Tatlas Struct Reference

Detailed Description

A collection of charts.

Note that charts and atlas are defined on a simplified cuiksystem. Recall that the system as defined in by the user (in the .cuik file) is the original system. This system is simplified and later dummified. Charts and atlas are defined in the intermeditate system (the simplified but not dummified). This is the smaller system in terms of variables and equations and, thus, the atlas is generated faster.

However, input (the seed from where to start the atlas or the goal for the path on the atlas) and output points (the path) are given in the original system and including only system variables. Therefore, all input points are processed to first find out the values of the dummy variables from the system ones and then the values of the variables in the simplified system. Output points undergo the reverse transformation.

See Also

chart.h,chart.c,atlas.c.

Definition at line 289 of file atlas.h.

Data Fields
TAtlasBase *	w
unsigned int	m
unsigned int	k
unsigned int	n
double	e
double	ce
double	r
boolean	simpleChart
unsigned int	nCores
boolean	parallel
unsigned int *	tp
unsigned int	maxCharts
unsigned int	currentChart
unsigned int	npCharts
Tchart **	charts
unsigned int	nrJ
unsigned int	ncJ
TJacobian	J
THessian *	H
Tbox *	ambient
unsigned int	mBifurcations
unsigned int	nBifurcations
unsigned int	npBifurcations
Tbifurcation **	bifurcation

Field Documentation

TAtlasBase* Tatlas::w

The world on which the atlas is defined

Definition at line 290 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindSingularPoint(), GeodesicDistance(), GetAtlasWorld(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), MinimizeOnAtlas(), NewChartFromPoint(), Newton2ManifoldPlane(), PlotAtlas(), PlotBifurcations(), RefineSingularPoint(), SaveChartCenters(), SaveSingularCharts(), SetAtlasTopology(), and TriangulateAtlas().

unsigned int Tatlas::m

Number of variables. Dimension of the ambient space.

Definition at line 292 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindPointInOtherBranch(), FindRightNullVector(), FindSingularPoint(), GeodesicDistance(), GetAtlasAmbientDim(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), LoadBifurcations(), MinimizeOnAtlas(), NewChartFromPoint(), Newton2ManifoldPlane(), RefineSingularPoint(), SaveAtlas(), SaveBifurcations(), SaveChartCenters(), and SetAtlasTopology().

unsigned int Tatlas::k

Dimension of the manifold

Definition at line 293 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindRightNullVector(), FindSingularPoint(), GetAtlasManifoldDim(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), PlotAtlas(), ReconstructAtlasPath(), RefineSingularPoint(), SaveAtlas(), SaveChartCenters(), and TriangulateAtlas().

unsigned int Tatlas::n

Number of equations (equalities) defining the manifold.

Definition at line 294 of file atlas.h.

Referenced by AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), DetermineChartNeighbours(), GeodesicDistance(), InitAtlas(), LoadAtlas(), Newton2ManifoldPlane(), and SaveAtlas().

double Tatlas::e

Maximum error for the linear approximation of the manifold.

Definition at line 295 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindSingularPoint(), GetAtlasError(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), and SaveAtlas().

double Tatlas::ce

Maximum cuvature error between the charts and the manifold

Definition at line 296 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindSingularPoint(), GetAtlasErrorCurv(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), and SaveAtlas().

double Tatlas::r

Radius around p (in tangent space) where the linearization holds.

Definition at line 297 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindPointInOtherBranch(), FindSingularPoint(), GetAtlasRadius(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), and SaveAtlas().

boolean Tatlas::simpleChart

TRUE if the atlas is to be defined on simple charts.

Definition at line 298 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindSingularPoint(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), PlotAtlas(), and SaveAtlas().

unsigned int Tatlas::nCores

Available computing cores.

Definition at line 300 of file atlas.h.

Referenced by AtlasAStar(), AtlasGBF(), BuildAtlasFromPoint(), InitAtlas(), and LoadAtlas().

boolean Tatlas::parallel

TRUE if it is worth to use parallelism. Right now ony the altas construction exploits parallelism.

Definition at line 301 of file atlas.h.

Referenced by AtlasAStar(), BuildAtlasFromPoint(), InitAtlas(), and LoadAtlas().

unsigned int* Tatlas::tp

Topology for each variable.

Definition at line 304 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), AtlasVolume(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), DeleteAtlas(), DetermineChartNeighbours(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindPointInOtherBranch(), FindSingularPoint(), GeodesicDistance(), InitAtlasFromPoint(), LoadAtlas(), NewChartFromPoint(), Newton2ManifoldPlane(), RandomPointInAtlas(), ReconstructAtlasPath(), RefineSingularPoint(), SaveChartCenters(), and SetAtlasTopology().

unsigned int Tatlas::maxCharts

Maximum numer of charts in the atlas. Expanded as needed.

