/*************************************************************************
        Initialization of internal structures.

        It assumes correctness of all parameters.

          -- ALGLIB --
             Copyright 02.03.2010 by Bochkanov Sergey
        *************************************************************************/
        private static void idwinit1(int n,
            int nx,
            int d,
            int nq,
            int nw,
            idwinterpolant z)
        {
            z.debugsolverfailures = 0;
            z.debugworstrcond = 1.0;
            z.debugbestrcond = 0;
            z.n = n;
            z.nx = nx;
            z.d = 0;
            if( d==1 )
            {
                z.d = 1;
            }
            if( d==2 )
            {
                z.d = 2;
            }
            if( d==-1 )
            {
                z.d = 1;
            }
            z.nw = nw;
            if( d==-1 )
            {
                z.q = new double[n, nx+1+nx];
            }
            if( d==0 )
            {
                z.q = new double[n, nx+1];
            }
            if( d==1 )
            {
                z.q = new double[n, nx+1+nx];
            }
            if( d==2 )
            {
                z.q = new double[n, nx+1+nx+(int)Math.Round(nx*(nx+1)*0.5)];
            }
            z.tbuf = new int[nw];
            z.rbuf = new double[nw];
            z.xybuf = new double[nw, nx+1];
            z.xbuf = new double[nx];
        }

        /*************************************************************************
        IDW model for noisy data.

        This subroutine may be used to handle noisy data, i.e. data with noise  in
        OUTPUT values.  It differs from IDWBuildModifiedShepard() in the following
        aspects:
        * nodal functions are not constrained to pass through  nodes:  Qi(xi)<>yi,
          i.e. we have fitting  instead  of  interpolation.
        * weights which are used during least  squares fitting stage are all equal
          to 1.0 (independently of distance)
        * "fast"-linear or constant nodal functions are not supported (either  not
          robust enough or too rigid)

        This problem require far more complex tuning than interpolation  problems.
        Below you can find some recommendations regarding this problem:
        * focus on tuning NQ; it controls noise reduction. As for NW, you can just
          make it equal to 2*NQ.
        * you can use cross-validation to determine optimal NQ.
        * optimal NQ is a result of complex tradeoff  between  noise  level  (more
          noise = larger NQ required) and underlying  function  complexity  (given
          fixed N, larger NQ means smoothing of compex features in the data).  For
          example, NQ=N will reduce noise to the minimum level possible,  but  you
          will end up with just constant/linear/quadratic (depending on  D)  least
          squares model for the whole dataset.

        INPUT PARAMETERS:
            XY  -   X and Y values, array[0..N-1,0..NX].
                    First NX columns contain X-values, last column contain
                    Y-values.
            N   -   number of nodes, N>0.
            NX  -   space dimension, NX>=1.
            D   -   nodal function degree, either:
                    * 1     linear model, least squares fitting. Simpe  model  for
                            datasets too small for quadratic models (or  for  very
                            noisy problems).
                    * 2     quadratic  model,  least  squares  fitting. Best model
                            available (if your dataset is large enough).
            NQ  -   number of points used to calculate nodal functions.  NQ should
                    be  significantly   larger   than  1.5  times  the  number  of
                    coefficients in a nodal function to overcome effects of noise:
                    * larger than 1.5*(1+NX) for linear model,
                    * larger than 3/4*(NX+2)*(NX+1) for quadratic model.
                    Values less than this threshold will be silently increased.
            NW  -   number of points used to calculate weights and to interpolate.
                    Required: >=2^NX+1, values less than this  threshold  will  be
                    silently increased.
                    Recommended value: about 2*NQ or larger

        OUTPUT PARAMETERS:
            Z   -   IDW interpolant.

        NOTES:
          * best results are obtained with quadratic models, linear models are not
            recommended to use unless you are pretty sure that it is what you want
          * this subroutine is always succeeds (as long as correct parameters  are
            passed).
          * see  'Multivariate  Interpolation  of Large Sets of Scattered Data' by
            Robert J. Renka for more information on this algorithm.


