#include "vtkLagrangeInterpolation.h"

#include "vtkMultiBaselineRegressionTest.h"

#include "vtkNew.h"
#include "vtkSmartPointer.h"
#include "vtkTable.h"
#include "vtkDoubleArray.h"

#include "vtkPointData.h"
#include "vtkPoints.h"
#include "vtkPolyData.h"
#include "vtkCellArray.h"
#include "vtkXMLPolyDataWriter.h"
#include "vtkVector.h"
#include "vtkVectorOperators.h"

#include "vtkAxis.h"
#include "vtkColor.h"
#include "vtkColorSeries.h"
#include "vtkRenderWindow.h"
#include "vtkChartXY.h"
#include "vtkPlot.h"
#include "vtkTable.h"
#include "vtkFloatArray.h"
#include "vtkContextView.h"
#include "vtkContextScene.h"
#include "vtkRegressionTestImage.h"
#include "vtkRenderWindowInteractor.h"

#include <vector>
#include <sstream>

#include <math.h>

#include "vtkTestConditionals.txx"

using namespace vtk;

template<int N, typename T, typename U>
void printShape(const int order[N], const T& rst, U& shape)
{
  if (N != 3 || order[0] != 2 || order[1] != 2 || order[2] != 2)
    {
    return;
    }

  std::cout << "  ";
  for (int i = 0; i < 3; ++ i)
    {
    std::cout.width(4);
    std::cout << " " << order[i];
    }
  std::cout << "  / (";
  for (int i = 0; i < 3; ++ i)
    {
    std::cout.width(3);
    std::cout << " " << (rst[i] >= 0 ? "+" : "") << rst[i];
    }
  std::cout << " ) :";
  typename U::const_iterator it;
  for (it = shape.begin(); it != shape.end(); ++it)
    {
    std::cout << " " << (*it > 0 ? "+" : "") << *it;
    }
  std::cout << "\n";
}

template<typename T>
bool testShape(const int order[3], T& shape, int nonzeroidx)
{
  typename T::const_iterator it;
  int i = 0;
  bool ok = true;

  if (order[0] != 2 || order[1] != 2 || order[2] != 2)
    {
    return ok;
    }

  for (it = shape.begin(); it != shape.end(); ++it, ++i)
    {
    bool tval = fabs(*it - (i == nonzeroidx ? 1.0 : 0.0)) < 1e-7;
    if (!tval)
      {
      std::cerr << "  ERROR: Expected shape[" << i << "] == " << (i == nonzeroidx ? 1 : 0) << " got " << *it << "\n";
      }
    ok &= tval;
    }
  return ok;
}

template<typename T, typename U>
void InsertTableRow(int& row, T& all, const U& shape)
{
  typename T::iterator ait = all.begin();
  (*ait)->SetValue(row, row);
  ++ait; // Advance past "X" column

  int delta = 0;
  typename U::const_iterator sit;
  for (sit = shape.begin(); ait != all.end() && sit != shape.end(); ++ait, ++sit, ++delta)
    {
    (*ait)->SetValue(row, *sit + 2.0 * delta);
    }
  ++row;
}

template<int N, typename T, typename U>
vtkSmartPointer<vtkTable> CreateShapeFunctionTable(const int order[N], T& testpts, U method)
{
  vtkIdType numtests = testpts->GetNumberOfPoints();

  vtkNew<vtkLagrangeInterpolation> interp;
  vtkSmartPointer<vtkTable> out = vtkSmartPointer<vtkTable>::New();
  int ss = 1;
  for (int oo = 0; oo < N; ++oo)
    {
    ss *= (order[oo] + 1);
    }
  int nd = 16;
  int nn = nd * (numtests - 1) + 1;
  double dd = 1. / nd;
  vtkNew<vtkDoubleArray> xcol;
  vtkNew<vtkDoubleArray> rst;
  xcol->SetName("X");
  xcol->SetNumberOfTuples(nn);
  rst->SetName("rst");
  rst->SetNumberOfComponents(3);
  rst->SetNumberOfTuples(nn);
  out->AddColumn(xcol.GetPointer());
  out->GetFieldData()->AddArray(rst.GetPointer());

