/*
** Computes Quasi Monte-Carlo sequence.
**
** Copyright © 2010-2020 Dynare Team
**
** This file is part of Dynare (can be used outside Dynare).
**
** Dynare is free software: you can redistribute it and/or modify
** it under the terms of the GNU General Public License as published by
** the Free Software Foundation, either version 3 of the License, or
** (at your option) any later version.
**
** Dynare is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
** GNU General Public License for more details.
**
** You should have received a copy of the GNU General Public License
** along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
**/

#include <string>

#include <dynmex.h>

#include "sobol.hh"
#include "gaussian.hh"

void
mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
  /*
  ** INPUTS:
  ** prhs[0]    [integer]    scalar, dimension.
  ** prhs[1]    [integer]    scalar, seed.
  ** prhs[2]    [integer]    scalar, sequence type:
  **                                   0 ⇒ uniform,
  **                                   1 ⇒ gaussian,
  **                                   2 ⇒ uniform on an hypershere.
  ** prhs[3]    [integer]    scalar, sequence size.
  ** prhs[4]    [double]     dimension×2 array, lower and upper bounds of the hypercube (default is 0-1 in all dimensions) if prhs[2]==0,
  **                         dimension×dimension array, covariance of the multivariate gaussian distribution of prhs[2]==1 (default is the identity matrix),
  **                         scalar, radius of the hypershere if prhs[2]==2 (default is one).
  **
  ** OUTPUTS:
  ** plhs[0]    [double]     sequence_size×dimension array, the Sobol sequence.
  ** plhs[1]    [integer]    scalar, seed.
  ** plhs[2]    [integer]    zero in case of success, one in case of error
  **
  */
  /*
  ** Check the number of input and output arguments.
  */
  if (nrhs < 3 || nrhs > 5)
    mexErrMsgTxt("qmc_sequence:: Five, four or three input arguments are required!");

  if (nlhs == 0)
    mexErrMsgTxt("qmc_sequence:: At least one output argument is required!");

  /*
  ** Test the first input argument and assign it to dimension.
  */
  if (!mxIsNumeric(prhs[0]))
    mexErrMsgTxt("qmc_sequence:: First input (dimension) has to be a positive integer!");

  int dimension = static_cast<int>(mxGetScalar(prhs[0]));
  /*
  ** Test the second input argument and assign it to seed.
  */
  if (!(mxIsNumeric(prhs[1]) && mxIsClass(prhs[1], "int64")))
    mexErrMsgTxt("qmc_sequence:: Second input (seed) has to be an integer [int64]!");

  int64_T seed = static_cast<int64_T>(mxGetScalar(prhs[1]));
  /*
  ** Test the third input argument and assign it to type (kind of QMC sequence).
  */
  int error_flag_3 = 0;
  if (!mxIsNumeric(prhs[2]))
    error_flag_3 = 1;

  int type = static_cast<int>(mxGetScalar(prhs[2]));
  if (!(type == 0 || type == 1 || type == 2))
    error_flag_3 = 1;

  if (error_flag_3 == 1)
    mexErrMsgTxt("qmc_sequence:: Third input (type of QMC sequence) has to be an integer equal to 0, 1 or 2!");

  /*
  ** Test dimension ≥ 2 when type==2
  */
  if (type == 2 && dimension < 2)
    mexErrMsgTxt("qmc_sequence:: First input (dimension) has to be greater than 1 for a uniform QMC on an hypershere!");

  else if (dimension > DIM_MAX)
    mexErrMsgTxt(("qmc_sequence:: First input (dimension) has to be smaller than " + to_string(DIM_MAX) + " !").c_str());

  /*
  ** Test the optional fourth input argument and assign it to sequence_size.
  */
  if (nrhs > 3 && !mxIsNumeric(prhs[3]))
    mexErrMsgTxt("qmc_sequence:: Fourth input (qmc sequence size) has to be a positive integer!");

  int sequence_size;
  if (nrhs > 3)
    sequence_size = static_cast<int>(mxGetScalar(prhs[3]));
  else
    sequence_size = 1;

