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Copy pathsolver.rs
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342 lines (309 loc) · 9.87 KB
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use feos_core::{log_iter, EosError, EosResult, Verbosity};
use ndarray::prelude::*;
use num_dual::linalg::{norm, LU};
use std::collections::VecDeque;
use std::fmt;
const DEFAULT_PARAMS_PICARD: SolverParameter = SolverParameter {
solver: DFTAlgorithm::PicardIteration(1.0),
log: false,
max_iter: 500,
tol: 1e-11,
beta: 0.15,
};
const DEFAULT_PARAMS_ANDERSON_LOG: SolverParameter = SolverParameter {
solver: DFTAlgorithm::AndersonMixing(100),
log: true,
max_iter: 50,
tol: 1e-5,
beta: 0.15,
};
const DEFAULT_PARAMS_ANDERSON: SolverParameter = SolverParameter {
solver: DFTAlgorithm::AndersonMixing(100),
log: false,
max_iter: 150,
tol: 1e-11,
beta: 0.15,
};
#[derive(Clone, Copy)]
struct SolverParameter {
solver: DFTAlgorithm,
log: bool,
max_iter: usize,
tol: f64,
beta: f64,
}
#[derive(Clone, Copy)]
enum DFTAlgorithm {
PicardIteration(f64),
AndersonMixing(usize),
}
/// Settings for the DFT solver.
#[derive(Clone)]
pub struct DFTSolver {
parameters: Vec<SolverParameter>,
pub verbosity: Verbosity,
}
impl Default for DFTSolver {
fn default() -> Self {
Self {
parameters: vec![DEFAULT_PARAMS_ANDERSON_LOG, DEFAULT_PARAMS_ANDERSON],
verbosity: Verbosity::None,
}
}
}
impl DFTSolver {
/// Create a new empty `DFTSolver` object.
pub fn new(verbosity: Verbosity) -> Self {
Self {
parameters: Vec::new(),
verbosity,
}
}
/// Add a Picard iteration to the solver.
pub fn picard_iteration(mut self, max_rel: Option<f64>) -> Self {
let mut algorithm = DEFAULT_PARAMS_PICARD;
if let Some(max_rel) = max_rel {
algorithm.solver = DFTAlgorithm::PicardIteration(max_rel);
}
self.parameters.push(algorithm);
self
}
/// Add Anderson mixing to the solver.
pub fn anderson_mixing(mut self, mmax: Option<usize>) -> Self {
let mut algorithm = DEFAULT_PARAMS_ANDERSON;
if let Some(mmax) = mmax {
algorithm.solver = DFTAlgorithm::AndersonMixing(mmax);
}
self.parameters.push(algorithm);
self
}
/// Iterate the logarithm of the density profile in the last solver.
pub fn log(mut self) -> Self {
self.parameters.last_mut().unwrap().log = true;
self
}
/// Set the maximum number of iterations for the last solver.
pub fn max_iter(mut self, max_iter: usize) -> Self {
self.parameters.last_mut().unwrap().max_iter = max_iter;
self
}
/// Set the tolerance for the last solver.
pub fn tol(mut self, tol: f64) -> Self {
self.parameters.last_mut().unwrap().tol = tol;
self
}
/// Set the damping factor for the last solver
pub fn beta(mut self, beta: f64) -> Self {
self.parameters.last_mut().unwrap().beta = beta;
self
}
pub(crate) fn solve<F>(&self, x: &mut Array1<f64>, residual: &mut F) -> EosResult<(bool, usize)>
where
F: FnMut(&Array1<f64>, ArrayViewMut1<f64>, bool) -> EosResult<()>,
{
log_iter!(self.verbosity, "solver | iter | residual ");
let mut converged = false;
let mut iterations = 0;
for algorithm in &self.parameters {
let (c, i) = algorithm.solve(x, residual, self.verbosity)?;
converged = c;
iterations += i;
}
Ok((converged, iterations))
}
}
impl SolverParameter {
fn solve<F>(
&self,
x: &mut Array1<f64>,
residual: &mut F,
verbosity: Verbosity,
) -> EosResult<(bool, usize)>
where
F: FnMut(&Array1<f64>, ArrayViewMut1<f64>, bool) -> EosResult<()>,
{
match self.solver {
DFTAlgorithm::PicardIteration(max_rel) => {
self.solve_picard(max_rel, x, residual, verbosity)
}
DFTAlgorithm::AndersonMixing(mmax) => self.solve_anderson(mmax, x, residual, verbosity),
}
}
fn solve_picard<F>(
&self,
max_rel: f64,
x: &mut Array1<f64>,
residual: &mut F,
verbosity: Verbosity,
) -> EosResult<(bool, usize)>
where
F: FnMut(&Array1<f64>, ArrayViewMut1<f64>, bool) -> EosResult<()>,
{
log_iter!(verbosity, "{:-<43}", "");
let mut resm = Array::zeros(x.raw_dim());
