// Gmsh - Copyright (C) 1997-2012 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
//
// Contributed by Cecile Piret

#include "GmshConfig.h"
#include "GRbf.h"
#include <math.h>
#include <vector>
#include "fullMatrix.h"
#include "Octree.h"
#include "SPoint3.h"
#include "SVector3.h"
#include "SBoundingBox3d.h"
#include "OS.h"
#include "MVertex.h"
#include "MVertexPositionSet.h"

#if defined(HAVE_SOLVER)
#include "linearSystem.h"
#endif

#if defined(HAVE_ANN)
#include <ANN/ANN.h>
#endif

static void SphereBB(void *a, double*mmin, double*mmax)
{
  Sphere *t = (Sphere *)a;
  mmin[0] = t->center.x()-t->radius;
  mmin[1] = t->center.y()-t->radius;
  mmin[2] = t->center.z()-t->radius;
  mmax[0] = t->center.x()+t->radius;
  mmax[1] = t->center.y()+t->radius;
  mmax[2] = t->center.z()+t->radius;
}

static void SphereCentroid(void *a, double*c)
{
  Sphere *t = (Sphere *)a;
  c[0] = t->center.x();
  c[1] = t->center.y();
  c[2] = t->center.z();
}

static int SphereInEle(void *a, double*c)
{
  Sphere *t = (Sphere *)a;
  double dist = sqrt((c[0]-t->center.x())*(c[0]-t->center.x())+
		     (c[1]-t->center.y())*(c[1]-t->center.y())+
		     (c[2]-t->center.z())*(c[2]-t->center.z()) );
  if(dist < t->radius){
    return 1;
  }
  return 0;
}

static void printNodes(std::set<MVertex *> myNodes)
{
  FILE * xyz = fopen("myNodes.pos","w");
  fprintf(xyz,"View \"\"{\n");
 for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end(); ++itv){
   MVertex *v = *itv;
   fprintf(xyz,"SP(%g,%g,%g){%d};\n", v->x(), v->y(), v->z(), v->getNum());
 }
 fprintf(xyz,"};\n");
 fclose(xyz);
}

static void exportParametrizedMesh(fullMatrix<double> &UV, int nbNodes)
{
  FILE *f = fopen ("UV.pos", "w");
  fprintf(f,"View  \" uv \" {\n");

  Msg::Info("*** RBF exporting 'UV.pos' ");
  for(int id = 0; id < nbNodes; id++){
    fprintf(f,"SP(%g,%g,%g){%d};\n", UV(id,0), UV(id,1), 0.0, id);
  }
  fprintf(f,"};\n");

  fclose(f);
}

GRbf::GRbf(double sizeBox, int variableEps, int rbfFun,
           std::map<MVertex*, SVector3> _normals,
           std::set<MVertex *> allNodes, std::vector<MVertex*> bcNodes, bool _isLocal)
  :  isLocal(_isLocal), _inUV(0), sBox(sizeBox), variableShapeParam(variableEps),
     radialFunctionIndex (rbfFun)

{
#if defined (HAVE_ANN)
  XYZkdtree = 0;
#endif

  allCenters.resize(allNodes.size(),3);
  double tol =  4.e-2*sBox;
  if (isLocal) tol = 1.e-15;

  // remove duplicate vertices
  // add bc nodes
  for(unsigned int i = 0; i < bcNodes.size(); i++){
    myNodes.insert(bcNodes[i]);
    //if (bcNodes.size()  > 20) i+=2;
  }

  // then create Mvertex position
  std::vector<MVertex*> vertices( allNodes.begin(), allNodes.end() );
  MVertexPositionSet pos(vertices);
  for(unsigned int i = 0; i < vertices.size(); i++){
    MVertex *v = vertices[i];
    pos.find(v->x(), v->y(), v->z(), tol);
    allCenters(i,0) = v->x()/sBox;
    allCenters(i,1) = v->y()/sBox;
    allCenters(i,2) = v->z()/sBox;
    _mapAllV.insert(std::make_pair(v, i));
  }
  // keep only no duplicate vertices
  for(unsigned int i = 0; i < vertices.size(); i++)
    if(vertices[i]->getIndex()) myNodes.insert(vertices[i]);

  // initialize with  points
  nbNodes= myNodes.size();
  centers.resize(nbNodes,3);
  normals.resize(nbNodes,3);
  int index = 0;
  double dist_min = 1.e6;
  for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end(); ++itv){
    MVertex *v1 = *itv;
    centers(index,0) = v1->x()/sBox;
    centers(index,1) = v1->y()/sBox;
    centers(index,2) = v1->z()/sBox;
    std::map<MVertex*, SVector3>::iterator itn = _normals.find(v1);
    if (itn != _normals.end()){
      normals(index,0) = itn->second.x();
      normals(index,1) = itn->second.y();
      normals(index,2) = itn->second.z();
    }
    _mapV.insert(std::make_pair(v1, index));
    for(std::set<MVertex *>::iterator itv2 = myNodes.begin(); itv2 !=myNodes.end(); itv2++){
      MVertex *v2 = *itv2;
      double dist = sqrt((v1->x()-v2->x())*(v1->x()-v2->x())+
                         (v1->y()-v2->y())*(v1->y()-v2->y())+
                         (v1->z()-v2->z())*(v1->z()-v2->z()))/sBox;
      if (dist < dist_min && *itv != *itv2 && dist > 1.e-5) dist_min = dist;
    }
    index++;
  }

  delta = dist_min/10.0;//0.33

  //radius = 1.0/15.0 //curvature setting
  radius= 1.0/6.0; //size 1 is non dim size

  Msg::Info("*****************************************");
  Msg::Info("*** RBF nbNodes=%d (all=%d) ", myNodes.size(), allNodes.size());
  Msg::Info("*** RBF rad=%g dist_min =%g", radius, dist_min);
  Msg::Info("*****************************************");

  printNodes(myNodes);

  if (!isLocal){
    matAInv.resize(nbNodes, nbNodes);
    matAInv = generateRbfMat(0,centers,centers);
    matAInv.invertInPlace();
  }

  extendedX.resize(3*nbNodes,3);
}

GRbf::~GRbf()
{
#if defined (HAVE_ANN)
  ANNpointArray XYZNodes = XYZkdtree->thePoints();
  ANNpointArray UVNodes = UVkdtree->thePoints();
  annDeallocPts(XYZNodes);
  annDeallocPts(UVNodes);
  delete XYZkdtree;
  delete UVkdtree;
#endif
}

void GRbf::buildXYZkdtree()
{
#if defined (HAVE_ANN)
  ANNpointArray XYZnodes = annAllocPts(nbNodes, 3);
  for(int i = 0; i < nbNodes; i++){
    XYZnodes[i][0] = centers(i,0);
    XYZnodes[i][1] = centers(i,1);
    XYZnodes[i][2] = centers(i,2);
  }
  XYZkdtree = new ANNkd_tree(XYZnodes, nbNodes, 3);
#endif
}

void GRbf::buildOctree(double radius)
{
  //printf("building octree radius = %g \n", radius);
  SBoundingBox3d bb;
  for (int i = 0; i < nbNodes; i++)
    bb += SPoint3(centers(i,0),centers(i,1), centers(i,2));
  double origin[3] = {bb.min().x(), bb.min().y(), bb.min().z()};
  double ssize[3] = {bb.max().x() - bb.min().x(),
                     bb.max().y() - bb.min().y(),
                     bb.max().z() - bb.min().z()};
  const int maxElePerBucket = 10;
  Octree *oct = Octree_Create(maxElePerBucket, origin, ssize, SphereBB,
			      SphereCentroid, SphereInEle);

