--- a/src/linops.rs Sun Apr 27 20:41:36 2025 -0500
+++ b/src/linops.rs Mon Apr 28 08:26:04 2025 -0500
@@ -2,38 +2,46 @@
Abstract linear operators.
*/
-use numeric_literals::replace_float_literals;
-use std::marker::PhantomData;
-use serde::Serialize;
-use crate::types::*;
-pub use crate::mapping::{Mapping, Space, Composition};
use crate::direct_product::Pair;
use crate::instance::Instance;
-use crate::norms::{NormExponent, PairNorm, L1, L2, Linfinity, Norm};
+pub use crate::mapping::{Composition, DifferentiableImpl, Mapping, Space};
+use crate::norms::{Linfinity, Norm, NormExponent, PairNorm, L1, L2};
+use crate::types::*;
+use numeric_literals::replace_float_literals;
+use serde::Serialize;
+use std::marker::PhantomData;
/// Trait for linear operators on `X`.
-pub trait Linear<X : Space> : Mapping<X>
-{ }
+pub trait Linear<X: Space>: Mapping<X> {}
+
+// impl<X: Space, A: Linear<X>> DifferentiableImpl<X> for A {
+// type Derivative = <Self as Mapping<X>>::Codomain;
+
+// /// Compute the differential of `self` at `x`, consuming the input.
+// fn differential_impl<I: Instance<X>>(&self, x: I) -> Self::Derivative {
+// self.apply(x)
+// }
+// }
/// Efficient in-place summation.
#[replace_float_literals(F::cast_from(literal))]
-pub trait AXPY<F, X = Self> : Space + std::ops::MulAssign<F>
+pub trait AXPY<F, X = Self>: Space + std::ops::MulAssign<F>
where
- F : Num,
- X : Space,
+ F: Num,
+ X: Space,
{
- type Owned : AXPY<F, X>;
+ type Owned: AXPY<F, X>;
/// Computes `y = βy + αx`, where `y` is `Self`.
- fn axpy<I : Instance<X>>(&mut self, α : F, x : I, β : F);
+ fn axpy<I: Instance<X>>(&mut self, α: F, x: I, β: F);
/// Copies `x` to `self`.
- fn copy_from<I : Instance<X>>(&mut self, x : I) {
+ fn copy_from<I: Instance<X>>(&mut self, x: I) {
self.axpy(1.0, x, 0.0)
}
/// Computes `y = αx`, where `y` is `Self`.
- fn scale_from<I : Instance<X>>(&mut self, α : F, x : I) {
+ fn scale_from<I: Instance<X>>(&mut self, α: F, x: I) {
self.axpy(α, x, 0.0)
}
@@ -46,37 +54,36 @@
/// Efficient in-place application for [`Linear`] operators.
#[replace_float_literals(F::cast_from(literal))]
-pub trait GEMV<F : Num, X : Space, Y = <Self as Mapping<X>>::Codomain> : Linear<X> {
+pub trait GEMV<F: Num, X: Space, Y = <Self as Mapping<X>>::Codomain>: Linear<X> {
/// Computes `y = αAx + βy`, where `A` is `Self`.
- fn gemv<I : Instance<X>>(&self, y : &mut Y, α : F, x : I, β : F);
+ fn gemv<I: Instance<X>>(&self, y: &mut Y, α: F, x: I, β: F);
#[inline]
/// Computes `y = Ax`, where `A` is `Self`
- fn apply_mut<I : Instance<X>>(&self, y : &mut Y, x : I){
+ fn apply_mut<I: Instance<X>>(&self, y: &mut Y, x: I) {
self.gemv(y, 1.0, x, 0.0)
}
#[inline]
/// Computes `y += Ax`, where `A` is `Self`
- fn apply_add<I : Instance<X>>(&self, y : &mut Y, x : I){
+ fn apply_add<I: Instance<X>>(&self, y: &mut Y, x: I) {
self.gemv(y, 1.0, x, 1.0)
}
}
-
/// Bounded linear operators
-pub trait BoundedLinear<X, XExp, CodExp, F = f64> : Linear<X>
+pub trait BoundedLinear<X, XExp, CodExp, F = f64>: Linear<X>
where
- F : Num,
- X : Space + Norm<F, XExp>,
- XExp : NormExponent,
- CodExp : NormExponent
+ F: Num,
+ X: Space + Norm<F, XExp>,
+ XExp: NormExponent,
+ CodExp: NormExponent,
{
/// A bound on the operator norm $\|A\|$ for the linear operator $A$=`self`.
/// This is not expected to be the norm, just any bound on it that can be
/// reasonably implemented. The [`NormExponent`] `xexp` indicates the norm
/// in `X`, and `codexp` in the codomain.
- fn opnorm_bound(&self, xexp : XExp, codexp : CodExp) -> F;
+ fn opnorm_bound(&self, xexp: XExp, codexp: CodExp) -> F;
}
// Linear operator application into mutable target. The [`AsRef`] bound
@@ -90,13 +97,15 @@
}*/
/// Trait for forming the adjoint operator of `Self`.
