qsym2/drivers/representation_analysis/

multideterminant.rs

//! Driver for symmetry analysis of multi-determinantal wavefunctions.

use std::collections::HashSet;
use std::fmt;
use std::hash::Hash;
use std::ops::Mul;

use anyhow::{self, bail, format_err};
use derive_builder::Builder;
use duplicate::duplicate_item;
use ndarray::{s, Array2};
use ndarray_linalg::types::Lapack;
use num_complex::{Complex, ComplexFloat};
use num_traits::Float;
use serde::{Deserialize, Serialize};

use crate::analysis::{
    log_overlap_eigenvalues, EigenvalueComparisonMode, Overlap, ProjectionDecomposition,
    RepAnalysis,
};
use crate::angmom::spinor_rotation_3d::{SpinConstraint, SpinOrbitCoupled, StructureConstraint};
use crate::chartab::chartab_group::CharacterProperties;
use crate::chartab::SubspaceDecomposable;
use crate::drivers::representation_analysis::angular_function::{
    find_angular_function_representation, find_spinor_function_representation,
    AngularFunctionRepAnalysisParams,
};
use crate::drivers::representation_analysis::{
    fn_construct_magnetic_group, fn_construct_unitary_group, log_bao, log_cc_transversal,
    CharacterTableDisplay, MagneticSymmetryAnalysisKind,
};
use crate::drivers::symmetry_group_detection::SymmetryGroupDetectionResult;
use crate::drivers::QSym2Driver;
use crate::group::{GroupProperties, MagneticRepresentedGroup, UnitaryRepresentedGroup};
use crate::io::format::{
    log_micsec_begin, log_micsec_end, log_subtitle, nice_bool, qsym2_output, write_subtitle,
    write_title, QSym2Output,
};
use crate::symmetry::symmetry_group::{
    MagneticRepresentedSymmetryGroup, SymmetryGroupProperties, UnitaryRepresentedSymmetryGroup,
};
use crate::symmetry::symmetry_transformation::SymmetryTransformationKind;
use crate::target::determinant::SlaterDeterminant;
use crate::target::noci::basis::{Basis, EagerBasis, OrbitBasis};
use crate::target::noci::multideterminant::multideterminant_analysis::MultiDeterminantSymmetryOrbit;
use crate::target::noci::multideterminant::MultiDeterminant;

#[cfg(test)]
#[path = "multideterminant_tests.rs"]
mod multideterminant_tests;

// ==================
// Struct definitions
// ==================

// ----------
// Parameters
// ----------

const fn default_true() -> bool {
    true
}
const fn default_symbolic() -> Option<CharacterTableDisplay> {
    Some(CharacterTableDisplay::Symbolic)
}

/// Structure containing control parameters for multi-determinantal wavefunction representation
/// analysis.
#[derive(Clone, Builder, Debug, Serialize, Deserialize)]
pub struct MultiDeterminantRepAnalysisParams<T: From<f64>> {
    /// Threshold for checking if subspace multiplicities are integral.
    pub integrality_threshold: T,

    /// Threshold for determining zero eigenvalues in the orbit overlap matrix.
    pub linear_independence_threshold: T,

    /// Option indicating if the magnetic group is to be used for symmetry analysis, and if so,
    /// whether unitary representations or unitary-antiunitary corepresentations should be used.
    #[builder(default = "None")]
    #[serde(default)]
    pub use_magnetic_group: Option<MagneticSymmetryAnalysisKind>,

    /// Boolean indicating if the double group is to be used for symmetry analysis.
    #[builder(default = "false")]
    #[serde(default)]
    pub use_double_group: bool,

    /// Boolean indicating if the Cayley table of the group, if available, should be used to speed
    /// up the computation of orbit overlap matrices.
    #[builder(default = "true")]
    #[serde(default = "default_true")]
    pub use_cayley_table: bool,

    /// The kind of symmetry transformation to be applied on the reference multi-determinantal
    /// wavefunction to generate the orbit for symmetry analysis.
    #[builder(default = "SymmetryTransformationKind::Spatial")]
    #[serde(default)]
    pub symmetry_transformation_kind: SymmetryTransformationKind,

    /// Option indicating if the character table of the group used for symmetry analysis is to be
    /// printed out.
    #[builder(default = "Some(CharacterTableDisplay::Symbolic)")]
    #[serde(default = "default_symbolic")]
    pub write_character_table: Option<CharacterTableDisplay>,