  std::vector<double> shape(ss);
  std::vector<vtkDoubleArray*> all(ss + 1);
  all[0] = xcol.GetPointer();
  for (int i = 0; i < ss; ++i)
    {
    vtkNew<vtkDoubleArray> col;
    std::ostringstream cname;
    cname << "Shape " << i;
    col->SetName(cname.str().c_str());
    col->SetNumberOfTuples(nn);
    all[i + 1] = col.GetPointer();
    out->AddColumn(col.GetPointer());
    }

  bool ok = true;
  int row = 0;
  for (unsigned i = 0; i < static_cast<unsigned>(numtests); ++i)
    {
    vtkVector3d pcoord(testpts->GetPoint(i));
    method(order, pcoord.GetData(), &shape[0]);
    printShape<N>(order, pcoord, shape);
    ok &= testShape(order, shape, i);
    rst->SetTuple(row, pcoord.GetData());
    InsertTableRow(row, all, shape);

    if (i + 1 < static_cast<unsigned>(numtests))
      { // Interpolate between this test point and next, saving to output table.
      vtkVector3d p0(testpts->GetPoint(i + 1));
      vtkVector3d p1(testpts->GetPoint(i));
      for (double xx = dd; xx < 1.0; xx += dd)
        {
        vtkVector3d xp = p0 * xx + p1 * (1. - xx);
        method(order, xp.GetData(), &shape[0]);
        rst->SetTuple(row, xp.GetData());
        InsertTableRow(row, all, shape);
        }
      }
    }
  if (!ok)
    {
    std::cerr << "ERROR: Failed test\n";
    }
  return out;
}

template<int N, typename T>
vtkSmartPointer<vtkPoints> CreatePrismaticPoints(const int order[N], T method)
{
  vtkSmartPointer<vtkPoints> pts;
  method(pts, order);

  vtkVector3d pt;
  for (int ii = 0; ii < pts->GetNumberOfPoints(); ++ii)
    {
    pts->GetPoint(ii, pt.GetData());
    //std::cout << "  " << ii << " " << pt[0] << " " << pt[1] << " " << pt[2] << "\n";
    }
  return pts;
}

vtkSmartPointer<vtkPoints> CreateHexPoints(int order[3])
{
  vtkSmartPointer<vtkPoints> pts;
  vtkLagrangeInterpolation::AppendHexahedronCollocationPoints(pts, order);

  vtkVector3d pt;
  for (int ii = 0; ii < pts->GetNumberOfPoints(); ++ii)
    {
    pts->GetPoint(ii, pt.GetData());
    //std::cout << "  " << ii << " " << pt[0] << " " << pt[1] << " " << pt[2] << "\n";
    }
  return pts;
}

template<typename T>
bool TestShapeFunctionImage(T& tab, int argc, char* argv[], const std::string& testImg)
{
  bool imageTest = !testImg.empty();
  bool interact = false;
  for (int a = 0; a < argc; ++a)
    {
    if (!strcmp(argv[a], "-I"))
      {
      interact = true;
      }
    }
  // Set up a 2D scene, add an XY chart to it
  vtkNew<vtkContextView> view;
  view->GetRenderWindow()->SetSize(800, 600);
  vtkNew<vtkChartXY> chart;
  view->GetScene()->AddItem(chart.GetPointer());

  vtkNew<vtkColorSeries> colors;
  colors->SetColorScheme(vtkColorSeries::BREWER_QUALITATIVE_DARK2);
  int nc = colors->GetNumberOfColors();