          -- ALGLIB PROJECT --
             Copyright 02.03.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void idwbuildnoisy(double[,] xy,
            int n,
            int nx,
            int d,
            int nq,
            int nw,
            idwinterpolant z)
        {
            int i = 0;
            int j = 0;
            int k = 0;
            int j2 = 0;
            int j3 = 0;
            double v = 0;
            int nc = 0;
            int offs = 0;
            double taskrcond = 0;
            double[] x = new double[0];
            double[] qrbuf = new double[0];
            double[,] qxybuf = new double[0,0];
            double[] y = new double[0];
            double[] w = new double[0];
            double[,] fmatrix = new double[0,0];
            double[] qsol = new double[0];
            int[] tags = new int[0];
            double[] temp = new double[0];
            int info = 0;
            int i_ = 0;

            
            //
            // these initializers are not really necessary,
            // but without them compiler complains about uninitialized locals
            //
            nc = 0;
            
            //
//.........这里部分代码省略.........

        /*************************************************************************
        Internal subroutine: K-th nodal function calculation

          -- ALGLIB --
             Copyright 02.03.2010 by Bochkanov Sergey
        *************************************************************************/
        private static double idwcalcq(idwinterpolant z,
            double[] x,
            int k)
        {
            double result = 0;
            int nx = 0;
            int i = 0;
            int j = 0;
            int offs = 0;

            nx = z.nx;
            
            //
            // constant member
            //
            result = z.q[k,nx];
            
            //
            // linear members
            //
            if( z.d>=1 )
            {
                for(i=0; i<=nx-1; i++)
                {
                    result = result+z.q[k,nx+1+i]*(x[i]-z.q[k,i]);
                }
            }
            
            //
            // quadratic members
            //
            if( z.d>=2 )
            {
                offs = nx+1+nx;
                for(i=0; i<=nx-1; i++)
                {
                    for(j=i; j<=nx-1; j++)
                    {
                        result = result+z.q[k,offs]*(x[i]-z.q[k,i])*(x[j]-z.q[k,j]);
                        offs = offs+1;
                    }
                }
            }
            return result;
        }

    /*************************************************************************
    IDW interpolation

    INPUT PARAMETERS:
        Z   -   IDW interpolant built with one of model building
                subroutines.
        X   -   array[0..NX-1], interpolation point

    Result:
        IDW interpolant Z(X)

      -- ALGLIB --
         Copyright 02.03.2010 by Bochkanov Sergey
    *************************************************************************/
    public static double idwcalc(idwinterpolant z, double[] x)
    {

        double result = idwint.idwcalc(z.innerobj, x);
        return result;
    }

        /*************************************************************************
        IDW interpolant using modified Shepard method for non-uniform datasets.

        This type of model uses  constant  nodal  functions and interpolates using
        all nodes which are closer than user-specified radius R. It  may  be  used
        when points distribution is non-uniform at the small scale, but it  is  at
        the distances as large as R.

        INPUT PARAMETERS:
            XY  -   X and Y values, array[0..N-1,0..NX].
                    First NX columns contain X-values, last column contain
                    Y-values.
            N   -   number of nodes, N>0.
            NX  -   space dimension, NX>=1.
            R   -   radius, R>0

        OUTPUT PARAMETERS:
            Z   -   IDW interpolant.

        NOTES:
        * if there is less than IDWKMin points within  R-ball,  algorithm  selects
          IDWKMin closest ones, so that continuity properties of  interpolant  are
          preserved even far from points.

          -- ALGLIB PROJECT --
             Copyright 11.04.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void idwbuildmodifiedshepardr(double[,] xy,
            int n,
            int nx,
            double r,
            idwinterpolant z)
        {
            int i = 0;
            int[] tags = new int[0];
            int i_ = 0;

            
            //
            // assertions
            //
            alglib.ap.assert(n>0, "IDWBuildModifiedShepardR: N<=0!");
            alglib.ap.assert(nx>=1, "IDWBuildModifiedShepardR: NX<1!");
            alglib.ap.assert((double)(r)>(double)(0), "IDWBuildModifiedShepardR: R<=0!");
            
            //
            // primary initialization of Z
            //
            idwinit1(n, nx, 0, 0, n, z);
            z.modeltype = 1;
            z.r = r;
            
            //
            // Create KD-tree
            //
            tags = new int[n];
            for(i=0; i<=n-1; i++)
            {
                tags[i] = i;
            }
            nearestneighbor.kdtreebuildtagged(xy, tags, n, nx, 1, 2, z.tree);
            
            //
            // build nodal functions
            //
            for(i=0; i<=n-1; i++)
            {
                for(i_=0; i_<=nx;i_++)
                {
                    z.q[i,i_] = xy[i,i_];
                }
            }
        }

        /*************************************************************************
        IDW interpolant using modified Shepard method for uniform point
        distributions.