  Sphere *_sph = new Sphere[nbNodes];
  for (int i = 0; i < nbNodes; i++){
    _sph[i].index = i;
    _sph[i].radius = radius;
    _sph[i].center = SPoint3(centers(i,0),centers(i,1), centers(i,2));
    Octree_Insert(&_sph[i], oct);
  }
  Octree_Arrange(oct);

  for (int i = 0; i < nbNodes; i++){
    std::vector<void*> l;
    double P[3] = {centers(i,0),centers(i,1), centers(i,2)};
    Octree_SearchAll(P, oct, &l);
    nodesInSphere[i].push_back(i);
    if (l.size() == 1) printf("*** WARNING: Found only %d sphere ! \n", (int)l.size());
    for (std::vector<void*>::iterator it = l.begin(); it != l.end(); it++) {
      Sphere *sph = (Sphere*) *it;
      if (sph->index != i) nodesInSphere[i].push_back(sph->index);
    }
    //printf("size node i =%d = %d \n", i , nodesInSphere[i].size());
  }

  Octree_Delete(oct);
  buildXYZkdtree();
}

// compute curvature from level set
void GRbf::curvatureRBF(const fullMatrix<double> &cntrs,
			fullMatrix<double> &curvature)
{
	
	
  fullMatrix<double> extX, surf, sx,sy,sz, sxx,syy,szz, sxy,sxz,syz,sLap;
  setup_level_set(cntrs,normals,extX, surf);

  evalRbfDer(1,extX,cntrs,surf,sx);
  evalRbfDer(2,extX,cntrs,surf,sy);
  evalRbfDer(3,extX,cntrs,surf,sz);
  evalRbfDer(222,extX,cntrs,surf,sLap);

  for (int i = 0; i < cntrs.size1(); i++) {
    double norm_grad_s = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
    double curv = -sLap(i,0)/norm_grad_s;
    curvature(i,0) = 0.5*fabs(curv)/sBox;
  }
	
	
	
}

void GRbf::computeCurvature(const fullMatrix<double> &cntrs,
			    std::map<MVertex*, double> &rbf_curv)
{
  fullMatrix<double> extX, surf, sx,sy,sz, allsx,allsy,allsz;
  setup_level_set(cntrs,normals,extX, surf);
  // Find derivatives of the surface interpolant
  evalRbfDer(1,extX,extX,surf,sx);
  evalRbfDer(2,extX,extX,surf,sy);
  evalRbfDer(3,extX,extX,surf,sz);
  
  for (int i = 0; i < extX.size1(); i++) {
    double norm_grad_s = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
    sx(i,0) = sx(i,0)/norm_grad_s;
    sy(i,0) = sy(i,0)/norm_grad_s;
    sz(i,0) = sz(i,0)/norm_grad_s;
  }

  fullMatrix<double> curvatureAll(allCenters.size1(), 1);
  evalRbfDer(1,extX,allCenters,sx,allsx);
  evalRbfDer(2,extX,allCenters,sy,allsy);
  evalRbfDer(3,extX,allCenters,sz,allsz);

  for (int i = 0; i < allCenters.size1(); i++) {
    curvatureAll(i,0) = 0.5*(allsx(i,0)+allsy(i,0)+allsz(i,0))/sBox;
  }

  //fill rbf_curv
  std::map<MVertex*, int>::iterator itm = _mapAllV.begin();
  for (; itm != _mapAllV.end(); itm++){
    int index = itm->second;
    rbf_curv.insert(std::make_pair(itm->first,curvatureAll(index,0)));
  }

}

void GRbf::computeLocalCurvature(const fullMatrix<double> &cntrs,
				 std::map<MVertex*, double> &rbf_curv)
{
  fullMatrix<double> extX, surf;  
  int numNodes = cntrs.size1();
  int numExtNodes = 3*numNodes;
  setup_level_set(cntrs,normals,extX, surf);

  if(nodesInSphere.size() == 0) buildOctree(radius);
  fullMatrix<double> curvature(cntrs.size1(), 1);
  fullMatrix<double> Dx(numExtNodes,numExtNodes),Dy(numExtNodes,numExtNodes),Dz(numExtNodes,numExtNodes),tempX,tempY,tempZ,sx(numExtNodes,1),sy(numExtNodes,1),sz(numExtNodes,1);
  fullMatrix<double> cluster_center(3,3);
  for (int i = 0; i < numNodes; ++i) {
    std::vector<int> &pts = nodesInSphere[i];
    int cluster_size = pts.size();
    fullMatrix<double> nodes_in_sph(3*cluster_size,3);
    
    cluster_center(0,0) = extX(i,0);
    cluster_center(0,1) = extX(i,1);
    cluster_center(0,2) = extX(i,2);

    cluster_center(1,0) = extX(i+numNodes,0);
    cluster_center(1,1) = extX(i+numNodes,1);
    cluster_center(1,2) = extX(i+numNodes,2);

    cluster_center(2,0) = extX(i+2*numNodes,0);
    cluster_center(2,1) = extX(i+2*numNodes,1);
    cluster_center(2,2) = extX(i+2*numNodes,2);

    for (int k=0; k< cluster_size; k++){
      nodes_in_sph(k,0) = extX(pts[k],0);
      nodes_in_sph(k,1) = extX(pts[k],1);
      nodes_in_sph(k,2) = extX(pts[k],2);

      nodes_in_sph(k+cluster_size,0) = extX(pts[k]+numNodes,0);
      nodes_in_sph(k+cluster_size,1) = extX(pts[k]+numNodes,1);
      nodes_in_sph(k+cluster_size,2) = extX(pts[k]+numNodes,2);

      nodes_in_sph(k+2*cluster_size,0) = extX(pts[k]+2*numNodes,0);
      nodes_in_sph(k+2*cluster_size,1) = extX(pts[k]+2*numNodes,1);
      nodes_in_sph(k+2*cluster_size,2) = extX(pts[k]+2*numNodes,2);
    }

    RbfOp(1,nodes_in_sph,cluster_center,tempX);
    RbfOp(2,nodes_in_sph,cluster_center,tempY);
    RbfOp(3,nodes_in_sph,cluster_center,tempZ);

    for (int k=0; k< cluster_size; k++){
      for (int j=0; j< 3; j++){
	Dx(i+j*numNodes,pts[k]) = tempX(j,k);
	Dy(i+j*numNodes,pts[k]) = tempY(j,k);
	Dz(i+j*numNodes,pts[k]) = tempZ(j,k);
	