  std::vector<vtkPlot*> plots;
  for (int c = 1; c < tab->GetNumberOfColumns(); ++c)
    {
    vtkPlot* plot = chart->AddPlot(vtkChart::LINE);
    vtkColor3ub cu = colors->GetColor((c - 1) % nc);
    plot->SetInputData(tab.GetPointer(), 0, c);
    plot->SetColor(cu.GetRed(), cu.GetGreen(), cu.GetBlue(), 255);
    plot->SetWidth(2.0);
    plots.push_back(plot);
    }

  chart->GetAxis(vtkAxis::LEFT)->SetTickLabelAlgorithm(vtkAxis::TICK_WILKINSON_EXTENDED);
  chart->GetAxis(vtkAxis::BOTTOM)->SetTickLabelAlgorithm(vtkAxis::TICK_WILKINSON_EXTENDED);
  view->GetRenderWindow()->SetMultiSamples(0);
  view->GetInteractor()->Initialize();
  view->GetRenderWindow()->Render();
  if (imageTest)
    {
    int retVal = RegressionTestWithImageName(argc, argv, view->GetRenderWindow(), testImg);
    if (retVal == vtkRegressionTester::DO_INTERACTOR)
      {
      view->GetRenderWindow()->SetMultiSamples(8);
      view->GetInteractor()->Start();
      }
    return retVal ? true : false;
    }
  if (interact)
    {
    view->GetRenderWindow()->SetMultiSamples(8);
    view->GetInteractor()->Start();
    }
  return true; // If asked not to do a regression test, we always succeed.
}

template<int N, typename T, typename U, typename V>
bool SumShapeFunctions(const int order[N], T tab, U world, V lpd)
{
  vtkDataArray* rst = tab->GetFieldData()->GetArray("rst");
  vtkIdType nr = tab->GetNumberOfRows();
  vtkIdType nc = tab->GetNumberOfColumns();
  vtkNew<vtkLagrangeInterpolation> interp;
  vtkNew<vtkPoints> ppt;
  vtkNew<vtkCellArray> polyline;
  vtkNew<vtkDoubleArray> time;
  vtkNew<vtkDoubleArray> du;
  vtkNew<vtkDoubleArray> dv;
  vtkNew<vtkDoubleArray> dw;
  du->SetName("dr");
  dv->SetName("ds");
  dw->SetName("dt");
  du->SetNumberOfComponents(3);
  dv->SetNumberOfComponents(3);
  dw->SetNumberOfComponents(3);
  du->SetNumberOfTuples(nr);
  dv->SetNumberOfTuples(nr);
  dw->SetNumberOfTuples(nr);
  ppt->SetNumberOfPoints(nr);
  time->SetName("T");
  time->SetNumberOfTuples(nr);
  std::vector<vtkIdType> conn;
  std::vector<double> derivs(N * (nc - 1)); // nc - 1 => skip the column holding the row number
  for (vtkIdType rr = 0; rr < nr; ++rr)
    {
    vtkVector3d pt(0,0,0); // Interpolated result point
    vtkVector3d dr[N]; // Interpolated derivatives
    for (int i = 0; i < N; ++i)
      {
      for (int j = 0; j < 3; ++j)
        {
        dr[i][j] = 0.0;
        }
      }
    vtkVector3d cp; // Lagrange control point
    cp[2] = 0.0;
    vtkVector3d uu; // Parametric coordinates of control point

