NearTree
Release 2.3.2
30 October 2010
(c) Copyright 2001, 2008, 2009, 2010 Larry Andrews. All rights reserved
based on
Larry Andrews, "A template for the nearest neighbor problem",
C/C++ Users Journal, Volume 19 , Issue 11 (November 2001), 40 - 49 (2001),
ISSN:1075-2838,
www.ddj.com/architect/184401449
Revised 12 Dec 2008, for sourceforge release, Larry Andrews and Herbert J.
Bernstein
8 Jan 2009 Release 1.0 LCA and HJB
11 Jan 2009 Release 1.0.1 LCA and HJB
21 March 2009 Release 2.0 LCA and HJB
30 May 2009 Release 2.1 LCA and HJB
4 June 2009 Release 2.1.1 LCA and HJB
7 June 2009 Release 2.1.2 LCA and HJB
7 July 2009 Release 2.1.3 LCA and HJB
29 November 2009 Release 2.1.4 LCA
23 April 2010 Release 2.1.5 LCA and HJB
18 July 2010 Release 2.2 HJB
25 July 2010 Release 2.2.1 HJB
31 August 2010 Release 2.3 LCA
7 September 2010 Release 2.3.1 LCA
30 October 2010 Release 2.3.2 LCA
YOU MAY REDISTRIBUTE NearTree UNDER THE TERMS OF THE LGPL
+------------------------------------------------------------------------------+
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| |
| This library is free software; you can redistribute it and/or modify it |
| under the terms of the GNU Lesser General Public License as published by the |
| Free Software Foundation; either version 2.1 of the License, or (at your |
| option) any later version. |
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| This library is distributed in the hope that it will be useful, but WITHOUT |
| ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| FITNESS FOR A PARTICULAR PURPOSE. See the GNU* Lesser General Public License |
| for more details. |
| |
| You should have received a copy of the GNU Lesser General Public License |
| along with this library; if not, write to the Free Software Foundation, |
| Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
+------------------------------------------------------------------------------+
This is a release of an API for finding nearest neighbors among points in
spaces of arbitrary dimensions. This release provides a C++ template,
TNear.h, and a C library, CNearTree.c, with example/test programs.
Release 2.3.2 adds optional returns of vectors of ordinals of found
objects
Release 2.3.1 adds Centroid method for Lloyd clustering.
Release 2.3 added methods for clustering.
Release 2.2.1 was a minor revision to Release 2.2 to add an include of
limits.h to TNear.h, primarily for MINGW use.
Release 2.2 added support for C code for fixed length string searches
using a hamming distance norm, and for spherical and hemispherical
geodesic norm based searches. Because of the addition of new type and norm
flags, the version 2.2 shared libraries cannot be used to support binaries
copiled against earlier headers and vice-versa.
Release 2.1.5 was a cleanup update to the 2.1 release of 30 May 2009 to
increase portability, in five stages (2.1.1 on 4 June 2009, 2.1.2 on 7
June 2009, 2.1.3 on 7 July 2009, 2.1.4 on 29 November 2009 and 2.1.5 on 23
April 2010) dealing with the following issues:
* Convert to use of a self-contained portable random-number generator
from Rob Harrison (2.1.1)
* Ensure wider use of const where appropriate (2.1.1)
* Correct typos and unclear wording in the README (2.1.2)
* Reorganize use of USE_LOCAL_HEADERS in CNearTreeTest.cpp (2.1.2)
* Change FAR macro to CNEARTREE_FAR (2.1.3)
* Add BelongsToPoints and SeparateByRadius (2.1.4)
* Fix dimensions for rhrand (2.1.5)
The 2.1 release was a minor update to the 2.0 release of 21 March 2009 to
deal with the following issues:
* Make delayed insertion the default
* Complete the containerization of TNear.h
* Add code for K-nearest/farthest in TNear.h and in CNearTree.c
* Correct the InAnnulus search filter
Release 2.0 was a major update to the 1.0 release of 8 January 2009 to
deal with the following issues:
* Replace use recursion with a stack, except in insertion logic
* Replace use of double with templated DistanceType (usually double)
* Provide constuctors to build NearTree from vectors, lists or sets
* Change "Insert" to "insert" for consistentcy with other containers
* Add access function "at" or array type references [], and provide
contents of a neartree as a vector
* Add iterator support
* Provide delayed insertion logic
* Functions added for searches outside of a sphere or in an annular
region
Our thanks to Nicolas Brodu for suggesting the more general handling of
the distance type.
Note: As Nicolas Brodu has noted, CNearTree is particularly well-suited to
multi-threaded applications. However, if the same CNearTree is to be
searched in multiple threads, it is important to complete all insertions
and/or delayed insertions before parallel execution of parallel searches.
