source: tags/3.3.6/HeuristicLab.ExtLibs/HeuristicLab.ALGLIB/3.1.0/ALGLIB-3.1.0/alglibmisc.cs @ 7585

/*************************************************************************
Copyright (c) Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.

This program 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 General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#pragma warning disable 162
#pragma warning disable 219
using System;

public partial class alglib
{


    /*************************************************************************
    Portable high quality random number generator state.
    Initialized with HQRNDRandomize() or HQRNDSeed().

    Fields:
        S1, S2      -   seed values
        V           -   precomputed value
        MagicV      -   'magic' value used to determine whether State structure
                        was correctly initialized.
    *************************************************************************/
    public class hqrndstate
    {
        //
        // Public declarations
        //

        public hqrndstate()
        {
            _innerobj = new hqrnd.hqrndstate();
        }

        //
        // Although some of declarations below are public, you should not use them
        // They are intended for internal use only
        //
        private hqrnd.hqrndstate _innerobj;
        public hqrnd.hqrndstate innerobj { get { return _innerobj; } }
        public hqrndstate(hqrnd.hqrndstate obj)
        {
            _innerobj = obj;
        }
    }

    /*************************************************************************
    HQRNDState  initialization  with  random  values  which come from standard
    RNG.

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static void hqrndrandomize(out hqrndstate state)
    {
        state = new hqrndstate();
        hqrnd.hqrndrandomize(state.innerobj);
        return;
    }

    /*************************************************************************
    HQRNDState initialization with seed values

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static void hqrndseed(int s1, int s2, out hqrndstate state)
    {
        state = new hqrndstate();
        hqrnd.hqrndseed(s1, s2, state.innerobj);
        return;
    }

    /*************************************************************************
    This function generates random real number in (0,1),
    not including interval boundaries

    State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static double hqrnduniformr(hqrndstate state)
    {

        double result = hqrnd.hqrnduniformr(state.innerobj);
        return result;
    }

    /*************************************************************************
    This function generates random integer number in [0, N)

    1. N must be less than HQRNDMax-1.
    2. State structure must be initialized with HQRNDRandomize() or HQRNDSeed()

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static int hqrnduniformi(hqrndstate state, int n)
    {

        int result = hqrnd.hqrnduniformi(state.innerobj, n);
        return result;
    }

    /*************************************************************************
    Random number generator: normal numbers

    This function generates one random number from normal distribution.
    Its performance is equal to that of HQRNDNormal2()

    State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static double hqrndnormal(hqrndstate state)
    {

        double result = hqrnd.hqrndnormal(state.innerobj);
        return result;
    }

    /*************************************************************************
    Random number generator: random X and Y such that X^2+Y^2=1

    State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static void hqrndunit2(hqrndstate state, out double x, out double y)
    {
        x = 0;
        y = 0;
        hqrnd.hqrndunit2(state.innerobj, ref x, ref y);
        return;
    }

    /*************************************************************************
    Random number generator: normal numbers

    This function generates two independent random numbers from normal
    distribution. Its performance is equal to that of HQRNDNormal()

    State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

      -- ALGLIB --
         Copyright 02.12.2009 by Bochkanov Sergey
    *************************************************************************/
    public static void hqrndnormal2(hqrndstate state, out double x1, out double x2)
    {
        x1 = 0;
        x2 = 0;
        hqrnd.hqrndnormal2(state.innerobj, ref x1, ref x2);
        return;
    }

    /*************************************************************************
    Random number generator: exponential distribution

    State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

      -- ALGLIB --
         Copyright 11.08.2007 by Bochkanov Sergey
    *************************************************************************/
    public static double hqrndexponential(hqrndstate state, double lambdav)
    {

        double result = hqrnd.hqrndexponential(state.innerobj, lambdav);
        return result;
    }

}
public partial class alglib
{


    /*************************************************************************

    *************************************************************************/
    public class kdtree
    {
        //
        // Public declarations
        //

        public kdtree()
        {
            _innerobj = new nearestneighbor.kdtree();
        }

        //
        // Although some of declarations below are public, you should not use them
        // They are intended for internal use only
        //
        private nearestneighbor.kdtree _innerobj;
        public nearestneighbor.kdtree innerobj { get { return _innerobj; } }
        public kdtree(nearestneighbor.kdtree obj)
        {
            _innerobj = obj;
        }
    }

    /*************************************************************************
    KD-tree creation

    This subroutine creates KD-tree from set of X-values and optional Y-values

    INPUT PARAMETERS
        XY      -   dataset, array[0..N-1,0..NX+NY-1].
                    one row corresponds to one point.
                    first NX columns contain X-values, next NY (NY may be zero)
                    columns may contain associated Y-values
        N       -   number of points, N>=1
        NX      -   space dimension, NX>=1.
        NY      -   number of optional Y-values, NY>=0.
        NormType-   norm type:
                    * 0 denotes infinity-norm
                    * 1 denotes 1-norm
                    * 2 denotes 2-norm (Euclidean norm)

    OUTPUT PARAMETERS
        KDT     -   KD-tree


    NOTES

    1. KD-tree  creation  have O(N*logN) complexity and O(N*(2*NX+NY))  memory
       requirements.
    2. Although KD-trees may be used with any combination of N  and  NX,  they
       are more efficient than brute-force search only when N >> 4^NX. So they
       are most useful in low-dimensional tasks (NX=2, NX=3). NX=1  is another
       inefficient case, because  simple  binary  search  (without  additional
       structures) is much more efficient in such tasks than KD-trees.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreebuild(double[,] xy, int n, int nx, int ny, int normtype, out kdtree kdt)
    {
        kdt = new kdtree();
        nearestneighbor.kdtreebuild(xy, n, nx, ny, normtype, kdt.innerobj);
        return;
    }
    public static void kdtreebuild(double[,] xy, int nx, int ny, int normtype, out kdtree kdt)
    {
        int n;

        kdt = new kdtree();
        n = ap.rows(xy);
        nearestneighbor.kdtreebuild(xy, n, nx, ny, normtype, kdt.innerobj);

        return;
    }

    /*************************************************************************
    KD-tree creation

    This  subroutine  creates  KD-tree  from set of X-values, integer tags and
    optional Y-values

    INPUT PARAMETERS
        XY      -   dataset, array[0..N-1,0..NX+NY-1].
                    one row corresponds to one point.
                    first NX columns contain X-values, next NY (NY may be zero)
                    columns may contain associated Y-values
        Tags    -   tags, array[0..N-1], contains integer tags associated
                    with points.
        N       -   number of points, N>=1
        NX      -   space dimension, NX>=1.
        NY      -   number of optional Y-values, NY>=0.
        NormType-   norm type:
                    * 0 denotes infinity-norm
                    * 1 denotes 1-norm
                    * 2 denotes 2-norm (Euclidean norm)

    OUTPUT PARAMETERS
        KDT     -   KD-tree

    NOTES

    1. KD-tree  creation  have O(N*logN) complexity and O(N*(2*NX+NY))  memory
       requirements.
    2. Although KD-trees may be used with any combination of N  and  NX,  they
       are more efficient than brute-force search only when N >> 4^NX. So they
       are most useful in low-dimensional tasks (NX=2, NX=3). NX=1  is another
       inefficient case, because  simple  binary  search  (without  additional
       structures) is much more efficient in such tasks than KD-trees.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreebuildtagged(double[,] xy, int[] tags, int n, int nx, int ny, int normtype, out kdtree kdt)
    {
        kdt = new kdtree();
        nearestneighbor.kdtreebuildtagged(xy, tags, n, nx, ny, normtype, kdt.innerobj);
        return;
    }
    public static void kdtreebuildtagged(double[,] xy, int[] tags, int nx, int ny, int normtype, out kdtree kdt)
    {
        int n;
        if( (ap.rows(xy)!=ap.len(tags)))
            throw new alglibexception("Error while calling 'kdtreebuildtagged': looks like one of arguments has wrong size");
        kdt = new kdtree();
        n = ap.rows(xy);
        nearestneighbor.kdtreebuildtagged(xy, tags, n, nx, ny, normtype, kdt.innerobj);

        return;
    }

    /*************************************************************************
    K-NN query: K nearest neighbors

    INPUT PARAMETERS
        KDT         -   KD-tree
        X           -   point, array[0..NX-1].
        K           -   number of neighbors to return, K>=1
        SelfMatch   -   whether self-matches are allowed:
                        * if True, nearest neighbor may be the point itself
                          (if it exists in original dataset)
                        * if False, then only points with non-zero distance
                          are returned
                        * if not given, considered True

    RESULT
        number of actual neighbors found (either K or N, if K>N).