	Dx(i+j*numNodes,pts[k]+numNodes) = tempX(j,k+cluster_size);
	Dy(i+j*numNodes,pts[k]+numNodes) = tempY(j,k+cluster_size);
	Dz(i+j*numNodes,pts[k]+numNodes) = tempZ(j,k+cluster_size);
	
	Dx(i+j*numNodes,pts[k]+2*numNodes) = tempX(j,k+2*cluster_size);
	Dy(i+j*numNodes,pts[k]+2*numNodes) = tempY(j,k+2*cluster_size);
	Dz(i+j*numNodes,pts[k]+2*numNodes) = tempZ(j,k+2*cluster_size);
      }
    }
  }

    sx.gemm(Dx,surf, 1.0, 0.0);
    sy.gemm(Dy,surf, 1.0, 0.0);
    sz.gemm(Dz,surf, 1.0, 0.0);

    for (int i = 0; i < numExtNodes; i++) {
      double norm_grad_s = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
      sx(i,0) = sx(i,0)/norm_grad_s;
      sy(i,0) = sy(i,0)/norm_grad_s;
      sz(i,0) = sz(i,0)/norm_grad_s;
    }
    sx.gemm(Dx,sx, 1.0, 0.0);
    sy.gemm(Dy,sy, 1.0, 0.0);
    sz.gemm(Dz,sz, 1.0, 0.0); 

    printf("sBox = %g ",sBox);
    for (int i = 0; i < numNodes; i++) {
      curvature(i,0) = 0.5*(sx(i,0)+sy(i,0)+sz(i,0))/sBox;
    }
  std::map<MVertex*, int>::iterator itm = _mapAllV.begin();
  for (; itm != _mapAllV.end(); itm++) {
    int index = itm->second;
    rbf_curv.insert(std::make_pair(itm->first, curvature(index,0)));
  }
}

double GRbf::evalRadialFnDer (int p, double dx, double dy, double dz, double ep)
{
  double r2 = dx*dx+dy*dy+dz*dz; //r^2
  switch (radialFunctionIndex) {
  case 0 : // GA
    switch (p) {
    case 0: return exp(-ep*ep*r2);
    case 1: return -2.0*ep*ep*dx*exp(-ep*ep*r2); // _x
    case 2: return -2.0*ep*ep*dy*exp(-ep*ep*r2); // _y
    case 3: return -2.0*ep*ep*dz*exp(-ep*ep*r2); // _z
    case 11: return -2.0*ep*ep*(1.0-2.0*ep*ep*dx*dx)*exp(-ep*ep*r2); // _xx
    case 12: return 4.0*ep*ep*ep*ep*dx*dy*exp(-ep*ep*r2); // _xy
    case 13: return 4.0*ep*ep*ep*ep*dx*dz*exp(-ep*ep*r2); // ...
    case 22: return -2.0*ep*ep*(1.0-2.0*ep*ep*dy*dy)*exp(-ep*ep*r2);
    case 23: return 4.0*ep*ep*ep*ep*dy*dz*exp(-ep*ep*r2);
    case 33: return -2.0*ep*ep*(1.0-2.0*ep*ep*dz*dz)*exp(-ep*ep*r2);
    case 222: return -2.0*ep*ep*(3.0-2.0*ep*ep*r2)*exp(-ep*ep*r2); //Laplacian
    }
  case 1 : //MQ
    switch (p) {
    case 0: return sqrt(1.0+ep*ep*r2);
    case 1: return ep*ep*dx/sqrt(1.0+ep*ep*r2);
    case 2: return ep*ep*dy/sqrt(1.0+ep*ep*r2);
    case 3: return ep*ep*dz/sqrt(1.0+ep*ep*r2);
    case 11: return ep*ep*(1.0+ep*ep*dy*dy+ep*ep*dz*dz)/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2)); // _xx
    case 12: return -ep*ep*ep*ep*dx*dy/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2)); // _xy
    case 13: return -ep*ep*ep*ep*dx*dz/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2)); // ...
    case 22: return ep*ep*(1.0+ep*ep*dx*dx+ep*ep*dz*dz)/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2));
    case 23: return -ep*ep*ep*ep*dy*dz/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2));
    case 33: return ep*ep*(1.0+ep*ep*dx*dx+ep*ep*dy*dy)/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2));
    case 222: return ep*ep*(3.0+ep*ep*2.0*r2)/sqrt((1.0+ep*ep*r2)*(1.0+ep*ep*r2)*(1.0+ep*ep*r2));
    }
  }
  return 0.;
}

fullMatrix<double> GRbf::generateRbfMat(int p,
					const fullMatrix<double> &nodes1,
					const fullMatrix<double> &nodes2)
{
  int m = nodes2.size1();
  int n = nodes1.size1();
  fullMatrix<double> rbfMat(m,n);

  //curvature setting double eps = 0.1/delta;
  double eps = 1.0/(delta*10);//2*sqrt(n/radius);////0.5/delta; //0.0677*(nbNodes^0.28)/min_dist; //0.5
  //printf("Shape parameter = %g   ", eps);
  //printf("delta = %g    ", delta);

  if (_inUV) eps = 0.4/deltaUV;
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      double dx = nodes2(i,0)-nodes1(j,0);
      double dy = nodes2(i,1)-nodes1(j,1);
      double dz = nodes2(i,2)-nodes1(j,2);
      rbfMat(i,j) = evalRadialFnDer(p,dx,dy,dz,eps);
    }
  }

  return rbfMat;
}

//DL matrix (B*inv A)
void GRbf::RbfOp(int p,
		const fullMatrix<double> &cntrs,
		const fullMatrix<double> &nodes,
		 fullMatrix<double> &D)
{
  fullMatrix<double> rbfInvA, rbfMatB;

  D.resize(nodes.size1(), cntrs.size1());

  if (isLocal){
    rbfInvA = generateRbfMat(0,cntrs,cntrs);
    rbfInvA.invertInPlace();
   }
   else{
     if (cntrs.size1() == nbNodes )
       rbfInvA = matAInv;
     else if (cntrs.size1() == 3*nbNodes )
       rbfInvA  = matAInv_nn;
     else{
       rbfInvA = generateRbfMat(0,cntrs,cntrs);
       rbfInvA.invertInPlace();
     }
   }
  rbfMatB = generateRbfMat(p,cntrs,nodes);
  D.gemm(rbfMatB, rbfInvA, 1.0, 0.0);
}

//U = DL * U
void GRbf::evalRbfDer(int p,
		     const fullMatrix<double> &cntrs,
		     const fullMatrix<double> &nodes,
		     const fullMatrix<double> &fValues,
		      fullMatrix<double> &fApprox)
{
  fApprox.resize(nodes.size1(),fValues.size2());
  fullMatrix<double> D;
  RbfOp(p,cntrs,nodes,D);
  fApprox.gemm(D,fValues, 1.0, 0.0);
}

void GRbf::setup_level_set(const fullMatrix<double> &cntrs,
			   const fullMatrix<double> &normals,
			   fullMatrix<double> &level_set_nodes,
			   fullMatrix<double> &level_set_funvals)
{
  int numNodes = cntrs.size1();
  int nTot = 3*numNodes;
  double normFactor;
  level_set_nodes.resize(nTot,3);
  level_set_funvals.resize(nTot,1);
  fullMatrix<double> ONES(numNodes+1,1), sx(numNodes,1), sy(numNodes,1);
  fullMatrix<double> sz(numNodes,1),norms(numNodes,3), cntrsPlus(numNodes+1,3);