----------------------------------------------------------------------
Contents
* Installation
* The C++ template: TNear.h
* The C NearTree API: CNearTree.c
* A Portable pseudo-random number generator: rhrand.h
----------------------------------------------------------------------
----------------------------------------------------------------------
Installation
The NearTree package is available at
www.sourceforge.net/projects/neartree. A source tarball is available at
downloads.sourceforge.net/neartree/NearTree-2.3.2.tar.gz. Later tarballs
may be available.
If you decide to simply use the TNear.h header to add nearest neighbor
support to C++ code under Visual Studio, be sure to also use the rhrand.h
and triple.h headers, and to define USE_LOCAL_HEADERS. For unix or MINGW,
you will need to use the Makefile and to have libtool on your system. Be
warned that the default libtool under Mac OS X will not work for this
installation.
When the source tarball is downloaded and unpacked, you should have a
directory NearTree-2.3.2. To see the current settings for a build execute
make
which should give the following information:
PLEASE READ README_NearTree.txt and lgpl.txt
Before making the NearTree libraries and example programs, check
that the chosen settings are correct
The current C++ and C compile commands are:
libtool --mode=compile g++ -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -I. -c
libtool --mode=compile gcc -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -I. -c
The C API, CNearTree.c, depends on the sourceforge project CVector
You are currently setup to use the system defaults for CVector
If that is not correct, define the variable CVECTOR_INCLUDE
The current library link command is:
libtool --mode=link gcc -version-info 3:0:0 \
-no-undefined -rpath /usr/local/lib
The current C++ and C library local, and C dynamic and static build commands are:
libtool --mode=link g++ -no-undefined -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -I.
libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -I.
libtool --mode=link gcc -no-undefined -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -shared -I/usr/local/include
libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic \
-DCNEARTREE_SAFE_TRIANG=1 -static-libtool-libs -I/usr/local/include
Before installing the NearTree library and example programs, check
that the install directory and install commands are correct:
The current values are :
/usr/local
libtool --mode=install cp
To compile the NearTree library and example programs type:
make clean
make all
To run a set of tests type:
make tests
To clean up the directories type:
make clean
To install the library and headers type:
make install
If these settings need to be changed, edit Makefile. On some systems, e.g.
Mac OS X, the default libtool is not appropriate. In that case you should
install a recent version of libtool. The CVector kit has been tested with
libtool versions 1.3.5 and 1.5.4. For MINGW, libtool version 2.2.6 and gcc
version 4 are needed to work with shared libraries (DLLs). If the system
libtool is not to be used, define the variable LIBTOOL to be the path to
the libtool executable, e.g. in bash
export LIBTOOL=$HOME/bin/libtool
or in the Makefie
LIBTOOL = $(HOME)/bin/libtool
If you need to include local header files using #include "..." instead of
#include <...>, define the variable USE_LOCAL_HEADERS
The triangle inequality that must be evaluated in building trees and
retrieving data may not be evaluated correctly if the range of the three
values is extremely large (>10**15 or so for doubles) or may be evaluated
differently by some compilers in different parts of a program (due to
differing usage of registers). The default in this API is to do the
triangle inequality three different ways under the control of
CNEARTREE_SAFE_TRIANG
#ifdef CNEARTREE_SAFE_TRIANG
#define TRIANG(a,b,c) ( (((b)+(c))-(a) >= 0) \
|| ((b)-((a)-(c)) >= 0) \
|| ((c)-((a)-(b)) >= 0))
#else
#define TRIANG(a,b,c) ( (((b)+(c))-(a) >= 0))
#endif
Problems with the unsafe definition of TRIANG have been seen in Linux
under gcc version 4 and in MS Window under VS 2003. There is a slight
performance hit from the triple test. If maximal speed is critical and
misidentification of nearest points by relative distance errors of about 1
part in 10**15 is not a serious problem, the definition of
-DCNEARTREE_SAFE_TRIANG=1 can be removed from the definition of CFLAGS in
the Makefile.
NOTE: A range of 10**15 is comparable to the diameter of the earth vs. the
separation of two bonded atoms.
----------------------------------------------------------------------
----------------------------------------------------------------------
The C++ template: TNear.h
This is a revised release of
template <typename T, typename DistanceType=double, int distMinValue=-1
> class CNearTree;
implementing the Nearest Neighbor algorithm after Kalantari and McDonald,
(IEEE Transactions on Software Engineering, v. SE-9, pp. 631-634,1983)
modified to use recursion for insertions and recursion (original version)
or a stack (current version) for searches instead of a double-linked tree
and simplified so that it does a bit less checking for things like is the
distance to the right less than the distance to the left; it was found
that these checks made little to no difference.
This template is used to contain a collection of objects. After the
collection has been loaded into this structure, it can be quickly queried
for which object is "closest" to some probe object of the same type. The
major restriction on applicability of the near-tree is that the algorithm
only works if the objects obey the triangle inequality. The triangle rule
states that the length of any side of a triangle cannot exceed the sum of
the lengths of the other two sides.