    /// Boolean indicating if the eigenvalues of the orbit overlap matrix are to be printed out.
    #[builder(default = "true")]
    #[serde(default = "default_true")]
    pub write_overlap_eigenvalues: bool,

    /// The comparison mode for filtering out orbit overlap eigenvalues.
    #[builder(default = "EigenvalueComparisonMode::Modulus")]
    #[serde(default)]
    pub eigenvalue_comparison_mode: EigenvalueComparisonMode,

    /// The finite order to which any infinite-order symmetry element is reduced, so that a finite
    /// subgroup of an infinite group can be used for the symmetry analysis.
    #[builder(default = "None")]
    #[serde(default)]
    pub infinite_order_to_finite: Option<u32>,
}

impl<T> MultiDeterminantRepAnalysisParams<T>
where
    T: Float + From<f64>,
{
    /// Returns a builder to construct a [`MultiDeterminantRepAnalysisParams`] structure.
    pub fn builder() -> MultiDeterminantRepAnalysisParamsBuilder<T> {
        MultiDeterminantRepAnalysisParamsBuilder::default()
    }
}

impl Default for MultiDeterminantRepAnalysisParams<f64> {
    fn default() -> Self {
        Self::builder()
            .integrality_threshold(1e-7)
            .linear_independence_threshold(1e-7)
            .build()
            .expect("Unable to construct a default `MultiDeterminantRepAnalysisParams<f64>`.")
    }
}

impl<T> fmt::Display for MultiDeterminantRepAnalysisParams<T>
where
    T: From<f64> + fmt::LowerExp + fmt::Debug,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        writeln!(
            f,
            "Integrality threshold: {:.3e}",
            self.integrality_threshold
        )?;
        writeln!(
            f,
            "Linear independence threshold: {:.3e}",
            self.linear_independence_threshold
        )?;
        writeln!(
            f,
            "Orbit eigenvalue comparison mode: {}",
            self.eigenvalue_comparison_mode
        )?;
        writeln!(
            f,
            "Write overlap eigenvalues: {}",
            nice_bool(self.write_overlap_eigenvalues)
        )?;
        writeln!(f)?;
        writeln!(
            f,
            "Use magnetic group for analysis: {}",
            match self.use_magnetic_group {
                None => "no",
                Some(MagneticSymmetryAnalysisKind::Representation) =>
                    "yes, using unitary representations",
                Some(MagneticSymmetryAnalysisKind::Corepresentation) =>
                    "yes, using magnetic corepresentations",
            }
        )?;
        writeln!(
            f,
            "Use double group for analysis: {}",
            nice_bool(self.use_double_group)
        )?;
        writeln!(
            f,
            "Use Cayley table for orbit overlap matrices: {}",
            nice_bool(self.use_cayley_table)
        )?;
        if let Some(finite_order) = self.infinite_order_to_finite {
            writeln!(f, "Infinite order to finite: {finite_order}")?;
        }
        writeln!(
            f,
            "Symmetry transformation kind: {}",
            self.symmetry_transformation_kind
        )?;
        writeln!(f)?;
        writeln!(
            f,
            "Write character table: {}",
            if let Some(chartab_display) = self.write_character_table.as_ref() {
                format!("yes, {}", chartab_display.to_string().to_lowercase())
            } else {
                "no".to_string()
            }
        )?;

        Ok(())
    }
}

// ------
// Result
// ------

/// Structure to contain multi-determinantal representation analysis results.
#[derive(Clone, Builder)]
pub struct MultiDeterminantRepAnalysisResult<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    /// The control parameters used to obtain this set of multi-determinantal wavefunction
    /// representation analysis results.
    parameters: &'a MultiDeterminantRepAnalysisParams<<T as ComplexFloat>::Real>,

    /// The multi-determinantal wavefunctions being analysed.
    multidets: Vec<&'a MultiDeterminant<'a, T, B, SC>>,

    /// The group used for the representation analysis.
    group: G,

    /// The deduced symmetries of the multi-determinantal wavefunctions.
    multidet_symmetries:
        Vec<Result<<G::CharTab as SubspaceDecomposable<T>>::Decomposition, String>>,