  //Computes the normal vectors to the surface at each node
  //Specifies the function values on the level set : 0 at all nodes (but add
  //a node to make the problem non sigular)
  for (int i=0;i<numNodes ; ++i){
    ONES(i,0) = 0.0;
    cntrsPlus(i,0) = cntrs(i,0);
    cntrsPlus(i,1) = cntrs(i,1);
    cntrsPlus(i,2) = cntrs(i,2);
  }	
  //Specifies the additional node position and its function value
  ONES(numNodes,0) = 1.0;
  cntrsPlus(numNodes,0) = cntrs(0,0)+10.*sBox;
  cntrsPlus(numNodes,1) = cntrs(0,1)+10.*sBox;
  cntrsPlus(numNodes,2) = cntrs(0,2)+10.*sBox;

  //printf("%g,%g,%g,%g;\n",sBox, cntrs(0,0), cntrs(0,1), cntrs(0,2));
	
  evalRbfDer(1,cntrsPlus,cntrs,ONES,sx);
  evalRbfDer(2,cntrsPlus,cntrs,ONES,sy);
  evalRbfDer(3,cntrsPlus,cntrs,ONES,sz);

  for (int i=0;i<numNodes ; ++i){

    normFactor = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
    sx(i,0) = sx(i,0)/normFactor;
    sy(i,0) = sy(i,0)/normFactor;
    sz(i,0) = sz(i,0)/normFactor;
    norms(i,0) = sx(i,0);norms(i,1) = sy(i,0);norms(i,2) = sz(i,0);

    //GMSH NORMALS
    // norms(i,0) = normals(i,0);
    // norms(i,1) = normals(i,1);
    // norms(i,2) = normals(i,2);
    //END GMSH NORMALS
  }

  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < 3; ++j){
      level_set_nodes(i,j) = cntrs(i,j);
      level_set_nodes(i+numNodes,j) = cntrs(i,j)-delta*norms(i,j);
      level_set_nodes(i+2*numNodes,j) = cntrs(i,j)+delta*norms(i,j);
    }
    level_set_funvals(i,0) = 0.0;
    level_set_funvals(i+numNodes,0) = -1;
    level_set_funvals(i+2*numNodes,0) = 1;
  }

  if (!isLocal)
    {
      matAInv_nn.resize(nTot, nTot);
      matAInv_nn = generateRbfMat(0,level_set_nodes,level_set_nodes);
      matAInv_nn.invertInPlace();
    }
}

void GRbf::RbfLapSurface_local_projection(const fullMatrix<double> &cntrs,
                                          const fullMatrix<double> &normals,
                                          fullMatrix<double> &Oper)
{
  isLocal = true;
  int numNodes = cntrs.size1();
  Oper.resize(numNodes,numNodes);

  if(nodesInSphere.size() == 0) buildOctree(radius);

  for (int i = 0; i < numNodes; ++i){
    std::vector<int> &pts = nodesInSphere[i];

    fullMatrix<double> nodes_in_sph(pts.size(),3), local_normals(pts.size(),3);
    fullMatrix<double> LocalOper;

    LocalOper.setAll(0.0);

    for (unsigned int k = 0; k < pts.size(); k++){
      nodes_in_sph(k, 0) = cntrs(pts[k], 0);
      nodes_in_sph(k, 1) = cntrs(pts[k], 1);
      nodes_in_sph(k, 2) = cntrs(pts[k], 2);
      local_normals(k, 0) = normals(pts[k], 0);
      local_normals(k, 1) = normals(pts[k], 1);
      local_normals(k, 2) = normals(pts[k], 2);
    }

    RbfLapSurface_global_projection(nodes_in_sph,local_normals, LocalOper);

    for (unsigned int j = 0; j < pts.size(); j++)
      Oper(i, pts[j]) = LocalOper(0, j);
  }
}

void GRbf::RbfLapSurface_global_projection2(const fullMatrix<double> &cntrs,
										const fullMatrix<double> &normals,
										fullMatrix<double> &Oper) {
	
	int numNodes = cntrs.size1();
	int nnTot = 3*numNodes;
	Oper.resize(numNodes,numNodes);
	
	fullMatrix<double> Dx(numNodes,numNodes),Dy(numNodes,numNodes),Dz(numNodes,numNodes),
    PDx(numNodes,numNodes),PDy(numNodes,numNodes),PDz(numNodes,numNodes),
    PDxx(numNodes,numNodes),PDyy(numNodes,numNodes),PDzz(numNodes,numNodes);
	
	fullMatrix<double> sx(nnTot,1),sy(nnTot,1),sz(nnTot,1); 
	fullMatrix<double> extX(nnTot,3), surf(nnTot,1);
	
	//Stage 1 : The Arbitrary surface
	setup_level_set(cntrs,normals,extX,surf);
	if (!isLocal) extendedX = extX;
	if (!isLocal) surfInterp = surf;
	
	//Computes the normal vectors to the surface at each node
	evalRbfDer(1,extX,extX,surf,sx);
	evalRbfDer(2,extX,extX,surf,sy);
	evalRbfDer(3,extX,extX,surf,sz);
	for (int i=0;i<nnTot ; ++i){
		double normFactor = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
		sx(i,0) = sx(i,0)/normFactor;
		sy(i,0) = sy(i,0)/normFactor;
		sz(i,0) = sz(i,0)/normFactor;
	}
	// Finds differentiation matrices
	RbfOp(1,cntrs,cntrs,Dx);
	RbfOp(2,cntrs,cntrs,Dy);
	RbfOp(3,cntrs,cntrs,Dz);
	
	// Fills up the operator matrix
	for (int i=0;i<numNodes ; ++i){
		for (int j=0;j<numNodes ; ++j){
			PDx(i,j) = (1-sx(i,0)*sx(i,0))*Dx(i,j)-sx(i,0)*sy(i,0)*Dy(i,j)-sx(i,0)*sz(i,0)*Dz(i,j);
			PDy(i,j) = -sx(i,0)*sy(i,0)*Dx(i,j)+(1-sy(i,0)*sy(i,0))*Dy(i,j)-sy(i,0)*sz(i,0)*Dz(i,j);
			PDz(i,j) =  -sx(i,0)*sz(i,0)*Dx(i,j)-sy(i,0)*sz(i,0)*Dy(i,j)+(1-sz(i,0)*sz(i,0))*Dz(i,j);
		}
	}
	PDx.mult(PDx,PDxx);
	PDy.mult(PDy,PDyy);
	PDz.mult(PDz,PDzz);
	for (int i=0;i<numNodes ; ++i){
		for (int j=0;j<numNodes ; ++j){
			Oper(i,j) = PDxx(i,j)+PDyy(i,j)+PDzz(i,j);
		}
	}
	
