template<typename Index, typename Value>
class TKDTree< Index, Value >

a kd-tree

Contents:

What is kd-tree
How to cosntruct kdtree - Pseudo code
Using TKDTree a. Creating the kd-tree and setting the data b. Navigating the kd-tree
TKDTree implementation - technical details a. The order of nodes in internal arrays b. Division algorithm c. The order of nodes in boundary related arrays

1. What is kdtree ? ( [http://en.wikipedia.org/wiki/Kd-tree] )

In computer science, a kd-tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. kd-trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbour searches). kd-trees are a special case of BSP trees.

A kd-tree uses only splitting planes that are perpendicular to one of the coordinate system axes. This differs from BSP trees, in which arbitrary splitting planes can be used. In addition, in the typical definition every node of a kd-tree, from the root to the leaves, stores a point. This differs from BSP trees, in which leaves are typically the only nodes that contain points (or other geometric primitives). As a consequence, each splitting plane must go through one of the points in the kd-tree. kd-trees are a variant that store data only in leaf nodes.

2. Constructing a classical kd-tree ( Pseudo code)

Since there are many possible ways to choose axis-aligned splitting planes, there are many different ways to construct kd-trees. The canonical method of kd-tree construction has the following constraints:

As one moves down the tree, one cycles through the axes used to select the splitting planes. (For example, the root would have an x-aligned plane, the root's children would both have y-aligned planes, the root's grandchildren would all have z-aligned planes, and so on.) At each step, the point selected to create the splitting plane is the median of the points being put into the kd-tree, with respect to their coordinates in the axis being used. (Note the assumption that we feed the entire set of points into the algorithm up-front.)

This method leads to a balanced kd-tree, in which each leaf node is about the same distance from the root. However, balanced trees are not necessarily optimal for all applications. The following pseudo-code illustrates this canonical construction procedure (NOTE, that the procedure used by the TKDTree class is a bit different, the following pseudo-code is given as a simple illustration of the concept):

function kdtree (list of points pointList, int depth)
{
    if pointList is empty
        return nil;
    else
    {
        // Select axis based on depth so that axis cycles through all valid values
        var int axis := depth mod k;
        // Sort point list and choose median as pivot element
        select median from pointList;
        // Create node and construct subtrees
        var tree_node node;
        node.location := median;
        node.leftChild := kdtree(points in pointList before median, depth+1);
        node.rightChild := kdtree(points in pointList after median, depth+1);
        return node;
    }
}

Our construction method is optimized to save memory, and differs a bit from the constraints above. In particular, the division axis is chosen as the one with the biggest spread, and the point to create the splitting plane is chosen so, that one of the two subtrees contains exactly 2^k terminal nodes and is a perfectly balanced binary tree, and, while at the same time, trying to keep the number of terminal nodes in the 2 subtrees as close as possible. The following section gives more details about our implementation.

3. Using TKDTree

3a. Creating the tree and setting the data

The interface of the TKDTree, that allows to set input data, has been developped to simplify using it together with TTree::Draw() functions. That's why the data has to be provided column-wise. For example:

{
TTree *datatree = ...
...
datatree->Draw("x:y:z", "selection", "goff");
//now make a kd-tree on the drawn variables
TKDTreeID *kdtree = new TKDTreeID(npoints, 3, 1);
kdtree->SetData(0, datatree->GetV1());
kdtree->SetData(1, datatree->GetV2());
kdtree->SetData(2, datatree->GetV3());
kdtree->Build();
}
NOTE, that this implementation of kd-tree doesn't support adding new points after the tree has been built
Of course, it's not necessary to use TTree::Draw(). What is important, is to have data columnwise.
An example with regular arrays:
{
Int_t npoints = 100000;
Int_t ndim = 3;
Int_t bsize = 1;
Double_t xmin = -0.5;
Double_t xmax = 0.5;
Double_t *data0 = new Double_t[npoints];
Double_t *data1 = new Double_t[npoints];
Double_t *data2 = new Double_t[npoints];
Double_t *y     = new Double_t[npoints];
for (Int_t i=0; i<npoints; i++){
   data0[i]=gRandom->Uniform(xmin, xmax);
   data1[i]=gRandom->Uniform(xmin, xmax);
   data2[i]=gRandom->Uniform(xmin, xmax);
}
TKDTreeID *kdtree = new TKDTreeID(npoints, ndim, bsize);
kdtree->SetData(0, data0);
kdtree->SetData(1, data1);
kdtree->SetData(2, data2);
kdtree->Build();
}