-pub trait Adjointable<X, Yʹ> : Linear<X>
+pub trait Adjointable<X, Yʹ>: Linear<X>
where
- X : Space,
- Yʹ : Space,
+ X: Space,
+ Yʹ: Space,
{
- type AdjointCodomain : Space;
- type Adjoint<'a> : Linear<Yʹ, Codomain=Self::AdjointCodomain> where Self : 'a;
+ type AdjointCodomain: Space;
+ type Adjoint<'a>: Linear<Yʹ, Codomain = Self::AdjointCodomain>
+ where
+ Self: 'a;
/// Form the adjoint operator of `self`.
fn adjoint(&self) -> Self::Adjoint<'_>;
@@ -112,144 +121,168 @@
/// We do not make additional restrictions on `Self::Preadjoint` (in particular, it
/// does not have to be adjointable) to allow `X` to be a subspace yet the preadjoint
/// have the full space as the codomain, etc.
-pub trait Preadjointable<X : Space, Ypre : Space> : Linear<X> {
- type PreadjointCodomain : Space;
- type Preadjoint<'a> : Linear<
- Ypre, Codomain=Self::PreadjointCodomain
- > where Self : 'a;
+pub trait Preadjointable<X: Space, Ypre: Space = <Self as Mapping<X>>::Codomain>:
+ Linear<X>
+{
+ type PreadjointCodomain: Space;
+ type Preadjoint<'a>: Linear<Ypre, Codomain = Self::PreadjointCodomain>
+ where
+ Self: 'a;
/// Form the adjoint operator of `self`.
fn preadjoint(&self) -> Self::Preadjoint<'_>;
}
/// Adjointable operators $A: X → Y$ between reflexive spaces $X$ and $Y$.
-pub trait SimplyAdjointable<X : Space> : Adjointable<X,<Self as Mapping<X>>::Codomain> {}
-impl<'a,X : Space, T> SimplyAdjointable<X> for T
-where T : Adjointable<X,<Self as Mapping<X>>::Codomain> {}
+pub trait SimplyAdjointable<X: Space>: Adjointable<X, <Self as Mapping<X>>::Codomain> {}
+impl<'a, X: Space, T> SimplyAdjointable<X> for T where
+ T: Adjointable<X, <Self as Mapping<X>>::Codomain>
+{
+}
/// The identity operator
-#[derive(Clone,Copy,Debug,Serialize,Eq,PartialEq)]
-pub struct IdOp<X> (PhantomData<X>);
+#[derive(Clone, Copy, Debug, Serialize, Eq, PartialEq)]
+pub struct IdOp<X>(PhantomData<X>);
impl<X> IdOp<X> {
- pub fn new() -> IdOp<X> { IdOp(PhantomData) }
+ pub fn new() -> IdOp<X> {
+ IdOp(PhantomData)
+ }
}
-impl<X : Clone + Space> Mapping<X> for IdOp<X> {
+impl<X: Clone + Space> Mapping<X> for IdOp<X> {
type Codomain = X;
- fn apply<I : Instance<X>>(&self, x : I) -> X {
+ fn apply<I: Instance<X>>(&self, x: I) -> X {
x.own()
}
}
-impl<X : Clone + Space> Linear<X> for IdOp<X>
-{ }
+impl<X: Clone + Space> Linear<X> for IdOp<X> {}
#[replace_float_literals(F::cast_from(literal))]
-impl<F : Num, X, Y> GEMV<F, X, Y> for IdOp<X>
+impl<F: Num, X, Y> GEMV<F, X, Y> for IdOp<X>
where
- Y : AXPY<F, X>,
- X : Clone + Space
+ Y: AXPY<F, X>,
+ X: Clone + Space,
{
// Computes `y = αAx + βy`, where `A` is `Self`.
- fn gemv<I : Instance<X>>(&self, y : &mut Y, α : F, x : I, β : F) {
+ fn gemv<I: Instance<X>>(&self, y: &mut Y, α: F, x: I, β: F) {
y.axpy(α, x, β)
}
- fn apply_mut<I : Instance<X>>(&self, y : &mut Y, x : I){
+ fn apply_mut<I: Instance<X>>(&self, y: &mut Y, x: I) {
y.copy_from(x);
}
}
impl<F, X, E> BoundedLinear<X, E, E, F> for IdOp<X>
where
- X : Space + Clone + Norm<F, E>,
- F : Num,
- E : NormExponent
+ X: Space + Clone + Norm<F, E>,
+ F: Num,
+ E: NormExponent,
{
- fn opnorm_bound(&self, _xexp : E, _codexp : E) -> F { F::ONE }
-}
-
-impl<X : Clone + Space> Adjointable<X,X> for IdOp<X> {
- type AdjointCodomain=X;
- type Adjoint<'a> = IdOp<X> where X : 'a;
-
- fn adjoint(&self) -> Self::Adjoint<'_> { IdOp::new() }
+ fn opnorm_bound(&self, _xexp: E, _codexp: E) -> F {
+ F::ONE
+ }
}
-impl<X : Clone + Space> Preadjointable<X,X> for IdOp<X> {
- type PreadjointCodomain=X;
- type Preadjoint<'a> = IdOp<X> where X : 'a;
+impl<X: Clone + Space> Adjointable<X, X> for IdOp<X> {
+ type AdjointCodomain = X;
+ type Adjoint<'a>
+ = IdOp<X>
+ where
+ X: 'a;
- fn preadjoint(&self) -> Self::Preadjoint<'_> { IdOp::new() }
+ fn adjoint(&self) -> Self::Adjoint<'_> {
+ IdOp::new()
+ }
}
+impl<X: Clone + Space> Preadjointable<X, X> for IdOp<X> {
+ type PreadjointCodomain = X;
+ type Preadjoint<'a>
+ = IdOp<X>
+ where
+ X: 'a;
+
+ fn preadjoint(&self) -> Self::Preadjoint<'_> {
+ IdOp::new()
+ }
+}
/// The zero operator
-#[derive(Clone,Copy,Debug,Serialize,Eq,PartialEq)]
+#[derive(Clone, Copy, Debug, Serialize, Eq, PartialEq)]
pub struct ZeroOp<'a, X, XD, Y, F> {
- zero : &'a Y, // TODO: don't pass this in `new`; maybe not even store.