    This  subroutine  performs  query  and  stores  its result in the internal
    structures of the KD-tree. You can use  following  subroutines  to  obtain
    these results:
    * KDTreeQueryResultsX() to get X-values
    * KDTreeQueryResultsXY() to get X- and Y-values
    * KDTreeQueryResultsTags() to get tag values
    * KDTreeQueryResultsDistances() to get distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static int kdtreequeryknn(kdtree kdt, double[] x, int k, bool selfmatch)
    {

        int result = nearestneighbor.kdtreequeryknn(kdt.innerobj, x, k, selfmatch);
        return result;
    }
    public static int kdtreequeryknn(kdtree kdt, double[] x, int k)
    {
        bool selfmatch;


        selfmatch = true;
        int result = nearestneighbor.kdtreequeryknn(kdt.innerobj, x, k, selfmatch);

        return result;
    }

    /*************************************************************************
    R-NN query: all points within R-sphere centered at X

    INPUT PARAMETERS
        KDT         -   KD-tree
        X           -   point, array[0..NX-1].
        R           -   radius of sphere (in corresponding norm), R>0
        SelfMatch   -   whether self-matches are allowed:
                        * if True, nearest neighbor may be the point itself
                          (if it exists in original dataset)
                        * if False, then only points with non-zero distance
                          are returned
                        * if not given, considered True

    RESULT
        number of neighbors found, >=0

    This  subroutine  performs  query  and  stores  its result in the internal
    structures of the KD-tree. You can use  following  subroutines  to  obtain
    actual results:
    * KDTreeQueryResultsX() to get X-values
    * KDTreeQueryResultsXY() to get X- and Y-values
    * KDTreeQueryResultsTags() to get tag values
    * KDTreeQueryResultsDistances() to get distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static int kdtreequeryrnn(kdtree kdt, double[] x, double r, bool selfmatch)
    {

        int result = nearestneighbor.kdtreequeryrnn(kdt.innerobj, x, r, selfmatch);
        return result;
    }
    public static int kdtreequeryrnn(kdtree kdt, double[] x, double r)
    {
        bool selfmatch;


        selfmatch = true;
        int result = nearestneighbor.kdtreequeryrnn(kdt.innerobj, x, r, selfmatch);

        return result;
    }

    /*************************************************************************
    K-NN query: approximate K nearest neighbors

    INPUT PARAMETERS
        KDT         -   KD-tree
        X           -   point, array[0..NX-1].
        K           -   number of neighbors to return, K>=1
        SelfMatch   -   whether self-matches are allowed:
                        * if True, nearest neighbor may be the point itself
                          (if it exists in original dataset)
                        * if False, then only points with non-zero distance
                          are returned
                        * if not given, considered True
        Eps         -   approximation factor, Eps>=0. eps-approximate  nearest
                        neighbor  is  a  neighbor  whose distance from X is at
                        most (1+eps) times distance of true nearest neighbor.

    RESULT
        number of actual neighbors found (either K or N, if K>N).

    NOTES
        significant performance gain may be achieved only when Eps  is  is  on
        the order of magnitude of 1 or larger.

    This  subroutine  performs  query  and  stores  its result in the internal
    structures of the KD-tree. You can use  following  subroutines  to  obtain
    these results:
    * KDTreeQueryResultsX() to get X-values
    * KDTreeQueryResultsXY() to get X- and Y-values
    * KDTreeQueryResultsTags() to get tag values
    * KDTreeQueryResultsDistances() to get distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static int kdtreequeryaknn(kdtree kdt, double[] x, int k, bool selfmatch, double eps)
    {

        int result = nearestneighbor.kdtreequeryaknn(kdt.innerobj, x, k, selfmatch, eps);
        return result;
    }
    public static int kdtreequeryaknn(kdtree kdt, double[] x, int k, double eps)
    {
        bool selfmatch;


        selfmatch = true;
        int result = nearestneighbor.kdtreequeryaknn(kdt.innerobj, x, k, selfmatch, eps);

        return result;
    }

    /*************************************************************************
    X-values from last query

    INPUT PARAMETERS
        KDT     -   KD-tree
        X       -   possibly pre-allocated buffer. If X is too small to store
                    result, it is resized. If size(X) is enough to store
                    result, it is left unchanged.

    OUTPUT PARAMETERS
        X       -   rows are filled with X-values

    NOTES
    1. points are ordered by distance from the query point (first = closest)
    2. if  XY is larger than required to store result, only leading part  will
       be overwritten; trailing part will be left unchanged. So  if  on  input
       XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
       XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
       you want function  to  resize  array  according  to  result  size,  use
       function with same name and suffix 'I'.

    SEE ALSO
    * KDTreeQueryResultsXY()            X- and Y-values
    * KDTreeQueryResultsTags()          tag values
    * KDTreeQueryResultsDistances()     distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsx(kdtree kdt, ref double[,] x)
    {

        nearestneighbor.kdtreequeryresultsx(kdt.innerobj, ref x);
        return;
    }

    /*************************************************************************
    X- and Y-values from last query

    INPUT PARAMETERS
        KDT     -   KD-tree
        XY      -   possibly pre-allocated buffer. If XY is too small to store
                    result, it is resized. If size(XY) is enough to store
                    result, it is left unchanged.

    OUTPUT PARAMETERS
        XY      -   rows are filled with points: first NX columns with
                    X-values, next NY columns - with Y-values.

    NOTES
    1. points are ordered by distance from the query point (first = closest)
    2. if  XY is larger than required to store result, only leading part  will
       be overwritten; trailing part will be left unchanged. So  if  on  input
       XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
       XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
       you want function  to  resize  array  according  to  result  size,  use
       function with same name and suffix 'I'.

    SEE ALSO
    * KDTreeQueryResultsX()             X-values
    * KDTreeQueryResultsTags()          tag values
    * KDTreeQueryResultsDistances()     distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsxy(kdtree kdt, ref double[,] xy)
    {

        nearestneighbor.kdtreequeryresultsxy(kdt.innerobj, ref xy);
        return;
    }

    /*************************************************************************
    Tags from last query

    INPUT PARAMETERS
        KDT     -   KD-tree
        Tags    -   possibly pre-allocated buffer. If X is too small to store
                    result, it is resized. If size(X) is enough to store
                    result, it is left unchanged.

    OUTPUT PARAMETERS
        Tags    -   filled with tags associated with points,
                    or, when no tags were supplied, with zeros

    NOTES
    1. points are ordered by distance from the query point (first = closest)
    2. if  XY is larger than required to store result, only leading part  will
       be overwritten; trailing part will be left unchanged. So  if  on  input
       XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
       XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
       you want function  to  resize  array  according  to  result  size,  use
       function with same name and suffix 'I'.

    SEE ALSO
    * KDTreeQueryResultsX()             X-values
    * KDTreeQueryResultsXY()            X- and Y-values
    * KDTreeQueryResultsDistances()     distances

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultstags(kdtree kdt, ref int[] tags)
    {

        nearestneighbor.kdtreequeryresultstags(kdt.innerobj, ref tags);
        return;
    }

    /*************************************************************************
    Distances from last query

    INPUT PARAMETERS
        KDT     -   KD-tree
        R       -   possibly pre-allocated buffer. If X is too small to store
                    result, it is resized. If size(X) is enough to store
                    result, it is left unchanged.

    OUTPUT PARAMETERS
        R       -   filled with distances (in corresponding norm)

    NOTES
    1. points are ordered by distance from the query point (first = closest)
    2. if  XY is larger than required to store result, only leading part  will
       be overwritten; trailing part will be left unchanged. So  if  on  input
       XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
       XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
       you want function  to  resize  array  according  to  result  size,  use
       function with same name and suffix 'I'.