    /// The overlap eigenvalues above and below the linear independence threshold for each
    /// multi-determinantal wavefunction symmetry deduction.
    multidet_symmetries_thresholds: Vec<(Option<T>, Option<T>)>,
}

impl<'a, G, T, B, SC> MultiDeterminantRepAnalysisResult<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Clone + Hash + Eq + fmt::Display,
{
    /// Returns a builder to construct a new [`MultiDeterminantRepAnalysisResultBuilder`]
    /// structure.
    fn builder() -> MultiDeterminantRepAnalysisResultBuilder<'a, G, T, B, SC> {
        MultiDeterminantRepAnalysisResultBuilder::default()
    }

    /// Returns the multi-determinantal wavefunction symmetries obtained from the analysis result.
    pub fn multidet_symmetries(
        &self,
    ) -> &Vec<Result<<G::CharTab as SubspaceDecomposable<T>>::Decomposition, String>> {
        &self.multidet_symmetries
    }
}

impl<'a, G, T, B, SC> fmt::Display for MultiDeterminantRepAnalysisResult<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug + fmt::Display,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Clone + Hash + Eq + fmt::Display,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write_subtitle(f, "Orbit-based symmetry analysis results")?;
        writeln!(f)?;
        writeln!(
            f,
            "> Group: {} ({})",
            self.group
                .finite_subgroup_name()
                .map(|subgroup_name| format!("{} > {}", self.group.name(), subgroup_name))
                .unwrap_or(self.group.name()),
            self.group.group_type().to_string().to_lowercase()
        )?;
        writeln!(f)?;

        let multidet_index_length = usize::try_from(self.multidets.len().ilog10() + 1).unwrap_or(4);
        let multidet_symmetry_length = self
            .multidet_symmetries
            .iter()
            .map(|multidet_sym| {
                multidet_sym
                    .as_ref()
                    .map(|sym| sym.to_string())
                    .unwrap_or_else(|err| err.clone())
                    .chars()
                    .count()
            })
            .max()
            .unwrap_or(0)
            .max(8);
        let multidet_energy_length = self
            .multidets
            .iter()
            .map(|multidet| {
                multidet
                    .energy()
                    .map(|v| format!("{v:+.7}").chars().count())
                    .unwrap_or(2)
            })
            .max()
            .unwrap_or(6)
            .max(6);

        let multidet_eig_above_length: usize = self
            .multidet_symmetries_thresholds
            .iter()
            .map(|(above, _)| {
                above
                    .as_ref()
                    .map(|eig| format!("{eig:+.3e}"))
                    .unwrap_or("--".to_string())
                    .chars()
                    .count()
            })
            .max()
            .unwrap_or(10)
            .max(10);

        let multidet_eig_below_length: usize = self
            .multidet_symmetries_thresholds
            .iter()
            .map(|(_, below)| {
                below
                    .as_ref()
                    .map(|eig| format!("{eig:+.3e}"))
                    .unwrap_or("--".to_string())
                    .chars()
                    .count()
            })
            .max()
            .unwrap_or(10)
            .max(10);

        let table_width = 10
            + multidet_index_length
            + multidet_energy_length
            + multidet_symmetry_length
            + multidet_eig_above_length
            + multidet_eig_below_length;

        writeln!(f, "> Multi-determinantal results")?;
        writeln!(
            f,
            "  Structure constraint: {}",
            self.multidets
                .get(0)
                .map(|multidet_0| multidet_0.structure_constraint().to_string().to_lowercase())
                .unwrap_or("--".to_string())
        )?;
        writeln!(f, "{}", "┈".repeat(table_width))?;
        writeln!(
            f,
            " {:>multidet_index_length$}  {:<multidet_energy_length$}  {:<multidet_symmetry_length$}  {:<multidet_eig_above_length$}  Eig. below",
            "#",
            "Energy",
            "Symmetry",
            "Eig. above",
        )?;
        writeln!(f, "{}", "┈".repeat(table_width))?;

        for (multidet_i, multidet) in self.multidets.iter().enumerate() {
            let multidet_energy_str = multidet
                .energy()
                .map(|multidet_energy| format!("{multidet_energy:>+multidet_energy_length$.7}"))
                .unwrap_or("--".to_string());
            let multidet_sym_str = self
                .multidet_symmetries
                .get(multidet_i)
                .ok_or_else(|| format!("Unable to retrieve the symmetry of multideterminantal wavefunction index `{multidet_i}`."))
                .and_then(|sym_res| sym_res.as_ref().map(|sym| sym.to_string()).map_err(|err| err.to_string()))
                .unwrap_or_else(|err| err);

