned(self.spikes)
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        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
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for &'a DiscreteMeasure<Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Borrowed(self.spikes.as_slice())
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        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()
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for EitherSlice<'a, Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        self
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        match self {
            EitherDecomp::Owned(v) => v.as_slice(),
            EitherDecomp::Borrowed(s) => s,
        }
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        match self {
            EitherDecomp::Owned(v) => v.into(),
            EitherDecomp::Borrowed(s) => s.into(),
        }
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for &'a EitherSlice<'a, Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        match self {
            EitherDecomp::Owned(v) => EitherDecomp::Borrowed(v.as_slice()),
            EitherDecomp::Borrowed(s) => EitherDecomp::Borrowed(s),
        }
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        match self {
            EitherDecomp::Owned(v) => v.as_slice(),
            EitherDecomp::Borrowed(s) => s,
        }
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        match self {
            EitherDecomp::Owned(v) => v.as_slice(),
            EitherDecomp::Borrowed(s) => s
        }.into()
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for SpikeSlice<'a, Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Borrowed(self)
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        self
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        self.into()
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for &'a SpikeSlice<'a, Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Borrowed(*self)
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        *self
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        (*self).into()
    }
}

impl<F : Num, Domain : Clone > Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for DeltaMeasure<Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Owned(vec![self])
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        std::slice::from_ref(self)
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        self.into()
    }
}

impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp>
for &'a DeltaMeasure<Domain, F>
{
    fn decompose<'b>(self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b>
    where Self : 'b, DiscreteMeasure<Domain, F> : 'b {
        EitherDecomp::Borrowed(std::slice::from_ref(self))
    }
  
    fn ref_instance(&self)
        -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_>
    {
        std::slice::from_ref(*self)
    }

    fn own(self) -> DiscreteMeasure<Domain, F> {
        self.into()
    }
}