Struct qsym2::group::UnitaryRepresentedGroup

pub struct UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>
where
    T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder,
    RowSymbol: LinearSpaceSymbol,
    ColSymbol: CollectionSymbol<CollectionElement = T>,
{ /* private fields */ }

Structure for managing groups with unitary representations.

Implementations

impl<T, RowSymbol, ColSymbol> UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, RowSymbol: LinearSpaceSymbol, ColSymbol: CollectionSymbol<CollectionElement = T>,

pub fn new(name: &str, elements: Vec<T>) -> Result<Self, Error>

Constructs a unitary-represented group from its elements.

Arguments

• name - A name to be given to the unitary-represented group.
• elements - A vector of all group elements.

Returns

A unitary-represented group with its Cayley table constructed and conjugacy classes determined.

Trait Implementations

impl<T, RowSymbol, ColSymbol> CharacterProperties for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where RowSymbol: LinearSpaceSymbol + Sync, ColSymbol: CollectionSymbol<CollectionElement = T> + Sync, T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder<Int = u32> + Pow<i32, Output = T>, for<'a, 'b> &'b T: Mul<&'a T, Output = T>,

type RowSymbol = RowSymbol

Type of the row-labelling symbols in the associated character table.

type CharTab = RepCharacterTable<RowSymbol, ColSymbol>

Type of the associated character table whose row-labelling symbol type is constrained to be the same as Self::RowSymbol.

fn character_table(&self) -> &Self::CharTab

Returns a shared reference to the character table of this group.

fn unitary_represented(&self) -> bool

Returns a boolean indicating if this character table contains irreducible representations of a unitary-represented group.

impl<T, RowSymbol, ColSymbol> ClassProperties for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, <Self as GroupProperties>::GroupElement: Inv, RowSymbol: LinearSpaceSymbol, ColSymbol: CollectionSymbol<CollectionElement = T>,

fn compute_class_structure(&mut self) -> Result<(), Error>

Compute the class structure of this unitary-represented group that is induced by the following equivalence relation:

    g \sim h \Leftrightarrow \exists u : h = u g u^{-1}.

type ClassSymbol = ColSymbol

The type of class symbols.

fn get_cc_index(&self, cc_idx: usize) -> Option<&HashSet<usize>>

Given a class index, returns an optional shared reference to the set containing the indices of all elements in that class.

fn get_cc_of_element_index(&self, e_idx: usize) -> Option<usize>

Given an element index, returns an optional index of the conjugacy class to which the element belongs.

fn get_cc_transversal(&self, cc_idx: usize) -> Option<Self::GroupElement>

Given a class index, returns an optional representative element of that conjugacy class.

fn get_index_of_cc_symbol(&self, cc_sym: &Self::ClassSymbol) -> Option<usize>

Given a conjugacy class symbol, returns the index of the corresponding conjugacy class.

fn get_cc_symbol_of_index(&self, cc_idx: usize) -> Option<Self::ClassSymbol>

Given a class index, returns its conjugacy class symbol, if any.

fn filter_cc_symbols<P: FnMut(&Self::ClassSymbol) -> bool>( &self, predicate: P, ) -> Vec<Self::ClassSymbol>

Given a predicate, returns conjugacy class symbols satisfying it.

fn set_class_symbols(&mut self, cc_symbols: &[Self::ClassSymbol])

Sets the conjugacy class symbols for this group.

fn get_inverse_cc(&self, cc_idx: usize) -> Option<usize>

Given a class index, returns an index for its inverse.

fn class_number(&self) -> usize

Returns the number of conjugacy classes in the group.

fn class_size(&self, cc_idx: usize) -> Option<usize>

Given a class index, returns its size.

fn class_matrix( &self, ctb_opt: Option<&Array2<usize>>, r: usize, ) -> Array2<usize>

The class matrix $\mathbf{N}_r$ for the conjugacy classes in the group.

impl<T, RowSymbol, ColSymbol> Clone for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder + Clone, RowSymbol: LinearSpaceSymbol + Clone, ColSymbol: CollectionSymbol<CollectionElement = T> + Clone,

fn clone(&self) -> UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<'de, T, RowSymbol, ColSymbol> Deserialize<'de> for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder + Deserialize<'de>, RowSymbol: LinearSpaceSymbol + Deserialize<'de>, ColSymbol: CollectionSymbol<CollectionElement = T> + Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T, RowSymbol, ColSymbol> GroupProperties for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, RowSymbol: LinearSpaceSymbol, ColSymbol: CollectionSymbol<CollectionElement = T>,

type GroupElement = T

The type of the elements in the group.

type ElementCollection = IndexSet<<UnitaryRepresentedGroup<T, RowSymbol, ColSymbol> as GroupProperties>::GroupElement>

fn name(&self) -> String

Returns the name of the group.

fn finite_subgroup_name(&self) -> Option<&String>

Returns the finite subgroup name of this group, if any.

fn get_index(&self, index: usize) -> Option<Self::GroupElement>

Given an index, returns the element associated with it, or None if the index is out of range.