CNearTree is the root class for the neartree. The actual data of the tree
is stored in NearTreeNode objects descending from a CNearTree.
The types of objects that can be stored in the tree is quite broad. The
biggest limitation is that the objects must reside in some sort of metric
space and must obey the triangle rule. They must also be all of the same
size because they are stored in an std::vector. If your application
requires object of varying storage, then your best way to use this code is
to store pointers or handles and to write your own distance functions.
Note that std::string is a pointer type variable and so can be stored
directly.
The type of the objects to be stored is the only required template
argument. The type of the distance measure (DistanceType) defaults to
double. If your application is for an integer type, then the type for
DistanceType can be your integer type. This has the potential for speeding
the calculations by avoiding FP computation. Other general types can be
used if desired, but you may need to also input a value of distMinValue.
The template argument distMinValue must be something that your class will
understand as a negative number. The default input is negative one.
Internally, that is cast to DistanceType. Since most uses will be for
DistanceType to be double, that is a simple conversion. Obviously, for
integer types, there is no problem either. The need for this value is to
have something internally that is recognizable as smaller than the
smallest "distance" that can exist between any two objects in your type.
For most users, there is no need to input anything other than the default,
-1. -1 must be castable to DistanceType. It seems unlikely that anyone
would actually need this optional parameter, but it is here for
completeness.
It is a design decision that this class cannot work for unsigned types.
Verifying the triangle rule for unsigned types is more complex. Sorry,
unsigned types are left as an exercise for the reader.
The user of this class needs to provide at least the following
functionality for the template to work. For the built-in numerics of C++,
they are provided by the system.
// conversion constructor from the templated class to
DistanceType Norm( ); DistanceType
// (usually will return a "length" of type double)
operator- ( ); // geometrical (vector) difference of two objects
// a copy constructor would be nice
// a constructor would be nice
// a destructor would be nice
The provided interface is:
#include <TNear.h>
CNearTree( void ) // constructor
instantiated by something like: CNearTree <T> vTree;
for some type T
CNearTree( const ContainerType<T> ) // constructor from containers, e.g. ...
CNearTree( const std::vector<T> ) // constructor
CNearTree( const std::list<T> ) // constructor
CNearTree( const std::set<T> ) // constructor
CNearTree( const CNearTree<T> ) // constructor
CNearTree( const ContainerType<T>, const ContainerType<T> )
// constructor merging 2 containers, e.g. ...
~CNearTree( void ) // destructor
void clear( void ) // clear the NearTree
template<typename InputContainer>
CNearTree& operator+=( const InputContainer&, o )
// add a container's contents to a NearTree
template<typename InputContainer>
CNearTree& operator-=( const InputContainer&, o )
// remove a container's contents from a NearTree
template<typename InputContainer>
CNearTree& set_symmetric_difference( const InputContainer&, o )
// remove the part of a container's
// contents from a NearTree that is
// already in the Neartree and add
// in the contents of the container
// that is not already in the Neartree
// i.e. the exclusive or
void insert( const T& t )
where t is an object of the type T
all inserts are delayed until a search is performed or
until an explicit call to CompleteDelayedInsertions
is called or a search is called. The purpose is to distribute
the objects a bit more randomly. Excessively ordered objects
leads to less than optimal trees.
Starting with the 2.1 release, places objects in a queue for
insertion later when CompleteDelayInsert is called. In
earlier releases the default was immediate insertion.
The following additional convenience insert template
allow insertion of containers of objects
template< typename InputContainer >
void insert( ContainerType ) // e. g. ...
void insert( const std::vector<T> )
void insert( const std::list<T> )
void insert( const std::set<T> )
void insert( const CNearTree<T> )
bool NearestNeighbor ( const DistanceType& dRadius, T& tClosest, const T& t ) const
dRadius is the largest radius within which to search; make it
very large if you want to include every point that was loaded.
tClosest is returned as the object that was found closest to the probe
point (if any were within radius dRadius of the probe)
t is the probe point, used to search in the group of points insert'ed
return value is true if some object was found within the search radius, false otherwise.
If false is returned, tClosest is invalid (at best).
iterator NearestNeighbor ( const DistanceType & dRadius, const T& t ) const
returns an iterator to the nearest point to the probe point t or end() if there is none
bool FarthestNeighbor ( T& tFarthest, const T& t ) const
tFarthest is returned as the object that was found farthest from the probe
point
t is the probe point, used to search in the group of points Insert'ed
return value is true if some object was found, false otherwise
If false is returned, tFarthest is invalid (at best).
iterator FarthestNeighbor ( T& const T& t ) const
returns an iterator to the nearest point to the probe point t or end() if there is none
bool FarthestNeighbor ( T& tFarthest, const T& t ) const
The following functions (BelongsToPoints, SeparateByRadius, FindInSphere, FindOutSphere,
and FindInAnnulus) all return a container (ContainerType) that can be any standard library
container (such as std::vector< T >) or CNearTree. In each case option arguments
allow a parallel vector of indices to be returned for each container, giving the
indices of the returned objects within the original NearTree.
