kd_tree.cpp

c++实现的KNN库:建立高维度的K-d tree,实现K邻域搜索

//----------------------------------------------------------------------
// File:			kd_tree.cpp
// Programmer:		Sunil Arya and David Mount
// Description:		Basic methods for kd-trees.
// Last modified:	01/04/05 (Version 1.0)
//----------------------------------------------------------------------
// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
// David Mount.  All Rights Reserved.
// 
// This software and related documentation is part of the Approximate
// Nearest Neighbor Library (ANN).  This software is provided under
// the provisions of the Lesser GNU Public License (LGPL).  See the
// file ../ReadMe.txt for further information.
// 
// The University of Maryland (U.M.) and the authors make no
// representations about the suitability or fitness of this software for
// any purpose.  It is provided "as is" without express or implied
// warranty.
//----------------------------------------------------------------------
// History:
//	Revision 0.1  03/04/98
//		Initial release
//	Revision 1.0  04/01/05
//		Increased aspect ratio bound (ANN_AR_TOOBIG) from 100 to 1000.
//		Fixed leaf counts to count trivial leaves.
//		Added optional pa, pi arguments to Skeleton kd_tree constructor
//			for use in load constructor.
//		Added annClose() to eliminate KD_TRIVIAL memory leak.
//----------------------------------------------------------------------

#include "kd_tree.h"					// kd-tree declarations
#include "kd_split.h"					// kd-tree splitting rules
#include "kd_util.h"					// kd-tree utilities
#include <ANN/ANNperf.h>				// performance evaluation

//----------------------------------------------------------------------
//	Global data
//
//	For some splitting rules, especially with small bucket sizes,
//	it is possible to generate a large number of empty leaf nodes.
//	To save storage we allocate a single trivial leaf node which
//	contains no points.  For messy coding reasons it is convenient
//	to have it reference a trivial point index.
//
//	KD_TRIVIAL is allocated when the first kd-tree is created.  It
//	must *never* deallocated (since it may be shared by more than
//	one tree).
//----------------------------------------------------------------------
static int				IDX_TRIVIAL[] = {0};	// trivial point index
ANNkd_leaf				*KD_TRIVIAL = NULL;		// trivial leaf node

//----------------------------------------------------------------------
//	Printing the kd-tree 
//		These routines print a kd-tree in reverse inorder (high then
//		root then low).  (This is so that if you look at the output
//		from the right side it appear from left to right in standard
//		inorder.)  When outputting leaves we output only the point
//		indices rather than the point coordinates. There is an option
//		to print the point coordinates separately.
//
//		The tree printing routine calls the printing routines on the
//		individual nodes of the tree, passing in the level or depth
//		in the tree.  The level in the tree is used to print indentation
//		for readability.
//----------------------------------------------------------------------

void ANNkd_split::print(				// print splitting node
		int level,						// depth of node in tree
		ostream &out)					// output stream
{
	child[ANN_HI]->print(level+1, out);	// print high child
	out << "    ";
	for (int i = 0; i < level; i++)		// print indentation
		out << "..";
	out << "Split cd=" << cut_dim << " cv=" << cut_val;
	out << " lbnd=" << cd_bnds[ANN_LO];
	out << " hbnd=" << cd_bnds[ANN_HI];
	out << "\n";
	child[ANN_LO]->print(level+1, out);	// print low child
}

void ANNkd_leaf::print(					// print leaf node
		int level,						// depth of node in tree
		ostream &out)					// output stream
{

	out << "    ";
	for (int i = 0; i < level; i++)		// print indentation
		out << "..";

	if (this == KD_TRIVIAL) {			// canonical trivial leaf node
		out << "Leaf (trivial)\n";
	}
	else{
		out << "Leaf n=" << n_pts << " <";
		for (int j = 0; j < n_pts; j++) {
			out << bkt[j];
			if (j < n_pts-1) out << ",";
		}
		out << ">\n";
	}
}

