Classes
struct	Tumbler

struct	HistogramParams
	Parameters of the histogram. More...

struct	HistPoint
	Point in the histogram. More...

class	LinearFunction
	Class representing an ordinary 1D linear function. More...

class	QuadraticFunction

struct	KsResult

Typedefs
using	ExtHistogramId = ExtendedEnum< HistogramId >

using	KsFunction = Function< StaticArray< Float, 4 >(PlotPoint)>

Enumerations
enum class	ComponentFlag { OVERLAP = 0 , SEPARATE_BY_FLAG = 1 << 0 , ESCAPE_VELOCITY = 1 << 1 , SORT_BY_MASS = 1 << 2 }

enum class	MoonEnum { LARGEST_FRAGMENT , RUNAWAY , MOON , IMPACTOR , UNOBSERVABLE }
	Potential relationship of the body with a respect to the largest remnant (fragment). More...

enum class	HistogramId { RADII = -1 , EQUIVALENT_MASS_RADII = -2 , VELOCITIES = -3 , ROTATIONAL_FREQUENCY = -4 , ROTATIONAL_PERIOD = -5 , ROTATIONAL_AXIS = -6 }
	Quantity from which the histogram is constructed. More...

enum class	HistogramSource { COMPONENTS , PARTICLES }
	Source data used to construct the histogram. More...

Functions
Array< Size >	findNeighbourCounts (const Storage &storage, const Float particleRadius)
	Finds the number of neighbours of each particle. More...

Size	findComponents (const Storage &storage, const Float particleRadius, const Flags< ComponentFlag > flags, Array< Size > &indices)
	Finds and marks connected components (a.k.a. separated bodies) in the array of vertices. More...

Array< Size >	findLargestComponent (const Storage &storage, const Float particleRadius, const Flags< ComponentFlag > flags)
	Returns the indices of particles belonging to the largest remnant. More...

Array< Tumbler >	findTumblers (const Storage &storage, const Float limit)
	Find all tumbling asteroids. More...

Array< MoonEnum >	findMoons (const Storage &storage, const Float radius=1._f, const Float limit=0._f)
	Find a potential satellites of the largest body. More...

Size	findMoonCount (ArrayView< const Float > m, ArrayView< const Vector > r, ArrayView< const Vector > v, const Size i, const Float radius=1._f, const Float limit=0._f)
	Find the number of moons of given body. More...

Vector	getCenterOfMass (ArrayView< const Float > m, ArrayView< const Vector > r, ArrayView< const Size > idxs=nullptr)
	Computes the center of mass. More...

SymmetricTensor	getInertiaTensor (ArrayView< const Float > m, ArrayView< const Vector > r, const Vector &r0, ArrayView< const Size > idxs=nullptr)
	Computes the total inertia tensor of particles with respect to given center. More...

SymmetricTensor	getInertiaTensor (ArrayView< const Float > m, ArrayView< const Vector > r, ArrayView< const Size > idxs=nullptr)
	Computes the total inertia tensor of particle with respect to their center of mass. More...

Vector	getAngularFrequency (ArrayView< const Float > m, ArrayView< const Vector > r, ArrayView< const Vector > v, const Vector &r0, const Vector &v0, ArrayView< const Size > idxs=nullptr)
	Computes the immediate vector of angular frequency of a rigid body. More...

Vector	getAngularFrequency (ArrayView< const Float > m, ArrayView< const Vector > r, ArrayView< const Vector > v, ArrayView< const Size > idxs=nullptr)

Float	getSphericity (IScheduler &scheduler, const Storage &strorage, const Float resolution=0.05_f)
	Computes the sphericity coefficient of a body. More...

Array< HistPoint >	getDifferentialHistogram (ArrayView< const Float > values, const HistogramParams &params)
	Computes the differential histogram from given values. More...

Array< HistPoint >	getDifferentialHistogram (const Storage &storage, const ExtHistogramId id, const HistogramSource source, const HistogramParams &params)
	Computes the differential histogram of particles in the storage. More...

Array< HistPoint >	getCumulativeHistogram (const Storage &storage, const ExtHistogramId id, const HistogramSource source, const HistogramParams &params)
	Computes cumulative (integral) histogram of particles in the storage. More...

LinearFunction	getLinearFit (ArrayView< const PlotPoint > points)
	Finds a linear fit to a set of points. More...

