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use{
crate::{MarkovChain, HasRng},
rand::Rng,
std::marker::PhantomData,
num_traits::AsPrimitive
};
#[cfg(feature = "serde_support")]
use serde::{Serialize, Deserialize};
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "serde_support", derive(Serialize, Deserialize))]
/// Errors encountered during Metropolis Algorithm
pub enum MetropolisError
{
/// Energy function for current state of ensemble returns None
InvalidState,
/// Invalid nan encountered
NAN,
/// m_beta cannot be infinitiy or minus infinity!
InfinitBeta,
}
#[derive(Clone)]
#[cfg_attr(feature = "serde_support", derive(Serialize, Deserialize))]
/// # Create a metropolis simulation
/// Citation see, e.g,
/// > M. E. J. Newman and G. T. Barkema, "Monte Carlo Methods in Statistical Physics"
/// *Clarendon Press*, 1999, ISBN: 978-0-19-8517979
///
/// # Explanation
/// * used for large-deviation simulations
/// * Performes markov chain using the markov chain trait
/// ## All `self.metropolis*` functions do the following
/// * Let the current state of the system (i.e., the ensemble) be S(i) with corresponding energy `E(i) = energy_fn(S(i))`.
/// * Now perform a markov step, such that the new system is S_new with energy E_new.
/// * The new state will be accepted (meaning S(i+1) = S_new) with probability:
/// `min[1.0, exp{m_beta * (E_new - E(i))}]`
/// * otherwise the new state will be rejected, meaning S(i + 1) = S(i).
/// * the `measure` function is called: `measure(S(i + 1))`
pub struct Metropolis<E, R, S, Res, T>
{
ensemble: E,
rng: R,
energy: T,
m_beta: f64,
step_size: usize,
counter: usize,
steps: Vec<S>,
marker_res: PhantomData<Res>,
}
impl<R, E, S, Res, T> Metropolis<E, R, S, Res, T>
where T: Copy + AsPrimitive<f64>
{
/// returns stored `m_beta` value (-β for metropolis)
pub fn m_beta(&self) -> f64 {
self.m_beta
}
/// sets m_beta (minus beta). Is related to the temperature: m_beta = -1 / temperature
pub fn set_m_beta(&mut self, m_beta: f64)
{
self.m_beta = m_beta;
}
/// sets m_beta according to m_beta = -1 / temperature
pub fn set_temperature(&mut self, temperature: f64)
{
self.m_beta = -1.0 / temperature;
}
/// returns stored value for `current_energy`
pub fn energy(&self) -> T {
self.energy
}
/// # set stored value for `current_energy`
/// * Will return Err() if you try to set the energy to nan
/// * otherwise it will set the stored `energy` and return Ok(())
/// # Important
/// * It is very unlikely that you need this function - Only use it, if you know what you are doing
/// ## Safety
/// This is not unsafe in the programming sense, but I chose to make it unsafe anyway to make the user
/// aknowledge that this will result in a logical error for the algorithms if
/// set to the incorrect energy
#[allow(clippy::result_unit_err)]
pub unsafe fn set_energy(&mut self, energy: T) -> Result<(),()>{
if (energy.as_()).is_nan() {
Err(())
} else {
self.energy = energy;
Ok(())
}
}
/// returns reference to ensemble
pub fn ensemble(&self) -> &E
{
&self.ensemble
}
/// returns mutable reference to ensemble
/// * use with care!
/// ## Safety
/// * if you change your ensemble, this might invalidate
/// the simulation!
