Compile-time calculation of shape classes' properties. More...

Data Structures
struct	AngleBoundsFunctor
	Metafunction calculating the smallest and largest angle that exist in a shape. More...

struct	minAngleFunctor
	Functor to find out the minimum angle among all shape class types passed as template arguments. More...

struct	allRotationPeriodicities
	Calculate the multiplicities of all rotations of a shape. More...

struct	maxShapeSizeFunctor
	Finds the largest size value of a set of symmetries. More...

struct	MappingsReturnType
	Data struct to collect the results of calculating the ideal index mappings between pairs of indices. More...

Typedefs
template<typename T , size_t size>
using	ArrayType = std::array< T, size >

using	AngleFunctionPtr = double(*)(const unsigned, const unsigned)

template<typename ShapeClass >
using	IndicesList = ArrayType< unsigned, ShapeClass::size >

using	IndexListStorageType = unsigned

template<typename ShapeClass >
using	RotationsSetType = Temple::DynamicSet< IndicesList< ShapeClass >, maxRotations< ShapeClass >()*2 >

template<typename ShapeClass >
using	ChainStructuresArrayType = Temple::DynamicArray< IndicesList< ShapeClass >, maxRotations< ShapeClass >()*2 >

template<typename ShapeClass >
using	ChainArrayType = Temple::DynamicArray< unsigned, maxRotations< ShapeClass >()*2 >

Functions
template<typename ShapeClass >
constexpr double	calculateSmallestAngle ()
	Calculates the minimum angle returned in a shape class. More...

template<typename ShapeClass >
constexpr auto	startingIndexSequence ()
	Generate an integer sequence to use with stereopermutations.

template<typename ShapeClass , size_t... Indices>
constexpr ArrayType< unsigned, ShapeClass::size >	applyRotationImpl (const ArrayType< unsigned, ShapeClass::size > &indices, const unsigned rotationFunctionIndex, std::index_sequence< Indices...>)
	Helper to perform applyRotation in constexpr fashion.

template<typename ShapeClass >
constexpr ArrayType< unsigned, ShapeClass::size >	applyRotation (const ArrayType< unsigned, ShapeClass::size > &indices, const unsigned rotationFunctionIndex)
	Applies a shape group rotation to an array of indices. More...

template<typename ShapeClass , unsigned rotationFunctionIndex>
constexpr unsigned	rotationPeriodicityImpl (const ArrayType< unsigned, ShapeClass::size > &runningIndices, const unsigned count)
	Helper to perform rotationPeriodicity in constexpr fashion.

template<typename ShapeClass , unsigned rotationFunctionIndex>
constexpr unsigned	rotationPeriodicity ()
	Determines the multiplicity of a shape group rotation. More...

template<typename ShapeClass , size_t... Inds>
constexpr ArrayType< unsigned, ShapeClass::rotations.size()>	rotationPeriodicitiesImpl (std::index_sequence< Inds...>)
	Helper function to calculate all rotation periodicities.

template<typename ShapeClass >
constexpr ArrayType< unsigned, ShapeClass::rotations.size()>	rotationPeriodicities ()
	Calculates all multiplicities of a shape group's rotations.

template<typename ShapeClass >
constexpr Temple::Vector	getCoordinates (const unsigned indexInSymmetry)
	Fetches the coordinates of an index in a shape. More...

constexpr double	getTetrahedronVolume (const Temple::Vector &i, const Temple::Vector &j, const Temple::Vector &k, const Temple::Vector &l)
	Calculates the volume of a tetrahedron spanned by four positions. More...

template<size_t size>
constexpr double	calculateAngularDistortion (const ArrayType< unsigned, size > &indexMapping, const size_t sourceSymmetrySize, const AngleFunctionPtr sourceAngleFunction, const AngleFunctionPtr targetAngleFunction)
	Calculates angular distortion caused by a shape transition mapping. More...

template<size_t size>
constexpr unsigned	propagateSymmetryPosition (const unsigned symmetryPosition, const ArrayType< unsigned, size > &indexMapping)
	Propagates shape positions trhough an index mapping. More...

template<typename ShapeClassFrom , typename ShapeClassTo >
constexpr double	calculateChiralDistortion (const ArrayType< unsigned, Temple::Math::max(ShapeClassFrom::size, ShapeClassTo::size) > &indexMapping)
	Calculates the chiral distortion caused by a shape transition. More...

template<size_t size>
constexpr ArrayType< unsigned, size >	symPosMapping (const ArrayType< unsigned, size > &mapping)
	Transform shape positions through a mapping. More...

template<typename ShapeClass >
constexpr unsigned	maxRotations ()

template<typename ShapeClass >
constexpr auto	generateAllRotations (const IndicesList< ShapeClass > &indices)
	Generates all rotations of a sequence of indices within a shape group. More...