for k in 1..=self.max_iter {
// calculate residual
residual(x, resm.view_mut(), self.log)?;
// calculate beta
let mut beta_min: Option<f64> = None;
let beta = (max_rel * (&*x / &resm).mapv(f64::abs)).mapv(|beta| {
if beta < self.beta {
beta_min = Some(beta_min.map_or(beta, |b| b.min(beta)));
beta
} else {
self.beta
}
});
// update solution
if self.log {
*x *= &(&resm * (-beta)).mapv(f64::exp);
} else {
*x -= &(&resm * beta);
}
// check for convergence
let res = norm(&resm) / (resm.len() as f64).sqrt();
log_iter!(
verbosity,
"Picard iteration {:3} | {:>4} | {:.6e} | {}",
if self.log { "log" } else { "" },
k,
res,
beta_min.unwrap_or(self.beta)
);
if res.is_nan() {
return Err(EosError::IterationFailed(String::from("Picard Iteration")));
}
if res < self.tol && beta_min.is_none() {
return Ok((true, k));
}
}
Ok((false, self.max_iter))
}
fn solve_anderson<F>(
&self,
mmax: usize,
x: &mut Array1<f64>,
residual: &mut F,
verbosity: Verbosity,
) -> EosResult<(bool, usize)>
where
F: FnMut(&Array1<f64>, ArrayViewMut1<f64>, bool) -> EosResult<()>,
{
log_iter!(verbosity, "{:-<43}", "");
let mut resm = VecDeque::with_capacity(mmax);
let mut xm = VecDeque::with_capacity(mmax);
let mut r;
let mut alpha;
for k in 1..=self.max_iter {
// drop old values
if resm.len() == mmax {
resm.pop_front();
xm.pop_front();
}
let m = resm.len() + 1;
// calculate residual
let mut res = Array::zeros(x.raw_dim());
residual(x, res.view_mut(), self.log)?;
resm.push_back(res);
// save x value
if self.log {
xm.push_back(x.mapv(f64::ln));
} else {
xm.push_back(x.clone());
}
// calculate alpha
r = Array::from_shape_fn((m + 1, m + 1), |(i, j)| match (i == m, j == m) {
(false, false) => (&resm[i] * &resm[j]).sum(),
(true, true) => 0.0,
_ => 1.0,
});
alpha = Array::zeros(m + 1);
alpha[m] = 1.0;
alpha = LU::new(r)?.solve(&alpha);
// r.solveh_inplace(&mut alpha)?;
// update solution
x.fill(0.0);
for i in 0..m {
*x += &(alpha[i] * (&xm[i] - &(self.beta * &resm[i])));
}
if self.log {
x.mapv_inplace(f64::exp);
} else {
x.mapv_inplace(f64::abs);
}
// check for convergence
let resv = &resm[m - 1];
let res = norm(resv) / (resv.len() as f64).sqrt();
log_iter!(
verbosity,
"Anderson mixing {:3} | {:>4} | {:.6e} ",
if self.log { "log" } else { "" },
k,
res
);
if res.is_nan() {
return Err(EosError::IterationFailed(String::from("Anderson Mixing")));
}
if res < self.tol {
return Ok((true, k));
}
}
Ok((false, self.max_iter))
}
}
impl fmt::Display for DFTAlgorithm {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self {
Self::PicardIteration(max_rel) => write!(f, "Picard Iteration (max_rel={})", max_rel),
Self::AndersonMixing(mmax) => write!(f, "Anderson Mixing (mmax={})", mmax),
}
}
}
impl fmt::Debug for DFTAlgorithm {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self {
Self::PicardIteration(_) => write!(f, "Picard Iteration"),
Self::AndersonMixing(_) => write!(f, "Anderson Mixing"),
}
}
}
impl fmt::Display for SolverParameter {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(
f,
"{} max_iter: {}, tol: {}, beta: {}",
self.solver, self.max_iter, self.tol, self.beta
)
}
}
impl fmt::Display for DFTSolver {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
for algorithm in &self.parameters {
writeln!(f, "{algorithm}")?;
}
Ok(())
}
}
impl DFTSolver {
pub fn _repr_markdown_(&self) -> String {
let mut res =
String::from("|solver|log|max_iter|tol|beta|mmax|max_rel|\n|-|:-:|-:|-:|-:|-:|-:|");
for algorithm in &self.parameters {
let (mmax, max_rel) = match algorithm.solver {
DFTAlgorithm::PicardIteration(max_rel) => (String::new(), max_rel.to_string()),
DFTAlgorithm::AndersonMixing(mmax) => (mmax.to_string(), String::new()),
};
res += &fmt::format(format_args!(
"\n|{:?}|{}|{}|{:e}|{}|{}|{}|",
algorithm.solver,
if algorithm.log { "x" } else { "" },
algorithm.max_iter,
algorithm.tol,
algorithm.beta,
mmax,
max_rel
));
}
res
}
}