	
}


void GRbf::RbfLapSurface_global_projection( const fullMatrix<double> &cntrs,
					   const fullMatrix<double> &normals,
					   fullMatrix<double> &Oper)
{
  int numNodes = cntrs.size1();
  Oper.resize(numNodes,numNodes);

  fullMatrix<double> sx(numNodes,1),sy(numNodes,1),sz(numNodes,1),
    Dx(numNodes,numNodes),Dy(numNodes,numNodes),Dz(numNodes,numNodes),
    PDx(numNodes,numNodes),PDy(numNodes,numNodes),PDz(numNodes,numNodes),
    PDxx(numNodes,numNodes),PDyy(numNodes,numNodes),PDzz(numNodes,numNodes);

  surfInterp.resize(numNodes,1);
  surfInterp.setAll(1.0);
  evalRbfDer(1,cntrs,cntrs,surfInterp,sx);
  evalRbfDer(2,cntrs,cntrs,surfInterp,sy);
  evalRbfDer(3,cntrs,cntrs,surfInterp,sz);

  // Normalizes
  double norm;
  for (int i = 0; i < numNodes;i++){
    norm = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
    sx(i,0) /= norm;
    sy(i,0) /= norm;
    sz(i,0) /= norm;
  }

  // Finds differentiation matrices
  RbfOp(1,cntrs,cntrs,Dx);
  RbfOp(2,cntrs,cntrs,Dy);
  RbfOp(3,cntrs,cntrs,Dz);

  // Fills up the operator matrix
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < numNodes; ++j){
      PDx(i,j) = (1-sx(i,0)*sx(i,0))*Dx(i,j)-sx(i,0)*sy(i,0)*Dy(i,j)-sx(i,0)*sz(i,0)*Dz(i,j);
      PDy(i,j) = -sx(i,0)*sy(i,0)*Dx(i,j)+(1-sy(i,0)*sy(i,0))*Dy(i,j)-sy(i,0)*sz(i,0)*Dz(i,j);
      PDz(i,j) =  -sx(i,0)*sz(i,0)*Dx(i,j)-sy(i,0)*sz(i,0)*Dy(i,j)+(1-sz(i,0)*sz(i,0))*Dz(i,j);
    }
  }
  PDx.mult(PDx,PDxx);
  PDy.mult(PDy,PDyy);
  PDz.mult(PDz,PDzz);
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < numNodes; ++j){
      Oper(i,j) = PDxx(i,j)+PDyy(i,j)+PDzz(i,j);
    }
  }
}

void GRbf::RbfLapSurface_local_CPM(bool isLow,
                                   const fullMatrix<double> &cntrs,
                                   const fullMatrix<double> &normals,
                                   fullMatrix<double> &Oper)
{
  isLocal = true;
  int numNodes = cntrs.size1();
  Oper.resize(3*numNodes,3*numNodes);

  buildOctree(radius);
  setup_level_set(cntrs,normals,extendedX,surfInterp);

  for (int i = 0; i < numNodes; ++i){
    std::vector<int> &pts = nodesInSphere[i];
    int nbp = pts.size();
    fullMatrix<double> nodes_in_sph(nbp,3), local_normals(nbp,3);
    fullMatrix<double> LocalOper;

    for (int k=0; k< nbp; k++){
      nodes_in_sph(k,0) = cntrs(pts[k],0);
      nodes_in_sph(k,1) = cntrs(pts[k],1);
      nodes_in_sph(k,2) = cntrs(pts[k],2);
      local_normals(k,0)=normals(pts[k],0);
      local_normals(k,1)=normals(pts[k],1);
      local_normals(k,2)=normals(pts[k],2);
    }

    LocalOper.setAll(0.0);
    if (isLow) RbfLapSurface_global_CPM_low(nodes_in_sph,local_normals,LocalOper);
    else       RbfLapSurface_global_CPM_high_2(nodes_in_sph,local_normals,LocalOper);
	  
    for (int j = 0; j < nbp; j++){
      Oper(i,pts[j])=LocalOper(0,j);
      Oper(i,pts[j]+numNodes)=LocalOper(0,j+nbp);
      Oper(i,pts[j]+2*numNodes)=LocalOper(0,j+2*nbp);

      Oper(i+numNodes,pts[j])=LocalOper(nbp,j);
      Oper(i+numNodes,pts[j]+numNodes)=LocalOper(nbp,j+nbp);
      Oper(i+numNodes,pts[j]+2*numNodes)=LocalOper(nbp,j+2*nbp);

      Oper(i+2*numNodes,pts[j])=LocalOper(2*nbp,j);
      Oper(i+2*numNodes,pts[j]+numNodes)=LocalOper(2*nbp,j+nbp);
      Oper(i+2*numNodes,pts[j]+2*numNodes)=LocalOper(2*nbp,j+2*nbp);
    }

  }
}

void GRbf::RbfLapSurface_local_CPM_sparse(std::vector<MVertex*> &bndVertices, bool isLow,
                                          const fullMatrix<double> &cntrs,
                                          const fullMatrix<double> &normals,
                                          linearSystem<double> &sys)
{
#if defined(HAVE_SOLVER)
  std::set<int> bndIndices;
  for (size_t i = 0; i < bndVertices.size(); ++i) {
    bndIndices.insert(_mapV[bndVertices[i]]);
  }
  isLocal = true;
  int numNodes = cntrs.size1();

  sys.setParameter("matrix_reuse", "same_matrix");
  sys.allocate(3 * numNodes);

  buildOctree(radius);
  //setup_level_set(cntrs,normals,extendedX,surfInterp);

  for (int i = 0; i < numNodes; ++i) {
    std::vector<int> &pts = nodesInSphere[i];
    if (bndIndices.count(i) > 0) {
      sys.insertInSparsityPattern(i, i);
      for (unsigned int j = 0; j < pts.size(); ++j) {
        sys.insertInSparsityPattern(i + numNodes, pts[j]);
        sys.insertInSparsityPattern(i + 2 * numNodes, pts[j]);
      }
    }
    else {
      for (unsigned int j = 0; j < pts.size(); ++j) {
        sys.insertInSparsityPattern(i, pts[j]);
        sys.insertInSparsityPattern(i + numNodes, pts[j]);
        sys.insertInSparsityPattern(i + 2 * numNodes, pts[j]);
      }
    }
  }
  for (int i = 0; i < numNodes; ++i){
    std::vector<int> &pts = nodesInSphere[i];
    int nbp = pts.size();
    fullMatrix<double> nodes_in_sph(nbp,3), local_normals(nbp,3);
    fullMatrix<double> LocalOper;

    for (int k = 0; k < nbp; k++){
      nodes_in_sph(k,0) = cntrs(pts[k],0);
      nodes_in_sph(k,1) = cntrs(pts[k],1);
      nodes_in_sph(k,2) = cntrs(pts[k],2);
      local_normals(k,0)=normals(pts[k],0);
      local_normals(k,1)=normals(pts[k],1);
      local_normals(k,2)=normals(pts[k],2);
    }

