/*
  This file is part of CDO. CDO is a collection of Operators to manipulate and analyse Climate model Data.

  Author: Cedrick Ansorge
          Uwe Schulzweida

*/

/*
   This module contains the following operators:

     Timeof        eof             EOF in spatial or time space
     Timeof        eofspatial      EOF in spatial space
     Timeof        eoftime         EOF in time space
*/
/*
 * TODO:
 * Role of the weights for eofs. Should not be mixed up with division with number of contributing values during summation.
 */

#ifdef _OPENMP
#include <omp.h>
#endif

#include "cdi.h"
#include "julian_date.h"

#include "cdo_options.h"
#include "process_int.h"
#include "param_conversion.h"
#include <mpim_grid.h>
#include "eigen_solution.h"
#include "eof_mode.h"

// No missing value support added so far!

static void
scale_eigvec_grid(Varray<double> &out, int tsID, size_t npack, const std::vector<size_t> &pack, const Varray<double> &weight,
                  const Varray2D<double> &covar, double sumWeights)
{
  for (size_t i = 0; i < npack; ++i) out[pack[i]] = covar[tsID][i] / std::sqrt(weight[pack[i]] / sumWeights);
}

static void
scale_eigvec_time(Varray<double> &out, int tsID, int numSteps, size_t npack, const std::vector<size_t> &pack,
                  const Varray<double> &weight, const Varray2D<double> &covar, const Varray2D<double> &data, double missval,
                  double sumWeights)
{
#ifdef _OPENMP
#pragma omp parallel for default(none) shared(npack, numSteps, tsID, pack, data, covar, out)
#endif
  for (size_t i = 0; i < npack; ++i)
    {
      double sum = 0.0;
      for (int j = 0; j < numSteps; ++j) sum += data[j][i] * covar[tsID][j];
      out[pack[i]] = sum;
    }
  /*
  for ( size_t j = 0; j < numSteps; ++j )
    {
      for ( size_t i = 0; i < npack; ++i )
        out[pack[i]] += data[j][i] * covar[tsID][j];
    }
  */

  // Normalizing
  double sum = 0.0;

#ifdef _OPENMP
#pragma omp parallel for default(none) reduction(+ : sum) shared(out, weight, pack, npack)
#endif
  for (size_t i = 0; i < npack; ++i)
    {
      // do not need to account for weights as eigenvectors are non-weighted
      sum += weight[pack[i]] * out[pack[i]] * out[pack[i]];
    }

  if (sum > 0.0)
    {
      sum = std::sqrt(sum / sumWeights);
#ifdef _OPENMP
#pragma omp parallel for default(none) shared(npack, pack, sum, out)
#endif
      for (size_t i = 0; i < npack; ++i) out[pack[i]] /= sum;
    }
  else
    {
#ifdef _OPENMP
#pragma omp parallel for default(none) shared(npack, pack, out, missval)
#endif
      for (size_t i = 0; i < npack; ++i) out[pack[i]] = missval;
    }
}

class EOFs : public Process
{
  enum
  {
    EOF_,
    EOF_TIME,
    EOF_SPATIAL
  };

public:
  using Process::Process;
  inline static CdoModule module = {
    .name = "EOFs",
    .operators = { { "eof", EOF_, 0, EOFsHelp }, { "eofspatial", EOF_SPATIAL, 0, EOFsHelp }, { "eoftime", EOF_TIME, 0, EOFsHelp } },
    .aliases = {},
    .mode = EXPOSED,     // Module mode: 0:intern 1:extern
    .number = CDI_REAL,  // Allowed number type
    .constraints = { 1, 2, OnlyFirst },
  };
  inline static RegisterEntry<EOFs> registration = RegisterEntry<EOFs>(module);

  struct eofdata_t
  {
    bool init = false;
    bool first_call = true;
    Varray<double> eigenValues;
    Varray2D<double> covar;
    Varray2D<double> data;
  };

  size_t numMissVals = 0;
  int gridSpace = 0, timeSpace = 0;
  double sum_w = 1.0;

  CdoStreamID streamID1;
  CdoStreamID streamID2;
  CdoStreamID streamID3;

  int vlistID1 = -1;
  int vlistID2 = -1;
  int vlistID3 = -1;

  int taxisID1;

  int gridID2;

  int calendar = CALENDAR_STANDARD;