            let (eig_above_str, eig_below_str) = self
                .multidet_symmetries_thresholds
                .get(multidet_i)
                .map(|(eig_above_opt, eig_below_opt)| {
                    (
                        eig_above_opt
                            .map(|eig_above| format!("{eig_above:>+.3e}"))
                            .unwrap_or("--".to_string()),
                        eig_below_opt
                            .map(|eig_below| format!("{eig_below:>+.3e}"))
                            .unwrap_or("--".to_string()),
                    )
                })
                .unwrap_or(("--".to_string(), "--".to_string()));
            writeln!(
                f,
                " {multidet_i:>multidet_index_length$}  \
                {multidet_energy_str:<multidet_energy_length$}  \
                {multidet_sym_str:<multidet_symmetry_length$}  \
                {eig_above_str:<multidet_eig_above_length$}  \
                {eig_below_str}"
            )?;
        }

        writeln!(f, "{}", "┈".repeat(table_width))?;
        writeln!(f)?;

        Ok(())
    }
}

impl<'a, G, T, B, SC> fmt::Debug for MultiDeterminantRepAnalysisResult<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug + fmt::Display,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Clone + Hash + Eq + fmt::Display,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        writeln!(f, "{self}")
    }
}

// ------
// Driver
// ------

// ~~~~~~~~~~~~~~~~~
// Struct definition
// ~~~~~~~~~~~~~~~~~

/// Driver structure for performing representation analysis on multi-determinantal wavefunctions.
#[derive(Clone, Builder)]
#[builder(build_fn(validate = "Self::validate"))]
pub struct MultiDeterminantRepAnalysisDriver<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    /// The control parameters for multi-determinantal wavefunction representation analysis.
    parameters: &'a MultiDeterminantRepAnalysisParams<<T as ComplexFloat>::Real>,

    /// The multi-determinantal wavefunctions to be analysed.
    multidets: Vec<&'a MultiDeterminant<'a, T, B, SC>>,

    /// The result from symmetry-group detection on the underlying molecular structure of the
    /// multi-determinantal wavefunctions.
    symmetry_group: &'a SymmetryGroupDetectionResult,

    /// The atomic-orbital overlap matrix of the underlying basis set used to describe the
    /// wavefunctions. This is either for a single component corresponding to the basis functions
    /// specified by the basis angular order structure in the determinants in [`Self::multidets`],
    /// or for *all* explicit components specified by the coefficients in the determinants.
    sao: &'a Array2<T>,

    /// The complex-symmetric atomic-orbital overlap matrix of the underlying basis set used to
    /// describe the wavefunctions. This is either for a single component corresponding to the basis
    /// functions specified by the basis angular order structure in the determinants, or for *all*
    /// explicit components specified by the coefficients in the determinants.This is required if
    /// antiunitary symmetry operations are involved. If none is provided, this will be assumed to
    /// be the same as [`Self::sao`].
    #[builder(default = "None")]
    sao_h: Option<&'a Array2<T>>,

    /// The control parameters for symmetry analysis of angular functions.
    angular_function_parameters: &'a AngularFunctionRepAnalysisParams,

    /// The result of the multi-determinantal wavefunction representation analysis.
    #[builder(setter(skip), default = "None")]
    result: Option<MultiDeterminantRepAnalysisResult<'a, G, T, B, SC>>,
}

impl<'a, G, T, B, SC> MultiDeterminantRepAnalysisDriverBuilder<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    fn validate(&self) -> Result<(), String> {
        let params = self.parameters.ok_or(
            "No multi-determinantal wavefunction representation analysis parameters found."
                .to_string(),
        )?;

        let sym_res = self
            .symmetry_group
            .ok_or("No symmetry group information found.".to_string())?;

        let sao = self.sao.ok_or("No SAO matrix found.".to_string())?;

        if let Some(sao_h) = self.sao_h.flatten() {
            if sao_h.shape() != sao.shape() {
                return Err("Mismatched shapes between `sao` and `sao_h`.".to_string());
            }
        }