By default, the kd-tree doesn't own the data and doesn't delete it with itself. If you want the
data to be deleted together with the kd-tree, call TKDTree::SetOwner(kTRUE).

Most functions of the kd-tree don't require the original data to be present after the tree
has been built. Check the functions documentation for more details.

3b. Navigating the kd-tree

Nodes of the tree are indexed top to bottom, left to right. The root node has index 0. Functions
TKDTree::GetLeft(Index inode), TKDTree::GetRight(Index inode) and TKDTree::GetParent(Index inode)
allow to find the children and the parent of a given node.

For a given node, one can find the indexes of the original points, contained in this node,
by calling the GetNodePointsIndexes(Index inode) function. Additionally, for terminal nodes,
there is a function GetPointsIndexes(Index inode) that returns a pointer to the relevant
part of the index array. To find the number of point in the node
(not only terminal), call TKDTree::GetNpointsNode(Index inode).

4. TKDtree implementation details - internal information, not needed to use the kd-tree.

4a. Order of nodes in the node information arrays:

TKDtree is optimized to minimize memory consumption. Nodes of the TKDTree do not store pointers to the left and right children or to the parent node, but instead there are several 1-d arrays of size fNNodes with information about the nodes. The order of the nodes information in the arrays is described below. It's important to understand it, if one's class needs to store some kind of additional information on the per node basis, for example, the fit function parameters.

Drawback: Insertion to the TKDtree is not supported.
Advantage: Random access is supported

As noted above, the construction of the kd-tree involves choosing the axis and the point on that axis to divide the remaining points approximately in half. The exact algorithm for choosing the division point is described in the next section. The sequence of divisions is recorded in the following arrays:

fAxix[fNNodes] - Division axis (0,1,2,3 ...)

fValue[fNNodes] - Division value

Given the index of a node in those arrays, it's easy to find the indices, corresponding to children nodes or the parent node: Suppose, the parent node is stored under the index inode. Then:

Left child index = inode*2+1
Right child index = (inode+1)*2

Suppose, that the child node is stored under the index inode. Then:

Parent index = inode/2

Number of division nodes and number of terminals : fNNodes = (fNPoints/fBucketSize)

The nodes are filled always from left side to the right side: Let inode be the index of a node, and irow - the index of a row The TKDTree looks the following way: Ideal case:

Number of _terminal_ nodes = 2^N,  N=3
           INode
irow 0     0                                                                   -  1 inode
irow 1     1                              2                                    -  2 inodes
irow 2     3              4               5               6                    -  4 inodes
irow 3     7       8      9      10       11     12       13      14           -  8 inodes

Non ideal case:

Number of _terminal_ nodes = 2^N+k,  N=3  k=1
          INode
irow 0     0                                                                   - 1 inode
irow 1     1                              2                                    - 2 inodes
irow 2     3              4               5               6                    - 3 inodes
irow 3     7       8      9      10       11     12       13      14           - 8 inodes
irow 4     15  16                                                              - 2 inodes

4b. The division algorithm:

As described above, the kd-tree is built by repeatingly dividing the given set of points into 2 smaller sets. The cut is made on the axis with the biggest spread, and the value on the axis, on which the cut is performed, is chosen based on the following formula: Suppose, we want to divide n nodes into 2 groups, left and right. Then the left and right will have the following number of nodes:

n=2^k+rest
Left  = 2^k-1 +  ((rest>2^k-2) ?  2^k-2      : rest)
Right = 2^k-1 +  ((rest>2^k-2) ?  rest-2^k-2 : 0)

For example, let n_nodes=67. Then, the closest 2^k=64, 2^k-1=32, 2^k-2=16. Left node gets 32+3=35 sub-nodes, and the right node gets 32 sub-nodes

The division process continues until all the nodes contain not more than a predefined number of points.