QuadraticFunction	getQuadraticFit (ArrayView< const PlotPoint > points)

Outcome	compareParticles (const Storage &test, const Storage &ref, const Float eps=1.e-6_f)
	Compares particle positions and state quantities of two storages. More...

Outcome	compareLargeSpheres (const Storage &test, const Storage &ref, const Float fraction, const Float maxDeviation, const Float eps=1.e-6_f)
	Compares the positions, velocities and radii of the largest particles in given states. More...

Float	correlationCoefficient (ArrayView< const PlotPoint > points)

Float	chiSquareDistribution (const Float chiSqr, const Float dof)

Float	chiSquareTest (ArrayView< const Float > measured, ArrayView< const Float > expected)

Float	kolmogorovSmirnovDistribution (const Float x)

KsResult	kolmogorovSmirnovTest (ArrayView< const Float > data, const Function< Float(Float)> &expectedCdf)
	One-dimensional Kolmogorov-Smirnov test with given CDF of expected probability distribution. More...

KsResult	kolmogorovSmirnovTest (ArrayView< const Float > data1, ArrayView< const Float > data2)

KsResult	kolmogorovSmirnovTest (ArrayView< const PlotPoint > data, const KsFunction &expected)
	Two-dimensional Kolmogorov-Smirnov test. More...

KsFunction	getUniformKsFunction (Interval rangeX, Interval rangeY)

Typedef Documentation

◆ ExtHistogramId

using Post::ExtHistogramId = typedef ExtendedEnum<HistogramId>

Definition at line 214 of file Analysis.h.

◆ KsFunction

using Post::KsFunction = typedef Function<StaticArray<Float, 4>(PlotPoint)>

Definition at line 30 of file StatisticTests.h.

Enumeration Type Documentation

◆ ComponentFlag

enum Post::ComponentFlag

strong

Enumerator
OVERLAP	Specifies that overlapping particles belong into the same component.
SEPARATE_BY_FLAG	Specifies that particles with different flag belong to different component, even if they overlap.
ESCAPE_VELOCITY	Specifies that the gravitationally bound particles belong to the same component. If used, the components are constructed in two steps; first, the initial components are created from overlapping particles. Then each pair of components is merged if their relative velocity is less then the escape velocity.
SORT_BY_MASS	If used, components are sorted by the total mass of the particles, i.e. component with index 0 will correspond to the largest remnant, index 1 will be the second largest body, etc.

Definition at line 39 of file Analysis.h.

◆ HistogramId

enum Post::HistogramId

strong

Quantity from which the histogram is constructed.

Beside the listed options, any QuantityId can be used, by casting to HistogramId enum. All values of HistogramId has to be negative to avoid clashes.

Enumerator
RADII	Particle radii or equivalent radii of components.
EQUIVALENT_MASS_RADII	Radii determined from particle masses and given reference density. This generally given more 'discretized' SFD, as masses of SPH particles are constant during the run, whereas radii (smoothing lenghts) or densities may change.
VELOCITIES	Particle velocities.
ROTATIONAL_FREQUENCY	Rotational frequency in revs/day.
ROTATIONAL_PERIOD	Rotational periods of particles (in hours) Todo: it should be in code units and then converted to hours on output!
ROTATIONAL_AXIS	Distribution of axis directions, from -pi to pi.

Definition at line 191 of file Analysis.h.

◆ HistogramSource

enum Post::HistogramSource

strong

Source data used to construct the histogram.

Enumerator
COMPONENTS	Equivalent radii of connected chunks of particles (SPH framework)
PARTICLES	Radii of individual particles, considering particles as spheres (N-body framework)

Definition at line 217 of file Analysis.h.

◆ MoonEnum

enum Post::MoonEnum

strong

Potential relationship of the body with a respect to the largest remnant (fragment).

Enumerator
LARGEST_FRAGMENT	This is the largest fragment (or remnant, depending on definition)
RUNAWAY	Body is on hyperbolic trajectory, ejected away from the largest remnant (fragment)
MOON	Body is on elliptical trajectory, it is a potential sattelite.
IMPACTOR	Body is on collisional course with the largest remnant (fragment)
UNOBSERVABLE	Body is smaller than the user-defined observational limit.

Definition at line 96 of file Analysis.h.

