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//! Molecular symmetry element detection for symmetric tops.
use std::collections::HashMap;
use anyhow::{self, ensure, format_err};
use approx;
use indexmap::IndexSet;
use itertools::Itertools;
use log;
use nalgebra::Vector3;
use crate::rotsym::RotationalSymmetry;
use crate::symmetry::symmetry_core::_search_proper_rotations;
use crate::symmetry::symmetry_element::{SymmetryElement, INV, ROT, SIG, TRROT, TRSIG};
use crate::symmetry::symmetry_element_order::{ElementOrder, ORDER_1, ORDER_2};
use crate::symmetry::symmetry_symbols::deduce_sigma_symbol;
use super::{PreSymmetry, Symmetry};
impl Symmetry {
/// Performs point-group detection analysis for a symmetric-top molecule.
///
/// The possible symmetric top point groups are:
///
/// * $`\mathcal{C}_{n}`$ (except $`\mathcal{C}_1`$ and $`\mathcal{C}_2`$),
/// * $`\mathcal{C}_{nv}`$ (except $`\mathcal{C}_{2v}`$),
/// * $`\mathcal{C}_{nh}`$ (except $`\mathcal{C}_{2h}`$),
/// * $`\mathcal{D}_{n}`$ (except $`\mathcal{D}_{2}`$),
/// * $`\mathcal{D}_{nh}`$ (except $`\mathcal{D}_{2h}`$),
/// * $`\mathcal{D}_{nd}`$, and
/// * $`\mathcal{S}_{2n}`$.
///
/// The exceptions are all Abelian groups (but not all Abelian groups are the
/// exceptions, *e.g.* $`\mathcal{S}_{2n}`$).
///
/// # Arguments
///
/// * `presym` - A pre-symmetry-analysis structure containing information about the molecular
/// system.
/// * `tr` - A flag indicating if time reversal should also be considered. A time-reversed
/// symmetry element will only be considered if its non-time-reversed version turns out to be
/// not a symmetry element.
#[allow(clippy::too_many_lines)]
pub(super) fn analyse_symmetric(
&mut self,
presym: &PreSymmetry,
tr: bool,
) -> Result<(), anyhow::Error> {
let (_mois, _principal_axes) = presym.recentred_molecule.calc_moi();
ensure!(
matches!(
presym.rotational_symmetry,
RotationalSymmetry::ProlateNonLinear
| RotationalSymmetry::OblateNonPlanar
| RotationalSymmetry::OblatePlanar
),
"Unexpected rotational symmetry -- expected: {} or {} or {}, actual: {}",
RotationalSymmetry::ProlateNonLinear,
RotationalSymmetry::OblateNonPlanar,
RotationalSymmetry::OblatePlanar,
presym.rotational_symmetry
);
_search_proper_rotations(presym, self, false, tr)?;
// Classify into point groups
let max_ord = self.get_max_proper_order();
let max_ord_u32 = match max_ord {
ElementOrder::Int(ord_i) => Some(ord_i),
ElementOrder::Inf => None,
}
.ok_or_else(|| format_err!("`{max_ord}` has an unexpected order value."))?;
let dihedral =
{
log::debug!("Checking dihedrality by counting C2 axes...");
if self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.contains_key(&ORDER_2)
|| self
.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.contains_key(&ORDER_2)
{
if max_ord > ORDER_2 {
ensure!(
self.get_proper(&max_ord)
.ok_or_else(|| format_err!(
"No proper elements of order `{max_ord}` found."
))?
.len()
== 1,
"More than one principal elements of order greater than 2 found."
);
let principal_axis = self.get_proper_principal_element().raw_axis();
let n_c2_perp = self
.get_proper(&ORDER_2)
.ok_or_else(|| {
format_err!("No proper elements of order `{ORDER_2}` found.")
})?
.iter()
.filter(|c2_ele| {
c2_ele.raw_axis().dot(principal_axis).abs() < presym.dist_threshold
})
.count();
log::debug!("Principal axis is C{max_ord}. Expected {max_ord} perpendicular C2 axes, found {n_c2_perp}.");
ElementOrder::Int(n_c2_perp.try_into().map_err(|_| {
format_err!("Unable to convert `{n_c2_perp}` to `u32`.")