    LocalOper.setAll(0.0);

    if (isLow) RbfLapSurface_global_CPM_low(nodes_in_sph,local_normals,LocalOper);
    else       RbfLapSurface_global_CPM_high_2(nodes_in_sph,local_normals,LocalOper);

    bool isBnd = (bndIndices.count(i) > 0);
    if (isBnd) {
      sys.addToMatrix(i, i, 1.);
    }
    for (int j = 0; j < nbp; j++){
      if (!isBnd) {
        sys.addToMatrix(i, pts[j], LocalOper(0,j));
        sys.addToMatrix(i, pts[j] + numNodes, LocalOper(0,j + nbp));
        sys.addToMatrix(i, pts[j] + 2 * numNodes, LocalOper(0,j + 2 * nbp));
      }

      sys.addToMatrix(i + numNodes, pts[j], LocalOper(nbp,j));
      sys.addToMatrix(i + numNodes, pts[j] + numNodes, LocalOper(nbp,j + nbp));
      sys.addToMatrix(i + numNodes, pts[j] + 2 * numNodes, LocalOper(nbp,j + 2 * nbp));

      sys.addToMatrix(i + 2 * numNodes, pts[j], LocalOper(2 * nbp,j));
      sys.addToMatrix(i + 2 * numNodes, pts[j] + numNodes, LocalOper(2 * nbp,j + nbp));
      sys.addToMatrix(i + 2 * numNodes, pts[j] + 2 * numNodes, LocalOper(2 * nbp,j + 2 * nbp));
    }
  }
#endif
}

// NEW METHOD #1 CPM GLOBAL HIGH
void GRbf::RbfLapSurface_global_CPM_high_2(const fullMatrix<double> &cntrs,
					   const fullMatrix<double> &normals,
					   fullMatrix<double> &Oper)
{
  Msg::Info("***Building Laplacian operator");
  int numNodes = cntrs.size1();
  int nnTot = 3*numNodes;
  Oper.resize(nnTot,nnTot);

  fullMatrix<double> sx, sy, sz, sxx, sxy, sxz,syy, syz, szz;
  fullMatrix<double> A, Ax, Ay, Az, Axx, Axy, Axz, Ayy, Ayz, Azz, Alap, AOper, extX, surf;

  setup_level_set(cntrs,normals,extX,surf);
  if (!isLocal) extendedX = extX;
  if (!isLocal) surfInterp = surf;

  // Find derivatives of the surface interpolant
  evalRbfDer(1,extX,cntrs,surf,sx);
  evalRbfDer(2,extX,cntrs,surf,sy);
  evalRbfDer(3,extX,cntrs,surf,sz);
  evalRbfDer(11,extX,cntrs,surf,sxx);
  evalRbfDer(12,extX,cntrs,surf,sxy);
  evalRbfDer(13,extX,cntrs,surf,sxz);
  evalRbfDer(22,extX,cntrs,surf,syy);
  evalRbfDer(23,extX,cntrs,surf,syz);
  evalRbfDer(33,extX,cntrs,surf,szz);

   // Finds differentiation matrices
  A=generateRbfMat(0,extX,extX);
  Ax=generateRbfMat(1,extX,cntrs);
  Ay=generateRbfMat(2,extX,cntrs);
  Az=generateRbfMat(3,extX,cntrs);
  Axx=generateRbfMat(11,extX,cntrs);
  Axy=generateRbfMat(12,extX,cntrs);
  Axz=generateRbfMat(13,extX,cntrs);
  Ayy=generateRbfMat(22,extX,cntrs);
  Ayz=generateRbfMat(23,extX,cntrs);
  Azz=generateRbfMat(33,extX,cntrs);
  Alap=generateRbfMat(222,extX,cntrs);

  // Fills up the operator matrix
  AOper.resize(nnTot, nnTot);
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < nnTot; ++j){
      AOper(i,j) = Alap(i,j);
      AOper(i+numNodes,j)=sx(i,0)*Ax(i,j)+sy(i,0)*Ay(i,j)+sz(i,0)*Az(i,j);
      AOper(i+2*numNodes,j)=sx(i,0)*sx(i,0)*Axx(i,j)+sy(i,0)*sy(i,0)*Ayy(i,j)+sz(i,0)*sz(i,0)*Azz(i,j)+2*sx(i,0)*sy(i,0)*Axy(i,j)+2*sx(i,0)*sz(i,0)*Axz(i,j)+2*sy(i,0)*sz(i,0)*Ayz(i,j)+(sx(i,0)*sxx(i,0)+sy(i,0)*sxy(i,0)+sz(i,0)*sxz(i,0))*Ax(i,j)+(sx(i,0)*sxy(i,0)+sy(i,0)*syy(i,0)+sz(i,0)*syz(i,0))*Ay(i,j)+(sx(i,0)*sxz(i,0)+sy(i,0)*syz(i,0)+sz(i,0)*szz(i,0))*Az(i,j);
    }
  }
  A.invertInPlace();
  Oper.gemm(AOper, A, 1.0, 0.0);

  Msg::Info("*** RBF built Laplacian operator");
}

//NEW METHOD #2 CPM GLOBAL HIGH
//Produces a nxn differentiation matrix (like the projection method)
//So the local method for this is the local projection method
void GRbf::RbfLapSurface_global_CPM_high(const fullMatrix<double> &cntrs,
					const fullMatrix<double> &normals,
					fullMatrix<double> &Oper)
{
  Msg::Debug("*** RBF ... building Laplacian operator");
  int numNodes = cntrs.size1();
  int nnTot = 3*numNodes;
  Oper.resize(numNodes,numNodes);

  fullMatrix<double> sx(numNodes,1), sy(numNodes,1), sz(numNodes,1), sxx(numNodes,1), sxy(numNodes,1), sxz(numNodes,1),syy(numNodes,1), syz(numNodes,1), szz(numNodes,1);
  fullMatrix<double> A(nnTot,nnTot), Ax(numNodes,nnTot), Ay(numNodes,nnTot), Az(numNodes,nnTot), Axx(numNodes,nnTot), Axy(numNodes,nnTot), Axz(numNodes,nnTot), Ayy(numNodes,nnTot), Ayz(numNodes,nnTot), Azz(numNodes,nnTot), Alap(numNodes,nnTot), AOper(nnTot,nnTot), Temp(numNodes,nnTot), extX(nnTot,3), surf(nnTot,1);

  setup_level_set(cntrs,normals,extX,surf);
  if (!isLocal) extendedX = extX;
  if (!isLocal) surfInterp = surf;

  // Find derivatives of the surface interpolant
  evalRbfDer(1,extX,cntrs,surf,sx);
  evalRbfDer(2,extX,cntrs,surf,sy);
  evalRbfDer(3,extX,cntrs,surf,sz);
  evalRbfDer(11,extX,cntrs,surf,sxx);
  evalRbfDer(12,extX,cntrs,surf,sxy);
  evalRbfDer(13,extX,cntrs,surf,sxz);
  evalRbfDer(22,extX,cntrs,surf,syy);
  evalRbfDer(23,extX,cntrs,surf,syz);
  evalRbfDer(33,extX,cntrs,surf,szz);