Function Documentation

◆ chiSquareDistribution()

Float Post::chiSquareDistribution	(	const Float	chiSqr,
		const Float	dof
	)

Definition at line 28 of file StatisticTests.cpp.

◆ chiSquareTest()

Float Post::chiSquareTest	(	ArrayView< const Float >	measured,
		ArrayView< const Float >	expected
	)

Definition at line 33 of file StatisticTests.cpp.

◆ compareLargeSpheres()

Outcome Post::compareLargeSpheres	(	const Storage &	test,
		const Storage &	ref,
		const Float	fraction,
		const Float	maxDeviation,
		const Float	eps = `1.e-6_f`
	)

Compares the positions, velocities and radii of the largest particles in given states.

If both states match, returns SUCCESS, otherwise returns an explanatory message. This comparison method in suitable for N-body simulations with merging. Function considers two states equal even if they differ by few particles.

Parameters

test	Particles to test
ref	Reference particles
fraction	Fraction of the largest particles to test. The rest is considered a "noise".
maxDeviation	Maximal difference in positions of matching particles
eps	Allowed relative error.

Definition at line 101 of file Compare.cpp.

◆ compareParticles()

NAMESPACE_SPH_BEGIN Outcome Post::compareParticles	(	const Storage &	test,
		const Storage &	ref,
		const Float	eps = `1.e-6_f`
	)

Compares particle positions and state quantities of two storages.

If both states match, returns SUCCESS, otherwise returns an explanatory message. This comparison method is mainly intended for SPH simulations.

Parameters

test	Particles to test
ref	Reference particles
eps	Allowed relative error.

Definition at line 9 of file Compare.cpp.

◆ correlationCoefficient()

NAMESPACE_SPH_BEGIN Float Post::correlationCoefficient ( ArrayView< const PlotPoint > points )

Definition at line 7 of file StatisticTests.cpp.

◆ findComponents()

Size Post::findComponents	(	const Storage &	storage,
		const Float	particleRadius,
		const Flags< ComponentFlag >	flags,
		Array< Size > &	indices
	)

Finds and marks connected components (a.k.a. separated bodies) in the array of vertices.

It is a useful function for finding bodies in simulations where we do not merge particles.

Parameters

storage	Storage containing the particles. Must also contain QuantityId::FLAG if SEPARATE_BY_FLAG option is used.
particleRadius	Size of particles in smoothing lengths.
flags	Flags specifying connectivity of components, etc; see emum ComponentFlag.
indices[out]	Array of indices from 0 to n-1, where n is the number of components. In the array, i-th index corresponds to component to which i-th particle belongs.

Returns: Number of components

Definition at line 86 of file Analysis.cpp.

◆ findLargestComponent()

Array< Size > Post::findLargestComponent	(	const Storage &	storage,
		const Float	particleRadius,
		const Flags< ComponentFlag >	flags
	)

Returns the indices of particles belonging to the largest remnant.

The returned indices are sorted.

Definition at line 216 of file Analysis.cpp.

◆ findMoonCount()

Size Post::findMoonCount	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		ArrayView< const Vector >	v,
		const Size	i,
		const Float	radius = `1._f`,
		const Float	limit = `0._f`
	)

Find the number of moons of given body.

Parameters

m	Masses of bodies, sorted in descending order.
r	Positions and radii of bodies, sorted by mass (in descending order)
v	Velocities of bodies, sorted by mass (in descending order)
i	Index of the queried body
radius	Radius multiplier, may be used to exclude moons with pericenter very close to the body.
limit	Limiting mass radio, moons with masses lower than limit*m[i] are excluded.

Definition at line 415 of file Analysis.cpp.

◆ findMoons()

Array< Post::MoonEnum > Post::findMoons	(	const Storage &	storage,
		const Float	radius = `1._f`,
		const Float	limit = `0._f`
	)

Find a potential satellites of the largest body.

The sattelites are mainly determined using the total energy of the bodies; if the energy is negative, the body is likely to be a sattelite. Note that the N-body interactions can eject bodies with negative energy away from the largest remnant (fragment), and also make a body with positive energy a future satellite (by decreasing the energy during close encounter with 3rd body). If the energy of a body is negative, a Keplerian ellipse (assuming 2-body problem) is computed and based on this ellipse, the body is either marked as moon or as impactor.