    SEE ALSO
    * KDTreeQueryResultsX()             X-values
    * KDTreeQueryResultsXY()            X- and Y-values
    * KDTreeQueryResultsTags()          tag values

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsdistances(kdtree kdt, ref double[] r)
    {

        nearestneighbor.kdtreequeryresultsdistances(kdt.innerobj, ref r);
        return;
    }

    /*************************************************************************
    X-values from last query; 'interactive' variant for languages like  Python
    which   support    constructs   like  "X = KDTreeQueryResultsXI(KDT)"  and
    interactive mode of interpreter.

    This function allocates new array on each call,  so  it  is  significantly
    slower than its 'non-interactive' counterpart, but it is  more  convenient
    when you call it from command line.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsxi(kdtree kdt, out double[,] x)
    {
        x = new double[0,0];
        nearestneighbor.kdtreequeryresultsxi(kdt.innerobj, ref x);
        return;
    }

    /*************************************************************************
    XY-values from last query; 'interactive' variant for languages like Python
    which   support    constructs   like "XY = KDTreeQueryResultsXYI(KDT)" and
    interactive mode of interpreter.

    This function allocates new array on each call,  so  it  is  significantly
    slower than its 'non-interactive' counterpart, but it is  more  convenient
    when you call it from command line.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsxyi(kdtree kdt, out double[,] xy)
    {
        xy = new double[0,0];
        nearestneighbor.kdtreequeryresultsxyi(kdt.innerobj, ref xy);
        return;
    }

    /*************************************************************************
    Tags  from  last  query;  'interactive' variant for languages like  Python
    which  support  constructs  like "Tags = KDTreeQueryResultsTagsI(KDT)" and
    interactive mode of interpreter.

    This function allocates new array on each call,  so  it  is  significantly
    slower than its 'non-interactive' counterpart, but it is  more  convenient
    when you call it from command line.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultstagsi(kdtree kdt, out int[] tags)
    {
        tags = new int[0];
        nearestneighbor.kdtreequeryresultstagsi(kdt.innerobj, ref tags);
        return;
    }

    /*************************************************************************
    Distances from last query; 'interactive' variant for languages like Python
    which  support  constructs   like  "R = KDTreeQueryResultsDistancesI(KDT)"
    and interactive mode of interpreter.

    This function allocates new array on each call,  so  it  is  significantly
    slower than its 'non-interactive' counterpart, but it is  more  convenient
    when you call it from command line.

      -- ALGLIB --
         Copyright 28.02.2010 by Bochkanov Sergey
    *************************************************************************/
    public static void kdtreequeryresultsdistancesi(kdtree kdt, out double[] r)
    {
        r = new double[0];
        nearestneighbor.kdtreequeryresultsdistancesi(kdt.innerobj, ref r);
        return;
    }

}
public partial class alglib
{
    public class hqrnd
    {
        /*************************************************************************
        Portable high quality random number generator state.
        Initialized with HQRNDRandomize() or HQRNDSeed().

        Fields:
            S1, S2      -   seed values
            V           -   precomputed value
            MagicV      -   'magic' value used to determine whether State structure
                            was correctly initialized.
        *************************************************************************/
        public class hqrndstate
        {
            public int s1;
            public int s2;
            public double v;
            public int magicv;
        };




        public const int hqrndmax = 2147483563;
        public const int hqrndm1 = 2147483563;
        public const int hqrndm2 = 2147483399;
        public const int hqrndmagic = 1634357784;


        /*************************************************************************
        HQRNDState  initialization  with  random  values  which come from standard
        RNG.

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void hqrndrandomize(hqrndstate state)
        {
            hqrndseed(math.randominteger(hqrndm1), math.randominteger(hqrndm2), state);
        }


        /*************************************************************************
        HQRNDState initialization with seed values

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void hqrndseed(int s1,
            int s2,
            hqrndstate state)
        {
            state.s1 = s1%(hqrndm1-1)+1;
            state.s2 = s2%(hqrndm2-1)+1;
            state.v = (double)1/(double)hqrndmax;
            state.magicv = hqrndmagic;
        }


        /*************************************************************************
        This function generates random real number in (0,1),
        not including interval boundaries

        State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static double hqrnduniformr(hqrndstate state)
        {
            double result = 0;

            result = state.v*hqrndintegerbase(state);
            return result;
        }


        /*************************************************************************
        This function generates random integer number in [0, N)

        1. N must be less than HQRNDMax-1.
        2. State structure must be initialized with HQRNDRandomize() or HQRNDSeed()

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static int hqrnduniformi(hqrndstate state,
            int n)
        {
            int result = 0;
            int mx = 0;

            
            //
            // Correct handling of N's close to RNDBaseMax
            // (avoiding skewed distributions for RNDBaseMax<>K*N)
            //
            ap.assert(n>0, "HQRNDUniformI: N<=0!");
            ap.assert(n<hqrndmax-1, "HQRNDUniformI: N>=RNDBaseMax-1!");
            mx = hqrndmax-1-(hqrndmax-1)%n;
            do
            {
                result = hqrndintegerbase(state)-1;
            }
            while( result>=mx );
            result = result%n;
            return result;
        }


        /*************************************************************************
        Random number generator: normal numbers

        This function generates one random number from normal distribution.
        Its performance is equal to that of HQRNDNormal2()

        State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static double hqrndnormal(hqrndstate state)
        {
            double result = 0;
            double v1 = 0;
            double v2 = 0;

            hqrndnormal2(state, ref v1, ref v2);
            result = v1;
            return result;
        }


        /*************************************************************************
        Random number generator: random X and Y such that X^2+Y^2=1

        State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void hqrndunit2(hqrndstate state,
            ref double x,
            ref double y)
        {
            double v = 0;
            double mx = 0;
            double mn = 0;

            x = 0;
            y = 0;

            do
            {
                hqrndnormal2(state, ref x, ref y);
            }
            while( !((double)(x)!=(double)(0) | (double)(y)!=(double)(0)) );
            mx = Math.Max(Math.Abs(x), Math.Abs(y));
            mn = Math.Min(Math.Abs(x), Math.Abs(y));
            v = mx*Math.Sqrt(1+math.sqr(mn/mx));
            x = x/v;
            y = y/v;
        }


        /*************************************************************************
        Random number generator: normal numbers

        This function generates two independent random numbers from normal
        distribution. Its performance is equal to that of HQRNDNormal()

        State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

          -- ALGLIB --
             Copyright 02.12.2009 by Bochkanov Sergey
        *************************************************************************/
        public static void hqrndnormal2(hqrndstate state,
            ref double x1,
            ref double x2)
        {
            double u = 0;
            double v = 0;
            double s = 0;

            x1 = 0;
            x2 = 0;

            while( true )
            {
                u = 2*hqrnduniformr(state)-1;
                v = 2*hqrnduniformr(state)-1;
                s = math.sqr(u)+math.sqr(v);
                if( (double)(s)>(double)(0) & (double)(s)<(double)(1) )
                {
                    
                    //
                    // two Sqrt's instead of one to
                    // avoid overflow when S is too small
                    //
                    s = Math.Sqrt(-(2*Math.Log(s)))/Math.Sqrt(s);
                    x1 = u*s;
                    x2 = v*s;
                    return;
                }
            }
        }


        /*************************************************************************
        Random number generator: exponential distribution

        State structure must be initialized with HQRNDRandomize() or HQRNDSeed().