- dual_or_predual_zero : XD,
- _phantoms : PhantomData<(X, Y, F)>,
+ zero: &'a Y, // TODO: don't pass this in `new`; maybe not even store.
+ dual_or_predual_zero: XD,
+ _phantoms: PhantomData<(X, Y, F)>,
}
// TODO: Need to make Zero in Instance.
-impl<'a, F : Num, X : Space, XD, Y : Space + Clone> ZeroOp<'a, X, XD, Y, F> {
- pub fn new(zero : &'a Y, dual_or_predual_zero : XD) -> Self {
- ZeroOp{ zero, dual_or_predual_zero, _phantoms : PhantomData }
+impl<'a, F: Num, X: Space, XD, Y: Space + Clone> ZeroOp<'a, X, XD, Y, F> {
+ pub fn new(zero: &'a Y, dual_or_predual_zero: XD) -> Self {
+ ZeroOp {
+ zero,
+ dual_or_predual_zero,
+ _phantoms: PhantomData,
+ }
}
}
-impl<'a, F : Num, X : Space, XD, Y : AXPY<F> + Clone> Mapping<X> for ZeroOp<'a, X, XD, Y, F> {
+impl<'a, F: Num, X: Space, XD, Y: AXPY<F> + Clone> Mapping<X> for ZeroOp<'a, X, XD, Y, F> {
type Codomain = Y;
- fn apply<I : Instance<X>>(&self, _x : I) -> Y {
+ fn apply<I: Instance<X>>(&self, _x: I) -> Y {
self.zero.clone()
}
}
-impl<'a, F : Num, X : Space, XD, Y : AXPY<F> + Clone> Linear<X> for ZeroOp<'a, X, XD, Y, F>
-{ }
+impl<'a, F: Num, X: Space, XD, Y: AXPY<F> + Clone> Linear<X> for ZeroOp<'a, X, XD, Y, F> {}
#[replace_float_literals(F::cast_from(literal))]
impl<'a, F, X, XD, Y> GEMV<F, X, Y> for ZeroOp<'a, X, XD, Y, F>
where
- F : Num,
- Y : AXPY<F, Y> + Clone,
- X : Space
+ F: Num,
+ Y: AXPY<F, Y> + Clone,
+ X: Space,
{
// Computes `y = αAx + βy`, where `A` is `Self`.
- fn gemv<I : Instance<X>>(&self, y : &mut Y, _α : F, _x : I, β : F) {
+ fn gemv<I: Instance<X>>(&self, y: &mut Y, _α: F, _x: I, β: F) {
*y *= β;
}
- fn apply_mut<I : Instance<X>>(&self, y : &mut Y, _x : I){
+ fn apply_mut<I: Instance<X>>(&self, y: &mut Y, _x: I) {
y.set_zero();
}
}
impl<'a, F, X, XD, Y, E1, E2> BoundedLinear<X, E1, E2, F> for ZeroOp<'a, X, XD, Y, F>
where
- X : Space + Norm<F, E1>,
- Y : AXPY<F> + Clone + Norm<F, E2>,
- F : Num,
- E1 : NormExponent,
- E2 : NormExponent,
+ X: Space + Norm<F, E1>,
+ Y: AXPY<F> + Clone + Norm<F, E2>,
+ F: Num,
+ E1: NormExponent,
+ E2: NormExponent,
{
- fn opnorm_bound(&self, _xexp : E1, _codexp : E2) -> F { F::ZERO }
+ fn opnorm_bound(&self, _xexp: E1, _codexp: E2) -> F {
+ F::ZERO
+ }
}
-impl<'a, F : Num, X, XD, Y, Yprime : Space> Adjointable<X, Yprime> for ZeroOp<'a, X, XD, Y, F>
+impl<'a, F: Num, X, XD, Y, Yprime: Space> Adjointable<X, Yprime> for ZeroOp<'a, X, XD, Y, F>
where
- X : Space,
- Y : AXPY<F> + Clone + 'static,
- XD : AXPY<F> + Clone + 'static,
+ X: Space,
+ Y: AXPY<F> + Clone + 'static,
+ XD: AXPY<F> + Clone + 'static,
{
type AdjointCodomain = XD;
- type Adjoint<'b> = ZeroOp<'b, Yprime, (), XD, F> where Self : 'b;
- // () means not (pre)adjointable.