  T_WEIGHT_MODE weightMode;
  T_EIGEN_MODE eigenMode;

  size_t numEigenFunctions = 0;

  int numVars;
  int numEigen;
  int numGrids;
  int numSteps = 1;

  size_t npack = SIZE_MAX;
  VarList varList1;
  std::vector<size_t> pack;
  Varray<double> in;
  std::vector<std::vector<eofdata_t>> eofData2D;
  Varray<double> weights;

public:
  void
  init() override
  {
    auto operatorID = cdo_operator_id();
    auto operfunc = cdo_operator_f1(operatorID);

    operator_input_arg("Number of eigen functions to write out");
    numEigen = parameter_to_int(cdo_operator_argv(0));

    eigenMode = get_eigenmode();
    weightMode = get_weightmode();

    streamID1 = cdo_open_read(0);
    vlistID1 = cdo_stream_inq_vlist(streamID1);
    taxisID1 = vlistInqTaxis(vlistID1);

    varList1 = VarList(vlistID1);

    auto gridID1 = varList1.vars[0].gridID;
    auto gridsizeMax = varList1.gridsizeMax();
    numVars = varList1.numVars();

    numGrids = vlistNumGrids(vlistID1);
    for (int index = 1; index < numGrids; ++index)
      if (vlistGrid(vlistID1, 0) != vlistGrid(vlistID1, index)) cdo_abort("Too many different grids!");

    // eigenvalues

    // Count number of timesteps if EOF_ or EOF_TIME
    if (operfunc == EOF_ || operfunc == EOF_TIME)
      {
        numSteps = vlistNtsteps(vlistID1);
        if (numSteps == 0) numSteps = 1;
        if (numSteps == -1)
          {
            numSteps = 0;
            while (cdo_stream_inq_timestep(streamID1, numSteps)) numSteps++;

            if (Options::cdoVerbose) cdo_print("Counted %d timeSteps", numSteps);

            cdo_stream_close(streamID1);

            streamID1 = cdo_open_read(0);
            vlistID1 = cdo_stream_inq_vlist(streamID1);
            taxisID1 = vlistInqTaxis(vlistID1);
          }
        else if (Options::cdoVerbose) { cdo_print("Found %d timeSteps", numSteps); }

        if ((size_t) numSteps < gridsizeMax || operfunc == EOF_TIME)
          {
            timeSpace = 1;
            gridSpace = 0;
          }
        else
          {
            timeSpace = 0;
            gridSpace = 1;
          }
      }
    else if (operfunc == EOF_SPATIAL)
      {
        timeSpace = 0;
        gridSpace = 1;
      }

    // reset the requested number of eigen-function to the maximum if neccessary
    if (timeSpace)
      {
        if (numEigen > numSteps)
          {
            cdo_warning("Solving in time-space:");
            cdo_warning("Number of eigen-functions to write out is bigger than number of time-steps.");
            cdo_warning("Setting numEigen to %d.", numSteps);
            cdo_warning("If You want to force a solution in grid-space use operator eofspatial");
            numEigen = numSteps;
          }
        numEigenFunctions = numSteps;
      }
    else if (gridSpace)
      {
        if (((double) gridsizeMax) * gridsizeMax > (double) SIZE_MAX) cdo_abort("Grid space too large!");

        if ((size_t) numEigen > gridsizeMax)
          {
            cdo_warning("Solving in spatial space");
            cdo_warning("Number of eigen-functions to write out is bigger than grid size");
            cdo_warning("Setting numEigen to %zu", gridsizeMax);
            cdo_warning("If You want to force a solution in time-space use operator eoftime");
            numEigen = gridsizeMax;
          }
        numEigenFunctions = gridsizeMax;
      }

    if (Options::cdoVerbose)
      cdo_print("Calculating %d eigenvectors and %zu eigenvalues in %s", numEigen, numEigenFunctions,
                (gridSpace == 1) ? "grid_space" : "time_space");

    weights = Varray<double>(gridsizeMax, 1.0);

    if (weightMode == WEIGHT_ON)
      {
        auto wstatus = gridcell_weights(gridID1, weights);
        if (wstatus != 0)
          {
            weightMode = WEIGHT_OFF;
            cdo_warning("Using constant grid cell area weights!");
          }
      }

    // allocation of temporary fields and output structures

    pack = std::vector<size_t>(gridsizeMax);
    in = Varray<double>(gridsizeMax);
    eofData2D.resize(numVars);

    if (Options::cdoVerbose)
      cdo_print("Allocate eigenvalue/eigenvector object with numSteps=%d and gridSize=%zu (%zu Bytes)", numSteps, gridsizeMax,
                numSteps * gridsizeMax * 8);

    for (int varID = 0; varID < numVars; ++varID)
      {
        auto numLevels = varList1.vars[varID].nlevels;
        eofData2D[varID].resize(numLevels);

        if (timeSpace)
          for (int levelID = 0; levelID < numLevels; ++levelID) eofData2D[varID][levelID].data.resize(numSteps);
      }
  }

  void
  run() override
  {
    int tsID = 0;