    rst->GetTuple(rr, uu.GetData());
    switch (N)
    {
    case 1: interp->Tensor1ShapeDerivatives(order, uu.GetData(), &derivs[0]); break;
    case 2: interp->Tensor2ShapeDerivatives(order, uu.GetData(), &derivs[0]); break;
    case 3: interp->Tensor3ShapeDerivatives(order, uu.GetData(), &derivs[0]); break;
    default:
      std::cerr << "Unsupported dimension " << N << ". No way to obtain derivatives.\n";
      break;
    }
    //std::cout << "r = " << uu[0] << " " << uu[1] << " " << uu[2] << "\n";
    for (int cc = 1; cc < nc; ++cc)
      {
      world->GetPoint(cc - 1, cp.GetData());
      /*
      if (rr < 2) {
        std::cout
          << "cc " << cc << " (" << cp[0] << " " << cp[1] << " " << cp[2] << ")  "
          << (tab->GetValue(rr, cc).ToDouble() - 2. * cc + 2) << "\n";
      }
      */
      // The "- 2.0 * cc + 2.0" accounts for the amount added to each
      // column to make the 2-D plot of shape functions simpler:
      pt = pt + (tab->GetValue(rr, cc).ToDouble() - 2.0 * cc + 2.0) * cp;

      dr[0] = dr[0] + derivs[N * (cc - 1)] * cp;
      //std::cout << "  dr += " << derivs[N * (cc - 1)] << " * (" << cp[0] << " " << cp[1] << " " << cp[2] << ")\n";
      if (N > 1)
        {
        dr[1] = dr[1] + derivs[N * (cc - 1) + 1] * cp;
        if (N > 2)
          {
          dr[2] = dr[2] + derivs[N * (cc - 1) + 2] * cp;
          }
        }
      }
    conn.push_back(rr);
    ppt->SetPoint(rr, pt.GetData());
    du->SetTuple(rr, dr[0].GetData());
    //std::cout << "  dr = (" << cp[0] << " " << cp[1] << " " << cp[2] << ")\n";
    if (N > 1)
      {
      dv->SetTuple(rr, dr[1].GetData());
      if (N > 2)
        {
        dw->SetTuple(rr, dr[2].GetData());
        }
      }
    time->SetValue(rr, rr);
    }
  polyline->InsertNextCell(
    static_cast<vtkIdType>(conn.size()),
    &conn[0]);
  lpd->Initialize();
  lpd->SetPoints(ppt.GetPointer());
  lpd->SetLines(polyline.GetPointer());
  lpd->GetPointData()->SetScalars(time.GetPointer());
  lpd->GetPointData()->AddArray(du.GetPointer());
  if (N > 1)
    {
    lpd->GetPointData()->AddArray(dv.GetPointer());
    if (N > 2)
      {
      lpd->GetPointData()->AddArray(dw.GetPointer());
      }
    }
  return true;
}

template<int N, typename T, typename U, typename V>
bool SumWedgeShapeFunctions(const int order[N], T tab, U world, V lpd)
{
  (void)order;
  vtkDataArray* rst = tab->GetFieldData()->GetArray("rst");
  vtkIdType nr = tab->GetNumberOfRows();
  vtkIdType nc = tab->GetNumberOfColumns();
  vtkNew<vtkLagrangeInterpolation> interp;
  vtkNew<vtkPoints> ppt;
  vtkNew<vtkCellArray> polyline;
  vtkNew<vtkDoubleArray> time;
  ppt->SetNumberOfPoints(nr);
  time->SetName("T");
  time->SetNumberOfTuples(nr);
  std::vector<vtkIdType> conn;
  for (vtkIdType rr = 0; rr < nr; ++rr)
    {
    vtkVector3d pt(0,0,0); // Interpolated result point
    vtkVector3d cp; // Lagrange control point
    cp[2] = 0.0;
    vtkVector3d uu; // Parametric coordinates of control point