+ type Adjoint<'b>
+ = ZeroOp<'b, Yprime, (), XD, F>
+ where
+ Self: 'b;
+ // () means not (pre)adjointable.
fn adjoint(&self) -> Self::Adjoint<'_> {
ZeroOp::new(&self.dual_or_predual_zero, ())
@@ -258,15 +291,18 @@
impl<'a, F, X, XD, Y, Ypre> Preadjointable<X, Ypre> for ZeroOp<'a, X, XD, Y, F>
where
- F : Num,
- X : Space,
- Y : AXPY<F> + Clone,
- Ypre : Space,
- XD : AXPY<F> + Clone + 'static,
+ F: Num,
+ X: Space,
+ Y: AXPY<F> + Clone,
+ Ypre: Space,
+ XD: AXPY<F> + Clone + 'static,
{
type PreadjointCodomain = XD;
- type Preadjoint<'b> = ZeroOp<'b, Ypre, (), XD, F> where Self : 'b;
- // () means not (pre)adjointable.
+ type Preadjoint<'b>
+ = ZeroOp<'b, Ypre, (), XD, F>
+ where
+ Self: 'b;
+ // () means not (pre)adjointable.
fn preadjoint(&self) -> Self::Preadjoint<'_> {
ZeroOp::new(&self.dual_or_predual_zero, ())
@@ -275,45 +311,46 @@
impl<S, T, E, X> Linear<X> for Composition<S, T, E>
where
- X : Space,
- T : Linear<X>,
- S : Linear<T::Codomain>
-{ }
+ X: Space,
+ T: Linear<X>,
+ S: Linear<T::Codomain>,
+{
+}
impl<F, S, T, E, X, Y> GEMV<F, X, Y> for Composition<S, T, E>
where
- F : Num,
- X : Space,
- T : Linear<X>,
- S : GEMV<F, T::Codomain, Y>,
+ F: Num,
+ X: Space,
+ T: Linear<X>,
+ S: GEMV<F, T::Codomain, Y>,
{
- fn gemv<I : Instance<X>>(&self, y : &mut Y, α : F, x : I, β : F) {
+ fn gemv<I: Instance<X>>(&self, y: &mut Y, α: F, x: I, β: F) {
self.outer.gemv(y, α, self.inner.apply(x), β)
}
/// Computes `y = Ax`, where `A` is `Self`
- fn apply_mut<I : Instance<X>>(&self, y : &mut Y, x : I){
+ fn apply_mut<I: Instance<X>>(&self, y: &mut Y, x: I) {
self.outer.apply_mut(y, self.inner.apply(x))
}
/// Computes `y += Ax`, where `A` is `Self`
- fn apply_add<I : Instance<X>>(&self, y : &mut Y, x : I){
+ fn apply_add<I: Instance<X>>(&self, y: &mut Y, x: I) {
self.outer.apply_add(y, self.inner.apply(x))
}
}
impl<F, S, T, X, Z, Xexp, Yexp, Zexp> BoundedLinear<X, Xexp, Yexp, F> for Composition<S, T, Zexp>
where
- F : Num,
- X : Space + Norm<F, Xexp>,
- Z : Space + Norm<F, Zexp>,
- Xexp : NormExponent,
- Yexp : NormExponent,
- Zexp : NormExponent,
- T : BoundedLinear<X, Xexp, Zexp, F, Codomain=Z>,
- S : BoundedLinear<Z, Zexp, Yexp, F>,
+ F: Num,
+ X: Space + Norm<F, Xexp>,
+ Z: Space + Norm<F, Zexp>,
+ Xexp: NormExponent,
+ Yexp: NormExponent,
+ Zexp: NormExponent,
+ T: BoundedLinear<X, Xexp, Zexp, F, Codomain = Z>,
+ S: BoundedLinear<Z, Zexp, Yexp, F>,
{
- fn opnorm_bound(&self, xexp : Xexp, yexp : Yexp) -> F {
+ fn opnorm_bound(&self, xexp: Xexp, yexp: Yexp) -> F {
let zexp = self.intermediate_norm_exponent;
self.outer.opnorm_bound(zexp, yexp) * self.inner.opnorm_bound(xexp, zexp)
}
@@ -326,17 +363,16 @@
impl<A, B, S, T> Mapping<Pair<A, B>> for RowOp<S, T>
where
- A : Space,
- B : Space,
- S : Mapping<A>,
- T : Mapping<B>,
- S::Codomain : Add<T::Codomain>,
- <S::Codomain as Add<T::Codomain>>::Output : Space,
-
+ A: Space,
+ B: Space,
+ S: Mapping<A>,
+ T: Mapping<B>,
+ S::Codomain: Add<T::Codomain>,
+ <S::Codomain as Add<T::Codomain>>::Output: Space,
{
type Codomain = <S::Codomain as Add<T::Codomain>>::Output;
- fn apply<I : Instance<Pair<A, B>>>(&self, x : I) -> Self::Codomain {
+ fn apply<I: Instance<Pair<A, B>>>(&self, x: I) -> Self::Codomain {