          -- ALGLIB --
             Copyright 11.08.2007 by Bochkanov Sergey
        *************************************************************************/
        public static double hqrndexponential(hqrndstate state,
            double lambdav)
        {
            double result = 0;

            ap.assert((double)(lambdav)>(double)(0), "HQRNDExponential: LambdaV<=0!");
            result = -(Math.Log(hqrnduniformr(state))/lambdav);
            return result;
        }


        /*************************************************************************

        L'Ecuyer, Efficient and portable combined random number generators
        *************************************************************************/
        private static int hqrndintegerbase(hqrndstate state)
        {
            int result = 0;
            int k = 0;

            ap.assert(state.magicv==hqrndmagic, "HQRNDIntegerBase: State is not correctly initialized!");
            k = state.s1/53668;
            state.s1 = 40014*(state.s1-k*53668)-k*12211;
            if( state.s1<0 )
            {
                state.s1 = state.s1+2147483563;
            }
            k = state.s2/52774;
            state.s2 = 40692*(state.s2-k*52774)-k*3791;
            if( state.s2<0 )
            {
                state.s2 = state.s2+2147483399;
            }
            
            //
            // Result
            //
            result = state.s1-state.s2;
            if( result<1 )
            {
                result = result+2147483562;
            }
            return result;
        }


    }
    public class nearestneighbor
    {
        public class kdtree
        {
            public int n;
            public int nx;
            public int ny;
            public int normtype;
            public int distmatrixtype;
            public double[,] xy;
            public int[] tags;
            public double[] boxmin;
            public double[] boxmax;
            public double[] curboxmin;
            public double[] curboxmax;
            public double curdist;
            public int[] nodes;
            public double[] splits;
            public double[] x;
            public int kneeded;
            public double rneeded;
            public bool selfmatch;
            public double approxf;
            public int kcur;
            public int[] idx;
            public double[] r;
            public double[] buf;
            public int debugcounter;
            public kdtree()
            {
                xy = new double[0,0];
                tags = new int[0];
                boxmin = new double[0];
                boxmax = new double[0];
                curboxmin = new double[0];
                curboxmax = new double[0];
                nodes = new int[0];
                splits = new double[0];
                x = new double[0];
                idx = new int[0];
                r = new double[0];
                buf = new double[0];
            }
        };




        public const int splitnodesize = 6;


        /*************************************************************************
        KD-tree creation

        This subroutine creates KD-tree from set of X-values and optional Y-values

        INPUT PARAMETERS
            XY      -   dataset, array[0..N-1,0..NX+NY-1].
                        one row corresponds to one point.
                        first NX columns contain X-values, next NY (NY may be zero)
                        columns may contain associated Y-values
            N       -   number of points, N>=1
            NX      -   space dimension, NX>=1.
            NY      -   number of optional Y-values, NY>=0.
            NormType-   norm type:
                        * 0 denotes infinity-norm
                        * 1 denotes 1-norm
                        * 2 denotes 2-norm (Euclidean norm)
                        
        OUTPUT PARAMETERS
            KDT     -   KD-tree
            
            
        NOTES

        1. KD-tree  creation  have O(N*logN) complexity and O(N*(2*NX+NY))  memory
           requirements.
        2. Although KD-trees may be used with any combination of N  and  NX,  they
           are more efficient than brute-force search only when N >> 4^NX. So they
           are most useful in low-dimensional tasks (NX=2, NX=3). NX=1  is another
           inefficient case, because  simple  binary  search  (without  additional
           structures) is much more efficient in such tasks than KD-trees.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreebuild(double[,] xy,
            int n,
            int nx,
            int ny,
            int normtype,
            kdtree kdt)
        {
            int[] tags = new int[0];
            int i = 0;

            ap.assert(n>=1, "KDTreeBuild: N<1!");
            ap.assert(nx>=1, "KDTreeBuild: NX<1!");
            ap.assert(ny>=0, "KDTreeBuild: NY<0!");
            ap.assert(normtype>=0 & normtype<=2, "KDTreeBuild: incorrect NormType!");
            ap.assert(ap.rows(xy)>=n, "KDTreeBuild: rows(X)<N!");
            ap.assert(ap.cols(xy)>=nx+ny, "KDTreeBuild: cols(X)<NX+NY!");
            ap.assert(apserv.apservisfinitematrix(xy, n, nx+ny), "KDTreeBuild: X contains infinite or NaN values!");
            tags = new int[n];
            for(i=0; i<=n-1; i++)
            {
                tags[i] = 0;
            }
            kdtreebuildtagged(xy, tags, n, nx, ny, normtype, kdt);
        }


        /*************************************************************************
        KD-tree creation

        This  subroutine  creates  KD-tree  from set of X-values, integer tags and
        optional Y-values

        INPUT PARAMETERS
            XY      -   dataset, array[0..N-1,0..NX+NY-1].
                        one row corresponds to one point.
                        first NX columns contain X-values, next NY (NY may be zero)
                        columns may contain associated Y-values
            Tags    -   tags, array[0..N-1], contains integer tags associated
                        with points.
            N       -   number of points, N>=1
            NX      -   space dimension, NX>=1.
            NY      -   number of optional Y-values, NY>=0.
            NormType-   norm type:
                        * 0 denotes infinity-norm
                        * 1 denotes 1-norm
                        * 2 denotes 2-norm (Euclidean norm)

        OUTPUT PARAMETERS
            KDT     -   KD-tree

        NOTES

        1. KD-tree  creation  have O(N*logN) complexity and O(N*(2*NX+NY))  memory
           requirements.
        2. Although KD-trees may be used with any combination of N  and  NX,  they
           are more efficient than brute-force search only when N >> 4^NX. So they
           are most useful in low-dimensional tasks (NX=2, NX=3). NX=1  is another
           inefficient case, because  simple  binary  search  (without  additional
           structures) is much more efficient in such tasks than KD-trees.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreebuildtagged(double[,] xy,
            int[] tags,
            int n,
            int nx,
            int ny,
            int normtype,
            kdtree kdt)
        {
            int i = 0;
            int j = 0;
            int maxnodes = 0;
            int nodesoffs = 0;
            int splitsoffs = 0;
            int i_ = 0;
            int i1_ = 0;

            ap.assert(n>=1, "KDTreeBuildTagged: N<1!");
            ap.assert(nx>=1, "KDTreeBuildTagged: NX<1!");
            ap.assert(ny>=0, "KDTreeBuildTagged: NY<0!");
            ap.assert(normtype>=0 & normtype<=2, "KDTreeBuildTagged: incorrect NormType!");
            ap.assert(ap.rows(xy)>=n, "KDTreeBuildTagged: rows(X)<N!");
            ap.assert(ap.cols(xy)>=nx+ny, "KDTreeBuildTagged: cols(X)<NX+NY!");
            ap.assert(apserv.apservisfinitematrix(xy, n, nx+ny), "KDTreeBuildTagged: X contains infinite or NaN values!");
            
            //
            // initialize
            //
            kdt.n = n;
            kdt.nx = nx;
            kdt.ny = ny;
            kdt.normtype = normtype;
            kdt.distmatrixtype = 0;
            kdt.xy = new double[n, 2*nx+ny];
            kdt.tags = new int[n];
            kdt.idx = new int[n];
            kdt.r = new double[n];
            kdt.x = new double[nx];
            kdt.buf = new double[Math.Max(n, nx)];
            
            //
            // Initial fill
            //
            for(i=0; i<=n-1; i++)
            {
                for(i_=0; i_<=nx-1;i_++)
                {
                    kdt.xy[i,i_] = xy[i,i_];
                }
                i1_ = (0) - (nx);
                for(i_=nx; i_<=2*nx+ny-1;i_++)
                {
                    kdt.xy[i,i_] = xy[i,i_+i1_];
                }
                kdt.tags[i] = tags[i];
            }
            
            //
            // Determine bounding box
            //
            kdt.boxmin = new double[nx];
            kdt.boxmax = new double[nx];
            kdt.curboxmin = new double[nx];
            kdt.curboxmax = new double[nx];
            for(i_=0; i_<=nx-1;i_++)
            {
                kdt.boxmin[i_] = kdt.xy[0,i_];
            }
            for(i_=0; i_<=nx-1;i_++)
            {
                kdt.boxmax[i_] = kdt.xy[0,i_];
            }
            for(i=1; i<=n-1; i++)
            {
                for(j=0; j<=nx-1; j++)
                {
                    kdt.boxmin[j] = Math.Min(kdt.boxmin[j], kdt.xy[i,j]);
                    kdt.boxmax[j] = Math.Max(kdt.boxmax[j], kdt.xy[i,j]);
                }
            }
            
            //
            // prepare tree structure
            // * MaxNodes=N because we guarantee no trivial splits, i.e.
            //   every split will generate two non-empty boxes
            //
            maxnodes = n;
            kdt.nodes = new int[splitnodesize*2*maxnodes];
            kdt.splits = new double[2*maxnodes];
            nodesoffs = 0;
            splitsoffs = 0;
            for(i_=0; i_<=nx-1;i_++)
            {
                kdt.curboxmin[i_] = kdt.boxmin[i_];
            }
            for(i_=0; i_<=nx-1;i_++)
            {
                kdt.curboxmax[i_] = kdt.boxmax[i_];
            }
            kdtreegeneratetreerec(kdt, ref nodesoffs, ref splitsoffs, 0, n, 8);
            
            //
            // Set current query size to 0
            //
            kdt.kcur = 0;
        }


        /*************************************************************************
        K-NN query: K nearest neighbors

        INPUT PARAMETERS
            KDT         -   KD-tree
            X           -   point, array[0..NX-1].
            K           -   number of neighbors to return, K>=1
            SelfMatch   -   whether self-matches are allowed:
                            * if True, nearest neighbor may be the point itself
                              (if it exists in original dataset)
                            * if False, then only points with non-zero distance
                              are returned
                            * if not given, considered True

        RESULT
            number of actual neighbors found (either K or N, if K>N).