void ANNkd_tree::Print(					// print entire tree
		ANNbool with_pts,				// print points as well?
		ostream &out)					// output stream
{
	out << "ANN Version " << ANNversion << "\n";
	if (with_pts) {						// print point coordinates
		out << "    Points:\n";
		for (int i = 0; i < n_pts; i++) {
			out << "\t" << i << ": ";
			annPrintPt(pts[i], dim, out);
			out << "\n";
		}
	}
	if (root == NULL)					// empty tree?
		out << "    Null tree.\n";
	else {
		root->print(0, out);			// invoke printing at root
	}
}

//----------------------------------------------------------------------
//	kd_tree statistics (for performance evaluation)
//		This routine compute various statistics information for
//		a kd-tree.  It is used by the implementors for performance
//		evaluation of the data structure.
//----------------------------------------------------------------------

#define MAX(a,b)		((a) > (b) ? (a) : (b))

void ANNkdStats::merge(const ANNkdStats &st)	// merge stats from child 
{
	n_lf += st.n_lf;			n_tl += st.n_tl;
	n_spl += st.n_spl;			n_shr += st.n_shr;
	depth = MAX(depth, st.depth);
	sum_ar += st.sum_ar;
}

//----------------------------------------------------------------------
//	Update statistics for nodes
//----------------------------------------------------------------------

const double ANN_AR_TOOBIG = 1000;				// too big an aspect ratio

void ANNkd_leaf::getStats(						// get subtree statistics
	int					dim,					// dimension of space
	ANNkdStats			&st,					// stats (modified)
	ANNorthRect			&bnd_box)				// bounding box
{
	st.reset();
	st.n_lf = 1;								// count this leaf
	if (this == KD_TRIVIAL) st.n_tl = 1;		// count trivial leaf
	double ar = annAspectRatio(dim, bnd_box);	// aspect ratio of leaf
												// incr sum (ignore outliers)
	st.sum_ar += float(ar < ANN_AR_TOOBIG ? ar : ANN_AR_TOOBIG);
}

void ANNkd_split::getStats(						// get subtree statistics
	int					dim,					// dimension of space
	ANNkdStats			&st,					// stats (modified)
	ANNorthRect			&bnd_box)				// bounding box
{
	ANNkdStats ch_stats;						// stats for children
												// get stats for low child
	ANNcoord hv = bnd_box.hi[cut_dim];			// save box bounds
	bnd_box.hi[cut_dim] = cut_val;				// upper bound for low child
	ch_stats.reset();							// reset
	child[ANN_LO]->getStats(dim, ch_stats, bnd_box);
	st.merge(ch_stats);							// merge them
	bnd_box.hi[cut_dim] = hv;					// restore bound
												// get stats for high child
	ANNcoord lv = bnd_box.lo[cut_dim];			// save box bounds
	bnd_box.lo[cut_dim] = cut_val;				// lower bound for high child
	ch_stats.reset();							// reset
	child[ANN_HI]->getStats(dim, ch_stats, bnd_box);
	st.merge(ch_stats);							// merge them
	bnd_box.lo[cut_dim] = lv;					// restore bound

	st.depth++;									// increment depth
	st.n_spl++;									// increment number of splits
}

//----------------------------------------------------------------------
//	getStats
//		Collects a number of statistics related to kd_tree or
//		bd_tree.
//----------------------------------------------------------------------

void ANNkd_tree::getStats(						// get tree statistics
	ANNkdStats			&st)					// stats (modified)
{
	st.reset(dim, n_pts, bkt_size);				// reset stats
												// create bounding box
	ANNorthRect bnd_box(dim, bnd_box_lo, bnd_box_hi);
	if (root != NULL) {							// if nonempty tree
		root->getStats(dim, st, bnd_box);		// get statistics
		st.avg_ar = st.sum_ar / st.n_lf;		// average leaf asp ratio
	}
}

