Struct argmin::solver::landweber::Landweber

pub struct Landweber<F> { /* private fields */ }

Landweber iteration

The Landweber iteration is a solver for ill-posed linear inverse problems.

In iteration k, the new parameter vector x_{k+1} is calculated from the previous parameter vector x_k and the gradient at x_k according to the following update rule:

x_{k+1} = x_k - omega * \nabla f(x_k)

Requirements on the optimization problem

The optimization problem is required to implement Gradient.

References

Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first kind. Amer. J. Math. 73, 615–624

https://en.wikipedia.org/wiki/Landweber_iteration

Implementations

impl<F> Landweber<F>

pub fn new(omega: F) -> Self

Construct a new instance of Landweber

Example

let omega: f64 = 0.5;
let landweber = Landweber::new(omega);

Trait Implementations

impl<F: Clone> Clone for Landweber<F>

fn clone(&self) -> Landweber<F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<'de, F> Deserialize<'de> for Landweber<F>where
    F: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where
    __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F> Serialize for Landweber<F>where
    F: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>where
    __S: Serializer,

Serialize this value into the given Serde serializer.

impl<O, F, P, G> Solver<O, IterState<P, G, (), (), F>> for Landweber<F>where
    O: Gradient<Param = P, Gradient = G>,
    P: Clone + ArgminScaledSub<G, F, P>,
    F: ArgminFloat,

const NAME: &'static str = "Landweber"

Name of the solver. Mainly used in Observers.

fn next_iter(
    &mut self,
    problem: &mut Problem<O>,
    state: IterState<P, G, (), (), F>
) -> Result<(IterState<P, G, (), (), F>, Option<KV>), Error>

Computes a single iteration of the algorithm and has access to the optimization problem definition and the internal state of the solver. Returns an updated state and optionally a KV which holds key-value pairs used in Observers.

fn init(
    &mut self,
    _problem: &mut Problem<O>,
    state: I
) -> Result<(I, Option<KV>), Error>

Initializes the algorithm.

fn terminate_internal(&mut self, state: &I) -> TerminationStatus

Checks whether basic termination reasons apply.

fn terminate(&mut self, _state: &I) -> TerminationStatus

Used to implement stopping criteria, in particular criteria which are not covered by (terminate_internal.

impl<F: Copy> Copy for Landweber<F>