4c. The order of nodes in boundary-related arrays

Some kd-tree based algorithms need to know the boundaries of each node. This information can be computed by calling the TKDTree::MakeBoundaries() function. It fills the following arrays:

fRange : array containing the boundaries of the domain: | 1st dimension (min + max) | 2nd dimension (min + max) | ... fBoundaries : nodes boundaries | 1st node {1st dim * 2 elements | 2nd dim * 2 elements | ...} | 2nd node {...} | ...

The nodes are arranged in the order described in section 3a.

Note: the storage of the TKDTree in a file which include also the contained data is not supported. One must store the data separatly in a file (e.g. using a TTree) and then re-creating the TKDTree from the data, after having read them from the file

Definition at line 11 of file TKDTree.h.

Public Member Functions
	TKDTree ()

	TKDTree (Index npoints, Index ndim, UInt_t bsize)

	TKDTree (Index npoints, Index ndim, UInt_t bsize, Value **data)
	Create a kd-tree from the provided data array. More...

	~TKDTree ()
	Destructor By default, the original data is not owned by kd-tree and is not deleted with it. More...

void	Build ()
	Build the kd-tree. More...

Double_t	Distance (const Value *point, Index ind, Int_t type=2) const
	Find the distance between point of the first argument and the point at index value ind Type argument specifies the metric: type=2 - L2 metric, type=1 - L1 metric. More...

void	DistanceToNode (const Value *point, Index inode, Value &min, Value &max, Int_t type=2)
	Find the minimal and maximal distance from a given point to a given node. More...

Int_t	GetLeft (Int_t inode) const

Int_t	GetRight (Int_t inode) const

Int_t	GetParent (Int_t inode) const

Index *	GetPointsIndexes (Int_t node) const
	return the indices of the points in that terminal node for all the nodes except last, the size is fBucketSize for the last node it's fOffsetfBucketSize More...

void	GetNodePointsIndexes (Int_t node, Int_t &first1, Int_t &last1, Int_t &first2, Int_t &last2) const
	Return the indices of points in that node Indices are returned as the first and last value of the part of indices array, that belong to this node Sometimes points are in 2 intervals, then the first and last value for the second one are returned in third and fourth parameter, otherwise first2 is set to 0 and last2 is set to -1 To iterate over all the points of the node #inode, one can do, for example: Index *indices = kdtree->GetPointsIndexes(); Int_t first1, last1, first2, last2; kdtree->GetPointsIndexes(inode, first1, last1, first2, last2); for (Int_t ipoint=first1; ipoint<=last1; ipoint++){ point = indices[ipoint]; //do something with point; } for (Int_t ipoint=first2; ipoint<=last2; ipoint++){ point = indices[ipoint]; //do something with point; }. More...

UChar_t	GetNodeAxis (Int_t id) const

Value	GetNodeValue (Int_t id) const

Int_t	GetNNodes () const

Int_t	GetTotalNodes () const

Value *	GetBoundaries ()
	Get the boundaries. More...

Value *	GetBoundariesExact ()
	Get the boundaries. More...

Value *	GetBoundary (const Int_t node)
	Get a boundary. More...

Value *	GetBoundaryExact (const Int_t node)
	Get a boundary. More...

Index	GetNPoints ()

Index	GetNDim ()

Index	GetNPointsNode (Int_t node) const
	Get number of points in this node for all the terminal nodes except last, the size is fBucketSize for the last node it's fOffsetfBucketSize, or if fOffsetfBucketSize==0, it's also fBucketSize. More...