/// * The metropolis functions do not calculate the energy of the current state
/// * Unsafe purely for logical reasons, in the programming sense this function didn't need to be unsafe
pub unsafe fn ensemble_mut(&mut self) -> &mut E
{
&mut self.ensemble
}
/// # returns stored value for the `counter`, i.e., where to resume iteration
/// * note: `counter` is a wrapping counter
/// * counter is increase each time, a markov step is performed, i.e,
/// each time `ensemble.m_steps(step_size)` is called, the counter will increase by 1
/// (**not** by step_size)
pub fn counter(&self) -> usize {
self.counter
}
/// # resets the `counter` to 0
/// * note: `counter` is a wrapping counter
pub fn reset_counter(&mut self) {
self.counter = 0;
}
/// return current `stepsize`
pub fn step_size(&self) -> usize {
self.step_size
}
/// * change the `stepsize`
/// * returns err if you try to set stepsize to `0`, because that would be invalid
#[allow(clippy::result_unit_err)]
pub fn set_step_size(&mut self, step_size: usize) -> Result<(),()>
{
if step_size == 0 {
Err(())
} else {
self.step_size = step_size;
Ok(())
}
}
}
impl<E, R, S, Res, T> Metropolis<E, R, S, Res, T>
where R: Rng,
E: MarkovChain<S, Res>,
T: Copy + AsPrimitive<f64>,
{
/// # Create a new Metropolis struct - used for Metropolis simulations
///
/// | | meaning |
/// |---------------|------------------------------------------------------------------------------|
/// | `rng` | the Rng used to decide, if a state should be accepted or rejected |
/// | `ensemble` | the ensemble that is explored with the markov chain |
/// | `energy` | current energy of the ensemble - cannot be NAN, should match `energy_fn(ensemble)` (see `metropolis*` functions) |
/// | `m_beta` | minus beta, has to be finite - used for acceptance, i.e., probability to accept a markov step from Energy E to Energy E_new is min[1.0, exp{m_beta * (E_new - E)}] |
/// | `step_size` | is used for each markov step, i.e., `ensemble.m_steps(stepsize)` is called |
///
/// * will return Err if `energy` is nan or `m_beta` is not finite
pub fn new_from_m_beta(
rng: R,
ensemble: E,
energy: T,
m_beta: f64,
step_size: usize,
) -> Result<Self, MetropolisError>
{
if (energy.as_()).is_nan() || m_beta.is_nan() {
return Err(MetropolisError::NAN);
}
if !m_beta.is_finite(){
return Err(MetropolisError::InfinitBeta);
}
let steps = Vec::with_capacity(step_size);
Ok(
Self{
ensemble,
rng,
energy,
m_beta,
steps,
marker_res: PhantomData::<Res>,
counter: 0,
step_size,
}
)
}
/// # Create a new Metropolis struct - used for Metropolis simulations
///
/// | | meaning |
/// |---------------|------------------------------------------------------------------------------|
/// | `rng` | the Rng used to decide, if a state should be accepted or rejected |
/// | `ensemble` | the ensemble that is explored with the markov chain |
/// | `energy` | current energy of the ensemble - cannot be NAN, should match `energy_fn(ensemble)` (see `metropolis*` functions) |
/// | `temperature` | m_beta = -1.0/temperature. Used for acceptance, i.e., probability to accept a markov step from Energy E to Energy E_new is min[1.0, exp{m_beta * (E_new - E)}] |
/// | `step_size` | is used for each markov step, i.e., `ensemble.m_steps(stepsize)` is called |
///
/// * will return Err if `energy` is nan or `m_beta` is not finite
pub fn new_from_temperature(
rng: R,
ensemble: E,
energy: T,
temperature: f64,
step_size: usize,
) -> Result<Self, MetropolisError>
{
if temperature.is_nan() {
return Err(MetropolisError::NAN);
}
Self::new_from_m_beta(
rng,
ensemble,
energy,
-1.0 / temperature,
step_size,
)
}
/// # Change, which markov chain is used for the metropolis simulations
/// * Use this if there are different ways to perform a markov chain for your problem
/// and you want to switch between them
pub fn change_markov_chain<S2, Res2>(self) -> Metropolis<E, R, S2, Res2, T>
where E: MarkovChain<S2, Res2>
{
Metropolis::<E, R, S2, Res2, T>{
ensemble: self.ensemble,
rng: self.rng,
energy: self.energy,
step_size: self.step_size,
m_beta: self.m_beta,
counter: self.counter,
steps: Vec::with_capacity(self.step_size),
marker_res: PhantomData::<Res2>,
}
}
/// Perform a single Metropolis step
#[inline(always)]
unsafe fn metropolis_step_unsafe<Energy>(&mut self, mut energy_fn: Energy)
where Energy: FnMut(&mut E) -> Option<T>
{
self.metropolis_step_efficient_unsafe(
|ensemble, _, _| energy_fn(ensemble)
)
}
#[inline(always)]
fn metropolis_step<Energy>(&mut self, mut energy_fn: Energy)
where Energy: FnMut(&E) -> Option<T>
{
unsafe {
self.metropolis_step_unsafe(
|ensemble| energy_fn(ensemble)
)
}
}
/// Perform a single Metropolis step
#[inline(always)]
unsafe fn metropolis_step_efficient_unsafe<Energy>(&mut self, mut energy_fn: Energy)
where Energy: FnMut(&mut E, T, &[S]) -> Option<T>
{
self.counter = self.counter.wrapping_add(1);
self.ensemble.m_steps(self.step_size, &mut self.steps);
let new_energy = match energy_fn(&mut self.ensemble, self.energy, &self.steps) {
None => {
self.ensemble.undo_steps_quiet(&self.steps);
return;
},
Some(e) => {
e
}
};
let a_prob = (self.m_beta * (new_energy.as_() - self.energy.as_())).exp();
let rejected = self.rng.gen::<f64>() > a_prob;
if rejected {
self.ensemble.undo_steps_quiet(&self.steps);
} else {
self.energy = new_energy;
}
}
/// Perform a single Metropolis step
#[inline(always)]
fn metropolis_step_efficient<Energy>(&mut self, mut energy_fn: Energy)
where Energy: FnMut(&E, T, &[S]) -> Option<T>
{
unsafe {
self.metropolis_step_efficient_unsafe(
|ensemble, energy, steps| energy_fn(ensemble, energy, steps)
)
}
}
/// # Metropolis Simulation
/// * [see](#all-selfmetropolis-functions-do-the-following)
/// * performs `self.counter..=step_target` markov steps
/// * `energy_fn(self.ensemble)` is assumed to equal `self.energy` at the beginning!