template<class ShapeClassFrom , class ShapeClassTo >
constexpr auto	symmetryTransitionMappings ()
	Calculates ideal index mappings for +1, 0 size transitions. More...

template<class ShapeClassFrom , class ShapeClassTo >
constexpr auto	ligandLossMappings (const unsigned deletedSymmetryPosition)
	Find index mappings for ligand loss situations. More...

template<typename SymmetrySource , typename SymmetryTarget >
constexpr std::enable_if_t < (SymmetryTarget::size <=7 &&(SymmetrySource::size==SymmetryTarget::size\|\|SymmetrySource::size+1==SymmetryTarget::size)), Temple::Optional < MappingsReturnType >>	calculateMapping ()
	If symmetries are adjacent, calculate their shape transition mapping.

template<typename SymmetrySource , typename SymmetryTarget >
constexpr std::enable_if_t < !(SymmetryTarget::size <=7 &&(SymmetrySource::size==SymmetryTarget::size\|\|SymmetrySource::size+1==SymmetryTarget::size)), Temple::Optional < MappingsReturnType >>	calculateMapping ()
	If symmetries are not adjacent, return a None.

template<typename ShapeClass >
constexpr unsigned	numUnlinkedStereopermutations (const unsigned nIdenticalLigands)
	Calculate stereopermutations for an unlinked shape. More...

template<typename ShapeClass >
constexpr bool	hasMultipleUnlinkedStereopermutations (const unsigned nIdenticalLigands)
	Calculates whether a shape has multiple stereopermutations. More...

Variables
constexpr double	floatingPointEqualityTolerance = 1e-4

constexpr unsigned	maxShapeSize
	The largest shape size defined in the library. More...

Detailed Description

Compile-time calculation of shape classes' properties.

Here we calculate various properties of shape classes (i.e. classes that fulfill the concepts::ShapeClass concept). Also, transition mappings can be calculated at compile time using functions in this namespace.

Data from Primitives.h takes two paths through this library: Shape classes, whose equivalent data members may have different type signatures, can be processed directly here and transformed. The data available in the shape classes is made available to runtime functions by smoothing over the type signatures, which are merely differences in array lengths, into static runtime datatypes such as vectors. Then, runtime functions can calculate the same properties as these available here, but by referring to shapes by their Name, not by the shape class type itself.

Function Documentation

template<typename ShapeClass >

constexpr ArrayType<unsigned, ShapeClass::size> Scine::Molassembler::Shapes::ConstexprProperties::applyRotation	(	const ArrayType< unsigned, ShapeClass::size > &	indices,
		const unsigned	rotationFunctionIndex
	)

Applies a shape group rotation to an array of indices.

Complexity \(\Theta(S)\)

template<size_t size>

constexpr double Scine::Molassembler::Shapes::ConstexprProperties::calculateAngularDistortion	(	const ArrayType< unsigned, size > &	indexMapping,
		const size_t	sourceSymmetrySize,
		const AngleFunctionPtr	sourceAngleFunction,
		const AngleFunctionPtr	targetAngleFunction
	)

Calculates angular distortion caused by a shape transition mapping.

Complexity \(\Theta(S^2)\)

Parameters

indexMapping	An integer sequence specifying how indices from the source shape are mapped to the target shape
sourceSymmetrySize	The size of the source shape
sourceAngleFunction	A pointer to the source shape's angle function
targetAngleFunction	A pointer to the target shape's angle function

template<typename ShapeClassFrom , typename ShapeClassTo >

constexpr double Scine::Molassembler::Shapes::ConstexprProperties::calculateChiralDistortion ( const ArrayType< unsigned, Temple::Math::max(ShapeClassFrom::size, ShapeClassTo::size) > & indexMapping )

Calculates the chiral distortion caused by a shape transition.

Calculate the chiral distortion between the source shape and the target shape specified by an index mapping.

Complexity \(\Theta(T)\) where \(T\) is the number of tetrahedra for the shape, typically small

Parameters

indexMapping The index mapping that specifies how indices are mapped from a source shape to a target shape

template<typename ShapeClass >

constexpr double Scine::Molassembler::Shapes::ConstexprProperties::calculateSmallestAngle ( )

Calculates the minimum angle returned in a shape class.

Template Parameters

ShapeClass A shape class

Complexity \(\Theta(S^2)\)

template<typename ShapeClass >

constexpr auto Scine::Molassembler::Shapes::ConstexprProperties::generateAllRotations ( const IndicesList< ShapeClass > & indices )

Generates all rotations of a sequence of indices within a shape group.

Template Parameters

ShapeClass a model of concepts::ShapeClass

Complexity At most maxRotation iterations

template<typename ShapeClass >

constexpr Temple::Vector Scine::Molassembler::Shapes::ConstexprProperties::getCoordinates ( const unsigned indexInSymmetry )

Fetches the coordinates of an index in a shape.