        This  subroutine  performs  query  and  stores  its result in the internal
        structures of the KD-tree. You can use  following  subroutines  to  obtain
        these results:
        * KDTreeQueryResultsX() to get X-values
        * KDTreeQueryResultsXY() to get X- and Y-values
        * KDTreeQueryResultsTags() to get tag values
        * KDTreeQueryResultsDistances() to get distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static int kdtreequeryknn(kdtree kdt,
            double[] x,
            int k,
            bool selfmatch)
        {
            int result = 0;

            ap.assert(k>=1, "KDTreeQueryKNN: K<1!");
            ap.assert(ap.len(x)>=kdt.nx, "KDTreeQueryKNN: Length(X)<NX!");
            ap.assert(apserv.isfinitevector(x, kdt.nx), "KDTreeQueryKNN: X contains infinite or NaN values!");
            result = kdtreequeryaknn(kdt, x, k, selfmatch, 0.0);
            return result;
        }


        /*************************************************************************
        R-NN query: all points within R-sphere centered at X

        INPUT PARAMETERS
            KDT         -   KD-tree
            X           -   point, array[0..NX-1].
            R           -   radius of sphere (in corresponding norm), R>0
            SelfMatch   -   whether self-matches are allowed:
                            * if True, nearest neighbor may be the point itself
                              (if it exists in original dataset)
                            * if False, then only points with non-zero distance
                              are returned
                            * if not given, considered True

        RESULT
            number of neighbors found, >=0

        This  subroutine  performs  query  and  stores  its result in the internal
        structures of the KD-tree. You can use  following  subroutines  to  obtain
        actual results:
        * KDTreeQueryResultsX() to get X-values
        * KDTreeQueryResultsXY() to get X- and Y-values
        * KDTreeQueryResultsTags() to get tag values
        * KDTreeQueryResultsDistances() to get distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static int kdtreequeryrnn(kdtree kdt,
            double[] x,
            double r,
            bool selfmatch)
        {
            int result = 0;
            int i = 0;
            int j = 0;

            ap.assert((double)(r)>(double)(0), "KDTreeQueryRNN: incorrect R!");
            ap.assert(ap.len(x)>=kdt.nx, "KDTreeQueryRNN: Length(X)<NX!");
            ap.assert(apserv.isfinitevector(x, kdt.nx), "KDTreeQueryRNN: X contains infinite or NaN values!");
            
            //
            // Prepare parameters
            //
            kdt.kneeded = 0;
            if( kdt.normtype!=2 )
            {
                kdt.rneeded = r;
            }
            else
            {
                kdt.rneeded = math.sqr(r);
            }
            kdt.selfmatch = selfmatch;
            kdt.approxf = 1;
            kdt.kcur = 0;
            
            //
            // calculate distance from point to current bounding box
            //
            kdtreeinitbox(kdt, x);
            
            //
            // call recursive search
            // results are returned as heap
            //
            kdtreequerynnrec(kdt, 0);
            
            //
            // pop from heap to generate ordered representation
            //
            // last element is not pop'ed because it is already in
            // its place
            //
            result = kdt.kcur;
            j = kdt.kcur;
            for(i=kdt.kcur; i>=2; i--)
            {
                tsort.tagheappopi(ref kdt.r, ref kdt.idx, ref j);
            }
            return result;
        }


        /*************************************************************************
        K-NN query: approximate K nearest neighbors

        INPUT PARAMETERS
            KDT         -   KD-tree
            X           -   point, array[0..NX-1].
            K           -   number of neighbors to return, K>=1
            SelfMatch   -   whether self-matches are allowed:
                            * if True, nearest neighbor may be the point itself
                              (if it exists in original dataset)
                            * if False, then only points with non-zero distance
                              are returned
                            * if not given, considered True
            Eps         -   approximation factor, Eps>=0. eps-approximate  nearest
                            neighbor  is  a  neighbor  whose distance from X is at
                            most (1+eps) times distance of true nearest neighbor.

        RESULT
            number of actual neighbors found (either K or N, if K>N).
            
        NOTES
            significant performance gain may be achieved only when Eps  is  is  on
            the order of magnitude of 1 or larger.

        This  subroutine  performs  query  and  stores  its result in the internal
        structures of the KD-tree. You can use  following  subroutines  to  obtain
        these results:
        * KDTreeQueryResultsX() to get X-values
        * KDTreeQueryResultsXY() to get X- and Y-values
        * KDTreeQueryResultsTags() to get tag values
        * KDTreeQueryResultsDistances() to get distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static int kdtreequeryaknn(kdtree kdt,
            double[] x,
            int k,
            bool selfmatch,
            double eps)
        {
            int result = 0;
            int i = 0;
            int j = 0;

            ap.assert(k>0, "KDTreeQueryAKNN: incorrect K!");
            ap.assert((double)(eps)>=(double)(0), "KDTreeQueryAKNN: incorrect Eps!");
            ap.assert(ap.len(x)>=kdt.nx, "KDTreeQueryAKNN: Length(X)<NX!");
            ap.assert(apserv.isfinitevector(x, kdt.nx), "KDTreeQueryAKNN: X contains infinite or NaN values!");
            
            //
            // Prepare parameters
            //
            k = Math.Min(k, kdt.n);
            kdt.kneeded = k;
            kdt.rneeded = 0;
            kdt.selfmatch = selfmatch;
            if( kdt.normtype==2 )
            {
                kdt.approxf = 1/math.sqr(1+eps);
            }
            else
            {
                kdt.approxf = 1/(1+eps);
            }
            kdt.kcur = 0;
            
            //
            // calculate distance from point to current bounding box
            //
            kdtreeinitbox(kdt, x);
            
            //
            // call recursive search
            // results are returned as heap
            //
            kdtreequerynnrec(kdt, 0);
            
            //
            // pop from heap to generate ordered representation
            //
            // last element is non pop'ed because it is already in
            // its place
            //
            result = kdt.kcur;
            j = kdt.kcur;
            for(i=kdt.kcur; i>=2; i--)
            {
                tsort.tagheappopi(ref kdt.r, ref kdt.idx, ref j);
            }
            return result;
        }


        /*************************************************************************
        X-values from last query

        INPUT PARAMETERS
            KDT     -   KD-tree
            X       -   possibly pre-allocated buffer. If X is too small to store
                        result, it is resized. If size(X) is enough to store
                        result, it is left unchanged.

        OUTPUT PARAMETERS
            X       -   rows are filled with X-values

        NOTES
        1. points are ordered by distance from the query point (first = closest)
        2. if  XY is larger than required to store result, only leading part  will
           be overwritten; trailing part will be left unchanged. So  if  on  input
           XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
           XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
           you want function  to  resize  array  according  to  result  size,  use
           function with same name and suffix 'I'.

        SEE ALSO
        * KDTreeQueryResultsXY()            X- and Y-values
        * KDTreeQueryResultsTags()          tag values
        * KDTreeQueryResultsDistances()     distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsx(kdtree kdt,
            ref double[,] x)
        {
            int i = 0;
            int k = 0;
            int i_ = 0;
            int i1_ = 0;

            if( kdt.kcur==0 )
            {
                return;
            }
            if( ap.rows(x)<kdt.kcur | ap.cols(x)<kdt.nx )
            {
                x = new double[kdt.kcur, kdt.nx];
            }
            k = kdt.kcur;
            for(i=0; i<=k-1; i++)
            {
                i1_ = (kdt.nx) - (0);
                for(i_=0; i_<=kdt.nx-1;i_++)
                {
                    x[i,i_] = kdt.xy[kdt.idx[i],i_+i1_];
                }
            }
        }


        /*************************************************************************
        X- and Y-values from last query

        INPUT PARAMETERS
            KDT     -   KD-tree
            XY      -   possibly pre-allocated buffer. If XY is too small to store
                        result, it is resized. If size(XY) is enough to store
                        result, it is left unchanged.

