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use std::{cmp::Ordering, marker::PhantomData};
use crate::Array;
use super::{Scs, Spectrum, State};
/// A folded spectrum.
#[derive(Debug, PartialEq)]
pub struct Folded<S: State> {
array: Array<Option<f64>>, // "lower" triangle is None,
state: PhantomData<S>,
}
impl<S: State> Folded<S> {
pub(super) fn from_spectrum(spectrum: &Spectrum<S>) -> Self {
let n = spectrum.elements();
let total_count = spectrum.shape().iter().sum::<usize>() - spectrum.shape().len();
// In general, this point divides the folding line. Since we are folding onto the "upper"
// part of the array, we want to fold anything "below" it onto something "above" it.
let mid_count = total_count / 2;
// The spectrum may or may not have a "diagonal", i.e. a hyperplane that falls exactly on
// the midpoint. If such a diagonal exists, we need to handle it as a special case when
// folding below.
//
// For example, in 1D a spectrum with five elements has a "diagonal", marked X:
// [-, -, X, -, -]
// Whereas on with four elements would not.
//
// In two dimensions, e.g. three-by-three elements has a diagonal:
// [-, -, X]
// [-, X, -]
// [X, -, -]
// whereas two-by-three would not. On the other hand, two-by-four has a diagonal:
// [-, -, X, -]
// [-, X, -, -]
//
// Note that even-ploidy data should always have a diagonal, whereas odd-ploidy data
// may or may not.
let has_diagonal = total_count % 2 == 0;
// Note that we cannot use the algorithm below in-place, since the reverse iterator
// may reach elements that have already been folded, which causes bugs. Hence we fold
// into a zero-initialised copy.
let mut array = Array::from_element(None, spectrum.shape().clone());
// We iterate over indices rather than values since we have to mutate on the array
// while looking at it from both directions.
(0..n).zip((0..n).rev()).for_each(|(i, rev_i)| {
let count = spectrum.shape().index_sum_from_flat_unchecked(i);
let src = spectrum.array.as_slice();
let dst = array.as_mut_slice();
match (count.cmp(&mid_count), has_diagonal) {
(Ordering::Less, _) | (Ordering::Equal, false) => {
// We are in the upper part of the spectrum that should be folded onto.
dst[i] = Some(src[i] + src[rev_i]);
}
(Ordering::Equal, true) => {
// We are on a diagonal, which must be handled as a special case:
// there are apparently different opinions on what the most correct
// thing to do is. This adopts the same strategy as e.g. in dadi.
dst[i] = Some(0.5 * src[i] + 0.5 * src[rev_i]);
}
(Ordering::Greater, _) => {
// We are in the lower part of the spectrum to be filled with None;
dst[i] = None;
}
}
});
Self {
array,
state: PhantomData,
}
}
/// Returns an unfolded spectrum based on the folded spectrum, filling the folded elements with
/// the provided element.
pub fn into_spectrum(&self, fill: f64) -> Spectrum<S> {
let data = Vec::from_iter(self.array.iter().map(|x| x.unwrap_or(fill)));
let shape = self.array.shape().clone();
let array = Array::new_unchecked(data, shape);
Scs::from(array).into_state_unchecked()
}
}
impl<S: State> Clone for Folded<S> {
fn clone(&self) -> Self {
Self {
array: self.array.clone(),
state: PhantomData,
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_fold_4() {
let scs = Scs::from_range(0..4, 4).unwrap();
let expected = Scs::new([3., 3., 0., 0.], 4).unwrap();
assert_eq!(scs.fold().into_spectrum(0.0), expected);
}
#[test]
fn test_fold_5() {
let scs = Scs::from_range(0..5, 5).unwrap();
let expected = Scs::new([4., 4., 2., -1., -1.], 5).unwrap();
assert_eq!(scs.fold().into_spectrum(-1.), expected);
}
#[test]
fn test_fold_3x3() {
let scs = Scs::from_range(0..9, [3, 3]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
8., 8., 4.,
8., 4., 0.,
4., 0., 0.,
],
[3, 3]
).unwrap();
assert_eq!(scs.fold().into_spectrum(0.0), expected);
}
#[test]
fn test_fold_2x4() {
let scs = Scs::from_range(0..8, [2, 4]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
7., 7., 3.5, f64::INFINITY,
7., 3.5, f64::INFINITY, f64::INFINITY,
],
[2, 4]
).unwrap();
assert_eq!(scs.fold().into_spectrum(f64::INFINITY), expected);
}
#[test]
fn test_fold_3x4() {
let scs = Scs::from_range(0..12, [3, 4]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
11., 11., 11., 0.,
11., 11., 0., 0.,
11., 0., 0., 0.,
],
[3, 4]
).unwrap();
assert_eq!(scs.fold().into_spectrum(0.), expected);
}
#[test]
fn test_fold_3x7() {
let scs = Scs::from_range(0..21, [3, 7]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
20., 20., 20., 20., 10., 0., 0.,
20., 20., 20., 10., 0., 0., 0.,
20., 20., 10., 0., 0., 0., 0.,
],
[3, 7]
).unwrap();
assert_eq!(scs.fold().into_spectrum(0.0), expected);
}
#[test]
fn test_fold_2x2x2() {
let scs = Scs::from_range(0..8, [2, 2, 2]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
7., 7.,
7., -1.,
7., -1.,
-1., -1.,
],
[2, 2, 2]
).unwrap();
assert_eq!(scs.fold().into_spectrum(-1.0), expected);
}
#[test]
fn test_fold_2x3x2() {
let scs = Scs::from_range(0..12, [2, 3, 2]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
11., 11.,
11., 5.5,
5.5, 0.,
11., 5.5,
5.5, 0.,
0., 0.,
],
[2, 3, 2]
).unwrap();
assert_eq!(scs.fold().into_spectrum(0.0), expected);
}
#[test]
fn test_fold_3x3x3() {
let scs = Scs::from_range(0..27, [3, 3, 3]).unwrap();
#[rustfmt::skip]
let expected = Scs::new(
[
26., 26., 26.,
26., 26., 13.,
26., 13., 0.,
26., 26., 13.,
26., 13., 0.,
13., 0., 0.,
26., 13., 0.,
13., 0., 0.,
0., 0., 0.,
],
[3, 3, 3]
).unwrap();
assert_eq!(scs.fold().into_spectrum(0.0), expected);
}
}