Definition at line 306 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), InitAtlas(), LoadAtlas(), and SaveAtlas().

unsigned int Tatlas::currentChart

Current number of charts in the atlas.

Definition at line 307 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), AtlasMemSize(), AtlasVolume(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), DeleteAtlas(), DetermineChartNeighbours(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), GetAtlasNumCharts(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), MinimizeOnAtlas(), PlotAtlas(), PostProcessNewCharts(), RandomPointInAtlas(), SaveAtlas(), SaveChartCenters(), SaveSingularCharts(), and TriangulateAtlas().

unsigned int Tatlas::npCharts

Number of charts already processed. Charts are added to atlas and latter on they are post-processed (search for neighbours, detect bifurcations, etc).

Definition at line 308 of file atlas.h.

Referenced by InitAtlas(), InitAtlasFromPoint(), and PostProcessNewCharts().

Tchart** Tatlas::charts

Set of local charts

Definition at line 311 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), AtlasMemSize(), AtlasVolume(), BuildAtlasFromPoint(), DefineChartsAtBifurcation(), DeleteAtlas(), DetectBifurcation(), DetermineChartNeighbours(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindRightNullVector(), FindSingularPoint(), GeodesicDistance(), GetAtlasChart(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), MinimizeOnAtlas(), NewChartFromPoint(), PlotAtlas(), PlotBifurcations(), RandomPointInAtlas(), ReconstructAtlasPath(), RefineSingularPoint(), SaveAtlas(), SaveChartCenters(), SaveSingularCharts(), and TriangulateAtlas().

unsigned int Tatlas::nrJ

Number of rows of the symbolic Jacobian.

Definition at line 313 of file atlas.h.

Referenced by FindRightNullVector(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), Newton2ManifoldPlane(), and RefineSingularPoint().

unsigned int Tatlas::ncJ

Number of columns of the symbolic Jacobian.

Definition at line 314 of file atlas.h.

Referenced by FindRightNullVector(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), Newton2ManifoldPlane(), and RefineSingularPoint().

TJacobian Tatlas::J

Symbolic Jacobian of the underlying system of equations. Cached to avoid recomputing it every time we define a new chart.

Definition at line 315 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), AtlasAStar(), AtlasGBF(), AtlasVolume(), DefineChartsAtBifurcation(), DeleteAtlas(), DetectBifurcation(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindRightNullVector(), FindSingularPoint(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), MinimizeOnAtlas(), NewChartFromPoint(), Newton2ManifoldPlane(), PlotAtlas(), ReconstructAtlasPath(), RefineSingularPoint(), and SaveChartCenters().

THessian* Tatlas::H

Hessian. Computed from the Jacobian. Only used when refining singular points (RefineSingularPoint)

Definition at line 318 of file atlas.h.

Referenced by DeleteAtlas(), InitAtlas(), LoadAtlas(), and RefineSingularPoint().

Tbox* Tatlas::ambient

Area where the manifold is defined. This can be used to clip a manifold. In general this is determined by the ranges of the variables.

Definition at line 320 of file atlas.h.

Referenced by AddChart2Atlas(), AddTrustedChart2Atlas(), DefineChartsAtBifurcation(), DeleteAtlas(), DetermineChartNeighbours(), ExtendAtlasFromPoint(), ExtendAtlasTowardPoint(), FindSingularPoint(), InitAtlas(), InitAtlasFromPoint(), LoadAtlas(), and NewChartFromPoint().

unsigned int Tatlas::mBifurcations

Maximum space for bifurcations in bifurcations. Enlarged as needed.

Definition at line 324 of file atlas.h.

Referenced by DeleteBifurcations(), DetectBifurcation(), InitAtlas(), LoadBifurcations(), and SaveBifurcations().

unsigned int Tatlas::nBifurcations

Current number of bifurcations.

Definition at line 325 of file atlas.h.

Referenced by DeleteBifurcations(), DetectBifurcation(), InitAtlas(), LoadBifurcations(), PlotBifurcations(), PostProcessNewCharts(), and SaveBifurcations().

unsigned int Tatlas::npBifurcations

Number of bifurcations already processed. The bifurcations are generated in groups when searching for neighbouring charts. We process them in groups too.

Definition at line 326 of file atlas.h.

Referenced by DeleteBifurcations(), InitAtlas(), LoadBifurcations(), PostProcessNewCharts(), ProcessBifurcation(), and SaveBifurcations().

Tbifurcation** Tatlas::bifurcation

The bifurcation information.

Definition at line 329 of file atlas.h.

Referenced by DefineChartsAtBifurcation(), DeleteBifurcations(), DetectBifurcation(), FindPointInOtherBranch(), FindRightNullVector(), FindSingularPoint(), InitAtlas(), LoadBifurcations(), PlotBifurcations(), RefineSingularPoint(), and SaveBifurcations().