template<typename ContainerType>
void BelongsToPoints ( const T& t1, const T& t2,
ContainerType& group1, ContainerType& group2 )
template<typename ContainerType>
void BelongsToPoints ( const T& t1, const T& t2,
ContainerType& group1, ContainerType& group2,
std::vector<size_t>& group1_ordinals, std::vector<size_t>& group2_ordinals)
returns the points closer to t1 than to t2 in group1 and the rest in group 2
if group1_ordinals and group2_ordinals are provided the ordinals of the
found objects in the object store are put into those vectors.
template<typename ContainerTypeInside, typename ContainerTypeOutside>
void SeparateByRadius ( const DistanceType radius, const T& probe,
ContainerTypeInside& inside, ContainerTypeOutside& outside )
template<typename ContainerTypeInside, typename ContainerTypeOutside>
void SeparateByRadius ( const DistanceType radius, const T& probe,
ContainerTypeInside& inside, ContainerTypeOutside& outside,
std::vector<size_t>& inside_ordinals, std::vector<size_t>& outside_ordinals)
return the points within radius of the probe in inside and the rest in outside
if inside_ordinals and outside_ordinals are provided the ordinals of the
found objects in the object store are put into those vectors.
long FindInSphere ( const DistanceType& dRadius,
ContainerType& tInside, const T& t ) const
long FindInSphere ( const DistanceType& dRadius,
ContainerType& tInside,
std::vector<size_t>& tIndices, const T& t ) const
dRadius is the radius within which to search; make it very large if you want to
include every point that was loaded;
tInside is returned as the container of objects that were found within a radius dRadius
of the probe point
if the tIndices argument is given it will ve returned as a parallel vector
of indices in the near tree of the objects returned.
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the search radius
long FindInSphere ( const DistanceType& dRadius,
CNearTree< T >& tInside, const T& t ) const
dRadius is the radius within which to search; make it very large if you want to
include every point that was loaded;
tInside is returned as the CNearTree of objects that were found within a radius dRadius
of the probe point
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the search radius
long FindOutSphere ( const DistanceType& dRadius,
ContainerType& tOutside, const T& t ) const
long FindOutSphere ( const DistanceType& dRadius,
ContainerType& tOutside,
std::vector<size_t>& tIndices, const T& t ) const
dRadius is the radius outside of which to search
tOutside is returned as the container of objects that were found at or outside of radius dRadius
of the probe point
if the tIndices argument is given it will ve returned as a parallel vector
of indices in the near tree of the objects returned.
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the search radius
long FindOutSphere ( const DistanceType& dRadius,
CNearTree< T >& tOutside, const T& t ) const
dRadius is the radius outside of which to search.
tClosest is returned as the CNearTree of objects that were found at or outside of a radius dRadius
of the probe point
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the search radius
long FindInAnnulus ( const DistanceType& dRadius1,
const DistanceType& dRadius2,
ContainerType& tInRing, const T& t ) const
long FindInAnnulus ( const DistanceType& dRadius1,
const DistanceType& dRadius2,
ContainerType& tInRing,
std::vector<size_t>& tIndices, const T& t ) const
dRadius1 and dRadius2 are the two radii between which to find data points
tInRing is returned as the container of objects that were found at or outside of a radius dRadius1
and at or inside of radius dRadius2 of the probe point
if the tIndices argument is given it will ve returned as a parallel vector
of indices in the near tree of the objects returned.
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the annulus
long FindInAnnulus ( const DistanceType& dRadius1,
const DistanceType& dRadius2,
CNearTree< T >& tInRing, const T& t ) const
dRadius1 and dRadius2 are the two radii between which to find data points
tInRing is returned as the CNearTree of objects that were found at or outside of a radius dRadius1
and at or inside of radius dRadius2 of the probe point
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the annulus
long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
ContainerType& tClosest, const T& t )
long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
ContainerType& tClosest,
std::vector<size_t>& tIndices, const T& t )
k is the maximum number of nearest neighbors to return. Finds this many if possible
dRadius within a sphere defined by dRadius, search for the k-nearest-neighbors
tClosest is returned ContainerType of the objects found within the sphere
if the tIndices argument is given it will ve returned as a parallel vector
of indices in the near tree of the objects returned.