        let multidets = self
            .multidets
            .as_ref()
            .ok_or("No multi-determinantal wavefunctions found.".to_string())?;
        let mut n_spatial_set = multidets
            .iter()
            .flat_map(|multidet| {
                multidet.basis().iter().map(|det_res| {
                    det_res.map(|det| {
                        (
                            det.bao().n_funcs(),
                            det.structure_constraint()
                                .n_explicit_comps_per_coefficient_matrix(),
                        )
                    })
                })
            })
            .collect::<Result<HashSet<(usize, usize)>, _>>()
            .map_err(|err| err.to_string())?;
        let (n_spatial, n_comps) = if n_spatial_set.len() == 1 {
            n_spatial_set
                .drain()
                .next()
                .ok_or("Unable to retrieve the number of spatial AO basis functions and the number of explicit components.".to_string())
        } else {
            Err("Inconsistent numbers of spatial AO basis functions and/or explicit components across multi-determinantal wavefunctions.".to_string())
        }?;

        let sym = if params.use_magnetic_group.is_some() {
            sym_res
                .magnetic_symmetry
                .as_ref()
                .ok_or("Magnetic symmetry requested for representation analysis, but no magnetic symmetry found.")?
        } else {
            &sym_res.unitary_symmetry
        };

        if sym.is_infinite() && params.infinite_order_to_finite.is_none() {
            Err(
                format!(
                    "Representation analysis cannot be performed using the entirety of the infinite group `{}`. \
                    Consider setting the parameter `infinite_order_to_finite` to restrict to a finite subgroup instead.",
                    sym.group_name.as_ref().expect("No symmetry group name found.")
                )
            )
        } else if (n_spatial != sao.nrows() || n_spatial != sao.ncols())
            && (n_spatial * n_comps != sao.nrows() || n_spatial * n_comps != sao.ncols())
        {
            Err("The dimensions of the SAO matrix do not match either the number of spatial AO basis functions or the number of spatial AO basis functions multiplied by the number of explicit components per coefficient matrix.".to_string())
        } else {
            Ok(())
        }
    }
}

// ~~~~~~~~~~~~~~~~~~~~~~
// Struct implementations
// ~~~~~~~~~~~~~~~~~~~~~~

// Generic for all symmetry groups G and wavefunction numeric type T
// '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

impl<'a, G, T, B, SC> MultiDeterminantRepAnalysisDriver<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Clone + Hash + Eq + fmt::Display,
{
    /// Returns a builder to construct a [`MultiDeterminantRepAnalysisDriver`] structure.
    pub fn builder() -> MultiDeterminantRepAnalysisDriverBuilder<'a, G, T, B, SC> {
        MultiDeterminantRepAnalysisDriverBuilder::default()
    }

    /// Constructs the appropriate atomic-orbital overlap matrix based on the structure constraint of
    /// the multi-determinantal wavefunctions and the provided overlap matrix.
    fn construct_sao(&self) -> Result<(Array2<T>, Option<Array2<T>>), anyhow::Error> {
        let mut structure_constraint_set = self
            .multidets
            .iter()
            .map(|multidet| multidet.structure_constraint())
            .collect::<HashSet<_>>();
        let structure_constraint = if structure_constraint_set.len() == 1 {
            structure_constraint_set.drain().next().ok_or(format_err!(
                "Unable to retrieve the structure constraint of the multi-determinantal wavefunctions."
            ))
        } else {
            Err(format_err!(
                "Inconsistent structure constraints across multi-determinantal wavefunctions."
            ))
        }?;

        let mut nbas_set = self
            .multidets
            .iter()
            .map(|multidet| {
                multidet
                    .basis()
                    .first()
                    .expect("Unable to obtain the first determinant in the basis.")
                    .bao()
                    .n_funcs()
            })
            .collect::<HashSet<_>>();
        let nbas = if nbas_set.len() == 1 {
            nbas_set.drain().next().ok_or(format_err!(
                "Unable to retrieve the number of basis functions describing the multi-determinantal wavefunctions."
            ))
        } else {
            Err(format_err!(
                "Inconsistent numbers of basis functions across multi-determinantal wavefunctions."
            ))
        }?;
        let ncomps = structure_constraint.n_explicit_comps_per_coefficient_matrix();
        let provided_dim = self.sao.nrows();

        if provided_dim == nbas {
            let sao = {
                let mut sao_mut = Array2::zeros((ncomps * nbas, ncomps * nbas));
                (0..ncomps).for_each(|icomp| {
                    let start = icomp * nbas;
                    let end = (icomp + 1) * nbas;
                    sao_mut
                        .slice_mut(s![start..end, start..end])
                        .assign(self.sao);
                });
                sao_mut
            };

            let sao_h = self.sao_h.map(|sao_h| {
                let mut sao_h_mut = Array2::zeros((ncomps * nbas, ncomps * nbas));
                (0..ncomps).for_each(|icomp| {
                    let start = icomp * nbas;
                    let end = (icomp + 1) * nbas;
                    sao_h_mut
                        .slice_mut(s![start..end, start..end])
                        .assign(sao_h);
                });
                sao_h_mut
            });