fn get_index_of(&self, g: &Self::GroupElement) -> Option<usize>

Given an element, returns its index in the group, or None if the element does not exist in the group.

fn contains(&self, g: &Self::GroupElement) -> bool

Checks if an element is a member of the group.

fn elements(&self) -> &Self::ElementCollection

Returns an iterable collection of the elements in the group.

fn is_abelian(&self) -> bool

Checks if this group is abelian.

fn order(&self) -> usize

Returns the order of the group.

fn cayley_table(&self) -> Option<&Array2<usize>>

Returns the Cayley table of the group, if any.

impl<T, RowSymbol, ColSymbol> IrrepCharTabConstruction for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where RowSymbol: LinearSpaceSymbol + Sync, ColSymbol: CollectionSymbol<CollectionElement = T> + Sync, T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder<Int = u32> + Pow<i32, Output = T>, for<'a, 'b> &'b T: Mul<&'a T, Output = T>,

fn set_irrep_character_table(&mut self, chartab: Self::CharTab)

Sets the irrep character table internally.

fn construct_irrep_character_table(&mut self)

Constructs the irrep character table for this group using the Burnside–Dixon algorithm with Schneider optimisation.

impl<O, I, D> ProjectionDecomposition<UnitaryRepresentedGroup<SymmetryOperation, MullikenIrrepSymbol, SymmetryClassSymbol<SymmetryOperation>>, I, Complex<f64>, D> for O

where O: RepAnalysis<UnitaryRepresentedSymmetryGroup, I, Complex<f64>, D>, D: Dimension, I: Overlap<Complex<f64>, D> + Clone, Self: Sync + Send, Self::OrbitIter: Iterator<Item = Result<I, Error>>,

fn calc_projection_compositions( &self, ) -> Result<Vec<(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)>, Error>

Calculates the irreducible compositions of the origin $\mathbf{v}$ of the orbit using the projection operator:

fn projections_to_string( &self, projections: &[(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)], integrality_threshold: <T as ComplexFloat>::Real, ) -> String

Converts a slice of tuples of irreducible row symbols and projection values to a nicely formatted table.

impl<O, I, D> ProjectionDecomposition<UnitaryRepresentedGroup<SymmetryOperation, MullikenIrrepSymbol, SymmetryClassSymbol<SymmetryOperation>>, I, f64, D> for O

where O: RepAnalysis<UnitaryRepresentedSymmetryGroup, I, f64, D>, D: Dimension, I: Overlap<f64, D> + Clone, Self: Sync + Send, Self::OrbitIter: Iterator<Item = Result<I, Error>>,

fn calc_projection_compositions( &self, ) -> Result<Vec<(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)>, Error>

Calculates the irreducible compositions of the origin $\mathbf{v}$ of the orbit using the projection operator:

fn projections_to_string( &self, projections: &[(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)], integrality_threshold: <T as ComplexFloat>::Real, ) -> String

Converts a slice of tuples of irreducible row symbols and projection values to a nicely formatted table.

impl<T, RowSymbol, ColSymbol> Serialize for UnitaryRepresentedGroup<T, RowSymbol, ColSymbol>

where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder + Serialize, RowSymbol: LinearSpaceSymbol + Serialize, ColSymbol: CollectionSymbol<CollectionElement = T> + Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl SymmetryGroupProperties for UnitaryRepresentedGroup<SymmetryOperation, MullikenIrrepSymbol, SymmetryClassSymbol<SymmetryOperation>>

fn from_molecular_symmetry( sym: &Symmetry, infinite_order_to_finite: Option<u32>, ) -> Result<Self, Error>

Constructs a unitary-represented group from molecular symmetry elements (not operations).

Arguments

• sym - A molecular symmetry struct.
• infinite_order_to_finite - Interpret infinite-order generating elements as finite-order generating elements to create a finite subgroup of an otherwise infinite group.

Returns

A unitary-represented group of the symmetry operations generated by sym.

fn to_double_group(&self) -> Result<Self, Error>

Constructs the double group of this unitary-represented group.

Returns

The unitary-represented double group.

fn canonicalise_character_table(&mut self)

Reorders and relabels the rows and columns of the constructed character table using Mulliken conventions for the irreducible representations.

fn deduce_finite_group_name(&mut self) -> String

Deduces the group name in Schönflies notation of a finite subgroup of an infinite molecular symmetry group.

fn all_unitary(&self) -> bool

Returns true if all elements in this group are unitary.

fn is_double_group(&self) -> bool

Returns true if all elements in this group are in $\mathsf{SU}'(2)$ or false if they are all in $\mathsf{O}(3)$.

fn group_type(&self) -> GroupType

Determines whether this group is an ordinary (double) group, a magnetic grey (double) group, or a magnetic black-and-white (double) group.

fn class_symbols_from_symmetry( &mut self, ) -> Vec<SymmetryClassSymbol<SymmetryOperation>>

Returns the conjugacy class symbols in this group based on molecular symmetry.