t is the probe point, used to search in the group of points insert'ed
return value is the count of the number of points found within the sphere
long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
CNearTree< T >& tClosest, const T& t )
k is the maximum number of nearest neighbors to return. Finds this many if possible
dRadius within a sphere defined by dRadius, search for the k-nearest-neighbors
tClosest is returned as the CNearTree of objects found within the sphere
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the sphere
long FindK_FarthestNeighbors ( const size_t k,
ContainerType& tFarthest, const T& t )
long FindK_FarthestNeighbors ( const size_t k,
ContainerType& tFarthest,
std::vector<size_t>& tIndices, const T& t )
k is the maximum number of farthest neighbors to return. Finds this many if possible
tFarthest is returned ContainerType of the objects found
if the tIndices argument is given it will ve returned as a parallel vector
of indices in the near tree of the objects returned.
t is the probe point, used to search in the group of points insert'ed
return value is the count of the number of points found within the sphere
long FindK_NearestNeighbors ( const size_t k, CNearTree< T >& tFarthest, const T& t )
k is the maximum number of farthest neighbors to return. Finds this many if possible
tFarthest is returned as the CNearTree of objects found
t is the probe point, used to search in the group of points Insert'ed
return value is the count of the number of points found within the sphere
----------------------------------------------------------------------
Access Functions:
T at ( const size_t n ) const
returns the n'th item of the internal data store
T operator[] ( const size_t n )
returns the n'th item of the internal data store
template<typename ContainerType>
operator ContainerType ( void ) const
returns all of the inserted objects in the tree in a container of type ContainerType.
ContainerType can be std::vector<T>, etc, or other containers, including CNearTree<T>.
The returned vector contents are not guaranteed to be returned in the order loaded.
iterator begin ( void ) const
returns an iterator to the beginning of the internal data store
iterator end ( void ) const
returns an iterator to the end of the data store (one beyond the last item)
iterator back ( void ) const
returns an iterator to the last data item of the internal data store
----------------------------------------------------------------------
Information and special operation functions:
void ImmediateInsert( const T&aamp; t )
insert places objects in a queue for insertion later when CompleteDelayInsert
is called or a search is called. ImmediateInsert inserts the data immediately
into the tree (with the potential of a less balanced tree). ImmediateInsert is not
intended for the ordinary user.
void CompleteDelayedInsert ( void )
completes insertion for all delayed objects. sqrt(n) of them are inserted by
random choice. The rest are inserted in linear order as originally queued.
CompleteDelayedInsert is invoked at the beginning of all searches, so the
average user will never need to call it.
size_t GetDeferredSize ( void )
returns the number of delayed objects that have not yet completed insertion. This is
mainly for information about details of the tree.
size_t GetTotalSize ( void )
returns the number of objects that have been insert'ed plus those DelayInsert'ed
size_t size ( void )
identical to GetTotalSize
size_t GetDepth ( void )
returns the maximum tree layers from the root. This is mainly for information about
details of the tree.
T Centroid ( void )
returns the centroid of a neartree.
bool empty ( void )
returns true if the tree is empty, otherwise false
----------------------------------------------------------------------
Iterators:
Random access iterators are provided for accessing the data in a CNearTree. The most important
expected use is to retrieve the objects returned from one of the sphere search functions that
can return a CNearTree. However, they can be used with any CNearTree.
They should function in a fashion essentially the same as STL iterators. There is no assurance
that data will be returned in the order it was loaded, just that it is accessible. This is the
list of iterators. The same set is avaiable for const_iterator.
iterator ( void ) { }; // constructor
iterator ( const const_iterator& s )
iterator& operator= ( const iterator& s )
iterator operator++ ( const int n )
iterator operator-- ( const int n )
iterator& operator++ ( void )
iterator& operator-- ( void )
iterator operator+ ( const long n ) const
iterator operator- ( const long n ) const
iterator& operator+= ( const long n )
iterator& operator-= ( const long n )
T operator* ( void ) const
bool operator== ( const iterator& t ) const
bool operator!= ( const iterator& t ) const
bool operator== ( const const_iterator& t ) const
bool operator!= ( const const_iterator& t ) const
bool operator> ( const iterator& t ) const
bool operator> ( const const_iterator& t ) const
bool operator< ( const iterator& t ) const
bool operator< ( const const_iterator& t ) const
const T * const operator-> ( void ) const
----------------------------------------------------------------------
So a complete program is:
#include "TNear.h"
#include <cstdio>
void main()
{
CNearTree< double > dT;
double dNear;
dT.Insert( 1.5 );
if ( dT.NearestNeighbor( 10000.0, dNear, 2.0 )) printf( "%f\n",double(dNear-2.0) );
}
and it should print 0.5 (that's how for 2.0 is from 1.5). For more
examples of the use of TNear.h, see main.cpp and CNearTreeTest.cpp.