            Ok((sao, sao_h))
        } else {
            assert_eq!(provided_dim, nbas * ncomps);
            Ok((self.sao.clone(), self.sao_h.cloned()))
        }
    }
}

// Specific for unitary-represented symmetry groups, but generic for wavefunction numeric type T
// '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

impl<'a, T, B, SC> MultiDeterminantRepAnalysisDriver<'a, UnitaryRepresentedSymmetryGroup, T, B, SC>
where
    T: ComplexFloat + Lapack + Sync + Send,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug + Sync + Send,
    for<'b> Complex<f64>: Mul<&'b T, Output = Complex<f64>>,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    fn_construct_unitary_group!(
        /// Constructs the unitary-represented group (which itself can be unitary or magnetic) ready
        /// for Slater determinant representation analysis.
        construct_unitary_group
    );
}

// Specific for magnetic-represented symmetry groups, but generic for wavefunction numeric type T
// ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

impl<'a, T, B, SC> MultiDeterminantRepAnalysisDriver<'a, MagneticRepresentedSymmetryGroup, T, B, SC>
where
    T: ComplexFloat + Lapack + Sync + Send,
    <T as ComplexFloat>::Real: From<f64> + Sync + Send + fmt::LowerExp + fmt::Debug,
    for<'b> Complex<f64>: Mul<&'b T, Output = Complex<f64>>,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    fn_construct_magnetic_group!(
        /// Constructs the magnetic-represented group (which itself can only be magnetic) ready for
        /// Slater determinant corepresentation analysis.
        construct_magnetic_group
    );
}

// Specific for unitary-represented and magnetic-represented symmetry groups and wavefunction numeric types f64 and C128
// '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

#[duplicate_item(
    duplicate!{
        [
            dtype_nested sctype_nested;
            [ f64 ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinOrbitCoupled ];
        ]
        duplicate!{
            [
                [
                    btype_nested [OrbitBasis<'a, UnitaryRepresentedSymmetryGroup, SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
                    calc_smat_nested [calc_smat_optimised]
                ]
                [
                    btype_nested [EagerBasis<SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
                    calc_smat_nested [calc_smat]
                ]
            ]
            [
                gtype_ [ UnitaryRepresentedSymmetryGroup ]
                dtype_ [ dtype_nested ]
                btype_ [ btype_nested ]
                sctype_ [ sctype_nested ]
                doc_sub_ [ "Performs representation analysis using a unitary-represented group and stores the result." ]
                analyse_fn_ [ analyse_representation ]
                construct_group_ [ self.construct_unitary_group()? ]
                calc_smat_ [ calc_smat_nested ]
                calc_projections_ [
                    log_subtitle("Multi-determinantal wavefunction projection decompositions");
                    qsym2_output!("");
                    qsym2_output!("  Projections are defined w.r.t. the following inner product:");
                    qsym2_output!("    {}", multidet_orbit.origin().overlap_definition());
                    qsym2_output!("");
                    multidet_orbit
                        .projections_to_string(
                            &multidet_orbit.calc_projection_compositions()?,
                            params.integrality_threshold,
                        )
                        .log_output_display();
                    qsym2_output!("");
                ]
            ]
        }
    }
    duplicate!{
        [
            dtype_nested sctype_nested;
            [ f64 ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinOrbitCoupled ];
        ]
        duplicate!{
            [
                [
                    btype_nested [OrbitBasis<'a, MagneticRepresentedSymmetryGroup, SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
                    calc_smat_nested [calc_smat_optimised]
                ]
                [
                    btype_nested [EagerBasis<SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
                    calc_smat_nested [calc_smat]
                ]
            ]
            [
                gtype_ [ MagneticRepresentedSymmetryGroup ]
                dtype_ [ dtype_nested ]
                btype_ [ btype_nested ]
                sctype_ [ sctype_nested ]
                doc_sub_ [ "Performs corepresentation analysis using a magnetic-represented group and stores the result." ]
                analyse_fn_ [ analyse_corepresentation ]
                construct_group_ [ self.construct_magnetic_group()? ]
                calc_smat_ [ calc_smat_nested ]
                calc_projections_ [ ]
            ]
        }
    }
)]
impl<'a> MultiDeterminantRepAnalysisDriver<'a, gtype_, dtype_, btype_, sctype_> {
    #[doc = doc_sub_]
    fn analyse_fn_(&mut self) -> Result<(), anyhow::Error> {
        let params = self.parameters;
        let (sao, sao_h) = self.construct_sao()?;
        let group = construct_group_;
        log_cc_transversal(&group);
        let _ = find_angular_function_representation(&group, self.angular_function_parameters);
        if group.is_double_group() {
            let _ = find_spinor_function_representation(&group, self.angular_function_parameters);
        }
        if let Some(det) = self
            .multidets
            .get(0)
            .and_then(|multidet| multidet.basis().first())
        {
            log_bao(det.bao());
        }