Int_t	GetRowT0 ()

Int_t	GetCrossNode ()
	smallest terminal row More...

Int_t	GetOffset ()
	cross node More...

Index *	GetIndPoints ()
	offset in fIndPoints More...

Index	GetBucketSize ()

void	FindNearestNeighbors (const Value point, Int_t k, Index ind, Value *dist)
	Find kNN nearest neighbors to the point in the first argument Returns 1 on success, 0 on failure Arrays ind and dist are provided by the user and are assumed to be at least kNN elements long. More...

Index	FindNode (const Value *point) const
	returns the index of the terminal node to which point belongs (index in the fAxis, fValue, etc arrays) returns -1 in case of failure More...

void	FindPoint (Value *point, Index &index, Int_t &iter)
	find the index of point works only if we keep fData pointers More...

void	FindInRange (Value *point, Value range, std::vector< Index > &res)
	Find all points in the sphere of a given radius "range" around the given point 1st argument - the point 2nd argument - radius of the shere 3rd argument - a vector, in which the results will be returned. More...

void	FindBNodeA (Value point, Value delta, Int_t &inode)
	find the smallest node covering the full range - start More...

Bool_t	IsTerminal (Index inode) const

Int_t	IsOwner ()

Value	KOrdStat (Index ntotal, Value a, Index k, Index index) const
	copy of the TMath::KOrdStat because I need an Index work array More...

void	MakeBoundaries (Value *range=0x0)
	Build boundaries for each node. More...

void	MakeBoundariesExact ()
	Build boundaries for each node. More...

void	SetData (Index npoints, Index ndim, UInt_t bsize, Value **data)
	Set the data array. See the constructor function comments for details. More...

Int_t	SetData (Index idim, Value *data)
	Set the coordinate #ndim of all points (the column #ndim of the data matrix) After setting all the data columns, proceed by calling Build() function Note, that calling this function after Build() is not possible Note also, that no checks on the array sizes is performed anywhere. More...

void	SetOwner (Int_t owner)

void	Spread (Index ntotal, Value a, Index index, Value &min, Value &max) const
	Calculate spread of the array a. More...

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)
	TObject copy ctor. More...

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual	~TObject ()
	TObject destructor. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current pad. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual Option_t *	GetOption () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsSortable () const

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz, void *vp)

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

void	SetBit (UInt_t f)

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

Protected Attributes
Int_t	fDataOwner

Int_t	fNNodes
	0 - not owner, 2 - owner of the pointer array, 1 - owner of the whole 2-d array More...

Int_t	fTotalNodes

Index	fNDim

Index	fNDimm

Index	fNPoints

Index	fBucketSize

UChar_t *	fAxis

Value *	fValue

Value *	fRange

Value **	fData

Value *	fBoundaries
	data points More...

Index *	fIndPoints
	nodes boundaries More...

Int_t	fRowT0
	array of points indexes More...

Int_t	fCrossNode
	smallest terminal row - first row that contains terminal nodes More...

Int_t	fOffset
	cross node - node that begins the last row (with terminal nodes only) More...

Private Member Functions
	TKDTree (const TKDTree &)

TKDTree< Index, Value > &	operator= (const TKDTree< Index, Value > &)

void	CookBoundaries (const Int_t node, Bool_t left)
	define index of this terminal node More...

void	UpdateNearestNeighbors (Index inode, const Value point, Int_t kNN, Index ind, Value *dist)
	Update the nearest neighbors values by examining the node inode. More...

void	UpdateRange (Index inode, Value *point, Value range, std::vector< Index > &res)
	Internal recursive function with the implementation of range searches. More...