})?) == max_ord
} else {
log::debug!("Principal axis is C2. Expected 3 C2 axes.");
max_ord == ORDER_2
&& self
.get_proper(&ORDER_2)
.ok_or_else(|| {
format_err!("No proper elements of order `{ORDER_2}` found.")
})?
.len()
== 3
}
} else {
false
}
};
if dihedral {
// Dihedral family
log::debug!("Dihedral family.");
// Principal axis is also a generator.
let principal_element = self.get_proper_principal_element().clone();
self.add_proper(
max_ord,
principal_element.raw_axis(),
true,
presym.dist_threshold,
principal_element.contains_time_reversal(),
);
// A C2 axis perpendicular to the principal axis is also a generator.
let perp_c2_element = &(*self
.get_proper(&ORDER_2)
.ok_or_else(|| format_err!("No C2 elements found."))?
.iter()
.find(|c2_ele| {
c2_ele.raw_axis().dot(principal_element.raw_axis()).abs()
< presym.dist_threshold
})
.ok_or_else(|| {
format_err!("No C2 axes perpendicular to the principal axis found.")
})?)
.clone();
self.add_proper(
ORDER_2,
perp_c2_element.raw_axis(),
true,
presym.dist_threshold,
perp_c2_element.contains_time_reversal(),
);
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, principal_element.raw_axis(), &SIG, tr)
{
// Dnh (n >= 2)
ensure!(
max_ord >= ORDER_2,
"Unexpected principal order smaller than 2."
);
log::debug!("Located σh.");
self.set_group_name(format!("D{max_ord}h"));
self.add_improper(
ORDER_1,
principal_element.raw_axis(),
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
self.add_improper(
ORDER_1,
principal_element.raw_axis(),
true,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
// Locate all other mirror planes and improper axes
// We take all the other mirror planes to be σv.
// It's really not worth trying to classify them into σv and σd,
// as this classification is more conventional than fundamental.
let non_id_c_elements = self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.values()
.chain(
self.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.values(),
)
.fold(vec![], |acc, c_eles| {
acc.into_iter()
.chain(
c_eles
.iter()
.filter(|ele| *ele.raw_proper_order() != ORDER_1)
.cloned(),
)
.collect()
});
if max_ord_u32 % 2 == 0 {
// Dnh, n even, an inversion centre is expected.
let z_vec = Vector3::new(0.0, 0.0, 1.0);
let inversion_check = presym.check_improper(&ORDER_2, &z_vec, &SIG, tr);
ensure!(
inversion_check.is_some(),
"Expected inversion centre not found."
);
self.add_improper(
ORDER_2,
&z_vec,
false,
SIG,
None,
presym.dist_threshold,
inversion_check
.ok_or_else(|| format_err!("Expected inversion centre not found."))?
.contains_time_reversal(),
);
for c_element in non_id_c_elements {
let principal_element = self.get_proper_principal_element();
let sigma_symbol = deduce_sigma_symbol(
c_element.raw_axis(),
principal_element,
presym.dist_threshold,
false,
);
// iCn
let icn_check = presym.check_improper(
c_element.raw_proper_order(),
c_element.raw_axis(),
&INV,
tr,
);
ensure!(
icn_check.is_some(),
"Expected improper element iCn not found."
);
self.add_improper(
*c_element.raw_proper_order(),
c_element.raw_axis(),
false,
INV,
sigma_symbol,
presym.dist_threshold,
icn_check
.ok_or_else(|| format_err!("Expected iCn not found."))?
.contains_time_reversal(),
);
}
} else {
// Dnh, n odd, only σh is expected.
let sigma_h = self
.get_sigma_elements("h")
.ok_or_else(|| format_err!("No σh found."))?
.into_iter()
.next()
.ok_or_else(|| format_err!("No σh found."))?