//----------------------------------------------------------------------
//	kd_tree destructor
//		The destructor just frees the various elements that were
//		allocated in the construction process.
//----------------------------------------------------------------------

ANNkd_tree::~ANNkd_tree()				// tree destructor
{
	if (root != NULL) delete root;
	if (pidx != NULL) delete [] pidx;
	if (bnd_box_lo != NULL) annDeallocPt(bnd_box_lo);
	if (bnd_box_hi != NULL) annDeallocPt(bnd_box_hi);
}

//----------------------------------------------------------------------
//	This is called with all use of ANN is finished.  It eliminates the
//	minor memory leak caused by the allocation of KD_TRIVIAL.
//----------------------------------------------------------------------
void annClose()				// close use of ANN
{
	if (KD_TRIVIAL != NULL) {
		delete KD_TRIVIAL;
		KD_TRIVIAL = NULL;
	}
}

//----------------------------------------------------------------------
//	kd_tree constructors
//		There is a skeleton kd-tree constructor which sets up a
//		trivial empty tree.	 The last optional argument allows
//		the routine to be passed a point index array which is
//		assumed to be of the proper size (n).  Otherwise, one is
//		allocated and initialized to the identity.	Warning: In
//		either case the destructor will deallocate this array.
//
//		As a kludge, we need to allocate KD_TRIVIAL if one has not
//		already been allocated.	 (This is because I'm too dumb to
//		figure out how to cause a pointer to be allocated at load
//		time.)
//----------------------------------------------------------------------

void ANNkd_tree::SkeletonTree(			// construct skeleton tree
		int n,							// number of points
		int dd,							// dimension
		int bs,							// bucket size
		ANNpointArray pa,				// point array
		ANNidxArray pi)					// point indices
{
	dim = dd;							// initialize basic elements
	n_pts = n;
	bkt_size = bs;
	pts = pa;							// initialize points array

	root = NULL;						// no associated tree yet

	if (pi == NULL) {					// point indices provided?
		pidx = new ANNidx[n];			// no, allocate space for point indices
		for (int i = 0; i < n; i++) {
			pidx[i] = i;				// initially identity
		}
	}
	else {
		pidx = pi;						// yes, use them
	}

	bnd_box_lo = bnd_box_hi = NULL;		// bounding box is nonexistent
	if (KD_TRIVIAL == NULL)				// no trivial leaf node yet?
		KD_TRIVIAL = new ANNkd_leaf(0, IDX_TRIVIAL);	// allocate it
}

ANNkd_tree::ANNkd_tree(					// basic constructor
		int n,							// number of points
		int dd,							// dimension
		int bs)							// bucket size
{  SkeletonTree(n, dd, bs);  }			// construct skeleton tree

//----------------------------------------------------------------------
//	rkd_tree - recursive procedure to build a kd-tree
//
//		Builds a kd-tree for points in pa as indexed through the
//		array pidx[0..n-1] (typically a subarray of the array used in
//		the top-level call).  This routine permutes the array pidx,
//		but does not alter pa[].
//
//		The construction is based on a standard algorithm for constructing
//		the kd-tree (see Friedman, Bentley, and Finkel, ``An algorithm for
//		finding best matches in logarithmic expected time,'' ACM Transactions
//		on Mathematical Software, 3(3):209-226, 1977).  The procedure
//		operates by a simple divide-and-conquer strategy, which determines
//		an appropriate orthogonal cutting plane (see below), and splits
//		the points.  When the number of points falls below the bucket size,
//		we simply store the points in a leaf node's bucket.
//
//		One of the arguments is a pointer to a splitting routine,
//		whose prototype is:
//		
//				void split(
//						ANNpointArray pa,  // complete point array
//						ANNidxArray pidx,  // point array (permuted on return)
//						ANNorthRect &bnds, // bounds of current cell
//						int n,			   // number of points
//						int dim,		   // dimension of space
//						int &cut_dim,	   // cutting dimension
//						ANNcoord &cut_val, // cutting value
//						int &n_lo)		   // no. of points on low side of cut
//
//		This procedure selects a cutting dimension and cutting value,
//		partitions pa about these values, and returns the number of
//		points on the low side of the cut.
//----------------------------------------------------------------------