Additional Inherited Members
Public Types inherited from TObject
enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Member Functions inherited from TObject
void	MakeZombie ()

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

#include <TKDTree.h>

Inheritance diagram for TKDTree< Index, Value >:

[legend]

Constructor & Destructor Documentation

template<typename Index, typename Value>

Value TKDTree< Index, Value >::TKDTree ( )

Definition at line 272 of file TKDTree.cxx.

template<typename Index , typename Value >

TKDTree< Index, Value >::TKDTree	(	Index	npoints,
		Index	ndim,
		UInt_t	bsize
	)

Definition at line 294 of file TKDTree.cxx.

template<typename Index , typename Value >

TKDTree< Index, Value >::TKDTree	(	Index	npoints,
		Index	ndim,
		UInt_t	bsize,
		Value **	data
	)

Create a kd-tree from the provided data array.

This function only sets the data, call Build() to build the tree!!! Parameteres:

npoints - total number of points. Adding points after the tree is built is not supported
ndim - number of dimensions
bsize - maximal number of points in the terminal nodes
data - the data array

The data should be placed columnwise (like in a TTree). The columnwise orientation is chosen to simplify the usage together with TTree::GetV1() like functions. An example of filling such an array for a 2d case: Double_t **data = new Double_t*[2]; data[0] = new Double_t[npoints]; data[1] = new Double_t[npoints]; for (Int_t i=0; i<npoints; i++){ data[0][i]=gRandom->Uniform(-1, 1); //fill the x-coordinate data[1][i]=gRandom->Uniform(-1, 1); //fill the y-coordinate }

By default, the kd-tree doesn't own the data. If you want the kd-tree to delete the data array, call kdtree->SetOwner(kTRUE).

Definition at line 346 of file TKDTree.cxx.

template<typename Index , typename Value >

TKDTree< Index, Value >::~TKDTree ( )

Destructor By default, the original data is not owned by kd-tree and is not deleted with it.

If you want to delete the data along with the kd-tree, call SetOwner(kTRUE).

Definition at line 375 of file TKDTree.cxx.

template<typename Index, typename Value>

TKDTree< Index, Value >::TKDTree ( const TKDTree< Index, Value > & )

private

Member Function Documentation

template<typename Index , typename Value >

void TKDTree< Index, Value >::Build ( )

Build the kd-tree.

calculate number of nodes
calculate first terminal row
initialize index array
non recursive building of the binary tree

The tree is divided recursively. See class description, section 4b for the details of the division alogrithm

Definition at line 413 of file TKDTree.cxx.

Referenced by TKDTreeBinning::SetNBins(), TestBuild(), TestConstr(), TestMembers(), TestNeighbors(), TestRange(), and TestSpeed().

template<typename Index , typename Value >

void TKDTree< Index, Value >::CookBoundaries	(	const Int_t	node,
		Bool_t	left
	)

private

define index of this terminal node

Definition at line 1076 of file TKDTree.cxx.

template<typename Index , typename Value >

Double_t TKDTree< Index, Value >::Distance	(	const Value *	point,
		Index	ind,
		Int_t	type = `2`
	)		const

Find the distance between point of the first argument and the point at index value ind Type argument specifies the metric: type=2 - L2 metric, type=1 - L1 metric.

Definition at line 617 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::DistanceToNode	(	const Value *	point,
		Index	inode,
		Value &	min,
		Value &	max,
		Int_t	type = `2`
	)

Find the minimal and maximal distance from a given point to a given node.

Type argument specifies the metric: type=2 - L2 metric, type=1 - L1 metric If the point is inside the node, both min and max are set to 0.

Definition at line 642 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::FindBNodeA	(	Value *	point,
		Value *	delta,
		Int_t &	inode
	)

find the smallest node covering the full range - start

Definition at line 1180 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::FindInRange	(	Value *	point,
		Value	range,
		std::vector< Index > &	res
	)

Find all points in the sphere of a given radius "range" around the given point 1st argument - the point 2nd argument - radius of the shere 3rd argument - a vector, in which the results will be returned.

Definition at line 756 of file TKDTree.cxx.