.clone();
_add_sigmahcn(self, &sigma_h, non_id_c_elements, presym, tr)?;
}
}
// end Dnh
else {
// Dnd
let sigmad_axes = self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.get(&ORDER_2)
.unwrap_or(&IndexSet::new())
.iter()
.chain(
self.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.get(&ORDER_2)
.unwrap_or(&IndexSet::new()),
)
.combinations(2)
.fold(vec![], |mut acc, c2_elements| {
let c2_axis_i = c2_elements[0].raw_axis();
let c2_axis_j = c2_elements[1].raw_axis();
let axis_p = (c2_axis_i + c2_axis_j).normalize();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &axis_p, &SIG, tr)
{
acc.push((axis_p, improper_kind.contains_time_reversal()));
};
let axis_m = (c2_axis_i - c2_axis_j).normalize();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &axis_m, &SIG, tr)
{
acc.push((axis_m, improper_kind.contains_time_reversal()));
};
acc
});
let mut count_sigmad = 0u32;
for (sigmad_axis, sigmad_axis_tr) in sigmad_axes {
count_sigmad += u32::from(self.add_improper(
ORDER_1,
&sigmad_axis,
false,
SIG,
Some("d".to_owned()),
presym.dist_threshold,
sigmad_axis_tr,
));
if count_sigmad == max_ord_u32 {
break;
}
}
log::debug!("Located {} σd.", count_sigmad);
if count_sigmad == max_ord_u32 {
// Dnd
let sigmads = self
.get_sigma_elements("d")
.ok_or_else(|| format_err!("No σd found."))?;
let sigmad = sigmads
.iter()
.next()
.ok_or_else(|| format_err!("No σd found."))?;
let sigmad_axis = *sigmad.raw_axis();
self.add_improper(
ORDER_1,
&sigmad_axis,
true,
SIG,
Some("d".to_owned()),
presym.dist_threshold,
sigmad.contains_time_reversal(),
);
self.set_group_name(format!("D{max_ord}d"));
if max_ord_u32 % 2 == 0 {
// Dnd, n even, only σd planes are present.
let non_id_c_elements = self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.values()
.chain(
self.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.values(),
)
.fold(vec![], |acc, c_eles| {
acc.into_iter()
.chain(
c_eles
.iter()
.filter(|ele| *ele.raw_proper_order() != ORDER_1)
.cloned(),
)
.collect()
});
for c_element in non_id_c_elements {
let double_order = ElementOrder::new(
2.0 * c_element.raw_proper_order().to_float(),
f64::EPSILON,
);
if let Some(improper_kind) =
presym.check_improper(&double_order, c_element.raw_axis(), &SIG, tr)
{
self.add_improper(
double_order,
c_element.raw_axis(),
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
}
}
} else {
// Dnd, n odd, an inversion centre is expected.
let vec_z = Vector3::new(0.0, 0.0, 1.0);
let inversion_check = presym.check_improper(&ORDER_2, &vec_z, &SIG, tr);
ensure!(
inversion_check.is_some(),
"Expected inversion centre not found."
);
self.add_improper(
ORDER_2,
&vec_z,
false,
SIG,
None,
presym.dist_threshold,
inversion_check
.ok_or_else(|| format_err!("Expected inversion centre not found."))?
.contains_time_reversal(),
);
let non_id_c_elements = self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.values()
.chain(
self.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.values(),
)
.fold(vec![], |acc, c_eles| {
acc.into_iter()
.chain(
c_eles
.iter()
.filter(|ele| *ele.raw_proper_order() != ORDER_1)
.cloned(),
)
.collect()
});
for c_element in non_id_c_elements {
let principal_element = self.get_proper_principal_element();
let sigma_symbol = deduce_sigma_symbol(
c_element.raw_axis(),
principal_element,
presym.dist_threshold,
true, // sigma_v forced to become sigma_d
);
let icn_check = presym.check_improper(
c_element.raw_proper_order(),
c_element.raw_axis(),
&INV,
tr,
);
ensure!(
icn_check.is_some(),
"Expected improper element iCn not found."
);
self.add_improper(
*c_element.raw_proper_order(),
c_element.raw_axis(),
false,
INV,
sigma_symbol,
presym.dist_threshold,
icn_check
.ok_or_else(|| format_err!("Expected iCn not found."))?
