src/measures/delta.rs

/*!
This module implementes delta measures, i.e., single spikes $\alpha \delta_x$ for some
location $x$ and mass $\alpha$.
*/

use super::base::*;
use crate::types::*;
use std::ops::{Div, Mul, DivAssign, MulAssign, Neg};
use serde::ser::{Serialize, Serializer, SerializeStruct};
use alg_tools::norms::Norm;
use alg_tools::linops::{Mapping, Linear};
use alg_tools::instance::{Instance, Space};

/// Representation of a delta measure.
///
/// This is a single spike $\alpha \delta\_x$ for some location $x$ in `Domain` and
/// a mass $\alpha$ in `F`.
#[derive(Clone,Copy,Debug)]
pub struct DeltaMeasure<Domain, F : Num> {
    // This causes [`csv`] to crash.
    //#[serde(flatten)]
    /// Location of the spike
    pub x : Domain,
    /// Mass of the spike
    pub α : F
}

const COORDINATE_NAMES : &'static [&'static str] = &[
    "x0", "x1", "x2", "x3", "x4", "x5", "x6", "x7"
];

// Need to manually implement serialisation as [`csv`] writer fails on
// structs with nested arrays as well as with #[serde(flatten)].
impl<F : Num, const N : usize> Serialize for DeltaMeasure<Loc<F, N>, F>
where
    F: Serialize,
{
    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
    where
        S: Serializer,
    {
        assert!(N <= COORDINATE_NAMES.len());

        let mut s = serializer.serialize_struct("DeltaMeasure", N+1)?;
        for (i, e) in (0..).zip(self.x.iter()) {
            s.serialize_field(COORDINATE_NAMES[i], e)?;
        }
        s.serialize_field("weight", &self.α)?;
        s.end()
    }
}


impl<Domain, F : Float> Measure<F> for DeltaMeasure<Domain, F> {
    type Domain = Domain;
}

impl<Domain, F : Float> Norm<F, Radon> for DeltaMeasure<Domain, F> {
    #[inline]
    fn norm(&self, _ : Radon) -> F {
        self.α.abs()
    }
}

// impl<Domain : PartialEq, F : Float> Dist<F, Radon> for DeltaMeasure<Domain, F> {
//     #[inline]
//     fn dist(&self, other : &Self, _ : Radon) -> F {
//         if self.x == other. x {
//             (self.α - other.α).abs()
//         } else {
//             self.α.abs() + other.α.abs()
//         }
//     }
// }

impl<Domain, G, F : Num> Mapping<G> for DeltaMeasure<Domain, F>
where
    Domain : Space,
    G::Codomain : Mul<F, Output=G::Codomain>,
    G : Mapping<Domain> + 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(|g̃| g̃.apply(&self.x) * self.α)
    }
}

impl<Domain, G, F : Num> Linear<G> for DeltaMeasure<Domain, F>
where
    Domain : Space,
    G::Codomain : Mul<F, Output=G::Codomain>,
    G : Mapping<Domain> + Clone + Space,
    for<'b> &'b Domain : Instance<Domain>,
{ }

// /// Partial blanket implementation of [`DeltaMeasure`] as a linear functional of [`Mapping`]s.
// /// A full blanket implementation is not possible due to annoying Rust limitations: only [`Apply`]
// /// on a reference is implemented, but a consuming [`Apply`] has to be implemented on a case-by-case
// /// basis, not because an implementation could not be written, but because the Rust trait system
// /// chokes up.
// impl<Domain, G, F : Num, V> Linear<G> for DeltaMeasure<Domain, F>
// where G: for<'a> Apply<&'a Domain, Output = V>,
//       V : Mul<F>,
//       Self: Apply<G, Output =  <V as Mul<F>>::Output> {
//     type Codomain = <V as Mul<F>>::Output;
// }

// impl<'b, Domain, G, F : Num, V> Apply<&'b G> for DeltaMeasure<Domain, F>
// where G: for<'a> Apply<&'a Domain, Output = V>,
//       V : Mul<F> {
//     type Output = <V as Mul<F>>::Output;

//     #[inline]
//     fn apply(&self, g : &'b G) -> Self::Output {
//         g.apply(&self.x) * self.α
//     }
// }

// /// Implementation of the necessary apply for BTFNs
// mod btfn_apply {
//     use super::*;
//     use alg_tools::bisection_tree::{BTFN, BTImpl, SupportGenerator, LocalAnalysis};

//     impl<F : Float, BT, G, V, const N : usize> Apply<BTFN<F, G, BT, N>>
//     for DeltaMeasure<Loc<F, N>, F>
//     where BT : BTImpl<F, N>,
//         G : SupportGenerator<F, N, Id=BT::Data>,
//         G::SupportType : LocalAnalysis<F, BT::Agg, N> + for<'a> Apply<&'a Loc<F, N>, Output = V>,
//         V : std::iter::Sum + Mul<F> {
        
//         type Output = <V as Mul<F>>::Output;

//         #[inline]
//         fn apply(&self, g : BTFN<F, G, BT, N>) -> Self::Output {
//             g.apply(&self.x) * self.α
//         }
//     }
// }


impl<D, Domain, F : Num> From<(D, F)> for DeltaMeasure<Domain, F>
where D : Into<Domain> {
    #[inline]
    fn from((x, α) : (D, F)) -> Self {
        DeltaMeasure{x: x.into(), α: α}
    }
}

impl<'a, Domain : Clone, F : Num> From<&'a DeltaMeasure<Domain, F>> for DeltaMeasure<Domain, F> {
    #[inline]
    fn from(d : &'a DeltaMeasure<Domain, F>) -> Self {
        d.clone()
    }
}


impl<Domain, F : Num> DeltaMeasure<Domain, F> {
    /// Set the mass of the spike.
    #[inline]
    pub fn set_mass(&mut self, α : F) {
        self.α = α
    }

