# Struct argmin::solver::landweber::Landweber

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

## 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§

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### impl<F> Landweber<F>

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#### 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§

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### impl<F: Clone> Clone for Landweber<F>

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

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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### impl<'de, F> Deserialize<'de> for Landweber<F>where F: Deserialize<'de>,

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

Deserialize this value from the given Serde deserializer. Read more
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### impl<F> Serialize for Landweber<F>where F: Serialize,

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

Serialize this value into the given Serde serializer. Read more
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### 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,

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#### const NAME: &'static str = "Landweber"

Name of the solver. Mainly used in Observers.
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#### 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.
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#### fn terminate_internal(&mut self, state: &I) -> TerminationStatus

Checks whether basic termination reasons apply. Read more
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#### fn terminate(&mut self, _state: &I) -> TerminationStatus

Used to implement stopping criteria, in particular criteria which are not covered by (terminate_internal. Read more
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## Blanket Implementations§

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### impl<T> Any for Twhere T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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### impl<T> Borrow<T> for Twhere T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere U: From<T>,

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#### fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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### impl<T> ToOwned for Twhere T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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