        OUTPUT PARAMETERS
            XY      -   rows are filled with points: first NX columns with
                        X-values, next NY columns - with Y-values.

        NOTES
        1. points are ordered by distance from the query point (first = closest)
        2. if  XY is larger than required to store result, only leading part  will
           be overwritten; trailing part will be left unchanged. So  if  on  input
           XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
           XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
           you want function  to  resize  array  according  to  result  size,  use
           function with same name and suffix 'I'.

        SEE ALSO
        * KDTreeQueryResultsX()             X-values
        * KDTreeQueryResultsTags()          tag values
        * KDTreeQueryResultsDistances()     distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsxy(kdtree kdt,
            ref double[,] xy)
        {
            int i = 0;
            int k = 0;
            int i_ = 0;
            int i1_ = 0;

            if( kdt.kcur==0 )
            {
                return;
            }
            if( ap.rows(xy)<kdt.kcur | ap.cols(xy)<kdt.nx+kdt.ny )
            {
                xy = new double[kdt.kcur, kdt.nx+kdt.ny];
            }
            k = kdt.kcur;
            for(i=0; i<=k-1; i++)
            {
                i1_ = (kdt.nx) - (0);
                for(i_=0; i_<=kdt.nx+kdt.ny-1;i_++)
                {
                    xy[i,i_] = kdt.xy[kdt.idx[i],i_+i1_];
                }
            }
        }


        /*************************************************************************
        Tags from last query

        INPUT PARAMETERS
            KDT     -   KD-tree
            Tags    -   possibly pre-allocated buffer. If X is too small to store
                        result, it is resized. If size(X) is enough to store
                        result, it is left unchanged.

        OUTPUT PARAMETERS
            Tags    -   filled with tags associated with points,
                        or, when no tags were supplied, with zeros

        NOTES
        1. points are ordered by distance from the query point (first = closest)
        2. if  XY is larger than required to store result, only leading part  will
           be overwritten; trailing part will be left unchanged. So  if  on  input
           XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
           XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
           you want function  to  resize  array  according  to  result  size,  use
           function with same name and suffix 'I'.

        SEE ALSO
        * KDTreeQueryResultsX()             X-values
        * KDTreeQueryResultsXY()            X- and Y-values
        * KDTreeQueryResultsDistances()     distances

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultstags(kdtree kdt,
            ref int[] tags)
        {
            int i = 0;
            int k = 0;

            if( kdt.kcur==0 )
            {
                return;
            }
            if( ap.len(tags)<kdt.kcur )
            {
                tags = new int[kdt.kcur];
            }
            k = kdt.kcur;
            for(i=0; i<=k-1; i++)
            {
                tags[i] = kdt.tags[kdt.idx[i]];
            }
        }


        /*************************************************************************
        Distances from last query

        INPUT PARAMETERS
            KDT     -   KD-tree
            R       -   possibly pre-allocated buffer. If X is too small to store
                        result, it is resized. If size(X) is enough to store
                        result, it is left unchanged.

        OUTPUT PARAMETERS
            R       -   filled with distances (in corresponding norm)

        NOTES
        1. points are ordered by distance from the query point (first = closest)
        2. if  XY is larger than required to store result, only leading part  will
           be overwritten; trailing part will be left unchanged. So  if  on  input
           XY = [[A,B],[C,D]], and result is [1,2],  then  on  exit  we  will  get
           XY = [[1,2],[C,D]]. This is done purposely to increase performance;  if
           you want function  to  resize  array  according  to  result  size,  use
           function with same name and suffix 'I'.

        SEE ALSO
        * KDTreeQueryResultsX()             X-values
        * KDTreeQueryResultsXY()            X- and Y-values
        * KDTreeQueryResultsTags()          tag values

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsdistances(kdtree kdt,
            ref double[] r)
        {
            int i = 0;
            int k = 0;

            if( kdt.kcur==0 )
            {
                return;
            }
            if( ap.len(r)<kdt.kcur )
            {
                r = new double[kdt.kcur];
            }
            k = kdt.kcur;
            
            //
            // unload norms
            //
            // Abs() call is used to handle cases with negative norms
            // (generated during KFN requests)
            //
            if( kdt.normtype==0 )
            {
                for(i=0; i<=k-1; i++)
                {
                    r[i] = Math.Abs(kdt.r[i]);
                }
            }
            if( kdt.normtype==1 )
            {
                for(i=0; i<=k-1; i++)
                {
                    r[i] = Math.Abs(kdt.r[i]);
                }
            }
            if( kdt.normtype==2 )
            {
                for(i=0; i<=k-1; i++)
                {
                    r[i] = Math.Sqrt(Math.Abs(kdt.r[i]));
                }
            }
        }


        /*************************************************************************
        X-values from last query; 'interactive' variant for languages like  Python
        which   support    constructs   like  "X = KDTreeQueryResultsXI(KDT)"  and
        interactive mode of interpreter.

        This function allocates new array on each call,  so  it  is  significantly
        slower than its 'non-interactive' counterpart, but it is  more  convenient
        when you call it from command line.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsxi(kdtree kdt,
            ref double[,] x)
        {
            x = new double[0,0];

            kdtreequeryresultsx(kdt, ref x);
        }


        /*************************************************************************
        XY-values from last query; 'interactive' variant for languages like Python
        which   support    constructs   like "XY = KDTreeQueryResultsXYI(KDT)" and
        interactive mode of interpreter.

        This function allocates new array on each call,  so  it  is  significantly
        slower than its 'non-interactive' counterpart, but it is  more  convenient
        when you call it from command line.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsxyi(kdtree kdt,
            ref double[,] xy)
        {
            xy = new double[0,0];

            kdtreequeryresultsxy(kdt, ref xy);
        }


        /*************************************************************************
        Tags  from  last  query;  'interactive' variant for languages like  Python
        which  support  constructs  like "Tags = KDTreeQueryResultsTagsI(KDT)" and
        interactive mode of interpreter.

        This function allocates new array on each call,  so  it  is  significantly
        slower than its 'non-interactive' counterpart, but it is  more  convenient
        when you call it from command line.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultstagsi(kdtree kdt,
            ref int[] tags)
        {
            tags = new int[0];

            kdtreequeryresultstags(kdt, ref tags);
        }


        /*************************************************************************
        Distances from last query; 'interactive' variant for languages like Python
        which  support  constructs   like  "R = KDTreeQueryResultsDistancesI(KDT)"
        and interactive mode of interpreter.

        This function allocates new array on each call,  so  it  is  significantly
        slower than its 'non-interactive' counterpart, but it is  more  convenient
        when you call it from command line.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void kdtreequeryresultsdistancesi(kdtree kdt,
            ref double[] r)
        {
            r = new double[0];

            kdtreequeryresultsdistances(kdt, ref r);
        }


        /*************************************************************************
        Rearranges nodes [I1,I2) using partition in D-th dimension with S as threshold.
        Returns split position I3: [I1,I3) and [I3,I2) are created as result.

        This subroutine doesn't create tree structures, just rearranges nodes.
        *************************************************************************/
        private static void kdtreesplit(kdtree kdt,
            int i1,
            int i2,
            int d,
            double s,
            ref int i3)
        {
            int i = 0;
            int j = 0;
            int ileft = 0;
            int iright = 0;
            double v = 0;

            i3 = 0;

            
            //
            // split XY/Tags in two parts:
            // * [ILeft,IRight] is non-processed part of XY/Tags
            //
            // After cycle is done, we have Ileft=IRight. We deal with
            // this element separately.
            //
            // After this, [I1,ILeft) contains left part, and [ILeft,I2)
            // contains right part.
            //
            ileft = i1;
            iright = i2-1;
            while( ileft<iright )
            {
                if( (double)(kdt.xy[ileft,d])<=(double)(s) )
                {
                    
                    //
                    // XY[ILeft] is on its place.
                    // Advance ILeft.
                    //
                    ileft = ileft+1;
                }
                else
                {
                    
                    //
                    // XY[ILeft,..] must be at IRight.
                    // Swap and advance IRight.
                    //
                    for(i=0; i<=2*kdt.nx+kdt.ny-1; i++)
                    {
                        v = kdt.xy[ileft,i];
                        kdt.xy[ileft,i] = kdt.xy[iright,i];
                        kdt.xy[iright,i] = v;
                    }
                    j = kdt.tags[ileft];
                    kdt.tags[ileft] = kdt.tags[iright];
                    kdt.tags[iright] = j;
                    iright = iright-1;
                }
            }
            if( (double)(kdt.xy[ileft,d])<=(double)(s) )
            {
                ileft = ileft+1;
            }
            else
            {
                iright = iright-1;
            }
            i3 = ileft;
        }


        /*************************************************************************
        Recursive kd-tree generation subroutine.