        let (multidet_symmetries, multidet_symmetries_thresholds): (Vec<_>, Vec<_>) = self.multidets
            .iter()
            .enumerate()
            .map(|(i, multidet)| {
                log_micsec_begin(&format!("Multi-determinantal wavefunction {i}"));
                qsym2_output!("");
                let res = MultiDeterminantSymmetryOrbit::builder()
                    .group(&group)
                    .origin(multidet)
                    .integrality_threshold(params.integrality_threshold)
                    .linear_independence_threshold(params.linear_independence_threshold)
                    .symmetry_transformation_kind(params.symmetry_transformation_kind.clone())
                    .eigenvalue_comparison_mode(params.eigenvalue_comparison_mode.clone())
                    .build()
                    .map_err(|err| format_err!(err))
                    .and_then(|mut multidet_orbit| {
                        multidet_orbit
                            .calc_smat_(Some(&sao), sao_h.as_ref(), params.use_cayley_table)?
                            .normalise_smat()?
                            .calc_xmat(false)?;
                        log_overlap_eigenvalues(
                            "Overlap eigenvalues",
                            multidet_orbit.smat_eigvals.as_ref().ok_or(format_err!("Orbit overlap eigenvalues not found."))?,
                            params.linear_independence_threshold,
                            &params.eigenvalue_comparison_mode
                        );
                        qsym2_output!("");
                        let multidet_symmetry_thresholds = multidet_orbit
                            .smat_eigvals
                            .as_ref()
                            .map(|eigvals| {
                                let mut eigvals_vec = eigvals.iter().collect::<Vec<_>>();
                                match multidet_orbit.eigenvalue_comparison_mode() {
                                    EigenvalueComparisonMode::Modulus => {
                                        eigvals_vec.sort_by(|a, b| {
                                            a.abs().partial_cmp(&b.abs()).expect("Unable to compare two eigenvalues based on their moduli.")
                                        });
                                    }
                                    EigenvalueComparisonMode::Real => {
                                        eigvals_vec.sort_by(|a, b| {
                                            a.re().partial_cmp(&b.re()).expect("Unable to compare two eigenvalues based on their real parts.")
                                        });
                                    }
                                }
                                let eigval_above = match multidet_orbit.eigenvalue_comparison_mode() {
                                    EigenvalueComparisonMode::Modulus => eigvals_vec
                                        .iter()
                                        .find(|val| {
                                            val.abs() >= multidet_orbit.linear_independence_threshold
                                        })
                                        .copied()
                                        .copied(),
                                    EigenvalueComparisonMode::Real => eigvals_vec
                                        .iter()
                                        .find(|val| {
                                            val.re() >= multidet_orbit.linear_independence_threshold
                                        })
                                        .copied()
                                        .copied(),
                                };
                                eigvals_vec.reverse();
                                let eigval_below = match multidet_orbit.eigenvalue_comparison_mode() {
                                    EigenvalueComparisonMode::Modulus => eigvals_vec
                                        .iter()
                                        .find(|val| {
                                            val.abs() < multidet_orbit.linear_independence_threshold
                                        })
                                        .copied()
                                        .copied(),
                                    EigenvalueComparisonMode::Real => eigvals_vec
                                        .iter()
                                        .find(|val| {
                                            val.re() < multidet_orbit.linear_independence_threshold
                                        })
                                        .copied()
                                        .copied(),
                                };
                                (eigval_above, eigval_below)
                            })
                            .unwrap_or((None, None));
                        let multidet_sym = multidet_orbit.analyse_rep().map_err(|err| err.to_string());
                        { calc_projections_ }
                        Ok((multidet_sym, multidet_symmetry_thresholds))
                    })
                    .unwrap_or_else(|err| (Err(err.to_string()), (None, None)));
                log_micsec_end(&format!("Multi-determinantal wavefunction {i}"));
                qsym2_output!("");
                res
            }).unzip();

