Struct qsym2::target::density::Density

pub struct Density<'a, T>
where
    T: ComplexFloat + Lapack,
{ /* private fields */ }

Structure to manage particle spatial densities.

Implementations

impl<'a, T> Density<'a, T>

where T: ComplexFloat + Clone + Lapack,

pub fn builder() -> DensityBuilder<'a, T>

Returns a builder to construct a new Density.

pub fn complex_symmetric(&self) -> bool

Returns the complex-symmetric boolean of the density.

pub fn bao(&self) -> &BasisAngularOrder<'_>

Returns the basis angular order information of the basis set in which the density matrix is expressed.

pub fn density_matrix(&self) -> &Array2<T>

Returns a shared reference to the density matrix.

pub fn threshold(&self) -> <T as ComplexFloat>::Real

Returns the threshold with which densities are compared.

Trait Implementations

impl<'a, T> Add<&Density<'a, T>> for &Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the + operator.

fn add(self, rhs: &Density<'a, T>) -> Self::Output

Performs the + operation.

impl<'a, T> Add<&Density<'a, T>> for Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl<'a, T> Add<Density<'a, T>> for &Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the + operator.

fn add(self, rhs: Density<'a, T>) -> Self::Output

Performs the + operation.

impl<'a, T> Add for Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<'a, T> Clone for Density<'a, T>

where T: ComplexFloat + Lapack + Clone,

fn clone(&self) -> Density<'a, T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a, T> ComplexConjugationTransformable for Density<'a, T>

where T: ComplexFloat + Lapack,

fn transform_cc_mut(&mut self) -> Result<&mut Self, TransformationError>

Performs a complex conjugation in-place.

fn transform_cc(&self) -> Result<Self, TransformationError>

Performs a complex conjugation and returns the complex-conjugated result.

impl<'a, T> Debug for Density<'a, T>

where T: Debug + ComplexFloat + Lapack, <T as ComplexFloat>::Real: Sum + From<u16> + Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, T> Display for Density<'a, T>

where T: Display + ComplexFloat + Lapack, <T as ComplexFloat>::Real: Sum + From<u16> + Display,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, T> From<Density<'a, T>> for Density<'a, Complex<T>>

where T: Float + FloatConst + Lapack, Complex<T>: Lapack,

fn from(value: Density<'a, T>) -> Self

Converts to this type from the input type.

impl<'a, G, T> Orbit<G, Density<'a, T>> for DensitySymmetryOrbit<'a, G, T>

where G: SymmetryGroupProperties, T: ComplexFloat + Debug + Lapack, Density<'a, T>: SymmetryTransformable,

type OrbitIter = OrbitIterator<'a, G, Density<'a, T>>

Type of the iterator over items in the orbit.

fn group(&self) -> &G

The group generating the orbit.

fn origin(&self) -> &Density<'a, T>

The origin of the orbit.

fn iter(&self) -> Self::OrbitIter

An iterator over items in the orbit arising from the action of the group on the origin.

impl<'a, T> Overlap<T, Dim<[usize; 4]>> for Density<'a, T>

where T: Lapack + ComplexFloat<Real = <T as Scalar>::Real> + Debug + Mul<<T as ComplexFloat>::Real, Output = T>, <T as ComplexFloat>::Real: Debug + RelativeEq<<T as ComplexFloat>::Real> + AbsDiffEq<Epsilon = <T as Scalar>::Real>,

fn overlap( &self, other: &Self, metric: Option<&Array4<T>>, metric_h: Option<&Array4<T>>, ) -> Result<T, Error>

Computes the overlap between two densities.

When one or both of the densities have been acted on by an antiunitary operation, the correct Hermitian or complex-symmetric metric will be chosen in the evalulation of the overlap.

Panics

Panics if self and other have mismatched spin constraints.

fn overlap_definition(&self) -> String

Returns the mathematical definition of the overlap between two densities.

fn complex_symmetric(&self) -> bool

If true, the inner product is bilinear and $\hat{\iota} = \hat{\kappa}$. If false, the inner product is sesquilinear and $\hat{\iota} = \mathrm{id}$.

impl<'a, T> PartialEq for Density<'a, T>

where T: ComplexFloat<Real = f64> + Lapack,

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, G, T> RepAnalysis<G, Density<'a, T>, T, Dim<[usize; 4]>> for DensitySymmetryOrbit<'a, G, T>

where G: SymmetryGroupProperties, G::CharTab: SubspaceDecomposable<T>, T: Lapack + ComplexFloat<Real = <T as Scalar>::Real> + Debug + Mul<<T as ComplexFloat>::Real, Output = T>, <T as ComplexFloat>::Real: Debug + Zero + From<u16> + ToPrimitive + RelativeEq<<T as ComplexFloat>::Real> + AbsDiffEq<Epsilon = <T as Scalar>::Real>, Density<'a, T>: SymmetryTransformable,

fn analyse_rep( &self, ) -> Result<<<G as CharacterProperties>::CharTab as SubspaceDecomposable<T>>::Decomposition, DecompositionError>

Reduces the representation or corepresentation spanned by the densities in the orbit to a direct sum of the irreducible representations or corepresentations of the generating symmetry group.

Returns

The decomposed result.