----------------------------------------------------------------------
----------------------------------------------------------------------
The C NearTree API: CNearTree.c
Synopsis
#include <CNearTree.h>
double CNearTreeDist ( CNearTreeHandle treehandle, void * coord1, void *
coord2 );
int CNearTreeSetNorm ( const CNearTreeHandle treehandle, int treenorm );
int CNearTreeNodeCreate ( const CNearTreeHandle treehandle,
CNearTreeNodeHandle * treenodehandle )
int CNearTreeCreate ( CNearTreeHandle * treehandle, size_t treedim, int
treetype );
int CNearTreeFree ( const CNearTreeHandle treehandle );
int CNearTreeClear ( CNearTreeHandle * treehandle );
int CNearTreeNodeFree ( CNearTreeNodeHandle * treenodehandle );
int CNearTreeInsert( const CNearTreeHandle treehandle, const void *
coord, const void * obj );
int CNearTreeNodeInsert ( const CNearTreeHandle treehandle,
CNearTreeNodeHandle treenodehandle, size_t index; size_t * depth );
int CNearTreeImmediateInsert ( const CNearTreeHandle treehandle, const
void * coord, const void * obj );
int CNearTreeDelayedInsert ( const CNearTreeHandle treehandle, const
void * coord, const void * obj ); /* ***DEPRECATED*** */
int CNearTreeCompleteDelayedInsert ( const CNearTreeHandle treehandle )
int CNearTreeZeroIfEmpty ( const CNearTreeHandle treehandle );
int CNearTreeGetSize ( const CNearTreeHandle treehandle, size_t * size
);
int CNearTreeGetDelayedSize ( const CNearTreeHandle treehandle, size_t *
size );
int CNearTreeGetDepth ( const CNearTreeHandle treehandle, size_t * depth
)
int CNearTreeNearestNeighbor ( const CNearTreeHandle treehandle, const
double dRadius, void * * coordClosest, void * * objClosest, const void *
coord );
int CNearTreeFarthestNeighbor ( const CNearTreeHandle treehandle, void *
* coordFarthest, void * * objFarthest, const void * coord );
int CNearTreeFindInSphere ( const CNearTreeHandle treehandle, const
double dRadius, CVectorHandle coordInside, CVectorHandle objInside,
const void * coord, int resetcount );
int CNearTreeFindTreeInSphere ( const CNearTreeHandle treehandle, const
double dRadius, CNearTreeHandle foundInside, const void * coord, int
resetcount )
int CNearTreeFindOutSphere ( const CNearTreeHandle treehandle, const
double dRadius, CVectorHandle coordOutside, CVectorHandle objOutside,
const void * coord, int resetcount );
int CNearTreeFindTreeOutSphere ( const CNearTreeHandle treehandle, const
double dRadius, CNearTreeHandle foundOutside, const void * coord, int
resetcount )
int CNearTreeFindInAnnulus ( const CNearTreeHandle treehandle, const
double dRadiusInner, const double dRadiusOuter, CVectorHandle
coordInRing, CVectorHandle objInRing, const void * coord, int resetcount
);
int CNearTreeFindTreeInAnnulus ( const CNearTreeHandle treehandle, const
double dRadiusInner, const double dRadiusOuter, CNearTreeHandle
foundInRing, const void * coord, int resetcount )
int CNearTreeFindKNearest ( const CNearTreeHandle treehandle, const
size_t k, const double dRadius, CVectorHandle coordClosest,
CVectorHandle objClosest, const void * coord, int resetcount );
int CNearTreeFindKTreeNearest ( const CNearTreeHandle treehandle, const
size_t k, const double dRadius, CNearTreeHandle foundClosest, const void
* coord, int resetcount )
int CNearTreeFindKFarthest ( const CNearTreeHandle treehandle, const
size_t k, const double dRadius, CVectorHandle coordFarthest,
CVectorHandle objFarthest, const void * coord, int resetcount );
int CNearTreeFindKTreeFarthest ( const CNearTreeHandle treehandle, const
size_t k, const double dRadius, CNearTreeHandle foundFarthest, const
void * coord, int resetcount )
int CNearTreeNearest ( const CNearTreeHandle treehandle, double *
dRadius, void * * coordClosest, void * * objClosest, const void * coord
);
int CNearTreeFindFarthest ( const CNearTreeHandle treehandle, double *
dRadius, void * * coordFarthest, void * * objFarthest, const void *
coord );
int CNearTreeObjects ( const CNearTreeHandle treehandle, CVectorHandle *
vectorhandle );
void * CNearTreeObjectAt ( const CNearTreeHandle treehandle, size_t
index );
int CNearTreeCoords ( const CNearTreeHandle treehandle, CVectorHandle *
vectorhandle );
void * CNearTreeCoordAt ( const CNearTreeHandle treehandle, size_t index
);
The NearTree API works with coordinate vectors in an arbitrary number of
dimensions. Each neartree is accessed by a pointer of type CNearTreeHandle
which points to a struct of type CNearTree, which points to a tree of
nodes of type CNearTreeNode:
typedef struct _CNearTreeNode {
size_t m_indexLeft; /* index of left coords in m_CoordStore
and of left object in m_ObjectStore */
size_t m_indexRight; /* index of right coords in m_CoordStore
and of right object in m_ObjectStore */
double m_dMaxLeft; /* longest distance from the left object
to anything below it in the tree */
double m_dMaxRight; /* longest distance from the right object
to anything below it in the tree */
struct _CNearTreeNode * m_pLeftBranch;
/* tree descending from the left object */
struct _CNearTreeNode * m_pRightBranch;
/* tree descending from the right object */
int m_iflags; /* flags */
} CNearTreeNode;
typedef CNearTreeNode * CNearTreeNodeHandle;
typedef struct {
CNearTreeNodeHandle m_ptTree; /* pointer to the actual tree */
size_t m_szdimension; /* dimension of the coordinates */
size_t m_szsize; /* size of this tree */
size_t m_szdepth; /* depth of this tree */
int m_iflags; /* flags */
CVectorHandle m_ObjectStore; /* all inserted objects */
CVectorHandle m_CoordStore; /* all inserted coordinates */
CVectorHandle m_DelayedIndices;/* objects queued for insertion */
} CNearTree;
typedef CNearTree FAR * CNearTreeHandle;
The internal operation of the API depends on the function CNearTreeDist
that returns the distance (L1, L2 or L-infinity) between two coordinate
vectors as a double according to the parameters of the given tree. Note
that the tree may store the coordinates as integers or as doubles, but the
distance is always computed as a double. If this function is replaced by a
user function, it is important that the replacement obey the triangle
inequality.