        let result = MultiDeterminantRepAnalysisResult::builder()
            .parameters(params)
            .multidets(self.multidets.clone())
            .group(group)
            .multidet_symmetries(multidet_symmetries)
            .multidet_symmetries_thresholds(multidet_symmetries_thresholds)
            .build()?;
        self.result = Some(result);

        Ok(())
    }
}

// ~~~~~~~~~~~~~~~~~~~~~
// Trait implementations
// ~~~~~~~~~~~~~~~~~~~~~

// Generic for all symmetry groups G, basis B, and wavefunction numeric type T
// '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

impl<'a, G, T, B, SC> fmt::Display for MultiDeterminantRepAnalysisDriver<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write_title(f, "Multi-determinantal Wavefunction Symmetry Analysis")?;
        writeln!(f)?;
        writeln!(f, "{}", self.parameters)?;
        Ok(())
    }
}

impl<'a, G, T, B, SC> fmt::Debug for MultiDeterminantRepAnalysisDriver<'a, G, T, B, SC>
where
    G: SymmetryGroupProperties + Clone,
    G::CharTab: SubspaceDecomposable<T>,
    T: ComplexFloat + Lapack,
    <T as ComplexFloat>::Real: From<f64> + fmt::LowerExp + fmt::Debug,
    B: Basis<SlaterDeterminant<'a, T, SC>> + Clone,
    SC: StructureConstraint + Hash + Eq + fmt::Display,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        writeln!(f, "{self}")
    }
}

// Specific for unitary/magnetic-represented groups and determinant numeric type f64/Complex<f64>
// ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

#[duplicate_item(
    duplicate!{
        [
            dtype_nested sctype_nested;
            [ f64 ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinOrbitCoupled ];
        ]
        duplicate!{
            [
                btype_nested;
                [OrbitBasis<'a, UnitaryRepresentedSymmetryGroup, SlaterDeterminant<'a, dtype_nested, sctype_nested>>];
                [EagerBasis<SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
            ]
            [
                gtype_ [ UnitaryRepresentedSymmetryGroup ]
                dtype_ [ dtype_nested ]
                btype_ [ btype_nested ]
                sctype_ [ sctype_nested ]
                analyse_fn_ [ analyse_representation ]
            ]
        }
    }
    duplicate!{
        [
            dtype_nested sctype_nested;
            [ f64 ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinConstraint ];
            [ Complex<f64> ] [ SpinOrbitCoupled ];
        ]
        duplicate!{
            [
                btype_nested;
                [OrbitBasis<'a, MagneticRepresentedSymmetryGroup, SlaterDeterminant<'a, dtype_nested, sctype_nested>>];
                [EagerBasis<SlaterDeterminant<'a, dtype_nested, sctype_nested>>]
            ]
            [
                gtype_ [ MagneticRepresentedSymmetryGroup ]
                dtype_ [ dtype_nested ]
                btype_ [ btype_nested ]
                sctype_ [ sctype_nested ]
                analyse_fn_ [ analyse_corepresentation ]
            ]
        }
    }
)]
impl<'a> QSym2Driver for MultiDeterminantRepAnalysisDriver<'a, gtype_, dtype_, btype_, sctype_> {
    type Params = MultiDeterminantRepAnalysisParams<f64>;

    type Outcome = MultiDeterminantRepAnalysisResult<'a, gtype_, dtype_, btype_, sctype_>;

    fn result(&self) -> Result<&Self::Outcome, anyhow::Error> {
        self.result.as_ref().ok_or_else(|| {
            format_err!(
                "No multi-determinantal wavefunction representation analysis results found."
            )
        })
    }

    fn run(&mut self) -> Result<(), anyhow::Error> {
        self.log_output_display();
        self.analyse_fn_()?;
        self.result()?.log_output_display();
        Ok(())
    }
}