Errors

Errors if the decomposition fails, e.g. because one or more calculated multiplicities are non-integral.

fn set_smat(&mut self, smat: Array2<T>)

Sets the overlap matrix between the items in the orbit.

fn smat(&self) -> Option<&Array2<T>>

Returns the overlap matrix between the items in the orbit.

fn xmat(&self) -> &Array2<T>

Returns the transformation matrix $\mathbf{X}$ for the overlap matrix $\mathbf{S}$ between the items in the orbit.

fn norm_preserving_scalar_map(&self, i: usize) -> Result<fn(_: T) -> T, Error>

Returns the norm-preserving scalar map $f$ for every element of the generating group defined by

fn integrality_threshold(&self) -> <T as ComplexFloat>::Real

Returns the threshold for integrality checks of irreducible representation or corepresentation multiplicities.

fn eigenvalue_comparison_mode(&self) -> &EigenvalueComparisonMode

Returns the enumerated type specifying the comparison mode for filtering out orbit overlap eigenvalues.

fn calc_smat( &mut self, metric: Option<&Array<T, D>>, metric_h: Option<&Array<T, D>>, use_cayley_table: bool, ) -> Result<&mut Self, Error>

Calculates and stores the overlap matrix between items in the orbit, with respect to a metric of the basis in which these items are expressed.

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

Normalises overlap matrix between items in the orbit such that its diagonal entries are unity.

fn calc_tmat(&self, op: &G::GroupElement) -> Result<Array2<T>, Error>

Computes the $\mathbf{T}(g)$ matrix for a particular element $g$ of the generating group.

fn calc_dmat(&self, op: &G::GroupElement) -> Result<Array2<T>, Error>

Computes the representation or corepresentation matrix $\mathbf{D}(g)$ for a particular element $g$ in the generating group in the basis of the orbit.

fn calc_character(&self, op: &G::GroupElement) -> Result<T, Error>

Computes the character of a particular element $g$ in the generating group in the basis of the orbit.

fn calc_characters( &self, ) -> Result<Vec<(<G as ClassProperties>::ClassSymbol, T)>, Error>

Computes the characters of the elements in a conjugacy-class transversal of the generating group in the basis of the orbit.

impl<'a, T> SpatialUnitaryTransformable for Density<'a, T>

where T: ComplexFloat + LinalgScalar + ScalarOperand + Copy + Lapack, f64: Into<T>,

fn transform_spatial_mut( &mut self, rmat: &Array2<f64>, perm: Option<&Permutation<usize>>, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation in-place.

fn transform_spatial( &self, rmat: &Array2<f64>, perm: Option<&Permutation<usize>>, ) -> Result<Self, TransformationError>

Performs a spatial transformation and returns the transformed result.

impl<'a, T> SpinUnitaryTransformable for Density<'a, T>

where T: ComplexFloat + Lapack,

fn transform_spin_mut( &mut self, _: &Array2<Complex<f64>>, ) -> Result<&mut Self, TransformationError>

Performs a spin transformation in-place.

Since densities are entirely spatial, spin transformations have no effect on them. This thus simply returns self without modification.

fn transform_spin( &self, dmat: &Array2<Complex<f64>>, ) -> Result<Self, TransformationError>

Performs a spin transformation and returns the transformed result.

impl<'a, T> Sub<&Density<'a, T>> for &Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the - operator.

fn sub(self, rhs: &Density<'a, T>) -> Self::Output

Performs the - operation.

impl<'a, T> Sub<&Density<'a, T>> for Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl<'a, T> Sub<Density<'a, T>> for &Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the - operator.

fn sub(self, rhs: Density<'a, T>) -> Self::Output

Performs the - operation.

impl<'a, T> Sub for Density<'a, T>

where T: ComplexFloat + Lapack,

type Output = Density<'a, T>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<'a, T> SymmetryTransformable for Density<'a, T>

where T: ComplexFloat + Lapack, Density<'a, T>: SpatialUnitaryTransformable + TimeReversalTransformable,

fn sym_permute_sites_spatial( &self, symop: &SymmetryOperation, ) -> Result<Permutation<usize>, TransformationError>

Determines the permutation of sites (e.g. atoms in molecules) due to the action of a symmetry operation.

fn sym_transform_spatial_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation in-place.

fn sym_transform_spatial( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation and returns the transformed result.

fn sym_transform_spatial_with_spintimerev_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation in-place, but with spin-including time reversal.

fn sym_transform_spatial_with_spintimerev( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation but with spin-including time reversal and returns the transformed result.

fn sym_transform_spin_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spin transformation according to a specified symmetry operation in-place.

fn sym_transform_spin( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spin transformation according to a specified symmetry operation and returns the transformed result.

fn sym_transform_spin_spatial_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a coupled spin-spatial transformation according to a specified symmetry operation in-place.

fn sym_transform_spin_spatial( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a coupled spin-spatial transformation according to a specified symmetry operation and returns the transformed result.

impl<'a, T> DefaultTimeReversalTransformable for Density<'a, T>

where T: ComplexFloat + Lapack,

impl<'a, T> Eq for Density<'a, T>

where T: ComplexFloat<Real = f64> + Lapack,