/// * if `energy_fn` returns None, the step will always be rejected
/// * after each acceptance/rejection, `measure` is called
/// # Note
/// * I assume, that the energy_fn never returns `nan` (when cast as f64)
/// If nan is possible, please check for that beforhand and return `None` in that case
/// * Maybe do the same for infinity, it is unlikely, that infinit energys make sense
pub fn metropolis<Energy, Mes>(
&mut self,
step_target: usize,
mut energy_fn: Energy,
mut measure: Mes,
)
where Energy: FnMut(&E) -> Option<T>,
Mes: FnMut(&Self),
{
for _ in self.counter..=step_target
{
self.metropolis_step(&mut energy_fn);
measure(self);
}
}
/// # Metropolis Simulation
/// * [see](#all-selfmetropolis-functions-do-the-following)
/// * performs `self.counter..=step_target` markov steps
/// * `energy_fn(self.ensemble)` is assumed to equal `self.energy` at the beginning!
/// * if `energy_fn` returns None, the step will always be rejected
/// * after each acceptance/rejection, `measure` is called
/// # Important
/// * if possible, prefere [`self.metropolis`](#method.metropolis) as it is safer
/// * use this, if your energy function needs mutable access, or `measure`needs mutable access.
/// Be careful though, this can invalidate the results of your simulation
/// # Safety
/// * I assume, that the energy_fn never returns `nan` (when cast as f64)
/// If nan is possible, please check for that beforhand and return `None` in that case
/// * Maybe do the same for infinity, it is unlikely, that infinit energys make sense
/// * Note: I chose to make this function unsafe to force users to aknowledge the (purely logical) limitations
/// regarding the usage of the mutable ensemble. From a programming point of view this will not lead to
/// any undefined behavior or such regardless of if the user fullfills the requirements
pub unsafe fn metropolis_unsafe<Energy, Mes>(
&mut self,
step_target: usize,
mut energy_fn: Energy,
mut measure: Mes,
)
where Energy: FnMut(&mut E) -> Option<T>,
Mes: FnMut(&mut Self),
{
for _ in self.counter..=step_target
{
self.metropolis_step_unsafe(&mut energy_fn);
measure(self);
}
}
/// # Metropolis Simulation
/// * [see](#all-selfmetropolis-functions-do-the-following)
/// * performs `self.counter..=step_target` markov steps
/// * `energy_fn(self.ensemble)` is assumed to equal `self.energy` at the beginning!
/// * if `energy_fn` returns None, the step will always be rejected
/// * after each acceptance/rejection, `measure` is called
/// # Difference to [`self.metropolis`](#method.metropolis)
/// * Function parameter of energy_fn: &ensemble, old_energy, &\[steps\] - that
/// means, you should prefere this, if you can calculate the new energy more efficient
/// by accessing the old energy and the information about what the markov step changed
/// # Note
/// * I assume, that the energy_fn never returns `nan` (when cast as f64)
/// If nan is possible, please check for that beforhand and return `None` in that case
/// * Maybe do the same for infinity, it is unlikely, that infinit energys make sense
pub fn metropolis_efficient<Energy, Mes>
(
&mut self,
step_target: usize,
mut energy_fn: Energy,
mut measure: Mes,
)
where Energy: FnMut(&E, T, &[S]) -> Option<T>,
Mes: FnMut(&Self),
{
for _ in self.counter..=step_target
{
self.metropolis_step_efficient(&mut energy_fn);
measure(self);
}
}
/// # Metropolis Simulation
/// * [see](#all-selfmetropolis-functions-do-the-following)
/// * performs `self.counter..=step_target` markov steps
/// * `energy_fn(self.ensemble)` is assumed to equal `self.energy` at the beginning!