    // read the data and create covariance matrices for each var & level
    while (true)
      {
        auto numFields = cdo_stream_inq_timestep(streamID1, tsID);
        if (numFields == 0) break;

        for (int fieldID = 0; fieldID < numFields; ++fieldID)
          {
            auto [varID, levelID] = cdo_inq_field(streamID1);
            cdo_read_field(streamID1, in.data(), &numMissVals);

            auto const &var1 = varList1.vars[varID];

            if (npack == SIZE_MAX)
              {
                npack = 0;
                for (size_t i = 0; i < var1.gridsize; ++i)
                  {
                    if (!fp_is_equal(weights[i], 0.0) && !fp_is_equal(weights[i], var1.missval)
                        && !fp_is_equal(in[i], var1.missval))
                      {
                        pack[npack] = i;
                        npack++;
                      }
                  }

                if (weightMode == WEIGHT_ON)
                  {
                    sum_w = 0.0;
                    for (size_t i = 0; i < npack; ++i) sum_w += weights[pack[i]];
                  }
              }

            {
              size_t ipack = 0;
              for (size_t i = 0; i < var1.gridsize; ++i)
                {
                  if (!fp_is_equal(weights[i], 0.0) && !fp_is_equal(weights[i], var1.missval) && !fp_is_equal(in[i], var1.missval))
                    {
                      if (pack[ipack] != i) cdo_abort("Missing values unsupported!");
                      ipack++;
                    }
                }
              if (ipack != npack) cdo_abort("Missing values unsupported!");
            }

            auto &eofData = eofData2D[varID][levelID];
            if (gridSpace)
              {
                if (!eofData.init)
                  {
                    if (Options::cdoVerbose)
                      cdo_print("Allocate covar-matrix with %zux%zu elements for %s [layer: %d] (%zu Bytes)", npack, npack,
                                var1.name, levelID + 1, npack * npack * 8);
                    eofData.covar.resize(npack);
                    for (size_t i = 0; i < npack; ++i) eofData.covar[i].resize(npack, 0.0);
                  }

                auto &covar = eofData.covar;
#ifdef _OPENMP
#pragma omp parallel for default(none) shared(npack, covar, in, pack)
#endif
                for (size_t ipack = 0; ipack < npack; ++ipack)
                  {
                    auto &covar_i = covar[ipack];
                    auto in_i = in[pack[ipack]];
                    for (size_t jpack = ipack; jpack < npack; ++jpack) covar_i[jpack] += in_i * in[pack[jpack]];
                  }
              }
            else if (timeSpace)
              {
                eofData.data[tsID].resize(npack);
                auto &data = eofData.data[tsID];

                for (size_t ipack = 0; ipack < npack; ipack++) data[ipack] = in[pack[ipack]];
              }

            eofData.init = true;
          }

        tsID++;
      }

    if (gridSpace) numSteps = tsID;

    if (tsID == 1) cdo_abort("File consists of only one timestep!");

    // write files with eigenvalues (ID3) and eigenvectors (ID2)

    // eigenvalues
    streamID2 = cdo_open_write(1);

    auto vDateTime0 = cdiDateTime_set(10101, 0);

    vlistID2 = vlistDuplicate(vlistID1);
    auto taxisID2 = taxisDuplicate(taxisID1);
    cdiDefKeyInt(taxisID2, CDI_GLOBAL, CDI_KEY_DATATYPE, CDI_DATATYPE_FLT64);
    taxisDefRdatetime(taxisID2, vDateTime0);
    vlistDefTaxis(vlistID2, taxisID2);

    gridID2 = gridCreate(GRID_LONLAT, 1);
    gridDefXsize(gridID2, 1);
    gridDefYsize(gridID2, 1);
    double xvals = 0.0, yvals = 0.0;
    gridDefXvals(gridID2, &xvals);
    gridDefYvals(gridID2, &yvals);
    for (int i = 0; i < numGrids; ++i) vlistChangeGridIndex(vlistID2, i, gridID2);

    // eigenvectors
    streamID3 = cdo_open_write(2);

    vlistID3 = vlistDuplicate(vlistID1);
    auto taxisID3 = taxisDuplicate(taxisID1);
    cdiDefKeyInt(taxisID3, CDI_GLOBAL, CDI_KEY_DATATYPE, CDI_DATATYPE_FLT64);
    taxisDefRdatetime(taxisID3, vDateTime0);
    vlistDefTaxis(vlistID3, taxisID3);

    cdo_def_vlist(streamID2, vlistID2);
    cdo_def_vlist(streamID3, vlistID3);

    auto julianDate = julianDate_encode(calendar, vDateTime0);