.contains_time_reversal(),
);
}
}
} else {
// Dn (n > 2)
self.set_group_name(format!("D{max_ord}"));
}
}
} else {
// Non-dihedral family
log::debug!("Non-dihedral family.");
// Locate mirror planes
let mut count_sigma = 0u32;
let sea_groups = &presym.sea_groups;
for sea_group in sea_groups.iter() {
if count_sigma == max_ord_u32 {
break;
}
if sea_group.len() < 2 {
continue;
}
for atom2s in sea_group.iter().combinations(2) {
if count_sigma == max_ord_u32 {
break;
}
let principal_element = self.get_proper_principal_element();
let normal =
(atom2s[0].coordinates.coords - atom2s[1].coordinates.coords).normalize();
if let Some(improper_kind) = presym.check_improper(&ORDER_1, &normal, &SIG, tr)
{
let sigma_symbol = deduce_sigma_symbol(
&normal,
principal_element,
presym.dist_threshold,
false,
);
count_sigma += u32::from(self.add_improper(
ORDER_1,
&normal,
false,
SIG,
sigma_symbol,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
}
}
}
if matches!(presym.rotational_symmetry, RotationalSymmetry::OblatePlanar) {
// Planar system. The plane of the system (perpendicular to the highest-MoI
// principal axis) might be a symmetry element: time-reversed in the presence of
// a magnetic field (which must also lie in this plane), or both in the absence
// of a magnetic field.
let (_, principal_axes) = presym.recentred_molecule.calc_moi();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &principal_axes[2], &SIG, tr)
{
if presym.recentred_molecule.magnetic_atoms.is_some() {
ensure!(
improper_kind.contains_time_reversal(),
"Expected time-reversed improper element not found."
);
}
count_sigma += u32::from(self.add_improper(
ORDER_1,
&principal_axes[2],
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
}
}
if count_sigma == max_ord_u32 {
if max_ord_u32 > 1 {
let principal_element = self.get_proper_principal_element();
// Cnv
let count_cn = self
.get_proper(&ElementOrder::Int(max_ord_u32))
.ok_or_else(|| {
format_err!("No proper elements found for potential C{max_ord_u32}v.")
})?
.len();
ensure!(
count_cn == 1,
"Unexpected number of C{max_ord_u32} axes -- expected: 1 -- actual: {count_cn}."
);
log::debug!("Found {} σv planes.", count_sigma);
if max_ord_u32 == 2 && principal_element.contains_time_reversal() {
// C2v, but with θ·C2
log::debug!("The C2 axis is actually θ·C2. The non-time-reversed σv will be reassigned as σh.");
let old_sigmas = self
.get_elements_mut(&SIG)
.and_then(|sigmas| sigmas.remove(&ORDER_1))
.ok_or_else(|| format_err!("No σv found."))?;
let old_sigma = old_sigmas
.iter()
.next()
.ok_or_else(|| format_err!("No σv found."))?;
self.add_improper(
ORDER_1,
old_sigma.raw_axis(),
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
old_sigma.contains_time_reversal(),
);
}
self.set_group_name(format!("C{max_ord}v"));
let principal_element = self.get_proper_principal_element();
let principal_element_axis = *principal_element.raw_axis();
self.add_proper(
max_ord,
&principal_element_axis,
true,
presym.dist_threshold,
principal_element.contains_time_reversal(),
);
// One of the σ's is also a generator. We prioritise the non-time-reversed one
// as the generator.
let mut sigmas = self
.get_sigma_elements("v")
.or_else(|| {
log::debug!("No σv found. Searching for σh instead.");
self.get_sigma_elements("h")
})
.ok_or_else(|| format_err!("No σh found either."))?
.into_iter()
.chain(self.get_sigma_elements("h").unwrap_or_default().into_iter())
.cloned()
.collect_vec();
sigmas.sort_by_key(SymmetryElement::contains_time_reversal);
let sigma = sigmas
.first()
.ok_or_else(|| format_err!("No σv or σh found."))?;
self.add_improper(
ORDER_1,
sigma.raw_axis(),
true,
SIG,
Some(sigma.additional_subscript.clone()),
presym.dist_threshold,
sigma.contains_time_reversal(),
);
} else {
// Cs
log::debug!("Found {} σ planes.", count_sigma);
self.set_group_name("Cs".to_owned());
let old_sigmas = if self.elements.contains_key(&SIG) {
self.get_elements_mut(&SIG)
.and_then(|sigmas| sigmas.remove(&ORDER_1))
.ok_or_else(|| format_err!("No σ found."))?
