[−][src]Struct argmin::solver::newton::newton_method::Newton
Newton's method iteratively finds the stationary points of a function f by using a second order approximation of f at the current point.
Example
use argmin::prelude::*; use argmin::solver::newton::Newton; use ndarray::{Array, Array1, Array2}; // Define cost function let cost = MyProblem {}; // Define initial parameter vector let init_param: Array1<f64> = Array1::from_vec(vec![-1.2, 1.0]); // Set up solver let mut solver = Newton::new(cost, init_param); // Set maximum number of iterations solver.set_max_iters(7); // Attach a logger solver.add_logger(ArgminSlogLogger::term()); // Run solver solver.run()?; // Wait a second (lets the logger flush everything before printing again) std::thread::sleep(std::time::Duration::from_secs(1)); // Print result println!("{:?}", solver.result());
References:
[0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization. Springer. ISBN 0-387-30303-0.
Methods
impl<O> Newton<O> where
O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
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O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
pub fn new(cost_function: O, init_param: O::Param) -> Self
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Constructor
pub fn set_gamma(&mut self, gamma: f64) -> Result<&mut Self, Error>
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set gamma
Trait Implementations
impl<O> Serialize for Newton<O> where
O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
O: Serialize,
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O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
O: Serialize,
fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
__S: Serializer,
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__S: Serializer,
impl<'de, O> Deserialize<'de> for Newton<O> where
O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
O: Deserialize<'de>,
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O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
O: Deserialize<'de>,
fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
__D: Deserializer<'de>,
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__D: Deserializer<'de>,
impl<O> ArgminSolver for Newton<O> where
O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
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O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
fn run(&mut self) -> Result<ArgminResult<Self::Param>, Error>
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Run the optimization algorithm
fn run_fast(&mut self) -> Result<ArgminResult<Self::Param>, Error>
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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>
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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>
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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>
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Computes the Hessian at parameter param
.
Returns an Err
if hessian
of ArgminOperator
is not implemented.
fn cur_param(&self) -> Self::Param
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Returns the current parameter vector.
fn cur_grad(&self) -> Self::Param
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Returns the most recently stored gradient.
fn cur_hessian(&self) -> Self::Hessian
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Returns the most recently stored Hessian.
fn set_cur_param(&mut self, param: Self::Param)
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Sets the current parameter to param
.
fn set_cur_grad(&mut self, grad: Self::Param)
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Sets the current gradient to grad
.
fn set_cur_hessian(&mut self, hessian: Self::Hessian)
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Sets the current Hessian to hessian
.
fn set_best_param(&mut self, param: Self::Param)
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Sets the best parameter vector to param
.
fn modify(&self, param: &Self::Param, factor: f64) -> Result<Self::Param, Error>
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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>
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Returns the result of the optimization.
fn set_max_iters(&mut self, iters: u64)
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Sets the maximum number of iterations to iters
.
fn max_iters(&self) -> u64
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Returns the maximum number of iterations.
fn increment_iter(&mut self)
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Increments the iteration counter.
fn cur_iter(&self) -> u64
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Returns the current number of iterations.
fn cur_cost(&self) -> f64
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Returns the most recently stored cost function value.
fn set_cur_cost(&mut self, cost: f64)
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Sets the current cost function value to cost
fn best_cost(&self) -> f64
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Returns the best cost function value obtained so far.
fn set_best_cost(&mut self, cost: f64)
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Sets the best cost function value.
fn set_target_cost(&mut self, cost: f64)
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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)
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Increments the counter for the computations of the cost function by 1.
fn increase_cost_func_count(&mut self, count: u64)
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Increases the counter for the computations of the cost function by count
.
fn cost_func_count(&self) -> u64
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Returns the current value of the counter for the computations of the cost function.
fn increment_grad_func_count(&mut self)
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Increments the counter for the computations of the gradient by 1.
fn increase_grad_func_count(&mut self, count: u64)
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Increases the counter for the computations of the gradient by count
.
fn grad_func_count(&self) -> u64
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Returns the current value of the counter for the computations of the gradient.
fn increment_hessian_func_count(&mut self)
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Increments the counter for the computations of the Hessian by 1.
fn increase_hessian_func_count(&mut self, count: u64)
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Increases the counter for the computations of the Hessian by count
.
fn hessian_func_count(&self) -> u64
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Returns the current value of the counter for the computations of the Hessian.
fn add_logger(&mut self, logger: Arc<dyn ArgminLog>)
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Attaches a logger which implements ArgminLog
to the solver.
fn add_writer(&mut self, writer: Arc<dyn ArgminWrite<Param = Self::Param>>)
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Attaches a writer which implements ArgminWrite
to the solver.
fn set_termination_reason(&mut self, reason: TerminationReason)
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Sets the TerminationReason
fn terminate(&mut self) -> TerminationReason
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Checks whether any of the conditions to terminate is true and terminates the algorithm.
fn base_reset(&mut self)
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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)
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Set checkpoint directory
fn set_checkpoint_name(&mut self, name: &str)
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Set checkpoint name
fn set_checkpoint_mode(&mut self, mode: CheckpointMode)
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Set checkpoint mode
fn from_checkpoint<P>(path: P) -> Result<Self, Error> where
P: AsRef<Path>,
Self: DeserializeOwned,
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P: AsRef<Path>,
Self: DeserializeOwned,
Load solver from checkpoint
impl<O> ArgminIter for Newton<O> where
O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
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O: ArgminOp,
O::Param: ArgminScaledSub<O::Param, f64, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
Auto Trait Implementations
impl<O> Send for Newton<O> where
<O as ArgminOp>::Hessian: Send,
<O as ArgminOp>::Param: Send,
<O as ArgminOp>::Hessian: Send,
<O as ArgminOp>::Param: Send,
impl<O> Sync for Newton<O> where
<O as ArgminOp>::Hessian: Sync,
<O as ArgminOp>::Param: Sync,
<O as ArgminOp>::Hessian: Sync,
<O as ArgminOp>::Param: Sync,
Blanket Implementations
impl<T, U> Into for T where
U: From<T>,
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U: From<T>,
impl<T> From for T
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impl<T, U> TryFrom for T where
U: Into<T>,
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U: Into<T>,
type Error = !
try_from
)The type returned in the event of a conversion error.
fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T> Borrow for T where
T: ?Sized,
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T: ?Sized,
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> BorrowMut for T where
T: ?Sized,
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T: ?Sized,
fn borrow_mut(&mut self) -> &mut T
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impl<T, U> TryInto for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
try_from
)The type returned in the event of a conversion error.
fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<T> DeserializeOwned for T where
T: Deserialize<'de>,
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T: Deserialize<'de>,