Struct argmin::solver::landweber::Landweber

pub struct Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp,  { /* fields omitted */ }

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)

Example

use argmin::prelude::*;
use argmin::solver::landweber::Landweber;

let operator = MyProblem {};
let init_param: Vec<f64> = vec![1.2, 1.2];
let omega = 0.001;

let mut solver = Landweber::new(operator, omega, init_param)?;
solver.set_max_iters(100);
solver.add_logger(ArgminSlogLogger::term());
solver.run()?;

println!("{:?}", solver.result());

References

[0] Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first kind. Amer. J. Math. 73, 615–624 [1] https://en.wikipedia.org/wiki/Landweber_iteration

Methods

impl<O> Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp, 

pub fn new(
    cost_function: O,
    omega: f64,
    init_param: O::Param
) -> Result<Self, Error>

Constructor

Trait Implementations

impl<'de, O> Deserialize<'de> for Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp,
    O: Deserialize<'de>, 

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

Deserialize this value from the given Serde deserializer.

impl<O> Serialize for Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp,
    O: 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> ArgminSolver for Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp, 

fn run(&mut self) -> Result<ArgminResult<Self::Param>, Error>

Run the optimization algorithm

fn run_fast(&mut self) -> Result<ArgminResult<Self::Param>, Error>

Run the essential parts of the optimization algorithm (no logging, no Ctrl-C handling)

fn apply(&mut self, param: &Self::Param) -> Result<Self::Output, Error>

Applies the cost function or operator to a parameter vector param. Returns an Err if apply of ArgminOperator is not implemented.

fn gradient(&mut self, param: &Self::Param) -> Result<Self::Param, Error>

Computes the gradient at parameter param. Returns an Err if gradient of ArgminOperator is not implemented.

fn hessian(&mut self, param: &Self::Param) -> Result<Self::Hessian, Error>

Computes the Hessian at parameter param. Returns an Err if hessian of ArgminOperator is not implemented.

fn cur_param(&self) -> Self::Param

Returns the current parameter vector.

fn cur_grad(&self) -> Self::Param

Returns the most recently stored gradient.

fn cur_hessian(&self) -> Self::Hessian

Returns the most recently stored Hessian.

fn set_cur_param(&mut self, param: Self::Param)

Sets the current parameter to param.

fn set_cur_grad(&mut self, grad: Self::Param)

Sets the current gradient to grad.

fn set_cur_hessian(&mut self, hessian: Self::Hessian)

Sets the current Hessian to hessian.

fn set_best_param(&mut self, param: Self::Param)

Sets the best parameter vector to param.

fn modify(&self, param: &Self::Param, factor: f64) -> Result<Self::Param, Error>

Modify the parameter vector by calling the modify method of the trait ArgminOperator. Will return an Err if modify is not implemented.

fn result(&self) -> ArgminResult<Self::Param>

Returns the result of the optimization.

fn set_max_iters(&mut self, iters: u64)

Sets the maximum number of iterations to iters.

fn max_iters(&self) -> u64

Returns the maximum number of iterations.

fn increment_iter(&mut self)

Increments the iteration counter.

fn cur_iter(&self) -> u64

Returns the current number of iterations.

fn cur_cost(&self) -> f64

Returns the most recently stored cost function value.

fn set_cur_cost(&mut self, cost: f64)

Sets the current cost function value to cost

fn best_cost(&self) -> f64

Returns the best cost function value obtained so far.

fn set_best_cost(&mut self, cost: f64)

Sets the best cost function value.

fn set_target_cost(&mut self, cost: f64)

Sets the target cost function value to cost. The optimization algorithm will be terminated when this limit is reached.

fn increment_cost_func_count(&mut self)

Increments the counter for the computations of the cost function by 1.

fn increase_cost_func_count(&mut self, count: u64)

Increases the counter for the computations of the cost function by count.

fn cost_func_count(&self) -> u64

Returns the current value of the counter for the computations of the cost function.

fn increment_grad_func_count(&mut self)

Increments the counter for the computations of the gradient by 1.

fn increase_grad_func_count(&mut self, count: u64)

Increases the counter for the computations of the gradient by count.

fn grad_func_count(&self) -> u64

Returns the current value of the counter for the computations of the gradient.

fn increment_hessian_func_count(&mut self)

Increments the counter for the computations of the Hessian by 1.

fn increase_hessian_func_count(&mut self, count: u64)

Increases the counter for the computations of the Hessian by count.

fn hessian_func_count(&self) -> u64

Returns the current value of the counter for the computations of the Hessian.

fn add_logger(&mut self, logger: Arc<dyn ArgminLog>)

Attaches a logger which implements ArgminLog to the solver.

fn add_writer(&mut self, writer: Arc<dyn ArgminWrite<Param = Self::Param>>)

Attaches a writer which implements ArgminWrite to the solver.

fn set_termination_reason(&mut self, reason: TerminationReason)

Sets the TerminationReason

fn terminate(&mut self) -> TerminationReason

Checks whether any of the conditions to terminate is true and terminates the algorithm.

fn base_reset(&mut self)

Resets the base field to it's initial conditions. This is helpful for implementing a solver which is initialized once, but called several times. It is recommended to only call this method inside the init function of ArgminNextIter.

fn set_checkpoint_dir(&mut self, dir: &str)

Set checkpoint directory

fn set_checkpoint_name(&mut self, name: &str)

Set checkpoint name

fn set_checkpoint_mode(&mut self, mode: CheckpointMode)

Set checkpoint mode

fn from_checkpoint<P>(path: P) -> Result<Self, Error> where
    P: AsRef<Path>,
    Self: DeserializeOwned, 

Load solver from checkpoint

impl<O> ArgminIter for Landweber<O> where
    O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
    O: ArgminOp, 

type Param = O::Param

Parameter vectors

type Output = O::Output

Output of the operator

type Hessian = O::Hessian

Hessian

fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error>

Computes one iteration of the algorithm.

fn init(&mut self) -> Result<(), Error>

Initializes the algorithm