A neartree is created by CNearTreeCreate and freed by CNearTreeFree.
treedim is the dimension of the coordinate vectors and treetype is one of
the three predefined constants CNEARTREE_TYPE_DOUBLE for double or
CNEARTREE_TYPE_INTEGER for integer or CNEARTREE_TYPE_STRING, optionally
ORed with CNEARTREE_NORM_L1, CNEARTREE_NORM_L2 or CNEARTREE_NORM_LINF for
L1, L2 or L-infinity norms, CNEARTREE_NORM_SPHERE or
CNEARTREE_NORM_HSPHERE for a spherical or hemispherical norm (L1-norm
combination of radial and spherical/hemisppherical triangle distances), or
CNEARTREE_NORM_HAMMING for the string-Hamming distance norm (add one for
each differing character position).
Starting with release 2.1, all insertions are delayed by default, unless
the insertions is done by a call to CNearTreeImmediateInsert. The
insertions that have been queued are completed by a call to
CNearTreeCompleteDelayedInsert or by any search. The insertions are
actually done in a randomized order, either for an initial block of
sqrt(#queue) by default, or for the entire queue if the flag
CNEARTREE_DEFER_ALL is ored with treetype. In addition, if the flag
CNEARTREE_DEFER_ALL is set, all inserts will be deferred, even in calls to
CNearTreeImmediateInsert. Alteratively, if minimal reorganization of the
order of the tree is desired on each insertion, CNEARTREE_FLIP should be
ored with treetype. When first created, a neartree has no right or left
node and with the dMax-below set to negative values so that any match
found will be stored since it will greater than the negative value. The
tree is then populated by calls to CNearTreeInsert, with each call
providing a coordinate vector coord and an optional object pointer obj.
The API copies the coordinate vector, but does not copy the object. Later,
when a search is requested or an explicit call to
CNearTreeCompleteDelayedInsert is made, the tree is populated in the order
left, right and then the nearer child, working from a randomized selection
from the items queued for insertion.
Optionally, the actual insertions may done immediately by calling
CNearTreeImmediateInsert instead of CNearTreeInsert. For upwards
compatability of the library for existing code, the deprecated
CNearTreeDelayedInsert is provided as an deprecated alternate call to
CNearTreeInsert.
The neartree is searched for the nearest or farthest coordinate vector in
the neartree to a given probe coordinate vector coord by
CNearTreeNearestNeighbor and CNearTreeFarthestNeighbor, respectively. The
given radius confines the search to a sphere around the probe. If more
than a single extremal coordinate point is needed, CNearTreeFindInSphere
can be used to obtain a CVector result vector of all the coordinate
vectors that satisfy the constraint of being within a specified radius, or
CNearTreeFindOutSphere can be used to obtain a CVector result vector of
all the coordinates that satisfy the constraint of being outside a
specified radius. CNearTreeFindIn Annulus can be used to obtain a CVector
result vector of all the coordinates that satisfy the constraint of being
between two specified radii from the probe. CNearTreeFindKNearest can be
used to obtain a CVector result vector of the k coordinates closest to the
probe point such that all results are within the specified radius of the
probe point, or CNearTreeFindKFarthest to obtain a CVector result vector
of the k coordinates farthest from the probe point such that all results
are at or outside the specified radius of the probe point. The vectors
themselves are not copied into the result vector. If the parameter
resetcount is true (non zero) the result vector is cleared before the
search. A parallel CVector result vector of the matching object pointers
is returned if objs is not NULL. Aternatives the forms
CNearTreeFindTreeInSphere, CNearTreeFindTreeOutSphere,
CNearTreeFindTreeInAnnulus, CNearTreeFindKTreeNearest,
CNearTreeFindKTreeFarthest can be used to obtain CNearTrees rather than
CVectors of results. The functions CNearTreeNearest and
CNearTreeFindFarthest implement CNearTreeNearestNeighbor and
CNearTreeFarthestNeighbor, respectively, adjusting the radius of the
search while the search is in progress, and are not normally used by users
Returns
If CNearTreeDist fails, it returns -1. Except for CNearTreeDist, all the
functions in the API return 0 ( CNEARTREE_SUCCESS ) for success. If
dynamic memory allocation fails, CNEARTREE_MALLOC_FAILED is returned. If a
call is made with an improper argument, CNEARTREE_BAD_ARGUMENT is
returned. If a search fails to find anything, CNEARTREE_NOT_FOUND is
returned. If there is a failure in an attempt to free a CNearTree,
CNEARTREE_FREE_FAILED is returned. If any of the internal call to CVector
fail, CNEARTREE_CVECTOR_FAILED is returned. For convenience in debugging,
the formerly negative values of this returns are now positive.