} else {
self.get_elements_mut(&TRSIG)
.and_then(|sigmas| sigmas.remove(&ORDER_1))
.ok_or_else(|| format_err!("No time-reversed σ found."))?
};
ensure!(
old_sigmas.len() == 1,
"Unexpected number of old σ mirror planes: {}.",
old_sigmas.len()
);
let old_sigma = old_sigmas
.into_iter()
.next()
.ok_or_else(|| format_err!("No σ found."))?;
self.add_improper(
ORDER_1,
old_sigma.raw_axis(),
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
old_sigma.contains_time_reversal(),
);
self.add_improper(
ORDER_1,
old_sigma.raw_axis(),
true,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
old_sigma.contains_time_reversal(),
);
}
} else {
let principal_element = self.get_proper_principal_element().clone();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, principal_element.raw_axis(), &SIG, tr)
{
// Cnh (n > 2)
ensure!(
count_sigma == 1,
"Unexpected number of σ mirror planes: {count_sigma}."
);
log::debug!("Found no σv planes but one σh plane.");
self.set_group_name(format!("C{max_ord}h"));
self.add_proper(
max_ord,
principal_element.raw_axis(),
true,
presym.dist_threshold,
principal_element.contains_time_reversal(),
);
self.add_improper(
ORDER_1,
principal_element.raw_axis(),
true,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
// Locate the remaining improper elements
let non_id_c_elements = self
.get_elements(&ROT)
.unwrap_or(&HashMap::new())
.values()
.chain(
self.get_elements(&TRROT)
.unwrap_or(&HashMap::new())
.values(),
)
.fold(vec![], |acc, c_eles| {
acc.into_iter()
.chain(
c_eles
.iter()
.filter(|ele| *ele.raw_proper_order() != ORDER_1)
.cloned(),
)
.collect()
});
if max_ord_u32 % 2 == 0 {
// Cnh, n even, an inversion centre is expected.
let vec_z = Vector3::new(0.0, 0.0, 1.0);
let inversion_check = presym.check_improper(&ORDER_2, &vec_z, &SIG, tr);
ensure!(
inversion_check.is_some(),
"Expected inversion centre not found."
);
self.add_improper(
ORDER_2,
&vec_z,
false,
SIG,
None,
presym.dist_threshold,
inversion_check
.ok_or_else(|| format_err!("Expected inversion centre not found."))?
.contains_time_reversal(),
);
for c_element in non_id_c_elements {
let principal_element = self.get_proper_principal_element();
let sigma_symbol = deduce_sigma_symbol(
c_element.raw_axis(),
principal_element,
presym.dist_threshold,
false,
);
// iCn
let icn_check = presym.check_improper(
c_element.raw_proper_order(),
c_element.raw_axis(),
&INV,
tr,
);
ensure!(
icn_check.is_some(),
"Expected improper element iCn not found."
);
self.add_improper(
*c_element.raw_proper_order(),
c_element.raw_axis(),
false,
INV,
sigma_symbol,
presym.dist_threshold,
icn_check
.ok_or_else(|| format_err!("Expected iCn not found."))?
.contains_time_reversal(),
);
}
} else {
// Cnh, n odd, only σh is present.
let sigma_h = self
.get_sigma_elements("h")
.ok_or_else(|| format_err!("No σh found."))?
.into_iter()
.next()
.ok_or_else(|| format_err!("No σh found."))?
.clone();
_add_sigmahcn(self, &sigma_h, non_id_c_elements, presym, tr)?;
}
} else {
let double_max_ord = ElementOrder::new(2.0 * max_ord.to_float(), f64::EPSILON);
if let Some(improper_kind) = presym.check_improper(
&double_max_ord,
principal_element.raw_axis(),
&SIG,
tr,
) {
// S2n
self.set_group_name(if double_max_ord == ElementOrder::Int(2) {
// S2 is Ci.