    /// Set the location of the spike.
    #[inline]
    pub fn set_location(&mut self, x : Domain) {
        self.x = x
    }

    /// Get the mass of the spike.
    #[inline]
    pub fn get_mass(&self) -> F {
        self.α
    }

    /// Get a mutable reference to the mass of the spike.
    #[inline]
    pub fn get_mass_mut(&mut self) -> &mut F {
        &mut self.α
    }

    /// Get a reference to the location of the spike.
    #[inline]
    pub fn get_location(&self) -> &Domain {
        &self.x
    }

    /// Get a mutable reference to the location of the spike.
    #[inline]
    pub fn get_location_mut(&mut self) -> &mut Domain {
        &mut self.x
    }
}

impl<Domain, F : Num> IntoIterator for DeltaMeasure<Domain, F> {
    type Item =  Self;
    type IntoIter =  std::iter::Once<Self>;

    #[inline]
    fn into_iter(self) -> Self::IntoIter {
        std::iter::once(self)
    }
}

impl<'a, Domain, F : Num> IntoIterator for &'a DeltaMeasure<Domain, F> {
    type Item =  Self;
    type IntoIter =  std::iter::Once<Self>;

    #[inline]
    fn into_iter(self) -> Self::IntoIter {
        std::iter::once(self)
    }
}


macro_rules! make_delta_scalarop_rhs {
    ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
        impl<F : Num, Domain> $trait<F> for DeltaMeasure<Domain, F> {
            type Output = Self;
            fn $fn(mut self, b : F) -> Self {
                self.α.$fn_assign(b);
                self
            }
        }

        impl<'a, F : Num, Domain> $trait<&'a F> for DeltaMeasure<Domain, F> {
            type Output = Self;
            fn $fn(mut self, b : &'a F) -> Self {
                self.α.$fn_assign(*b);
                self
            }
        }

        impl<'b, F : Num, Domain : Clone> $trait<F> for &'b DeltaMeasure<Domain, F> {
            type Output = DeltaMeasure<Domain, F>;
            fn $fn(self, b : F) -> Self::Output {
                DeltaMeasure { α : self.α.$fn(b), x : self.x.clone() }
            }
        }

        impl<'a, 'b, F : Num, Domain : Clone> $trait<&'a F> for &'b DeltaMeasure<Domain, F> {
            type Output = DeltaMeasure<Domain, F>;
            fn $fn(self, b : &'a F) -> Self::Output {
                DeltaMeasure { α : self.α.$fn(*b), x : self.x.clone() }
            }
        }

        impl<F : Num, Domain> $trait_assign<F> for DeltaMeasure<Domain, F> {
            fn $fn_assign(&mut self, b : F) {
                self.α.$fn_assign(b)
            }
        }

        impl<'a, F : Num, Domain> $trait_assign<&'a F> for DeltaMeasure<Domain, F> {
            fn $fn_assign(&mut self, b : &'a F) {
                self.α.$fn_assign(*b)
            }
        }
    }
}

make_delta_scalarop_rhs!(Mul, mul, MulAssign, mul_assign);
make_delta_scalarop_rhs!(Div, div, DivAssign, div_assign);

macro_rules! make_delta_scalarop_lhs {
    ($trait:ident, $fn:ident; $($f:ident)+) => { $(
        impl<Domain> $trait<DeltaMeasure<Domain, $f>> for $f {
            type Output = DeltaMeasure<Domain, $f>;
            fn $fn(self, mut δ : DeltaMeasure<Domain, $f>) -> Self::Output {
                δ.α = self.$fn(δ.α);
                δ
            }
        }

        impl<'a, Domain : Clone> $trait<&'a DeltaMeasure<Domain, $f>> for $f {
            type Output = DeltaMeasure<Domain, $f>;
            fn $fn(self, δ : &'a DeltaMeasure<Domain, $f>) -> Self::Output {
                DeltaMeasure{ x : δ.x.clone(), α : self.$fn(δ.α) }
            }
        }

        impl<'b, Domain> $trait<DeltaMeasure<Domain, $f>> for &'b $f {
            type Output = DeltaMeasure<Domain, $f>;
            fn $fn(self, mut δ : DeltaMeasure<Domain, $f>) -> Self::Output {
                δ.α = self.$fn(δ.α);
                δ
            }
        }

        impl<'a, 'b, Domain : Clone> $trait<&'a DeltaMeasure<Domain, $f>> for &'b $f {
            type Output = DeltaMeasure<Domain, $f>;
            fn $fn(self, δ : &'a DeltaMeasure<Domain, $f>) -> Self::Output {
                DeltaMeasure{ x : δ.x.clone(), α : self.$fn(δ.α) }
            }
        }
    )+ }
}

make_delta_scalarop_lhs!(Mul, mul; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize);
make_delta_scalarop_lhs!(Div, div; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize);

macro_rules! make_delta_unary {
    ($trait:ident, $fn:ident, $type:ty) => {
        impl<'a, F : Num + Neg<Output=F>, Domain : Clone> Neg for $type {
            type Output = DeltaMeasure<Domain, F>;
            fn $fn(self) -> Self::Output {
                let mut tmp = self.clone();
                tmp.α = tmp.α.$fn();
                tmp
            }
        }
    }
}

make_delta_unary!(Neg, neg, DeltaMeasure<Domain, F>);
make_delta_unary!(Neg, neg, &'a DeltaMeasure<Domain, F>);