Referenced by TestRange().

template<typename Index , typename Value >

void TKDTree< Index, Value >::FindNearestNeighbors	(	const Value *	point,
		Int_t	k,
		Index *	ind,
		Value *	dist
	)

Find kNN nearest neighbors to the point in the first argument Returns 1 on success, 0 on failure Arrays ind and dist are provided by the user and are assumed to be at least kNN elements long.

Definition at line 550 of file TKDTree.cxx.

Referenced by TestNeighbors().

template<typename Index , typename Value >

Index TKDTree< Index, Value >::FindNode ( const Value * point ) const

returns the index of the terminal node to which point belongs (index in the fAxis, fValue, etc arrays) returns -1 in case of failure

Definition at line 679 of file TKDTree.cxx.

Referenced by TKDTreeBinning::FindBin().

template<typename Index , typename Value >

void TKDTree< Index, Value >::FindPoint	(	Value *	point,
		Index &	index,
		Int_t &	iter
	)

find the index of point works only if we keep fData pointers

Definition at line 710 of file TKDTree.cxx.

template<typename Index , typename Value >

Value * TKDTree< Index, Value >::GetBoundaries ( )

Get the boundaries.

Definition at line 1192 of file TKDTree.cxx.

template<typename Index , typename Value >

Value * TKDTree< Index, Value >::GetBoundariesExact ( )

Get the boundaries.

Definition at line 1203 of file TKDTree.cxx.

template<typename Index , typename Value >

Value * TKDTree< Index, Value >::GetBoundary ( const Int_t node )

Get a boundary.

Definition at line 1213 of file TKDTree.cxx.

Referenced by TKDTreeBinning::SetBinsEdges().

template<typename Index , typename Value >

Value * TKDTree< Index, Value >::GetBoundaryExact ( const Int_t node )

Get a boundary.

Definition at line 1223 of file TKDTree.cxx.

template<typename Index, typename Value>

Index TKDTree< Index, Value >::GetBucketSize ( )

inline

Definition at line 50 of file TKDTree.h.

Referenced by TKDTreeBinning::SetBinsContent().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetCrossNode ( )

inline

smallest terminal row

Definition at line 47 of file TKDTree.h.

Referenced by TestMembers().

template<typename Index, typename Value>

Index* TKDTree< Index, Value >::GetIndPoints ( )

inline

offset in fIndPoints

Definition at line 49 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetLeft ( Int_t inode ) const

inline

Definition at line 26 of file TKDTree.h.

template<typename Index, typename Value>

Index TKDTree< Index, Value >::GetNDim ( )

inline

Definition at line 42 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetNNodes ( ) const

inline

Definition at line 35 of file TKDTree.h.

Referenced by TKDTreeBinning::FindBin(), TKDTreeBinning::SetBinsEdges(), TestConstr(), TestMembers(), and TestSpeed().

template<typename Index, typename Value>

UChar_t TKDTree< Index, Value >::GetNodeAxis ( Int_t id ) const

inline

Definition at line 33 of file TKDTree.h.

template<typename Index , typename Value >

void TKDTree< Index, Value >::GetNodePointsIndexes	(	Int_t	node,
		Int_t &	first1,
		Int_t &	last1,
		Int_t &	first2,
		Int_t &	last2
	)		const

Return the indices of points in that node Indices are returned as the first and last value of the part of indices array, that belong to this node Sometimes points are in 2 intervals, then the first and last value for the second one are returned in third and fourth parameter, otherwise first2 is set to 0 and last2 is set to -1 To iterate over all the points of the node #inode, one can do, for example: Index *indices = kdtree->GetPointsIndexes(); Int_t first1, last1, first2, last2; kdtree->GetPointsIndexes(inode, first1, last1, first2, last2); for (Int_t ipoint=first1; ipoint<=last1; ipoint++){ point = indices[ipoint]; //do something with point; } for (Int_t ipoint=first2; ipoint<=last2; ipoint++){ point = indices[ipoint]; //do something with point; }.

Definition at line 848 of file TKDTree.cxx.

template<typename Index, typename Value>

Value TKDTree< Index, Value >::GetNodeValue ( Int_t id ) const

inline

Definition at line 34 of file TKDTree.h.

