Trait qsym2::analysis::ProjectionDecomposition

source · 
pub trait ProjectionDecomposition<G, I, T, D>: RepAnalysis<G, I, T, D>
where
    T: ComplexFloat + Lapack + Debug,
    <T as ComplexFloat>::Real: ToPrimitive,
    G: GroupProperties + ClassProperties + CharacterProperties + Sync + Send,
    <G as CharacterProperties>::RowSymbol: Sync + Send,
    G::GroupElement: Display,
    G::CharTab: SubspaceDecomposable<T>,
    D: Dimension,
    I: Overlap<T, D> + Clone,
    Self: Sync + Send,
    Self::OrbitIter: Iterator<Item = Result<I, Error>>,
    for<'a> Complex<f64>: Mul<&'a T, Output = Complex<f64>>,
{
    // Provided methods
    fn calc_projection_compositions(
        &self,
    ) -> Result<Vec<(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)>, Error> { ... }
    fn projections_to_string(
        &self,
        projections: &[(<<G as CharacterProperties>::CharTab as CharacterTable>::RowSymbol, Complex<f64>)],
        integrality_threshold: <T as ComplexFloat>::Real,
    ) -> String { ... }
}
Expand description

Trait for decomposing the origin of an orbit into the irreducible components of the generating group using the projection operator.

Provided Methods§

source

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:

p_{\Gamma} =
    \frac{\dim \Gamma}{\lvert \mathcal{G} \rvert}
    \sum_{i=1}^{\lvert \mathcal{G} \rvert}
        \chi_{\Gamma}^{*}(\hat{g}_i)
        \braket{ \mathbf{v} | \hat{g}_i \mathbf{v} }

At the moment, this only works for unitary irreducible representations because of the presence of the characters $\chi_{\Gamma}(\hat{g}_i)$ which can only be tabulated for unitary operations.

§Returns

A vector of tuples, each of which contains the irreducible row label and the corresponding projection value.

source

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.

§Arguments
  • projections - A slice of tuples of irreducible row symbols and projection values.
  • integrality_threshold - Threshold for ascertaining the integrality of projection values.
§Returns

A string of a nicely formatted table.

Object Safety§

This trait is not object safe.

Implementors§