  /*
  ** Test the optional fifth input argument and assign it to lower_and_upper_bounds.
  */
  if (nrhs > 4 && type == 0 && mxGetN(prhs[4]) != 2) // Sequence of uniformly distributed numbers in an hypercube
    mexErrMsgTxt("qmc_sequence:: The fifth input argument must be an array with two columns!");

  if (nrhs > 4 && type == 0 && static_cast<int>(mxGetM(prhs[4])) != dimension)
    mexErrMsgTxt("qmc_sequence:: The fourth input argument must be an array with a number of lines equal to dimension (first input argument)!");

  if (nrhs > 4 && type == 1 && !(static_cast<int>(mxGetN(prhs[4])) == dimension
                                 && static_cast<int>(mxGetM(prhs[4])) == dimension)) // Sequence of normally distributed numbers
    mexErrMsgTxt("qmc_sequence:: The fifth input argument must be a squared matrix (whose dimension is given by the first input argument)!");

  if (nrhs > 4 && type == 2 && !(mxGetN(prhs[4]) == 1 && mxGetM(prhs[4]) == 1)) // Sequence of uniformly distributed numbers on a hypershere
    mexErrMsgTxt("qmc_sequence:: The fifth input argument must be a positive scalar!");

  const double *lower_bounds = nullptr, *upper_bounds = nullptr;
  int unit_hypercube_flag = 1;
  if (type == 0 && nrhs > 4)
    {
      lower_bounds = mxGetPr(prhs[4]);
      upper_bounds = lower_bounds + dimension;
      unit_hypercube_flag = 0;
    }
  const double *cholcov = nullptr;
  int identity_covariance_matrix = 1;
  if (type == 1 && nrhs > 4)
    {
      cholcov = mxGetPr(prhs[4]);
      identity_covariance_matrix = 0;
    }
  double radius = 1.0;
  int unit_radius = 1;
  if (type == 2 && nrhs > 4)
    {
      radius = *mxGetPr(prhs[4]);
      unit_radius = 0;
    }
  /*
  ** Initialize outputs of the mex file.
  */
  plhs[0] = mxCreateDoubleMatrix(dimension, sequence_size, mxREAL);
  double *qmc_draws = mxGetPr(plhs[0]);
  int64_T seed_out;

  if (sequence_size == 1)
    {
      next_sobol(dimension, &seed, qmc_draws);
      seed_out = seed;
    }
  else
    seed_out = sobol_block(dimension, sequence_size, seed, qmc_draws);

  if (type == 0 && unit_hypercube_flag == 0) // Uniform QMC sequence in an hypercube
    expand_unit_hypercube(dimension, sequence_size, qmc_draws, lower_bounds, upper_bounds);
  else if (type == 1) // Normal QMC sequence in ℝⁿ
    {
      if (identity_covariance_matrix == 1)
        icdfm(dimension*sequence_size, qmc_draws);
      else
        icdfmSigma(dimension, sequence_size, qmc_draws, cholcov);
    }
  else if (type == 2) // Uniform QMC sequence on a hypershere
    {
      if (unit_radius == 1)
        usphere(dimension, sequence_size, qmc_draws);
      else
        usphereRadius(dimension, sequence_size, radius, qmc_draws);
    }

  if (nlhs >= 2)
    {
      plhs[1] = mxCreateNumericMatrix(1, 1, mxINT64_CLASS, mxREAL);
#if MX_HAS_INTERLEAVED_COMPLEX
      *mxGetInt64s(plhs[1]) = seed_out;
#else
      *(static_cast<int64_T *>(mxGetData(plhs[1]))) = seed_out;
#endif
    }
  if (nlhs >= 3)
    plhs[2] = mxCreateDoubleScalar(0);
}