Referenced by TestConstr().

template<typename Index, typename Value>

Index TKDTree< Index, Value >::GetNPoints ( )

inline

Definition at line 41 of file TKDTree.h.

template<typename Index , typename Value >

Index TKDTree< Index, Value >::GetNPointsNode ( Int_t node ) const

Get number of points in this node for all the terminal nodes except last, the size is fBucketSize for the last node it's fOffsetfBucketSize, or if fOffsetfBucketSize==0, it's also fBucketSize.

Definition at line 902 of file TKDTree.cxx.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetOffset ( )

inline

cross node

Definition at line 48 of file TKDTree.h.

Referenced by TestMembers().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetParent ( Int_t inode ) const

inline

Definition at line 28 of file TKDTree.h.

template<typename Index , typename Value >

Index * TKDTree< Index, Value >::GetPointsIndexes ( Int_t node ) const

return the indices of the points in that terminal node for all the nodes except last, the size is fBucketSize for the last node it's fOffsetfBucketSize

Definition at line 819 of file TKDTree.cxx.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetRight ( Int_t inode ) const

inline

Definition at line 27 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetRowT0 ( )

inline

Definition at line 46 of file TKDTree.h.

Referenced by TestMembers().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::GetTotalNodes ( ) const

inline

Definition at line 36 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::IsOwner ( )

inline

Definition at line 59 of file TKDTree.h.

template<typename Index, typename Value>

Bool_t TKDTree< Index, Value >::IsTerminal ( Index inode ) const

inline

Definition at line 58 of file TKDTree.h.

template<typename Index , typename Value >

Value TKDTree< Index, Value >::KOrdStat	(	Index	ntotal,
		Value *	a,
		Index	k,
		Index *	index
	)		const

copy of the TMath::KOrdStat because I need an Index work array

Definition at line 987 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::MakeBoundaries ( Value * range = 0x0 )

Build boundaries for each node.

Note, that the boundaries here are built based on the splitting planes of the kd-tree, and don't necessarily pass through the points of the original dataset. For the latter functionality see function MakeBoundariesExact() Boundaries can be retrieved by calling GetBoundary(inode) function that would return an array of boundaries for the specified node, or GetBoundaries() function that would return the complete array.

Definition at line 1041 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::MakeBoundariesExact ( )

Build boundaries for each node.

Unlike MakeBoundaries() function the boundaries built here always pass through a point of the original dataset So, for example, for a terminal node with just one point minimum and maximum for each dimension are the same. Boundaries can be retrieved by calling GetBoundaryExact(inode) function that would return an array of boundaries for the specified node, or GetBoundaries() function that would return the complete array.

Definition at line 1121 of file TKDTree.cxx.

template<typename Index, typename Value>

TKDTree<Index, Value>& TKDTree< Index, Value >::operator= ( const TKDTree< Index, Value > & )

private

template<typename Index , typename Value >

void TKDTree< Index, Value >::SetData	(	Index	npoints,
		Index	ndim,
		UInt_t	bsize,
		Value **	data
	)

Set the data array. See the constructor function comments for details.

Definition at line 925 of file TKDTree.cxx.

Referenced by TKDTreeBinning::SetTreeData(), TestConstr(), TestMembers(), TestNeighbors(), and TestRange().

template<typename Index , typename Value >

Int_t TKDTree< Index, Value >::SetData	(	Index	idim,
		Value *	data
	)

Set the coordinate #ndim of all points (the column #ndim of the data matrix) After setting all the data columns, proceed by calling Build() function Note, that calling this function after Build() is not possible Note also, that no checks on the array sizes is performed anywhere.

Definition at line 950 of file TKDTree.cxx.

template<typename Index, typename Value>

void TKDTree< Index, Value >::SetOwner ( Int_t owner )

inline

Definition at line 67 of file TKDTree.h.

template<typename Index , typename Value >

void TKDTree< Index, Value >::Spread	(	Index	ntotal,
		Value *	a,
		Index *	index,
		Value &	min,
		Value &	max
	)		const

Calculate spread of the array a.