    Varray<double> &out = in;

    int numStepsOut = (npack < (size_t) numSteps) ? npack : numSteps;

    for (tsID = 0; tsID < numStepsOut; ++tsID)
      {
        julianDate = julianDate_add_seconds(julianDate, 60);
        vDateTime0 = julianDate_decode(calendar, julianDate);

        taxisDefVdatetime(taxisID2, vDateTime0);
        cdo_def_timestep(streamID2, tsID);

        if (tsID < numEigen)
          {
            taxisDefVdatetime(taxisID3, vDateTime0);
            cdo_def_timestep(streamID3, tsID);
          }

        for (int varID = 0; varID < numVars; ++varID)
          {
            const auto &var1 = varList1.vars[varID];

            for (int levelID = 0; levelID < var1.nlevels; ++levelID)
              {
                auto &eofData = eofData2D[varID][levelID];
                const auto &data = eofData.data;
                auto &covar = eofData.covar;

                if (eofData.first_call)
                  {
                    eofData.first_call = false;

                    if (gridSpace)
                      {
                        if (Options::cdoVerbose) cdo_print("Processing level %d of %s", levelID + 1, var1.name);

                        eofData.eigenValues.resize(npack);

                        for (size_t ipack = 0; ipack < npack; ++ipack)
                          {
                            auto i = pack[ipack];
                            for (size_t jpack = 0; jpack < npack; ++jpack)
                              {
                                if (jpack < ipack) { covar[ipack][jpack] = covar[jpack][ipack]; }
                                else
                                  {
                                    auto j = pack[jpack];
                                    covar[ipack][jpack] = covar[ipack][jpack] *                                    // covariance
                                                          std::sqrt(weights[i]) * std::sqrt(weights[j]) / sum_w /  // weights
                                                          numSteps;  // number of data contributing
                                  }
                              }
                          }
                      }
                    else if (timeSpace)
                      {
                        if (Options::cdoVerbose)
                          cdo_print("Allocate covar-matrix with %dx%d elements (npack=%zu) for %s [layer: %d] (%zu Bytes)",
                                    numSteps, numSteps, npack, var1.name, levelID + 1, numSteps * numSteps * sizeof(double));

                        covar.resize(numSteps);
                        for (int i = 0; i < numSteps; ++i) covar[i].resize(numSteps);

                        eofData.eigenValues.resize(numSteps);

#ifdef _OPENMP
#pragma omp parallel for default(none) shared(numSteps, data, covar, weights, npack, pack, sum_w) schedule(static)
#endif
                        for (int j1 = 0; j1 < numSteps; ++j1)
                          {
                            const auto &df1p = data[j1];
                            for (int j2 = j1; j2 < numSteps; ++j2)
                              {
                                const auto &df2p = data[j2];
                                double sum = 0.0;
                                for (size_t i = 0; i < npack; ++i) sum += weights[pack[i]] * df1p[i] * df2p[i];
                                covar[j2][j1] = covar[j1][j2] = sum / sum_w / numSteps;
                              }
                          }
                      }

                    // Solve the eigen problem
                    auto &eigenValues = eofData.eigenValues;
                    if (eigenMode == JACOBI)
                      // TODO: use return status (>0 okay, -1 did not converge at all)
                      parallel_eigen_solution_of_symmetric_matrix(covar, eigenValues, numEigenFunctions, __func__);
                    else
                      eigen_solution_of_symmetric_matrix(covar, eigenValues, numEigenFunctions, __func__);

                    // NOW: covar contains the eigenvectors, eig_val the eigenvalues

                    for (size_t i = 0; i < var1.gridsize; ++i) out[i] = var1.missval;

                    // for ( int i = 0; i < n; i++ ) eig_val[i] *= sum_w;
                  }  // first_call

                if (tsID < numEigen)
                  {
                    if (gridSpace)
                      scale_eigvec_grid(out, tsID, npack, pack, weights, covar, sum_w);
                    else if (timeSpace)
                      scale_eigvec_time(out, tsID, numSteps, npack, pack, weights, covar, data, var1.missval, sum_w);

                    numMissVals = varray_num_mv(var1.gridsize, out, var1.missval);
                    cdo_def_field(streamID3, varID, levelID);
                    cdo_write_field(streamID3, out.data(), numMissVals);
                  }  // loop numEigen

                auto eigenValues = eofData.eigenValues.data();

                numMissVals = (fp_is_equal(eigenValues[tsID], var1.missval)) ? 1 : 0;

                cdo_def_field(streamID2, varID, levelID);
                cdo_write_field(streamID2, &eigenValues[tsID], numMissVals);
              }  // loop nlevs
          }  // loop nvars
      }
  }

  void
  close() override
  {
    cdo_stream_close(streamID3);
    cdo_stream_close(streamID2);
    cdo_stream_close(streamID1);

    vlistDestroy(vlistID2);
    vlistDestroy(vlistID3);
  }
};