ANNkd_ptr rkd_tree(				// recursive construction of kd-tree
	ANNpointArray		pa,				// point array
	ANNidxArray			pidx,			// point indices to store in subtree
	int					n,				// number of points
	int					dim,			// dimension of space
	int					bsp,			// bucket space
	ANNorthRect			&bnd_box,		// bounding box for current node
	ANNkd_splitter		splitter)		// splitting routine
{
	if (n <= bsp) {						// n small, make a leaf node
		if (n == 0)						// empty leaf node
			return KD_TRIVIAL;			// return (canonical) empty leaf
		else							// construct the node and return
			return new ANNkd_leaf(n, pidx); 
	}
	else {								// n large, make a splitting node
		int cd;							// cutting dimension
		ANNcoord cv;					// cutting value
		int n_lo;						// number on low side of cut
		ANNkd_node *lo, *hi;			// low and high children

										// invoke splitting procedure
		(*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo);

		ANNcoord lv = bnd_box.lo[cd];	// save bounds for cutting dimension
		ANNcoord hv = bnd_box.hi[cd];

		bnd_box.hi[cd] = cv;			// modify bounds for left subtree
		lo = rkd_tree(					// build left subtree
				pa, pidx, n_lo,			// ...from pidx[0..n_lo-1]
				dim, bsp, bnd_box, splitter);
		bnd_box.hi[cd] = hv;			// restore bounds

		bnd_box.lo[cd] = cv;			// modify bounds for right subtree
		hi = rkd_tree(					// build right subtree
				pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1]
				dim, bsp, bnd_box, splitter);
		bnd_box.lo[cd] = lv;			// restore bounds

										// create the splitting node
		ANNkd_split *ptr = new ANNkd_split(cd, cv, lv, hv, lo, hi);

		return ptr;						// return pointer to this node
	}
} 

//----------------------------------------------------------------------
// kd-tree constructor
//		This is the main constructor for kd-trees given a set of points.
//		It first builds a skeleton tree, then computes the bounding box
//		of the data points, and then invokes rkd_tree() to actually
//		build the tree, passing it the appropriate splitting routine.
//----------------------------------------------------------------------

ANNkd_tree::ANNkd_tree(					// construct from point array
	ANNpointArray		pa,				// point array (with at least n pts)
	int					n,				// number of points
	int					dd,				// dimension
	int					bs,				// bucket size
	ANNsplitRule		split)			// splitting method
{
	SkeletonTree(n, dd, bs);			// set up the basic stuff
	pts = pa;							// where the points are
	if (n == 0) return;					// no points--no sweat

	ANNorthRect bnd_box(dd);			// bounding box for points
	annEnclRect(pa, pidx, n, dd, bnd_box);// construct bounding rectangle
										// copy to tree structure
	bnd_box_lo = annCopyPt(dd, bnd_box.lo);
	bnd_box_hi = annCopyPt(dd, bnd_box.hi);

	switch (split) {					// build by rule
	case ANN_KD_STD:					// standard kd-splitting rule
		root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split);
		break;
	case ANN_KD_MIDPT:					// midpoint split
		root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split);
		break;
	case ANN_KD_FAIR:					// fair split
		root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split);
		break;
	case ANN_KD_SUGGEST:				// best (in our opinion)
	case ANN_KD_SL_MIDPT:				// sliding midpoint split
		root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split);
		break;
	case ANN_KD_SL_FAIR:				// sliding fair split
		root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_fair_split);
		break;
	default:
		annError("Illegal splitting method", ANNabort);
	}
}