Definition at line 970 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::UpdateNearestNeighbors	(	Index	inode,
		const Value *	point,
		Int_t	kNN,
		Index *	ind,
		Value *	dist
	)

private

Update the nearest neighbors values by examining the node inode.

Definition at line 570 of file TKDTree.cxx.

template<typename Index , typename Value >

void TKDTree< Index, Value >::UpdateRange	(	Index	inode,
		Value *	point,
		Value	range,
		std::vector< Index > &	res
	)

private

Internal recursive function with the implementation of range searches.

Definition at line 766 of file TKDTree.cxx.

Member Data Documentation

template<typename Index, typename Value>

UChar_t* TKDTree< Index, Value >::fAxis

protected

Definition at line 86 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetNodeAxis().

template<typename Index, typename Value>

Value* TKDTree< Index, Value >::fBoundaries

protected

data points

Definition at line 91 of file TKDTree.h.

template<typename Index, typename Value>

Index TKDTree< Index, Value >::fBucketSize

protected

Definition at line 85 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetBucketSize().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fCrossNode

protected

smallest terminal row - first row that contains terminal nodes

Definition at line 96 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetCrossNode().

template<typename Index, typename Value>

Value** TKDTree< Index, Value >::fData

protected

Definition at line 90 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fDataOwner

protected

Definition at line 79 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::IsOwner(), and TKDTree< Index, Value >::SetOwner().

template<typename Index, typename Value>

Index* TKDTree< Index, Value >::fIndPoints

protected

nodes boundaries

Definition at line 94 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetIndPoints().

template<typename Index, typename Value>

Index TKDTree< Index, Value >::fNDim

protected

Definition at line 82 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetNDim().

template<typename Index, typename Value>

Index TKDTree< Index, Value >::fNDimm

protected

Definition at line 83 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fNNodes

protected

0 - not owner, 2 - owner of the pointer array, 1 - owner of the whole 2-d array

Definition at line 80 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetNNodes(), TKDTree< Index, Value >::GetNodeAxis(), TKDTree< Index, Value >::GetNodeValue(), and TKDTree< Index, Value >::IsTerminal().

template<typename Index, typename Value>

Index TKDTree< Index, Value >::fNPoints

protected

Definition at line 84 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetNPoints().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fOffset

protected

cross node - node that begins the last row (with terminal nodes only)

Definition at line 97 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetOffset().

template<typename Index, typename Value>

Value* TKDTree< Index, Value >::fRange

protected

Definition at line 89 of file TKDTree.h.

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fRowT0

protected

array of points indexes

Definition at line 95 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetRowT0().

template<typename Index, typename Value>

Int_t TKDTree< Index, Value >::fTotalNodes

protected

Definition at line 81 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetTotalNodes().

template<typename Index, typename Value>

Value* TKDTree< Index, Value >::fValue

protected

Definition at line 87 of file TKDTree.h.

Referenced by TKDTree< Index, Value >::GetNodeValue().

Collaboration diagram for TKDTree< Index, Value >:

[legend]

The documentation for this class was generated from the following files:

math/mathcore/inc/TKDTree.h
math/mathcore/src/TKDTree.cxx

template<typename Index, typename Value> class TKDTree< Index, Value >

1. What is kdtree ? ( [http://en.wikipedia.org/wiki/Kd-tree] )

2. Constructing a classical kd-tree ( Pseudo code)

3. Using TKDTree

3a. Creating the tree and setting the data

3b. Navigating the kd-tree

4. TKDtree implementation details - internal information, not needed to use the kd-tree.

4a. Order of nodes in the node information arrays:

4b. The division algorithm:

4c. The order of nodes in boundary-related arrays

Public Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename Index, typename Value>
class TKDTree< Index, Value >