  // Finds differentiation matrices
  A=generateRbfMat(0,extX,extX);
  Ax=generateRbfMat(1,extX,cntrs);
  Ay=generateRbfMat(2,extX,cntrs);
  Az=generateRbfMat(3,extX,cntrs);
  Axx=generateRbfMat(11,extX,cntrs);
  Axy=generateRbfMat(12,extX,cntrs);
  Axz=generateRbfMat(13,extX,cntrs);
  Ayy=generateRbfMat(22,extX,cntrs);
  Ayz=generateRbfMat(23,extX,cntrs);
  Azz=generateRbfMat(33,extX,cntrs);
  Alap=generateRbfMat(222,extX,cntrs);

  // Fills up the operator matrix
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < nnTot; ++j){
      AOper(i,j) = A(i,j);
      AOper(i+numNodes,j)=sx(i,0)*Ax(i,j)+sy(i,0)*Ay(i,j)+sz(i,0)*Az(i,j);
      AOper(i+2*numNodes,j)=sx(i,0)*sx(i,0)*Axx(i,j)+sy(i,0)*sy(i,0)*Ayy(i,j)+sz(i,0)*sz(i,0)*Azz(i,j)+2*sx(i,0)*sy(i,0)*Axy(i,j)+2*sx(i,0)*sz(i,0)*Axz(i,j)+2*sy(i,0)*sz(i,0)*Ayz(i,j)+(sx(i,0)*sxx(i,0)+sy(i,0)*sxy(i,0)+sz(i,0)*sxz(i,0))*Ax(i,j)+(sx(i,0)*sxy(i,0)+sy(i,0)*syy(i,0)+sz(i,0)*syz(i,0))*Ay(i,j)+(sx(i,0)*sxz(i,0)+sy(i,0)*syz(i,0)+sz(i,0)*szz(i,0))*Az(i,j);
    }
  }
  AOper.invertInPlace();
  Alap.mult(AOper,Temp);
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < numNodes; ++j){
      Oper(i,j) = Temp(i,j);
    }
  }
  Msg::Info("*** RBF built Laplacian operator");
}

void GRbf::RbfLapSurface_global_CPM_low(const fullMatrix<double> &cntrs,
                                        const fullMatrix<double> &normals,
                                        fullMatrix<double> &Oper)
{
  int numNodes = cntrs.size1();
  int nnTot = 3*numNodes;
  Oper.resize(nnTot,nnTot);

  fullMatrix<double> sx(nnTot,1),sy(nnTot,1),sz(nnTot,1);
  fullMatrix<double> PLap(numNodes,nnTot), extX(nnTot,3), surf(nnTot,1);
  fullMatrix<double> norm(nnTot,3), extRBFX(2*numNodes,3), Ix2extX(2*numNodes,nnTot);

  //Stage 1 : The Arbitrary surface
  setup_level_set(cntrs,normals,extX,surf);
  if (!isLocal) extendedX = extX;
  if (!isLocal) surfInterp = surf;

  //Computes the normal vectors to the surface at each node
  evalRbfDer(1,extX,extX,surf,sx);
  evalRbfDer(2,extX,extX,surf,sy);
  evalRbfDer(3,extX,extX,surf,sz);
  for (int i = 0; i < nnTot; ++i){
    double normFactor = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
    sx(i,0) = sx(i,0)/normFactor;
    sy(i,0) = sy(i,0)/normFactor;
    sz(i,0) = sz(i,0)/normFactor;
    norm(i,0) = sx(i,0);norm(i,1) = sy(i,0);norm(i,2) = sz(i,0);
  }

  //Computes the inside and outside layers nodes of the surface
  for (int i = 0; i < numNodes; ++i){
    for (int j = 0; j < 3; ++j){
      extRBFX(i,j) = cntrs(i,j)-delta*norm(i,j);
      extRBFX(i+numNodes,j) = cntrs(i,j)+delta*norm(i,j);
    }
  }

  //Computes the gradient operators
  RbfOp(0,extX,extRBFX,Ix2extX); //'0' for interpolation
  RbfOp(222,extX,cntrs,PLap); //'222' for the Laplacian

  // Fills up the operator matrix
  for (int i = 0; i < numNodes; i++){
    for (int j = 0; j < nnTot; ++j){
      Oper(i,j) = PLap(i,j);
      double del = (i == j) ? -1.0: 0.0;
      //double pos1 = (i+numNodes == j) ? 1.0: 0.0;
      //double pos2 = (i+2*numNodes == j) ? 1.0: 0.0;
      Oper(i+numNodes,j) = del +Ix2extX(i,j);//+  pos1; //
      Oper(i+2*numNodes,j) = del + Ix2extX(i+numNodes,j); //+ pos2; //
    }
  }

}

void GRbf::solveHarmonicMap_sparse(linearSystem<double> &sys, int numNodes,
                                   const std::vector<MVertex*> &bcNodes,
                                   const std::vector<double> &coords,
                                   std::map<MVertex*, SPoint3> &rbf_param)
{
#if defined(HAVE_SOLVER)
  Msg::Info("*** RBF ... solving map");
	printf("system = %p\n", &sys);
  int nb = numNodes * 3;
  UV.resize(nb,2);
  for (int j = 0; j < 2; ++j) {
    sys.zeroRightHandSide();
    //UNIT CIRCLE
    for (unsigned int i = 0; i < bcNodes.size(); i++) {
      std::set<MVertex *>::iterator itN = myNodes.find(bcNodes[i]);
      if (itN != myNodes.end()){
        std::map<MVertex*, int>::iterator itm = _mapV.find(bcNodes[i]);
        double theta = 2 * M_PI * coords[i];
        int iFix = itm->second;
        sys.addToRightHandSide(iFix, ((j == 0) ? cos(theta) : sin(theta)));
      }
    }
    sys.systemSolve();
	for (int i = 0; i < nbNodes; ++i) {
      sys.getFromSolution(i, UV(i, j));
    }
  }

  //SQUARE
 // for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end(); ++itv){
 //   MVertex *v = *itv;
 //   if (v->getNum() == 1){ //2900){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 0.0;
 //     F(iFix,1) = 0.0;
 //   }
 //   if (v->getNum() == 2){//1911){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 1.0;
 //     F(iFix,1) = 0.0;
 //   }
 //   if (v->getNum() == 3){//4844){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 1.0;
 //     F(iFix,1) = 1.0;
 //   }
 //   if (v->getNum() == 4){//3187){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 0.0;
 //     F(iFix,1) = 1.0;
 //   }
 // }

  //ANN UVtree
#if defined (HAVE_ANN)
  double dist_min = 1.e6;
  ANNpointArray UVnodes = annAllocPts(nbNodes, 3);
  for(int i = 0; i < nbNodes; i++){
    UVnodes[i][0] = UV(i,0);
    UVnodes[i][1] = UV(i,1);
    UVnodes[i][2] = 0.0;
    for(int j = i+1; j < nbNodes; j++){
      double dist = sqrt((UV(i,0)-UV(j,0))*(UV(i,0)-UV(j,0))+
    			 (UV(i,1)-UV(j,1))*(UV(i,1)-UV(j,1)));
      if (dist<dist_min) dist_min = dist;
    }
  }
  deltaUV = 0.6*dist_min;
  UVkdtree = new ANNkd_tree(UVnodes, nbNodes, 3);
#endif