The function is mainly intended for post-reaccumulation analysis of the created asteroidal family. Satellites determined during reaccumulation can be very uncertain, as explained above. The storage must contains positions (with velocities) and masses of the bodies. The bodies do not have to be sorted, the largest remnant (or fragment) is defined as the most massive body.

Parameters

storage	Storage containing bodies of the asteroidal family
radius	Relative radius of bodies, multiplying the radius stored in h-component. Used only in collision detection; value 0 turns it off completely.
limit	Relative observational limit, with a respect to the largest remnant (fragment). Bodies with radius smaller than \({\rm limit} \cdot R_{\rm lr}\) are marked as UNOBSERVABLE, regardless their bound status. Must be in interval [0, 1>.

Returns: Array of the same size of storage, marking each body in the storage; see MoonEnum.

Definition at line 367 of file Analysis.cpp.

◆ findNeighbourCounts()

NAMESPACE_SPH_BEGIN Array< Size > Post::findNeighbourCounts	(	const Storage &	storage,
		const Float	particleRadius
	)

Finds the number of neighbours of each particle.

Note that each particle searches neighbours up to the distance given by their smoothing length, so the relation "A is a neighbour of B" might not be symmetrical.

Parameters

storage	Storage containing the particles.
particleRadius	Size of particles in smoothing lengths.

Returns: Number of neighbours of each particle.

Definition at line 22 of file Analysis.cpp.

◆ findTumblers()

Array< Post::Tumbler > Post::findTumblers	(	const Storage &	storage,
		const Float	limit
	)

Find all tumbling asteroids.

Limit specifies the required misalignment angle (in radians) for asteroid to be considered a tumbler. Note that tumbling begins to be detectable for the misalignment angle larger than 15 degrees with high accuracy data (Henych, 2013).

Definition at line 441 of file Analysis.cpp.

◆ getAngularFrequency() [1/2]

Vector Post::getAngularFrequency	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		ArrayView< const Vector >	v,
		ArrayView< const Size >	idxs = `nullptr`
	)

Definition at line 541 of file Analysis.cpp.

◆ getAngularFrequency() [2/2]

Vector Post::getAngularFrequency	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		ArrayView< const Vector >	v,
		const Vector &	r0,
		const Vector &	v0,
		ArrayView< const Size >	idxs = `nullptr`
	)

Computes the immediate vector of angular frequency of a rigid body.

Definition at line 514 of file Analysis.cpp.

◆ getCenterOfMass()

Vector Post::getCenterOfMass	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		ArrayView< const Size >	idxs = `nullptr`
	)

Computes the center of mass.

Definition at line 461 of file Analysis.cpp.

◆ getCumulativeHistogram()

Array< Post::HistPoint > Post::getCumulativeHistogram	(	const Storage &	storage,
		const ExtHistogramId	id,
		const HistogramSource	source,
		const HistogramParams &	params
	)

Computes cumulative (integral) histogram of particles in the storage.

Parameters

storage	Storage containing particle data.
id	Specifies the quantity for which the histogram is constructed.
source	Specifies the input bodies, see HistogramSource.
params	Parameters of the histogram.

Definition at line 814 of file Analysis.cpp.

◆ getDifferentialHistogram() [1/2]

Array< Post::HistPoint > Post::getDifferentialHistogram	(	ArrayView< const Float >	values,
		const HistogramParams &	params
	)

Computes the differential histogram from given values.

Note that only bin count and input range are used from the histogram parameters. No cut-offs are applied.

Definition at line 861 of file Analysis.cpp.

◆ getDifferentialHistogram() [2/2]

Array< Post::HistPoint > Post::getDifferentialHistogram	(	const Storage &	storage,
		const ExtHistogramId	id,
		const HistogramSource	source,
		const HistogramParams &	params
	)

Computes the differential histogram of particles in the storage.

Definition at line 852 of file Analysis.cpp.

◆ getInertiaTensor() [1/2]

SymmetricTensor Post::getInertiaTensor	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		ArrayView< const Size >	idxs = `nullptr`
	)

Computes the total inertia tensor of particle with respect to their center of mass.

Definition at line 506 of file Analysis.cpp.