let Pair(a, b) = x.decompose();
self.0.apply(a) + self.1.apply(b)
}
@@ -344,38 +380,38 @@
impl<A, B, S, T> Linear<Pair<A, B>> for RowOp<S, T>
where
- A : Space,
- B : Space,
- S : Linear<A>,
- T : Linear<B>,
- S::Codomain : Add<T::Codomain>,
- <S::Codomain as Add<T::Codomain>>::Output : Space,
-{ }
-
+ A: Space,
+ B: Space,
+ S: Linear<A>,
+ T: Linear<B>,
+ S::Codomain: Add<T::Codomain>,
+ <S::Codomain as Add<T::Codomain>>::Output: Space,
+{
+}
impl<'b, F, S, T, Y, U, V> GEMV<F, Pair<U, V>, Y> for RowOp<S, T>
where
- U : Space,
- V : Space,
- S : GEMV<F, U, Y>,
- T : GEMV<F, V, Y>,
- F : Num,
- Self : Linear<Pair<U, V>, Codomain=Y>
+ U: Space,
+ V: Space,
+ S: GEMV<F, U, Y>,
+ T: GEMV<F, V, Y>,
+ F: Num,
+ Self: Linear<Pair<U, V>, Codomain = Y>,
{
- fn gemv<I : Instance<Pair<U, V>>>(&self, y : &mut Y, α : F, x : I, β : F) {
+ fn gemv<I: Instance<Pair<U, V>>>(&self, y: &mut Y, α: F, x: I, β: F) {
let Pair(u, v) = x.decompose();
self.0.gemv(y, α, u, β);
self.1.gemv(y, α, v, F::ONE);
}
- fn apply_mut<I : Instance<Pair<U, V>>>(&self, y : &mut Y, x : I) {
+ fn apply_mut<I: Instance<Pair<U, V>>>(&self, y: &mut Y, x: I) {
let Pair(u, v) = x.decompose();
self.0.apply_mut(y, u);
self.1.apply_add(y, v);
}
/// Computes `y += Ax`, where `A` is `Self`
- fn apply_add<I : Instance<Pair<U, V>>>(&self, y : &mut Y, x : I) {
+ fn apply_add<I: Instance<Pair<U, V>>>(&self, y: &mut Y, x: I) {
let Pair(u, v) = x.decompose();
self.0.apply_add(y, u);
self.1.apply_add(y, v);
@@ -387,129 +423,137 @@
impl<A, S, T> Mapping<A> for ColOp<S, T>
where
- A : Space,
- S : Mapping<A>,
- T : Mapping<A>,
+ A: Space,
+ S: Mapping<A>,
+ T: Mapping<A>,
{
type Codomain = Pair<S::Codomain, T::Codomain>;
- fn apply<I : Instance<A>>(&self, a : I) -> Self::Codomain {
+ fn apply<I: Instance<A>>(&self, a: I) -> Self::Codomain {
Pair(self.0.apply(a.ref_instance()), self.1.apply(a))
}
}
impl<A, S, T> Linear<A> for ColOp<S, T>
where
- A : Space,
- S : Mapping<A>,
- T : Mapping<A>,
-{ }
+ A: Space,
+ S: Mapping<A>,
+ T: Mapping<A>,
+{
+}
impl<F, S, T, A, B, X> GEMV<F, X, Pair<A, B>> for ColOp<S, T>
where
- X : Space,
- S : GEMV<F, X, A>,
- T : GEMV<F, X, B>,
- F : Num,
- Self : Linear<X, Codomain=Pair<A, B>>
+ X: Space,
+ S: GEMV<F, X, A>,
+ T: GEMV<F, X, B>,
+ F: Num,
+ Self: Linear<X, Codomain = Pair<A, B>>,
{
- fn gemv<I : Instance<X>>(&self, y : &mut Pair<A, B>, α : F, x : I, β : F) {
+ fn gemv<I: Instance<X>>(&self, y: &mut Pair<A, B>, α: F, x: I, β: F) {
self.0.gemv(&mut y.0, α, x.ref_instance(), β);
self.1.gemv(&mut y.1, α, x, β);
}
- fn apply_mut<I : Instance<X>>(&self, y : &mut Pair<A, B>, x : I){
+ fn apply_mut<I: Instance<X>>(&self, y: &mut Pair<A, B>, x: I) {
self.0.apply_mut(&mut y.0, x.ref_instance());
self.1.apply_mut(&mut y.1, x);
}
/// Computes `y += Ax`, where `A` is `Self`
- fn apply_add<I : Instance<X>>(&self, y : &mut Pair<A, B>, x : I){
+ fn apply_add<I: Instance<X>>(&self, y: &mut Pair<A, B>, x: I) {
self.0.apply_add(&mut y.0, x.ref_instance());
self.1.apply_add(&mut y.1, x);
}
}
-
-impl<A, B, Yʹ, S, T> Adjointable<Pair<A,B>, Yʹ> for RowOp<S, T>
+impl<A, B, Yʹ, S, T> Adjointable<Pair<A, B>, Yʹ> for RowOp<S, T>
where
- A : Space,
- B : Space,
- Yʹ : Space,