    rst->GetTuple(rr, uu.GetData());
    //std::cout << "r = " << uu[0] << " " << uu[1] << " " << uu[2] << "\n";
    for (int cc = 1; cc < nc; ++cc)
      {
      world->GetPoint(cc - 1, cp.GetData());
      /*
      if (rr < 2) {
        std::cout
          << "cc " << cc << " (" << cp[0] << " " << cp[1] << " " << cp[2] << ")  "
          << (tab->GetValue(rr, cc).ToDouble() - 2. * cc + 2) << "\n";
      }
      */
      // The "- 2.0 * cc + 2.0" accounts for the amount added to each
      // column to make the 2-D plot of shape functions simpler:
      pt = pt + (tab->GetValue(rr, cc).ToDouble() - 2.0 * cc + 2.0) * cp;
      }
    conn.push_back(rr);
    ppt->SetPoint(rr, pt.GetData());
    time->SetValue(rr, rr);
    }
  polyline->InsertNextCell(
    static_cast<vtkIdType>(conn.size()),
    &conn[0]);
  lpd->Initialize();
  lpd->SetPoints(ppt.GetPointer());
  lpd->SetLines(polyline.GetPointer());
  lpd->GetPointData()->SetScalars(time.GetPointer());
  return true;
}

static bool SnapFace(vtkPoints* pts)
{
  int face1PtIds[] = {
    1, 2, 5, 6,
    9, 13, 17, 18,
    21
  };
  /*
  double face1PtDeltaX[] = {
    -0.20, -0.20, -0.20, -0.20,
    -0.10, -0.10, -0.10, -0.10,
    0.0
  };
  double face1PtDeltaY[] = {
    -0.20, +0.20, -0.20, +0.20,
     0.00,  0.00, -0.10, +0.10,
    0.0
  };
  double face1PtDeltaZ[] = {
    -0.20, -0.20, +0.20, +0.20,
    -0.10, +0.10,  0.00,  0.00,
    0.0
  };
  */
  double face1PtDeltaX[] = {
    -0.10, -0.10, -0.10, -0.10,
    -0.05, -0.05, -0.05, -0.05,
    0.0
  };
  double face1PtDeltaY[] = {
    -0.10, +0.10, -0.10, +0.10,
     0.00,  0.00, -0.05, +0.05,
    0.0
  };
  double face1PtDeltaZ[] = {
    -0.10, -0.10, +0.10, +0.10,
    -0.05, +0.05,  0.00,  0.00,
    0.0
  };
  vtkVector3d xx;
  for (unsigned ii = 0; ii < sizeof(face1PtIds) / sizeof(face1PtIds[0]); ++ii)
    {
    pts->GetPoint(face1PtIds[ii], xx.GetData());
    xx[0] += face1PtDeltaX[ii];
    xx[1] += face1PtDeltaY[ii];
    xx[2] += face1PtDeltaZ[ii];
    pts->SetPoint(face1PtIds[ii], xx.GetData());
    }
  return true;
}

template<typename T>
void Dump(T& pts)
{
  vtkIdType np = pts->GetNumberOfPoints();
  for (vtkIdType i = 0; i < np; ++i)
    {
    vtkVector3d p;
    pts->GetPoint(i, p.GetData());
    std::cout << "  " << i << "  " << p[0] << " " << p[1] << " " << p[2] << "\n";
    }
}

template<typename T>
bool SetupPoints(T& pts)
{
  pts->SetNumberOfPoints(2);
  pts->SetPoint(0,  0, 0, 0);
  pts->SetPoint(1,  1, 1, 0);
  pts->SetPoint(2,  2, 0, 0);
  return true;
}

int LagrangeInterpolation(int argc, char* argv[])
{
  bool ok = true;

  vtkSmartPointer<vtkTable> tab;
  vtkSmartPointer<vtkPoints> pts;
  vtkSmartPointer<vtkPoints> world = vtkSmartPointer<vtkPoints>::New();
  vtkSmartPointer<vtkPolyData> lpd = vtkSmartPointer<vtkPolyData>::New();

  int order5[1] = {2};
  ok &= testEqual(
    vtkLagrangeInterpolation::NumberOfIntervals<1>(order5), 2,
    "NumberOfIntervals: 1-D order 2 has 2 intervals");
  pts = CreatePrismaticPoints<1>(order5, vtkLagrangeInterpolation::AppendCurveCollocationPoints);
  tab = CreateShapeFunctionTable<1>(order5, pts, vtkLagrangeInterpolation::Tensor1ShapeFunctions);
  //tab->Dump(10,-1);
  // Dump(pts);
  world->DeepCopy(pts);
  ok &= SetupPoints(world);
  // Dump(world);
  ok &= SumShapeFunctions<1>(order5, tab, world, lpd); // Populate lpd with points interpolated from tab using world.