  //interpolate
  fullMatrix<double> UVall(allCenters.size1(), 3);
  evalRbfDer(0,centers,allCenters,UV,UVall);

  //fill rbf_param
  std::map<MVertex*, int>::iterator itm = _mapAllV.begin();
  for (; itm != _mapAllV.end(); itm++){
    int index = itm->second;
    SPoint3 coords(UVall(index,0), UVall(index,1), 0.0);
    rbf_param.insert(std::make_pair(itm->first,coords));
  }

  Msg::Info("*** RBF solved map");
  exportParametrizedMesh(UV, nbNodes);
#endif
}

void GRbf::solveHarmonicMap(fullMatrix<double> Oper,
			    std::vector<MVertex*> bcNodes,
			    std::vector<double> coords,
			    std::map<MVertex*, SPoint3> &rbf_param)
{
  Msg::Info("*** RBF ... solving map");
  int nb = Oper.size2();
  UV.resize(nb,2);

  fullMatrix<double> F(nb,2);
  F.scale(0.0);

  //UNIT CIRCLE
  for (unsigned int i = 0; i < bcNodes.size(); i++){
     std::set<MVertex *>::iterator itN = myNodes.find(bcNodes[i]);
      if (itN != myNodes.end()){
  	std::map<MVertex*, int>::iterator itm = _mapV.find(bcNodes[i]);
  	double theta = 2 * M_PI * coords[i];
  	int iFix = itm->second;
  	for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
  	Oper(iFix,iFix) = 1.0;
  	F(iFix,0) = cos(theta);
  	F(iFix,1) = sin(theta);
    }
  }

  //SQUARE
 // for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end(); ++itv){
 //   MVertex *v = *itv;
 //   if (v->getNum() == 1){ //2900){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 0.0;
 //     F(iFix,1) = 0.0;
 //   }
 //   if (v->getNum() == 2){//1911){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 1.0;
 //     F(iFix,1) = 0.0;
 //   }
 //   if (v->getNum() == 3){//4844){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 1.0;
 //     F(iFix,1) = 1.0;
 //   }
 //   if (v->getNum() == 4){//3187){
 //     std::map<MVertex*, int>::iterator itm = _mapV.find(v);
 //     int iFix = itm->second;
 //     for (int j = 0; j < nb; ++j) Oper(iFix,j) = 0.0;
 //     Oper(iFix,iFix) = 1.0;
 //     F(iFix,0) = 0.0;
 //     F(iFix,1) = 1.0;
 //   }
 // }

  Oper.invertInPlace();
  Oper.mult(F, UV);

  //ANN UVtree
#if defined (HAVE_ANN)
  double dist_min = 1.e6;
  ANNpointArray UVnodes = annAllocPts(nbNodes, 3);
  for(int i = 0; i < nbNodes; i++){
    UVnodes[i][0] = UV(i,0);
    UVnodes[i][1] = UV(i,1);
    UVnodes[i][2] = 0.0;
    for(int j = i+1; j < nbNodes; j++){
      double dist = sqrt((UV(i,0)-UV(j,0))*(UV(i,0)-UV(j,0))+
    			 (UV(i,1)-UV(j,1))*(UV(i,1)-UV(j,1)));
      if (dist<dist_min) dist_min = dist;
    }
  }
  deltaUV = 0.6*dist_min;
  UVkdtree = new ANNkd_tree(UVnodes, nbNodes, 3);
#endif

  //interpolate
  fullMatrix<double> UVall(allCenters.size1(), 3);
  evalRbfDer(0,centers,allCenters,UV,UVall);

  //fill rbf_param
  std::map<MVertex*, int>::iterator itm = _mapAllV.begin();
  for (; itm != _mapAllV.end(); itm++){
    int index = itm->second;
    SPoint3 coords(UVall(index,0), UVall(index,1), 0.0);
    rbf_param.insert(std::make_pair(itm->first,coords));
  }

  Msg::Info("*** RBF solved map");
  exportParametrizedMesh(UV, nbNodes);
}

bool GRbf::UVStoXYZ(const double  u_eval, const double v_eval,
		    double &XX, double &YY, double &ZZ,
		    SVector3 &dXdu, SVector3& dXdv, int num_neighbours)
{
  if (u_eval == lastU && v_eval == lastV){
    XX = lastX;
    YY = lastY;
    ZZ = lastZ;
    dXdu = lastDXDU;
    dXdv = lastDXDV;
    return true;
  }

  num_neighbours = std::min(100, nbNodes);
  fullMatrix<double> u_vec(num_neighbours,3), xyz_local(num_neighbours,3);
  fullMatrix<double> u_vec_eval(1, 3), nodes_eval(1,3), xu(1,3), xv(1,3);
  u_vec_eval(0,0) = u_eval;
  u_vec_eval(0,1) = v_eval;
  u_vec_eval(0,2) = 0.0;

  double dist_min  = 1.e6;

#if defined (HAVE_ANN)
  double uvw[3] = { u_eval, v_eval, 0.0 };
  ANNidxArray index = new ANNidx[num_neighbours];
  ANNdistArray dist = new ANNdist[num_neighbours];
  UVkdtree->annkSearch(uvw, num_neighbours, index, dist);

  for (int i = 0; i < num_neighbours; i++){

    u_vec(i,0) = UV(index[i],0);
    u_vec(i,1) = UV(index[i],1);
    u_vec(i,2) = 0.0;

    xyz_local(i,0) = extendedX(index[i],0);
    xyz_local(i,1) = extendedX(index[i],1);
    xyz_local(i,2) = extendedX(index[i],2);

    for (int j = i+1; j < num_neighbours; j++){
      double dist = sqrt((UV(index[i],0)-UV(index[j],0))*(UV(index[i],0)-UV(index[j],0))+
    			 (UV(index[i],1)-UV(index[j],1))*(UV(index[i],1)-UV(index[j],1)));
      if (dist<dist_min && dist > 1.e-5) dist_min = dist;
    }
  }
  delete [] index;
  delete [] dist;
#endif

  _inUV = 1;
  deltaUV = 0.3*dist_min;
  evalRbfDer(0, u_vec, u_vec_eval,xyz_local, nodes_eval);
  evalRbfDer(1, u_vec, u_vec_eval,xyz_local, xu);
  evalRbfDer(2, u_vec, u_vec_eval,xyz_local, xv);
  _inUV= 0;

  XX = nodes_eval(0,0)*sBox;
  YY = nodes_eval(0,1)*sBox;
  ZZ = nodes_eval(0,2)*sBox;
  dXdu = SVector3(xu(0,0)*sBox, xu(0,1)*sBox, xu(0,2)*sBox);
  dXdv = SVector3(xv(0,0)*sBox, xv(0,1)*sBox, xv(0,2)*sBox);

  //store last computation
  lastU = u_eval;
  lastV = v_eval;
  lastX = XX;
  lastY = YY;
  lastZ = ZZ;
  lastDXDU = dXdu;
  lastDXDV = dXdv;
  return true;
}