Fetches the coordinates of an index in a shape, properly handling the boost::none -> origin mapping.

Complexity \(\Theta(1)\)

constexpr double Scine::Molassembler::Shapes::ConstexprProperties::getTetrahedronVolume	(	const Temple::Vector &	i,
		const Temple::Vector &	j,
		const Temple::Vector &	k,
		const Temple::Vector &	l
	)

Calculates the volume of a tetrahedron spanned by four positions.

Complexity \(\Theta(1)\)

template<typename ShapeClass >

constexpr bool Scine::Molassembler::Shapes::ConstexprProperties::hasMultipleUnlinkedStereopermutations ( const unsigned nIdenticalLigands )

Calculates whether a shape has multiple stereopermutations.

Complexity \(\Theta(S!)\)

Template Parameters

ShapeClass The shape for which to calculate this property.

Parameters

nIdenticalLigands The number of ligands whose ranking is identical. E.g. 0 generates ABCDEF, 3 generates AAABCD, etc. for octahedral.

template<class ShapeClassFrom , class ShapeClassTo >

constexpr auto Scine::Molassembler::Shapes::ConstexprProperties::ligandLossMappings ( const unsigned deletedSymmetryPosition )

Find index mappings for ligand loss situations.

Complexity \(\Theta(S!)\)

Template Parameters

ShapeClassFrom	A model of concepts::ShapeClass
ShapeClassTo	A model of concepts::ShapeClass

template<typename ShapeClass >

constexpr unsigned Scine::Molassembler::Shapes::ConstexprProperties::maxRotations ( )

Calculate a lower bound on non-superimposable rotations a shape class can produce for entirely unequal indices

Complexity \(\Theta(R M S)\) where \(R\) is the number of rotations of the shape, \(M\) is the largest multiplicity of those rotations and \(S\) is the size of the shape

Template Parameters

ShapeClass A shape class as defined in Primitives.h

template<typename ShapeClass >

constexpr unsigned Scine::Molassembler::Shapes::ConstexprProperties::numUnlinkedStereopermutations ( const unsigned nIdenticalLigands )

Calculate stereopermutations for an unlinked shape.

Complexity \(\Theta(S!)\)

Template Parameters

ShapeClass A model of concepts::ShapeClass

Parameters

nIdenticalLigands The number of ligands whose ranking is identical. E.g. 0 generates ABCDEF, 3 generates AAABCD, etc. for octahedral.

template<size_t size>

constexpr unsigned Scine::Molassembler::Shapes::ConstexprProperties::propagateSymmetryPosition	(	const unsigned	symmetryPosition,
		const ArrayType< unsigned, size > &	indexMapping
	)

Propagates shape positions trhough an index mapping.

Propagates a source shape position through an index mapping, properly handling the origin placeholder special unsigned value.

Complexity \(\Theta(S)\)

Parameters

symmetryPosition	The shape position to be mapped
indexMapping	The index mapping that specifies how indices are mapped from a source shape to a target shape

template<typename ShapeClass , unsigned rotationFunctionIndex>

constexpr unsigned Scine::Molassembler::Shapes::ConstexprProperties::rotationPeriodicity ( )

Determines the multiplicity of a shape group rotation.

Calculates the multiplicity of a shape group's rotation specified via an index in that shape's list of rotations

Complexity \(\Theta(M S)\) where \(M\) is the multiplicity of the rotation and \(S\) is the shape size

Template Parameters

ShapeClass a model of concepts::ShapeClass

template<class ShapeClassFrom , class ShapeClassTo >

constexpr auto Scine::Molassembler::Shapes::ConstexprProperties::symmetryTransitionMappings ( )

Calculates ideal index mappings for +1, 0 size transitions.

Calculates the ideal index mappings for transitions in which a ligand is added or the shape size stays the same.

Complexity \(\Theta(S!)\)

Template Parameters

ShapeClassFrom	A model of concepts::ShapeClass
ShapeClassTo	A model of concepts::ShapeClass

template<size_t size>

constexpr ArrayType<unsigned, size> Scine::Molassembler::Shapes::ConstexprProperties::symPosMapping ( const ArrayType< unsigned, size > & mapping )

Transform shape positions through a mapping.

Writes the indices of the original shape in the mapping into the target shape's indexing scheme.

Complexity \(\Theta(S)\)

Parameters

mapping An index mapping that specifies how indices are mapped from a source shape to a target shape

Variable Documentation

constexpr unsigned Scine::Molassembler::Shapes::ConstexprProperties::maxShapeSize

Initial value:

= Temple::Tuples::unpackToFunction<
  Shapes::Data::allShapeDataTypes,
  maxShapeSizeFunctor
>()

The largest shape size defined in the library.

Data Structures

Typedefs

Functions

Variables

Detailed Description

Function Documentation

Variable Documentation