◆ getInertiaTensor() [2/2]

SymmetricTensor Post::getInertiaTensor	(	ArrayView< const Float >	m,
		ArrayView< const Vector >	r,
		const Vector &	r0,
		ArrayView< const Size >	idxs = `nullptr`
	)

Computes the total inertia tensor of particles with respect to given center.

Definition at line 484 of file Analysis.cpp.

◆ getLinearFit()

Post::LinearFunction Post::getLinearFit ( ArrayView< const PlotPoint > points )

Finds a linear fit to a set of points.

The set of points must have at least two elements and they must not coincide.

Returns: Function representing the linear fit.

Definition at line 914 of file Analysis.cpp.

◆ getQuadraticFit()

Post::QuadraticFunction Post::getQuadraticFit ( ArrayView< const PlotPoint > points )

Definition at line 935 of file Analysis.cpp.

◆ getSphericity()

Float Post::getSphericity	(	IScheduler &	scheduler,
		const Storage &	strorage,
		const Float	resolution = `0.05_f`
	)

Computes the sphericity coefficient of a body.

Sphericity is defined as the ratio of the surface area of a sphere (with the same volume as the given body) to the surface area of the body ([Wadell_1935]). This value is equal to 1 for sphere (and only for sphere); the lower the value, the more the body is "aspheric". The sphericity is useful for quantification of "roundness"; the ratio of semi-axes, for example, can be easily 1 even for cube, definitely not a round body.

Note that the sphericity depends on resolution, small-scale topograpy will always cause the sphericity to decrease! When comparing sphericities, it is necessary to use the same resolution for the compared bodies.

Parameters

scheduler	Scheduler potentially used for parallelization.
storage	Storage containing particle positions, optionally also masses and densities.
resolution	Relative resolution used to compute the sphericity.

Returns: Wadell's sphericity value for the body.

Definition at line 550 of file Analysis.cpp.

◆ getUniformKsFunction()

Post::KsFunction Post::getUniformKsFunction	(	Interval	rangeX,
		Interval	rangeY
	)

Definition at line 167 of file StatisticTests.cpp.

◆ kolmogorovSmirnovDistribution()

Float Post::kolmogorovSmirnovDistribution ( const Float x )

Definition at line 53 of file StatisticTests.cpp.

◆ kolmogorovSmirnovTest() [1/3]

Post::KsResult Post::kolmogorovSmirnovTest	(	ArrayView< const Float >	data,
		const Function< Float(Float)> &	expectedCdf
	)

One-dimensional Kolmogorov-Smirnov test with given CDF of expected probability distribution.

Definition at line 92 of file StatisticTests.cpp.

◆ kolmogorovSmirnovTest() [2/3]

Post::KsResult Post::kolmogorovSmirnovTest	(	ArrayView< const Float >	data1,
		ArrayView< const Float >	data2
	)

Definition at line 111 of file StatisticTests.cpp.

◆ kolmogorovSmirnovTest() [3/3]

Post::KsResult Post::kolmogorovSmirnovTest	(	ArrayView< const PlotPoint >	data,
		const KsFunction &	expected
	)

Two-dimensional Kolmogorov-Smirnov test.

Definition at line 149 of file StatisticTests.cpp.

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ ExtHistogramId

◆ KsFunction

Enumeration Type Documentation

◆ ComponentFlag

◆ HistogramId

◆ HistogramSource

◆ MoonEnum

Function Documentation

◆ chiSquareDistribution()

◆ chiSquareTest()

◆ compareLargeSpheres()

◆ compareParticles()

◆ correlationCoefficient()

◆ findComponents()

◆ findLargestComponent()

◆ findMoonCount()

◆ findMoons()

◆ findNeighbourCounts()

◆ findTumblers()

◆ getAngularFrequency() [1/2]

◆ getAngularFrequency() [2/2]

◆ getCenterOfMass()

◆ getCumulativeHistogram()

◆ getDifferentialHistogram() [1/2]

◆ getDifferentialHistogram() [2/2]

◆ getInertiaTensor() [1/2]

◆ getInertiaTensor() [2/2]

◆ getLinearFit()

◆ getQuadraticFit()

◆ getSphericity()

◆ getUniformKsFunction()

◆ kolmogorovSmirnovDistribution()

◆ kolmogorovSmirnovTest() [1/3]

◆ kolmogorovSmirnovTest() [2/3]

◆ kolmogorovSmirnovTest() [3/3]