  /*
  vtkNew<vtkXMLPolyDataWriter> wri;
  wri->SetInputDataObject(lpd.GetPointer());
  wri->SetFileName("/tmp/curve5.vtp");
  wri->Write();
  */

  int order222[3] = {2, 2, 2};
  pts = CreatePrismaticPoints<3>(order222, vtkLagrangeInterpolation::AppendHexahedronCollocationPoints);
  tab = CreateShapeFunctionTable<3>(order222, pts, vtkLagrangeInterpolation::Tensor3ShapeFunctions);
  world->DeepCopy(pts);
  ok &= TestShapeFunctionImage(tab, argc, argv, "LagrangeInterpolation.png");
  ok &= SnapFace(world); // Deform the parameter-space coordinates of the hex DOFs into a world-coordinate hex.
  ok &= SumShapeFunctions<3>(order222, tab, world, lpd); // Populate lpd with points interpolated from tab using world.

  /*
  //vtkNew<vtkXMLPolyDataWriter> wri;
  wri->SetInputDataObject(lpd.GetPointer());
  wri->SetFileName("/tmp/hexcurve.vtp");
  wri->Write();
  */

  int order333[3] = {3, 3, 3};
  ok &= testEqual(
    vtkLagrangeInterpolation::NumberOfIntervals<3>(order333), 27,
    "NumberOfIntervals: 3-D order 3 has 27 intervals");
  pts = CreatePrismaticPoints<3>(order333, vtkLagrangeInterpolation::AppendHexahedronCollocationPoints);
  tab = CreateShapeFunctionTable<3>(order333, pts, vtkLagrangeInterpolation::Tensor3ShapeFunctions);
  ok &= TestShapeFunctionImage(tab, argc, argv, "LagrangeInterpolation_333hex.png");

  int order531[3] = {5, 3, 1};
  pts = CreatePrismaticPoints<3>(order531, vtkLagrangeInterpolation::AppendHexahedronCollocationPoints);
  tab = CreateShapeFunctionTable<3>(order531, pts, vtkLagrangeInterpolation::Tensor3ShapeFunctions);
  ok &= TestShapeFunctionImage(tab, argc, argv, "LagrangeInterpolation_531hex.png");

  int order44[2] = {4, 4};
  ok &= testEqual(
    vtkLagrangeInterpolation::NumberOfIntervals<2>(order44), 16,
    "NumberOfIntervals: 2-D order 4 has 16 intervals");
  pts = CreatePrismaticPoints<2>(order44, vtkLagrangeInterpolation::AppendQuadrilateralCollocationPoints);

  pts = CreatePrismaticPoints<3>(order333, vtkLagrangeInterpolation::AppendWedgeCollocationPoints);
  tab = CreateShapeFunctionTable<3>(order333, pts, vtkLagrangeInterpolation::WedgeShapeFunctions);
  world->DeepCopy(pts);
  ok &= TestShapeFunctionImage(tab, argc, argv, "LagrangeInterpolation_333wedge.png");
  //ok &= SnapFace(world); // Deform the parameter-space coordinates of the hex DOFs into a world-coordinate hex.
  ok &= SumWedgeShapeFunctions<3>(order333, tab, world, lpd); // Populate lpd with points interpolated from tab using world.

  /*
  //vtkNew<vtkXMLPolyDataWriter> wri;
  wri->SetInputDataObject(lpd.GetPointer());
  wri->SetFileName("/tmp/wedgecurve.vtp");
  wri->Write();
  */

  return ok ? 0 : 1;
}