        INPUT PARAMETERS:
            XY  -   X and Y values, array[0..N-1,0..NX].
                    First NX columns contain X-values, last column contain
                    Y-values.
            N   -   number of nodes, N>0.
            NX  -   space dimension, NX>=1.
            D   -   nodal function type, either:
                    * 0     constant  model.  Just  for  demonstration only, worst
                            model ever.
                    * 1     linear model, least squares fitting. Simpe  model  for
                            datasets too small for quadratic models
                    * 2     quadratic  model,  least  squares  fitting. Best model
                            available (if your dataset is large enough).
                    * -1    "fast"  linear  model,  use  with  caution!!!   It  is
                            significantly  faster than linear/quadratic and better
                            than constant model. But it is less robust (especially
                            in the presence of noise).
            NQ  -   number of points used to calculate  nodal  functions  (ignored
                    for constant models). NQ should be LARGER than:
                    * max(1.5*(1+NX),2^NX+1) for linear model,
                    * max(3/4*(NX+2)*(NX+1),2^NX+1) for quadratic model.
                    Values less than this threshold will be silently increased.
            NW  -   number of points used to calculate weights and to interpolate.
                    Required: >=2^NX+1, values less than this  threshold  will  be
                    silently increased.
                    Recommended value: about 2*NQ

        OUTPUT PARAMETERS:
            Z   -   IDW interpolant.
            
        NOTES:
          * best results are obtained with quadratic models, worst - with constant
            models
          * when N is large, NQ and NW must be significantly smaller than  N  both
            to obtain optimal performance and to obtain optimal accuracy. In 2  or
            3-dimensional tasks NQ=15 and NW=25 are good values to start with.
          * NQ  and  NW  may  be  greater  than  N.  In  such  cases  they will be
            automatically decreased.
          * this subroutine is always succeeds (as long as correct parameters  are
            passed).
          * see  'Multivariate  Interpolation  of Large Sets of Scattered Data' by
            Robert J. Renka for more information on this algorithm.
          * this subroutine assumes that point distribution is uniform at the small
            scales.  If  it  isn't  -  for  example,  points are concentrated along
            "lines", but "lines" distribution is uniform at the larger scale - then
            you should use IDWBuildModifiedShepardR()


          -- ALGLIB PROJECT --
             Copyright 02.03.2010 by Bochkanov Sergey
        *************************************************************************/
        public static void idwbuildmodifiedshepard(double[,] xy,
            int n,
            int nx,
            int d,
            int nq,
            int nw,
            idwinterpolant z)
        {
            int i = 0;
            int j = 0;
            int k = 0;
            int j2 = 0;
            int j3 = 0;
            double v = 0;
            double r = 0;
            double s = 0;
            double d0 = 0;
            double di = 0;
            double v1 = 0;
            double v2 = 0;
            int nc = 0;
            int offs = 0;
            double[] x = new double[0];
            double[] qrbuf = new double[0];
            double[,] qxybuf = new double[0,0];
            double[] y = new double[0];
            double[,] fmatrix = new double[0,0];
            double[] w = new double[0];
            double[] qsol = new double[0];
            double[] temp = new double[0];
            int[] tags = new int[0];
            int info = 0;
            double taskrcond = 0;
            int i_ = 0;

            
            //
            // these initializers are not really necessary,
            // but without them compiler complains about uninitialized locals
            //
            nc = 0;
            
            //
            // assertions
            //
//.........这里部分代码省略.........

 public override alglib.apobject make_copy()
 {
     idwinterpolant _result = new idwinterpolant();
     _result.n = n;
     _result.nx = nx;
     _result.d = d;
     _result.r = r;
     _result.nw = nw;
     _result.tree = (nearestneighbor.kdtree)tree.make_copy();
     _result.modeltype = modeltype;
     _result.q = (double[,])q.Clone();
     _result.xbuf = (double[])xbuf.Clone();
     _result.tbuf = (int[])tbuf.Clone();
     _result.rbuf = (double[])rbuf.Clone();
     _result.xybuf = (double[,])xybuf.Clone();
     _result.debugsolverfailures = debugsolverfailures;
     _result.debugworstrcond = debugworstrcond;
     _result.debugbestrcond = debugbestrcond;
     return _result;
 }