/// * if `energy_fn` returns None, the step will always be rejected
/// * after each acceptance/rejection, `measure` is called
/// # Difference to [`self.metropolis`](#method.metropolis)
/// * Function parameter of energy_fn: &ensemble, old_energy, &\[steps\] - that
/// means, you should prefere this, if you can calculate the new energy more efficient
/// by accessing the old energy and the information about what the markov step changed
/// # Safety
/// * I assume, that the energy_fn never returns `nan` (when cast as f64)
/// If nan is possible, please check for that beforhand and return `None` in that case
/// * Maybe do the same for infinity, it is unlikely, that infinite energys make sense
pub unsafe fn metropolis_efficient_unsafe<Energy, Mes>
(
&mut self,
step_target: usize,
mut energy_fn: Energy,
mut measure: Mes,
)
where Energy: Fn(&mut E, T, &[S]) -> Option<T>,
Mes: FnMut(&mut Self),
{
for _ in self.counter..=step_target
{
self.metropolis_step_efficient_unsafe(&mut energy_fn);
measure(self);
}
}
/// # Metropolis Simulation
/// * [see](#all-selfmetropolis-functions-do-the-following)
/// * checks `condition(self)` after each `metropolis_step(&mut energy_fn)`
/// and returns when `false` is returned by the condition
/// * `energy_fn(self.ensemble)` is assumed to equal `self.energy` at the beginning!
/// * if `energy_fn` returns None, the step will always be rejected
/// * after each acceptance/rejection, `measure` is called
/// # Note
/// * I assume, that the energy_fn never returns `nan` (when cast as f64)
/// If nan is possible, please check for that beforhand and return `None` in that case
/// * Maybe do the same for infinity, it is unlikely, that infinit energys make sense
pub fn metropolis_while<Energy, Mes, Cond>(
&mut self,
mut energy_fn: Energy,
mut measure: Mes,
mut condition: Cond,
)
where Energy: FnMut(&E) -> Option<T>,
Mes: FnMut(&Self),
Cond: FnMut(&Self) -> bool,
{
while condition(self) {
self.metropolis_step(&mut energy_fn);
measure(self);
}
}
/// # Metropolis simulation
/// * almost the same as [`metropolis_while`](`crate::metropolis::Metropolis::metropolis_while`)
/// ## Difference
/// * `energy_fn` now works with a mutable reference of `E` (the ensemble).
/// ## Note
/// * prefere [`metropolis_while`](`crate::metropolis::Metropolis::metropolis_while`) as it is safer.
/// * the changeing of the Ensemble must not affect subsequent Energy calculations - otherwise the
/// logic of the algorithm breaks down
/// ## Safety
/// * Note: I chose to make this function unsafe to force users to aknowledge the (purely logical) limitations
/// regarding the usage of the mutable ensemble. From a programming point of view this will not lead to
/// any undefined behavior or such regardless of if the user fullfills the requirements
pub unsafe fn metropolis_while_unsafe<Energy, Mes, Cond>(
&mut self,
mut energy_fn: Energy,
mut measure: Mes,
mut condition: Cond,
)
where Energy: FnMut(&mut E) -> Option<T>,
Mes: FnMut(&mut Self),
Cond: FnMut(&mut Self) -> bool,
{
while condition(self) {
self.metropolis_step_unsafe(&mut energy_fn);
measure(self);
}
}
/// # Metropolis simulation
/// * similar to [`metropolis_while`](crate::metropolis::Metropolis::metropolis_while`)
/// ## Difference
/// * energy fn can use the old energy and the performed markov steps to more efficiently calculate the current Energy
pub fn metropolis_efficient_while<Energy, Mes, Cond>(
&mut self,
mut energy_fn: Energy,
mut measure: Mes,
mut condition: Cond,
)
where Energy: FnMut(&E, T, &[S]) -> Option<T>,
Mes: FnMut(&Self),
Cond: FnMut(&Self) -> bool,
{
while condition(self) {
self.metropolis_step_efficient(&mut energy_fn);
measure(self);
}
}
/// # Metropolis simulation
/// * similar to [`metropolis_efficient_while`](`crate::metropolis::Metropolis::metropolis_efficient_while`)
/// ## Difference
/// * now `energy_fn` works with a mutable reference of the ensemble instead
/// * This is intended for usages in which the energy can be calculated much more efficiently using a
/// mutable reference than an immutable one
/// ## Safety
/// * Only use this, if it is absolutly nessessary. The ensemble must not be changed in a way,
/// which affects successive energy calculations (or the markov steps)
pub unsafe fn metropolis_efficient_while_unsafe<Energy, Mes, Cond>(
&mut self,
mut energy_fn: Energy,
mut measure: Mes,
mut condition: Cond,
)
where Energy: FnMut(&mut E, T, &[S]) -> Option<T>,
Mes: FnMut(&mut Self),
Cond: FnMut(&mut Self) -> bool,
{
while condition(self) {
self.metropolis_step_efficient_unsafe(&mut energy_fn);
measure(self);
}
}
}
impl<E, R, S, Res, T> HasRng<R> for Metropolis<E, R, S, Res, T>
where R: Rng
{
fn rng(&mut self) -> &mut R {
&mut self.rng
}
fn swap_rng(&mut self, rng: &mut R) {
std::mem::swap(&mut self.rng,rng);
}
}