- S : Adjointable<A, Yʹ>,
- T : Adjointable<B, Yʹ>,
- Self : Linear<Pair<A, B>>,
+ A: Space,
+ B: Space,
+ Yʹ: Space,
+ S: Adjointable<A, Yʹ>,
+ T: Adjointable<B, Yʹ>,
+ Self: Linear<Pair<A, B>>,
// for<'a> ColOp<S::Adjoint<'a>, T::Adjoint<'a>> : Linear<
// Yʹ,
// Codomain=Pair<S::AdjointCodomain, T::AdjointCodomain>
// >,
{
type AdjointCodomain = Pair<S::AdjointCodomain, T::AdjointCodomain>;
- type Adjoint<'a> = ColOp<S::Adjoint<'a>, T::Adjoint<'a>> where Self : 'a;
+ type Adjoint<'a>
+ = ColOp<S::Adjoint<'a>, T::Adjoint<'a>>
+ where
+ Self: 'a;
fn adjoint(&self) -> Self::Adjoint<'_> {
ColOp(self.0.adjoint(), self.1.adjoint())
}
}
-impl<A, B, Yʹ, S, T> Preadjointable<Pair<A,B>, Yʹ> for RowOp<S, T>
+impl<A, B, Yʹ, S, T> Preadjointable<Pair<A, B>, Yʹ> for RowOp<S, T>
where
- A : Space,
- B : Space,
- Yʹ : Space,
- S : Preadjointable<A, Yʹ>,
- T : Preadjointable<B, Yʹ>,
- Self : Linear<Pair<A, B>>,
- for<'a> ColOp<S::Preadjoint<'a>, T::Preadjoint<'a>> : Linear<
- Yʹ, Codomain=Pair<S::PreadjointCodomain, T::PreadjointCodomain>,
- >,
+ A: Space,
+ B: Space,
+ Yʹ: Space,
+ S: Preadjointable<A, Yʹ>,
+ T: Preadjointable<B, Yʹ>,
+ Self: Linear<Pair<A, B>>,
+ for<'a> ColOp<S::Preadjoint<'a>, T::Preadjoint<'a>>:
+ Linear<Yʹ, Codomain = Pair<S::PreadjointCodomain, T::PreadjointCodomain>>,
{
type PreadjointCodomain = Pair<S::PreadjointCodomain, T::PreadjointCodomain>;
- type Preadjoint<'a> = ColOp<S::Preadjoint<'a>, T::Preadjoint<'a>> where Self : 'a;
+ type Preadjoint<'a>
+ = ColOp<S::Preadjoint<'a>, T::Preadjoint<'a>>
+ where
+ Self: 'a;
fn preadjoint(&self) -> Self::Preadjoint<'_> {
ColOp(self.0.preadjoint(), self.1.preadjoint())
}
}
-
-impl<A, Xʹ, Yʹ, R, S, T> Adjointable<A,Pair<Xʹ,Yʹ>> for ColOp<S, T>
+impl<A, Xʹ, Yʹ, R, S, T> Adjointable<A, Pair<Xʹ, Yʹ>> for ColOp<S, T>
where
- A : Space,
- Xʹ : Space,
- Yʹ : Space,
- R : Space + ClosedAdd,
- S : Adjointable<A, Xʹ, AdjointCodomain = R>,
- T : Adjointable<A, Yʹ, AdjointCodomain = R>,
- Self : Linear<A>,
+ A: Space,
+ Xʹ: Space,
+ Yʹ: Space,
+ R: Space + ClosedAdd,
+ S: Adjointable<A, Xʹ, AdjointCodomain = R>,
+ T: Adjointable<A, Yʹ, AdjointCodomain = R>,
+ Self: Linear<A>,
// for<'a> RowOp<S::Adjoint<'a>, T::Adjoint<'a>> : Linear<
// Pair<Xʹ,Yʹ>,
// Codomain=R,
// >,
{
type AdjointCodomain = R;
- type Adjoint<'a> = RowOp<S::Adjoint<'a>, T::Adjoint<'a>> where Self : 'a;
+ type Adjoint<'a>
+ = RowOp<S::Adjoint<'a>, T::Adjoint<'a>>
+ where
+ Self: 'a;
fn adjoint(&self) -> Self::Adjoint<'_> {
RowOp(self.0.adjoint(), self.1.adjoint())
}
}
-impl<A, Xʹ, Yʹ, R, S, T> Preadjointable<A,Pair<Xʹ,Yʹ>> for ColOp<S, T>
+impl<A, Xʹ, Yʹ, R, S, T> Preadjointable<A, Pair<Xʹ, Yʹ>> for ColOp<S, T>
where
- A : Space,
- Xʹ : Space,
- Yʹ : Space,
- R : Space + ClosedAdd,
- S : Preadjointable<A, Xʹ, PreadjointCodomain = R>,
- T : Preadjointable<A, Yʹ, PreadjointCodomain = R>,
- Self : Linear<A>,
- for<'a> RowOp<S::Preadjoint<'a>, T::Preadjoint<'a>> : Linear<
- Pair<Xʹ,Yʹ>, Codomain = R,
- >,
+ A: Space,
+ Xʹ: Space,
+ Yʹ: Space,
+ R: Space + ClosedAdd,
+ S: Preadjointable<A, Xʹ, PreadjointCodomain = R>,
+ T: Preadjointable<A, Yʹ, PreadjointCodomain = R>,
+ Self: Linear<A>,
+ for<'a> RowOp<S::Preadjoint<'a>, T::Preadjoint<'a>>: Linear<Pair<Xʹ, Yʹ>, Codomain = R>,
