dynare/mex/sources/sobol/gaussian.hh

/* Generates gaussian random deviates from uniform random deviates.
**
** Pseudo code of the algorithm is given at http://home.online.no/~pjacklam/notes/invnorm
**
** Copyright © 2010-2019 Dynare Team
**
** This file is part of 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 <https://www.gnu.org/licenses/>.
**
** AUTHOR(S): stephane DOT adjemian AT univ DASH lemans DOT fr
*/

#include <cmath>
#include <limits>
#include <algorithm>

#include <omp.h>

#include <dynblas.h>

using namespace std;

constexpr double lb = .02425;
constexpr double ub = .97575;

template<typename T>
T
icdf(const T uniform)
/*
**  This function invert the gaussian cumulative distribution function.
**
*/
{
  static T A[6] =
    {
     -3.969683028665376e+01,
     2.209460984245205e+02,
     -2.759285104469687e+02,
     1.383577518672690e+02,
     -3.066479806614716e+01,
     2.506628277459239e+00
    };
  static T B[5] =
    {
     -5.447609879822406e+01,
     1.615858368580409e+02,
     -1.556989798598866e+02,
     6.680131188771972e+01,
     -1.328068155288572e+01
    };
  static T C[6] =
    {
     -7.784894002430293e-03,
     -3.223964580411365e-01,
     -2.400758277161838e+00,
     -2.549732539343734e+00,
     4.374664141464968e+00,
     2.938163982698783e+00
    };
  static T D[4] =
    {
     7.784695709041462e-03,
     3.224671290700398e-01,
     2.445134137142996e+00,
     3.754408661907416e+00
    };
  T gaussian = static_cast<T>(0.0);
  if (0 < uniform && uniform < lb)
    {
      T tmp;
      tmp = sqrt(-2*log(uniform));
      gaussian = (((((C[0]*tmp+C[1])*tmp+C[2])*tmp+C[3])*tmp+C[4])*tmp+C[5])/((((D[0]*tmp+D[1])*tmp+D[2])*tmp+D[3])*tmp+1);
    }
  else
    {
      if (lb <= uniform && uniform <= ub)
        {
          T tmp, TMP;
          tmp = uniform - .5;
          TMP = tmp*tmp;
          gaussian = (((((A[0]*TMP+A[1])*TMP+A[2])*TMP+A[3])*TMP+A[4])*TMP+A[5])*tmp/(((((B[0]*TMP+B[1])*TMP+B[2])*TMP+B[3])*TMP+B[4])*TMP+1);
        }
      else
        {
          if (ub < uniform && uniform < 1)
            {
              T tmp;
              tmp = sqrt(-2*log(1-uniform));
              gaussian = -(((((C[0]*tmp+C[1])*tmp+C[2])*tmp+C[3])*tmp+C[4])*tmp+C[5])/((((D[0]*tmp+D[1])*tmp+D[2])*tmp+D[3])*tmp+1);
            }
        }
    }
  if (0 < uniform && uniform < 1)
    {
      T tmp, tmp_;
      tmp = .5*erfc(-gaussian/sqrt(2.0))-uniform;
      tmp_ = tmp*sqrt(2*M_PI)*exp(.5*gaussian*gaussian);
      gaussian = gaussian - tmp_/(1+.5*gaussian*tmp_);
    }
  if (uniform == 0)
    gaussian = -numeric_limits<T>::infinity();

  if (uniform == 1)
    gaussian = numeric_limits<T>::infinity();

  return gaussian;
}

template<typename T>
void
icdfm(int n, T *U)
{
#pragma omp parallel for
  for (int i = 0; i < n; i++)
    U[i] = icdf(U[i]);
  return;
}

template<typename T>
void
icdfmSigma(int d, int n, T *U, const double *LowerCholSigma)
{
  double one = 1.0;
  double zero = 0.0;
  blas_int dd(d);
  blas_int nn(n);
  icdfm(n*d, U);
  double tmp[n*d];
  dgemm("N", "N", &dd, &nn, &dd, &one, LowerCholSigma, &dd, U, &dd, &zero, tmp, &dd);
  copy_n(tmp, d*n, U);
}

template<typename T>
void
usphere(int d, int n, T *U)
{
  icdfm(n*d, U);
#pragma omp parallel for
  for (int j = 0; j < n; j++) // sequence index.
    {
      int k = j*d;
      double norm = 0.0;
      for (int i = 0; i < d; i++) // dimension index.
        norm = norm + U[k+i]*U[k+i];

      norm = sqrt(norm);
      for (int i = 0; i < d; i++) // dimension index.
        U[k+i] = U[k+i]/norm;
    }
}

template<typename T>
void
usphereRadius(int d, int n, double radius, T *U)
{
  icdfm(n*d, U);
#pragma omp parallel for
  for (int j = 0; j < n; j++) // sequence index.
    {
      int k = j*d;
      double norm = 0.0;
      for (int i = 0; i < d; i++) // dimension index.
        norm = norm + U[k+i]*U[k+i];

      norm = sqrt(norm);
      for (int i = 0; i < d; i++) // dimension index.
        U[k+i] = radius*U[k+i]/norm;
    }
}