        PARAMETERS
            KDT         tree
            NodesOffs   unused part of Nodes[] which must be filled by tree
            SplitsOffs  unused part of Splits[]
            I1, I2      points from [I1,I2) are processed
            
        NodesOffs[] and SplitsOffs[] must be large enough.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        private static void kdtreegeneratetreerec(kdtree kdt,
            ref int nodesoffs,
            ref int splitsoffs,
            int i1,
            int i2,
            int maxleafsize)
        {
            int n = 0;
            int nx = 0;
            int ny = 0;
            int i = 0;
            int j = 0;
            int oldoffs = 0;
            int i3 = 0;
            int cntless = 0;
            int cntgreater = 0;
            double minv = 0;
            double maxv = 0;
            int minidx = 0;
            int maxidx = 0;
            int d = 0;
            double ds = 0;
            double s = 0;
            double v = 0;
            int i_ = 0;
            int i1_ = 0;

            ap.assert(i2>i1, "KDTreeGenerateTreeRec: internal error");
            
            //
            // Generate leaf if needed
            //
            if( i2-i1<=maxleafsize )
            {
                kdt.nodes[nodesoffs+0] = i2-i1;
                kdt.nodes[nodesoffs+1] = i1;
                nodesoffs = nodesoffs+2;
                return;
            }
            
            //
            // Load values for easier access
            //
            nx = kdt.nx;
            ny = kdt.ny;
            
            //
            // select dimension to split:
            // * D is a dimension number
            //
            d = 0;
            ds = kdt.curboxmax[0]-kdt.curboxmin[0];
            for(i=1; i<=nx-1; i++)
            {
                v = kdt.curboxmax[i]-kdt.curboxmin[i];
                if( (double)(v)>(double)(ds) )
                {
                    ds = v;
                    d = i;
                }
            }
            
            //
            // Select split position S using sliding midpoint rule,
            // rearrange points into [I1,I3) and [I3,I2)
            //
            s = kdt.curboxmin[d]+0.5*ds;
            i1_ = (i1) - (0);
            for(i_=0; i_<=i2-i1-1;i_++)
            {
                kdt.buf[i_] = kdt.xy[i_+i1_,d];
            }
            n = i2-i1;
            cntless = 0;
            cntgreater = 0;
            minv = kdt.buf[0];
            maxv = kdt.buf[0];
            minidx = i1;
            maxidx = i1;
            for(i=0; i<=n-1; i++)
            {
                v = kdt.buf[i];
                if( (double)(v)<(double)(minv) )
                {
                    minv = v;
                    minidx = i1+i;
                }
                if( (double)(v)>(double)(maxv) )
                {
                    maxv = v;
                    maxidx = i1+i;
                }
                if( (double)(v)<(double)(s) )
                {
                    cntless = cntless+1;
                }
                if( (double)(v)>(double)(s) )
                {
                    cntgreater = cntgreater+1;
                }
            }
            if( cntless>0 & cntgreater>0 )
            {
                
                //
                // normal midpoint split
                //
                kdtreesplit(kdt, i1, i2, d, s, ref i3);
            }
            else
            {
                
                //
                // sliding midpoint
                //
                if( cntless==0 )
                {
                    
                    //
                    // 1. move split to MinV,
                    // 2. place one point to the left bin (move to I1),
                    //    others - to the right bin
                    //
                    s = minv;
                    if( minidx!=i1 )
                    {
                        for(i=0; i<=2*kdt.nx+kdt.ny-1; i++)
                        {
                            v = kdt.xy[minidx,i];
                            kdt.xy[minidx,i] = kdt.xy[i1,i];
                            kdt.xy[i1,i] = v;
                        }
                        j = kdt.tags[minidx];
                        kdt.tags[minidx] = kdt.tags[i1];
                        kdt.tags[i1] = j;
                    }
                    i3 = i1+1;
                }
                else
                {
                    
                    //
                    // 1. move split to MaxV,
                    // 2. place one point to the right bin (move to I2-1),
                    //    others - to the left bin
                    //
                    s = maxv;
                    if( maxidx!=i2-1 )
                    {
                        for(i=0; i<=2*kdt.nx+kdt.ny-1; i++)
                        {
                            v = kdt.xy[maxidx,i];
                            kdt.xy[maxidx,i] = kdt.xy[i2-1,i];
                            kdt.xy[i2-1,i] = v;
                        }
                        j = kdt.tags[maxidx];
                        kdt.tags[maxidx] = kdt.tags[i2-1];
                        kdt.tags[i2-1] = j;
                    }
                    i3 = i2-1;
                }
            }
            
            //
            // Generate 'split' node
            //
            kdt.nodes[nodesoffs+0] = 0;
            kdt.nodes[nodesoffs+1] = d;
            kdt.nodes[nodesoffs+2] = splitsoffs;
            kdt.splits[splitsoffs+0] = s;
            oldoffs = nodesoffs;
            nodesoffs = nodesoffs+splitnodesize;
            splitsoffs = splitsoffs+1;
            
            //
            // Recirsive generation:
            // * update CurBox
            // * call subroutine
            // * restore CurBox
            //
            kdt.nodes[oldoffs+3] = nodesoffs;
            v = kdt.curboxmax[d];
            kdt.curboxmax[d] = s;
            kdtreegeneratetreerec(kdt, ref nodesoffs, ref splitsoffs, i1, i3, maxleafsize);
            kdt.curboxmax[d] = v;
            kdt.nodes[oldoffs+4] = nodesoffs;
            v = kdt.curboxmin[d];
            kdt.curboxmin[d] = s;
            kdtreegeneratetreerec(kdt, ref nodesoffs, ref splitsoffs, i3, i2, maxleafsize);
            kdt.curboxmin[d] = v;
        }


        /*************************************************************************
        Recursive subroutine for NN queries.

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        private static void kdtreequerynnrec(kdtree kdt,
            int offs)
        {
            double ptdist = 0;
            int i = 0;
            int j = 0;
            int nx = 0;
            int i1 = 0;
            int i2 = 0;
            int d = 0;
            double s = 0;
            double v = 0;
            double t1 = 0;
            int childbestoffs = 0;
            int childworstoffs = 0;
            int childoffs = 0;
            double prevdist = 0;
            bool todive = new bool();
            bool bestisleft = new bool();
            bool updatemin = new bool();

            
            //
            // Leaf node.
            // Process points.
            //
            if( kdt.nodes[offs]>0 )
            {
                i1 = kdt.nodes[offs+1];
                i2 = i1+kdt.nodes[offs];
                for(i=i1; i<=i2-1; i++)
                {
                    
                    //
                    // Calculate distance
                    //
                    ptdist = 0;
                    nx = kdt.nx;
                    if( kdt.normtype==0 )
                    {
                        for(j=0; j<=nx-1; j++)
                        {
                            ptdist = Math.Max(ptdist, Math.Abs(kdt.xy[i,j]-kdt.x[j]));
                        }
                    }
                    if( kdt.normtype==1 )
                    {
                        for(j=0; j<=nx-1; j++)
                        {
                            ptdist = ptdist+Math.Abs(kdt.xy[i,j]-kdt.x[j]);
                        }
                    }
                    if( kdt.normtype==2 )
                    {
                        for(j=0; j<=nx-1; j++)
                        {
                            ptdist = ptdist+math.sqr(kdt.xy[i,j]-kdt.x[j]);
                        }
                    }
                    