{
type PreadjointCodomain = R;
- type Preadjoint<'a> = RowOp<S::Preadjoint<'a>, T::Preadjoint<'a>> where Self : 'a;
+ type Preadjoint<'a>
+ = RowOp<S::Preadjoint<'a>, T::Preadjoint<'a>>
+ where
+ Self: 'a;
fn preadjoint(&self) -> Self::Preadjoint<'_> {
RowOp(self.0.preadjoint(), self.1.preadjoint())
@@ -521,14 +565,14 @@
impl<A, B, S, T> Mapping<Pair<A, B>> for DiagOp<S, T>
where
- A : Space,
- B : Space,
- S : Mapping<A>,
- T : Mapping<B>,
+ A: Space,
+ B: Space,
+ S: Mapping<A>,
+ T: Mapping<B>,
{
type Codomain = Pair<S::Codomain, T::Codomain>;
- fn apply<I : Instance<Pair<A, B>>>(&self, x : I) -> Self::Codomain {
+ fn apply<I: Instance<Pair<A, B>>>(&self, x: I) -> Self::Codomain {
let Pair(a, b) = x.decompose();
Pair(self.0.apply(a), self.1.apply(b))
}
@@ -536,81 +580,84 @@
impl<A, B, S, T> Linear<Pair<A, B>> for DiagOp<S, T>
where
- A : Space,
- B : Space,
- S : Linear<A>,
- T : Linear<B>,
-{ }
+ A: Space,
+ B: Space,
+ S: Linear<A>,
+ T: Linear<B>,
+{
+}
impl<F, S, T, A, B, U, V> GEMV<F, Pair<U, V>, Pair<A, B>> for DiagOp<S, T>
where
- A : Space,
- B : Space,
- U : Space,
- V : Space,
- S : GEMV<F, U, A>,
- T : GEMV<F, V, B>,
- F : Num,
- Self : Linear<Pair<U, V>, Codomain=Pair<A, B>>,
+ A: Space,
+ B: Space,
+ U: Space,
+ V: Space,
+ S: GEMV<F, U, A>,
+ T: GEMV<F, V, B>,
+ F: Num,
+ Self: Linear<Pair<U, V>, Codomain = Pair<A, B>>,
{
- fn gemv<I : Instance<Pair<U, V>>>(&self, y : &mut Pair<A, B>, α : F, x : I, β : F) {
+ fn gemv<I: Instance<Pair<U, V>>>(&self, y: &mut Pair<A, B>, α: F, x: I, β: F) {
let Pair(u, v) = x.decompose();
self.0.gemv(&mut y.0, α, u, β);
self.1.gemv(&mut y.1, α, v, β);
}
- fn apply_mut<I : Instance<Pair<U, V>>>(&self, y : &mut Pair<A, B>, x : I){
+ fn apply_mut<I: Instance<Pair<U, V>>>(&self, y: &mut Pair<A, B>, x: I) {
let Pair(u, v) = x.decompose();
self.0.apply_mut(&mut y.0, u);
self.1.apply_mut(&mut y.1, v);
}
/// Computes `y += Ax`, where `A` is `Self`
- fn apply_add<I : Instance<Pair<U, V>>>(&self, y : &mut Pair<A, B>, x : I){
+ fn apply_add<I: Instance<Pair<U, V>>>(&self, y: &mut Pair<A, B>, x: I) {
let Pair(u, v) = x.decompose();
self.0.apply_add(&mut y.0, u);
self.1.apply_add(&mut y.1, v);
}
}
-impl<A, B, Xʹ, Yʹ, R, S, T> Adjointable<Pair<A,B>, Pair<Xʹ,Yʹ>> for DiagOp<S, T>
+impl<A, B, Xʹ, Yʹ, R, S, T> Adjointable<Pair<A, B>, Pair<Xʹ, Yʹ>> for DiagOp<S, T>
where
- A : Space,
- B : Space,
+ A: Space,
+ B: Space,
Xʹ: Space,
- Yʹ : Space,
- R : Space,
- S : Adjointable<A, Xʹ>,
- T : Adjointable<B, Yʹ>,
- Self : Linear<Pair<A, B>>,
- for<'a> DiagOp<S::Adjoint<'a>, T::Adjoint<'a>> : Linear<
- Pair<Xʹ,Yʹ>, Codomain=R,
- >,
+ Yʹ: Space,
+ R: Space,
+ S: Adjointable<A, Xʹ>,
+ T: Adjointable<B, Yʹ>,
+ Self: Linear<Pair<A, B>>,
+ for<'a> DiagOp<S::Adjoint<'a>, T::Adjoint<'a>>: Linear<Pair<Xʹ, Yʹ>, Codomain = R>,
{
type AdjointCodomain = R;
- type Adjoint<'a> = DiagOp<S::Adjoint<'a>, T::Adjoint<'a>> where Self : 'a;
+ type Adjoint<'a>
+ = DiagOp<S::Adjoint<'a>, T::Adjoint<'a>>
+ where
+ Self: 'a;
fn adjoint(&self) -> Self::Adjoint<'_> {
DiagOp(self.0.adjoint(), self.1.adjoint())
}
}
-impl<A, B, Xʹ, Yʹ, R, S, T> Preadjointable<Pair<A,B>, Pair<Xʹ,Yʹ>> for DiagOp<S, T>