"Ci".to_string()
} else {
format!("S{double_max_ord}")
});
self.add_improper(
double_max_ord,
principal_element.raw_axis(),
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
self.add_improper(
double_max_ord,
principal_element.raw_axis(),
true,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
// Locate the remaining improper symmetry elements
if max_ord_u32 % 2 != 0 {
// Odd rotation sub groups, an inversion centre is expected.
let vec_z = Vector3::new(0.0, 0.0, 1.0);
let inversion_check = presym.check_improper(&ORDER_2, &vec_z, &SIG, tr);
ensure!(
inversion_check.is_some(),
"Expected inversion centre not found."
);
self.add_improper(
ORDER_2,
&vec_z,
false,
SIG,
None,
presym.dist_threshold,
inversion_check
.ok_or_else(|| {
format_err!("Expected inversion centre not found.")
})?
.contains_time_reversal(),
);
}
} else {
// Cn (n > 2)
self.set_group_name(format!("C{max_ord}"));
self.add_proper(
max_ord,
principal_element.raw_axis(),
true,
presym.dist_threshold,
principal_element.contains_time_reversal(),
);
}
}
}
}
Ok(())
}
}
/// Adds improper elements constructed as a product between a $`\sigma_h`$ and a
/// rotation axis.
///
/// The constructed improper elements will be added to `sym`.
///
/// # Arguments
///
/// * `sym` - A symmetry struct to store the improper rotation elements found.
/// * `sigma_h` - A $`\sigma_h`$ mirror plane.
/// * `non_id_c_elements` - A vector of non-identity rotation elements to
/// consider.
/// * `presym` - A pre-symmetry-analysis struct containing information about
/// the molecular system.
fn _add_sigmahcn(
sym: &mut Symmetry,
sigma_h: &SymmetryElement,
non_id_c_elements: Vec<SymmetryElement>,
presym: &PreSymmetry,
tr: bool,
) -> Result<(), anyhow::Error> {
let au = sigma_h.contains_antiunitary();
ensure!(sigma_h.is_o3_mirror_plane(au), "Expected σh not found.");
for c_element in non_id_c_elements {
if approx::relative_eq!(
c_element.raw_axis().cross(sigma_h.raw_axis()).norm(),
0.0,
epsilon = presym.dist_threshold,
max_relative = presym.dist_threshold
) {
// Cn is orthogonal to σh. The product Cn * σh is Sn.
log::debug!("Cn is orthogonal to σh.");
let sn_check =
presym.check_improper(c_element.raw_proper_order(), c_element.raw_axis(), &SIG, tr);
ensure!(sn_check.is_some(), "Expected Sn not found.");
let sigma_symbol = if *c_element.raw_proper_order() == ORDER_1 {
Some("h".to_owned())
} else {
None
};
sym.add_improper(
*c_element.raw_proper_order(),
c_element.raw_axis(),
false,
SIG,
sigma_symbol,
presym.dist_threshold,
sn_check
.ok_or_else(|| format_err!("Expected Sn axis not found."))?
.contains_time_reversal(),
);
} else {
// Cn is C2 and is contained in σh.
// The product σh * C2 is a σv plane.
ensure!(
approx::relative_eq!(
c_element.raw_axis().dot(sigma_h.raw_axis()).abs(),
0.0,
epsilon = presym.dist_threshold,
max_relative = presym.dist_threshold
),
"C2 is not contained in σh."
);
ensure!(*c_element.raw_proper_order() == ORDER_2, "Cn is not C2.");
log::debug!("Cn is C2 and must therefore be contained in σh.");
let s_axis = c_element.raw_axis().cross(sigma_h.raw_axis()).normalize();
let sigmav_check = presym.check_improper(&ORDER_1, &s_axis, &SIG, tr);
ensure!(sigmav_check.is_some(), "Expected σv not found.");
sym.add_improper(
ORDER_1,
&s_axis,
false,
SIG,
Some("v".to_owned()),
presym.dist_threshold,
sigmav_check
.ok_or_else(|| format_err!("Expected σv not found."))?
.contains_time_reversal(),
);
}
}
Ok(())
}