src/forward_model/bias.rs

/*!
Simple parametric forward model.
 */

use numeric_literals::replace_float_literals;
use alg_tools::types::{Float, ClosedAdd};
use alg_tools::mapping::Space;
use alg_tools::direct_product::Pair;
use alg_tools::linops::{Linear, RowOp, ColOp, IdOp, ZeroOp, AXPY};
use alg_tools::error::DynError;
use alg_tools::norms::{L2, Norm, PairNorm, NormExponent};
use crate::types::L2Squared;
use crate::measures::RNDM;
use super::{ForwardModel, AdjointProductBoundedBy, AdjointProductPairBoundedBy, LipschitzValues};
use crate::transport::TransportLipschitz;

impl<Domain, F, A, E> ForwardModel<Pair<Domain, A::Observable>, F, PairNorm<E, L2, L2>>
for RowOp<A, IdOp<A::Observable>>
where
    E : NormExponent,
    Domain : Space + Norm<F, E>,
    F : Float,
    A::Observable : ClosedAdd + Norm<F, L2> + 'static,
    A : ForwardModel<Domain, F, E> + 'static
{
    type Observable = A::Observable;

    fn write_observable(&self, b : &Self::Observable, prefix : String) -> DynError {
        self.0.write_observable(b, prefix)
    }

    /// Returns a zero observable
    fn zero_observable(&self) -> Self::Observable {
        self.0.zero_observable()
    }
}

#[replace_float_literals(F::cast_from(literal))]
impl<Domain, F, A, D, Z> AdjointProductPairBoundedBy<Pair<Domain, Z>, D, IdOp<Z>>
for RowOp<A, IdOp<Z>>
where
    Domain : Space,
    F : Float,
    Z : Clone + Space + ClosedAdd,
    A : AdjointProductBoundedBy<Domain, D, FloatType=F, Codomain = Z>,
    D : Linear<Domain>,
    A::Codomain : ClosedAdd,
{
    type FloatType = F;

    fn adjoint_product_pair_bound(&self, d : &D, _ : &IdOp<Z>) -> Option<(F, F)> {
        self.0.adjoint_product_bound(d).map(|l_0| {
            // [A_*; B_*][A, B] = [A_*A, A_* B; B_* A, B_* B] ≤ diag(2A_*A, 2B_*B)
            // ≤ diag(2l_A𝒟_A, 2l_B𝒟_B), where now 𝒟_B=Id and l_B=1.
            (2.0 * l_0, 2.0)
        })
    }
}

/// This `impl` is bit of an abuse as the codomain of `Apre` is a [`Pair`] of a measure predual,
/// to which this `impl` applies, and another space.
impl<F, Apre, Z> LipschitzValues
for ColOp<Apre, IdOp<Z>>
where
    F : Float,
    Z : Clone + Space + ClosedAdd,
    Apre : LipschitzValues<FloatType = F>,
{
    type FloatType = F;
    /// Return (if one exists) a factor $L$ such that $A_*z$ is $L$-Lipschitz for all
    /// $z$ in the unit ball.
    fn value_unit_lipschitz_factor(&self) -> Option<Self::FloatType> {
        self.0.value_unit_lipschitz_factor()
    }

    /// Return (if one exists) a factor $L$ such that $∇A_*z$ is $L$-Lipschitz for all
    /// $z$ in the unit ball.
    fn value_diff_unit_lipschitz_factor(&self) -> Option<Self::FloatType> {
        self.0.value_diff_unit_lipschitz_factor()
    }
}


impl<'a, F : Float, Y : Space, XD, const N : usize> TransportLipschitz<L2Squared> for
ZeroOp<'a, RNDM<F, N>, XD, Y, F> {
    type FloatType = F;

    fn transport_lipschitz_factor(&self, _ : L2Squared) -> Self::FloatType {
        F::ZERO
    }
}


/// TODO: should assume `D` to be positive semi-definite and self-adjoint.
#[replace_float_literals(F::cast_from(literal))]
impl<'a, F, D, XD, Y, const N : usize> AdjointProductBoundedBy<RNDM<F, N>, D>
for ZeroOp<'a, RNDM<F, N>, XD, Y, F>
where
    F : Float,
    Y : AXPY<F> + Clone,
    D : Linear<RNDM<F, N>>,
{
    type FloatType = F;
    /// Return $L$ such that $A_*A ≤ L𝒟$ is bounded by some `other` operator $𝒟$.
    fn adjoint_product_bound(&self, _ : &D) -> Option<F> {
        Some(0.0)
    }
}