+impl<A, B, Xʹ, Yʹ, R, S, T> Preadjointable<Pair<A, B>, Pair<Xʹ, Yʹ>> for DiagOp<S, T>
where
- A : Space,
- B : Space,
+ A: Space,
+ B: Space,
Xʹ: Space,
- Yʹ : Space,
- R : Space,
- S : Preadjointable<A, Xʹ>,
- T : Preadjointable<B, Yʹ>,
- Self : Linear<Pair<A, B>>,
- for<'a> DiagOp<S::Preadjoint<'a>, T::Preadjoint<'a>> : Linear<
- Pair<Xʹ,Yʹ>, Codomain=R,
- >,
+ Yʹ: Space,
+ R: Space,
+ S: Preadjointable<A, Xʹ>,
+ T: Preadjointable<B, Yʹ>,
+ Self: Linear<Pair<A, B>>,
+ for<'a> DiagOp<S::Preadjoint<'a>, T::Preadjoint<'a>>: Linear<Pair<Xʹ, Yʹ>, Codomain = R>,
{
type PreadjointCodomain = R;
- type Preadjoint<'a> = DiagOp<S::Preadjoint<'a>, T::Preadjoint<'a>> where Self : 'a;
+ type Preadjoint<'a>
+ = DiagOp<S::Preadjoint<'a>, T::Preadjoint<'a>>
+ where
+ Self: 'a;
fn preadjoint(&self) -> Self::Preadjoint<'_> {
DiagOp(self.0.preadjoint(), self.1.preadjoint())
@@ -620,28 +667,26 @@
/// Block operator
pub type BlockOp<S11, S12, S21, S22> = ColOp<RowOp<S11, S12>, RowOp<S21, S22>>;
-
macro_rules! pairnorm {
($expj:ty) => {
impl<F, A, B, S, T, ExpA, ExpB, ExpR>
- BoundedLinear<Pair<A, B>, PairNorm<ExpA, ExpB, $expj>, ExpR, F>
- for RowOp<S, T>
+ BoundedLinear<Pair<A, B>, PairNorm<ExpA, ExpB, $expj>, ExpR, F> for RowOp<S, T>
where
- F : Float,
- A : Space + Norm<F, ExpA>,
- B : Space + Norm<F, ExpB>,
- S : BoundedLinear<A, ExpA, ExpR, F>,
- T : BoundedLinear<B, ExpB, ExpR, F>,
- S::Codomain : Add<T::Codomain>,
- <S::Codomain as Add<T::Codomain>>::Output : Space,
- ExpA : NormExponent,
- ExpB : NormExponent,
- ExpR : NormExponent,
+ F: Float,
+ A: Space + Norm<F, ExpA>,
+ B: Space + Norm<F, ExpB>,
+ S: BoundedLinear<A, ExpA, ExpR, F>,
+ T: BoundedLinear<B, ExpB, ExpR, F>,
+ S::Codomain: Add<T::Codomain>,
+ <S::Codomain as Add<T::Codomain>>::Output: Space,
+ ExpA: NormExponent,
+ ExpB: NormExponent,
+ ExpR: NormExponent,
{
fn opnorm_bound(
&self,
- PairNorm(expa, expb, _) : PairNorm<ExpA, ExpB, $expj>,
- expr : ExpR
+ PairNorm(expa, expb, _): PairNorm<ExpA, ExpB, $expj>,
+ expr: ExpR,
) -> F {
// An application of the triangle inequality bounds the norm by the maximum
// of the individual norms. A simple observation shows this to be exact.
@@ -650,23 +695,22 @@
na.max(nb)
}
}
-
- impl<F, A, S, T, ExpA, ExpS, ExpT>
- BoundedLinear<A, ExpA, PairNorm<ExpS, ExpT, $expj>, F>
- for ColOp<S, T>
+
+ impl<F, A, S, T, ExpA, ExpS, ExpT> BoundedLinear<A, ExpA, PairNorm<ExpS, ExpT, $expj>, F>
+ for ColOp<S, T>
where
- F : Float,
- A : Space + Norm<F, ExpA>,
- S : BoundedLinear<A, ExpA, ExpS, F>,
- T : BoundedLinear<A, ExpA, ExpT, F>,
- ExpA : NormExponent,
- ExpS : NormExponent,
- ExpT : NormExponent,
+ F: Float,
+ A: Space + Norm<F, ExpA>,
+ S: BoundedLinear<A, ExpA, ExpS, F>,
+ T: BoundedLinear<A, ExpA, ExpT, F>,
+ ExpA: NormExponent,
+ ExpS: NormExponent,
+ ExpT: NormExponent,
{
fn opnorm_bound(
&self,
- expa : ExpA,
- PairNorm(exps, expt, _) : PairNorm<ExpS, ExpT, $expj>
+ expa: ExpA,
+ PairNorm(exps, expt, _): PairNorm<ExpS, ExpT, $expj>,
) -> F {
// This is based on the rule for RowOp and ‖A^*‖ = ‖A‖, hence,
// for A=[S; T], ‖A‖=‖[S^*, T^*]‖ ≤ max{‖S^*‖, ‖T^*‖} = max{‖S‖, ‖T‖}
@@ -675,10 +719,9 @@
ns.max(nt)
}
}
- }
+ };
}
pairnorm!(L1);
pairnorm!(L2);
pairnorm!(Linfinity);
-