Examples
To create a neartree for 3-dimensional vectors of doubles:
#include <CNearTree.h>
CNearTreeHandle treehandle;
int bReturn;
...
bReturn = !CNearTreeCreate(&treehandle,3,CNEARTREE_TYPE_DOUBLE);
To insert a copy of a 3-dimensional vector of doubles into this tree, with
no associated object:
double v[3];
...
v[0] = 1.; v[1] = 2.; v[2] = 3.;
bReturn = !CNearTreeInsert(treehandle,&v[0],NULL);
To search for the nearest neighbor to a probe vector vSearch in a radius
of 3., returning a pointer to the resulting vector in vBest:
double * vBest;
void * vvBest;
double vSearch[3];
double dRad = =3.;
...
if ( !CNearTreeNearestNeighbor(treehandle,dRad,&vvBest,NULL,vSearch))
{ vBest = (double *)vvBest; }
Note the use of a separate void * vvBest instead of a cast of &vBest to
avoid compiler type punning warnings.
For more examples of the use of CNearTree.c, see main.c and
CNearTreeTest.c in the release kit.
----------------------------------------------------------------------
----------------------------------------------------------------------
A Portable pseudo-random number generator: rhrand.h
rhrand.h is a portable pseudo-random number generator based one by Rob
Harrison, derived from "one in J.M.Hammersley and D.C. Handscomb, 'Monte
Carlo Methods,' Methuen & Co., London and Wiley & Sons, New York, 1964,
p47". See also, D. E. Knuth "The Art of Computer Programming", Volume 2,
"Seminumerical Alogorithms, Third Edition, Addison-Wesley, Reading MA,
1997.
rhrand.h is a header file in which a C++ class, RHrand, is defined, and a
C struct typedef CRHrand is defined.
The C++ interface is
static const int RHRAND_MAX = 32767; /* the integer range accessible as RHrand::RHRAND_MAX */
RHrand(void) /* the default constructor */
RHrand( const int iseed ) /* a constructor to start with the given seed */
~RHrand( void) /* a destructor */
void srandom( const int iseed) /* reset the generator based on the given seed */
double urand( void ) /* return a random double uniformly distributed in [0,1) */
int random ( void ) /* return a random integer uniformly distributed in [0, RHRAND_MAX-1] */
In C++ code, typical use is
#include <rhhand.h>
RHrand rhr;
...
x = rhr.urand();
The C interface is suppressed in RHRAND_NOCCODE is defined. Otherwise the
C interface is based on defining a struct of type CRHRrand and calling
macros that refer to a handle of type RCRHrandHandle.
typedef struct CRHrand_ { /* the struct used in random number generattion */
double buffer[55];
int indx;
int jndx;
int kndx;
double dTemp;
} CRHrand;
typedef CRHrand * CRHrandHandle; /* the type to be used in maro calls */
#define CRHRAND_MAX 32767 /* the integer range */
#define CRHrandSrandom(randhandle,iseed) ...
/* a macro to call to initialize CHRrandHandle randhandle
using see int iseed */
#define CRHrandUrand(randhandle) ... /* a macro to return a random double uniformly distributed in [0,1) */
#define CRHrandRandom(randhandle) ((int)(CRHrandUrand(randhandle)*(double)CRHRAND_MAX))
/* a macro to return a random integer uniformly distributed in
[0, CRHRAND_MAX-1] */
Typical use is
#include <rhhand.h>
CRHrand rhr;
...
CRHrandSrandom(&rhr, 0 );
...
x = CRHrandUrand(&rhr);
----------------------------------------------------------------------
----------------------------------------------------------------------
Updated 31 September 2010
andrewsl@ix.netcom.com.com