                    //
                    // Skip points with zero distance if self-matches are turned off
                    //
                    if( (double)(ptdist)==(double)(0) & !kdt.selfmatch )
                    {
                        continue;
                    }
                    
                    //
                    // We CAN'T process point if R-criterion isn't satisfied,
                    // i.e. (RNeeded<>0) AND (PtDist>R).
                    //
                    if( (double)(kdt.rneeded)==(double)(0) | (double)(ptdist)<=(double)(kdt.rneeded) )
                    {
                        
                        //
                        // R-criterion is satisfied, we must either:
                        // * replace worst point, if (KNeeded<>0) AND (KCur=KNeeded)
                        //   (or skip, if worst point is better)
                        // * add point without replacement otherwise
                        //
                        if( kdt.kcur<kdt.kneeded | kdt.kneeded==0 )
                        {
                            
                            //
                            // add current point to heap without replacement
                            //
                            tsort.tagheappushi(ref kdt.r, ref kdt.idx, ref kdt.kcur, ptdist, i);
                        }
                        else
                        {
                            
                            //
                            // New points are added or not, depending on their distance.
                            // If added, they replace element at the top of the heap
                            //
                            if( (double)(ptdist)<(double)(kdt.r[0]) )
                            {
                                if( kdt.kneeded==1 )
                                {
                                    kdt.idx[0] = i;
                                    kdt.r[0] = ptdist;
                                }
                                else
                                {
                                    tsort.tagheapreplacetopi(ref kdt.r, ref kdt.idx, kdt.kneeded, ptdist, i);
                                }
                            }
                        }
                    }
                }
                return;
            }
            
            //
            // Simple split
            //
            if( kdt.nodes[offs]==0 )
            {
                
                //
                // Load:
                // * D  dimension to split
                // * S  split position
                //
                d = kdt.nodes[offs+1];
                s = kdt.splits[kdt.nodes[offs+2]];
                
                //
                // Calculate:
                // * ChildBestOffs      child box with best chances
                // * ChildWorstOffs     child box with worst chances
                //
                if( (double)(kdt.x[d])<=(double)(s) )
                {
                    childbestoffs = kdt.nodes[offs+3];
                    childworstoffs = kdt.nodes[offs+4];
                    bestisleft = true;
                }
                else
                {
                    childbestoffs = kdt.nodes[offs+4];
                    childworstoffs = kdt.nodes[offs+3];
                    bestisleft = false;
                }
                
                //
                // Navigate through childs
                //
                for(i=0; i<=1; i++)
                {
                    
                    //
                    // Select child to process:
                    // * ChildOffs      current child offset in Nodes[]
                    // * UpdateMin      whether minimum or maximum value
                    //                  of bounding box is changed on update
                    //
                    if( i==0 )
                    {
                        childoffs = childbestoffs;
                        updatemin = !bestisleft;
                    }
                    else
                    {
                        updatemin = bestisleft;
                        childoffs = childworstoffs;
                    }
                    
                    //
                    // Update bounding box and current distance
                    //
                    if( updatemin )
                    {
                        prevdist = kdt.curdist;
                        t1 = kdt.x[d];
                        v = kdt.curboxmin[d];
                        if( (double)(t1)<=(double)(s) )
                        {
                            if( kdt.normtype==0 )
                            {
                                kdt.curdist = Math.Max(kdt.curdist, s-t1);
                            }
                            if( kdt.normtype==1 )
                            {
                                kdt.curdist = kdt.curdist-Math.Max(v-t1, 0)+s-t1;
                            }
                            if( kdt.normtype==2 )
                            {
                                kdt.curdist = kdt.curdist-math.sqr(Math.Max(v-t1, 0))+math.sqr(s-t1);
                            }
                        }
                        kdt.curboxmin[d] = s;
                    }
                    else
                    {
                        prevdist = kdt.curdist;
                        t1 = kdt.x[d];
                        v = kdt.curboxmax[d];
                        if( (double)(t1)>=(double)(s) )
                        {
                            if( kdt.normtype==0 )
                            {
                                kdt.curdist = Math.Max(kdt.curdist, t1-s);
                            }
                            if( kdt.normtype==1 )
                            {
                                kdt.curdist = kdt.curdist-Math.Max(t1-v, 0)+t1-s;
                            }
                            if( kdt.normtype==2 )
                            {
                                kdt.curdist = kdt.curdist-math.sqr(Math.Max(t1-v, 0))+math.sqr(t1-s);
                            }
                        }
                        kdt.curboxmax[d] = s;
                    }
                    
                    //
                    // Decide: to dive into cell or not to dive
                    //
                    if( (double)(kdt.rneeded)!=(double)(0) & (double)(kdt.curdist)>(double)(kdt.rneeded) )
                    {
                        todive = false;
                    }
                    else
                    {
                        if( kdt.kcur<kdt.kneeded | kdt.kneeded==0 )
                        {
                            
                            //
                            // KCur<KNeeded (i.e. not all points are found)
                            //
                            todive = true;
                        }
                        else
                        {
                            
                            //
                            // KCur=KNeeded, decide to dive or not to dive
                            // using point position relative to bounding box.
                            //
                            todive = (double)(kdt.curdist)<=(double)(kdt.r[0]*kdt.approxf);
                        }
                    }
                    if( todive )
                    {
                        kdtreequerynnrec(kdt, childoffs);
                    }
                    
                    //
                    // Restore bounding box and distance
                    //
                    if( updatemin )
                    {
                        kdt.curboxmin[d] = v;
                    }
                    else
                    {
                        kdt.curboxmax[d] = v;
                    }
                    kdt.curdist = prevdist;
                }
                return;
            }
        }


        /*************************************************************************
        Copies X[] to KDT.X[]
        Loads distance from X[] to bounding box.
        Initializes CurBox[].

          -- ALGLIB --
             Copyright 28.02.2010 by Bochkanov Sergey
        *************************************************************************/
        private static void kdtreeinitbox(kdtree kdt,
            double[] x)
        {
            int i = 0;
            double vx = 0;
            double vmin = 0;
            double vmax = 0;

            
            //
            // calculate distance from point to current bounding box
            //
            kdt.curdist = 0;
            if( kdt.normtype==0 )
            {
                for(i=0; i<=kdt.nx-1; i++)
                {
                    vx = x[i];
                    vmin = kdt.boxmin[i];
                    vmax = kdt.boxmax[i];
                    kdt.x[i] = vx;
                    kdt.curboxmin[i] = vmin;
                    kdt.curboxmax[i] = vmax;
                    if( (double)(vx)<(double)(vmin) )
                    {
                        kdt.curdist = Math.Max(kdt.curdist, vmin-vx);
                    }
                    else
                    {
                        if( (double)(vx)>(double)(vmax) )
                        {
                            kdt.curdist = Math.Max(kdt.curdist, vx-vmax);
                        }
                    }
                }
            }
            if( kdt.normtype==1 )
            {
                for(i=0; i<=kdt.nx-1; i++)
                {
                    vx = x[i];
                    vmin = kdt.boxmin[i];
                    vmax = kdt.boxmax[i];
                    kdt.x[i] = vx;
                    kdt.curboxmin[i] = vmin;
                    kdt.curboxmax[i] = vmax;
                    if( (double)(vx)<(double)(vmin) )
                    {
                        kdt.curdist = kdt.curdist+vmin-vx;
                    }
                    else
                    {
                        if( (double)(vx)>(double)(vmax) )
                        {
                            kdt.curdist = kdt.curdist+vx-vmax;
                        }
                    }
                }
            }
            if( kdt.normtype==2 )
            {
                for(i=0; i<=kdt.nx-1; i++)
                {
                    vx = x[i];
                    vmin = kdt.boxmin[i];
                    vmax = kdt.boxmax[i];
                    kdt.x[i] = vx;
                    kdt.curboxmin[i] = vmin;
                    kdt.curboxmax[i] = vmax;
                    if( (double)(vx)<(double)(vmin) )
                    {
                        kdt.curdist = kdt.curdist+math.sqr(vmin-vx);
                    }
                    else
                    {
                        if( (double)(vx)>(double)(vmax) )
                        {
                            kdt.curdist = kdt.curdist+math.sqr(vx-vmax);
                        }
                    }
                }
            }
        }


    }
}