libhealpix-cxx-dev 3.11.2-7.1ubuntu1 / usr / include / healpix_cxx / sharp_geomhelpers.c

/*
 *  This file is part of libsharp.
 *
 *  libsharp 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 2 of the License, or
 *  (at your option) any later version.
 *
 *  libsharp 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 libsharp; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

/*
 *  libsharp is being developed at the Max-Planck-Institut fuer Astrophysik
 *  and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
 *  (DLR).
 */

/*! \file sharp_geomhelpers.c
 *  Spherical transform library
 *
 *  Copyright (C) 2006-2012 Max-Planck-Society<br>
 *  Copyright (C) 2007-2008 Pavel Holoborodko (for gauss_legendre_tbl)
 *  \author Martin Reinecke \author Pavel Holoborodko
 */

#include <math.h>
#include "sharp_geomhelpers.h"
#include "c_utils.h"
#include "ls_fft.h"

void sharp_make_weighted_healpix_geom_info (int nside, int stride,
  const double *weight, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;
  ptrdiff_t npix=(ptrdiff_t)nside*nside*12;
  ptrdiff_t ncap=2*(ptrdiff_t)nside*(nside-1);
  int nrings=4*nside-1;

  double *theta=RALLOC(double,nrings);
  double *weight_=RALLOC(double,nrings);
  int *nph=RALLOC(int,nrings);
  double *phi0=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);
  for (int m=0; m<nrings; ++m)
    {
    int ring=m+1;
    ptrdiff_t northring = (ring>2*nside) ? 4*nside-ring : ring;
    stride_[m] = stride;
    if (northring < nside)
      {
      theta[m] = 2*asin(northring/(sqrt(6.)*nside));
      nph[m] = 4*northring;
      phi0[m] = pi/nph[m];
      ofs[m] = 2*northring*(northring-1)*stride;
      }
    else
      {
      double fact1 = (8.*nside)/npix;
      double costheta = (2*nside-northring)*fact1;
      theta[m] = acos(costheta);
      nph[m] = 4*nside;
      if ((northring-nside) & 1)
        phi0[m] = 0;
      else
        phi0[m] = pi/nph[m];
      ofs[m] = (ncap + (northring-nside)*nph[m])*stride;
      }
    if (northring != ring) /* southern hemisphere */
      {
      theta[m] = pi-theta[m];
      ofs[m] = (npix - nph[m])*stride - ofs[m];
      }
    weight_[m]=4.*pi/npix*((weight==NULL) ? 1. : weight[northring-1]);
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0, theta, weight_,
    geom_info);

  DEALLOC(theta);
  DEALLOC(weight_);
  DEALLOC(nph);
  DEALLOC(phi0);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }

static inline double one_minus_x2 (double x)
  { return (fabs(x)>0.1) ? (1.+x)*(1.-x) : 1.-x*x; }

/* Function adapted from GNU GSL file glfixed.c
   Original author: Pavel Holoborodko (http://www.holoborodko.com)

   Adjustments by M. Reinecke
    - adjusted interface (keep epsilon internal, return full number of points)
    - removed precomputed tables
    - tweaked Newton iteration to obtain higher accuracy */
static void gauss_legendre_tbl(int n, double *x, double *w)
  {
  const double pi = 3.141592653589793238462643383279502884197;
  const double eps = 3e-14;
  int m = (n+1)>>1;

  double t0 = 1 - (1-1./n) / (8.*n*n);
  double t1 = 1./(4.*n+2.);

#pragma omp parallel
{
  int i;
#pragma omp for schedule(dynamic,100)
  for (i=1; i<=m; ++i)
    {
    double x0 = cos(pi * ((i<<2)-1) * t1) * t0;

    int dobreak=0;
    int j=0;
    double dpdx;
    while(1)
      {
      double P_1 = 1.0;
      double P0 = x0;
      double dx, x1;

      for (int k=2; k<=n; k++)
        {
        double P_2 = P_1;
        P_1 = P0;
//        P0 = ((2*k-1)*x0*P_1-(k-1)*P_2)/k;
        P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2);
        }

      dpdx = (P_1 - x0*P0) * n / one_minus_x2(x0);

      /* Newton step */
      x1 = x0 - P0/dpdx;
      dx = x0-x1;
      x0 = x1;
      if (dobreak) break;

      if (fabs(dx)<=eps) dobreak=1;
      UTIL_ASSERT(++j<100,"convergence problem");
      }

    x[i-1] = -x0;
    x[n-i] = x0;
    w[i-1] = w[n-i] = 2. / (one_minus_x2(x0) * dpdx * dpdx);
    }
} // end of parallel region
  }

void sharp_make_gauss_geom_info (int nrings, int nphi, double phi0,
  int stride_lon, int stride_lat, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;

  double *theta=RALLOC(double,nrings);
  double *weight=RALLOC(double,nrings);
  int *nph=RALLOC(int,nrings);
  double *phi0_=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);

  gauss_legendre_tbl(nrings,theta,weight);
  for (int m=0; m<nrings; ++m)
    {
    theta[m] = acos(-theta[m]);
    nph[m]=nphi;
    phi0_[m]=phi0;
    ofs[m]=(ptrdiff_t)m*stride_lat;
    stride_[m]=stride_lon;
    weight[m]*=2*pi/nphi;
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, weight,
    geom_info);

  DEALLOC(theta);
  DEALLOC(weight);
  DEALLOC(nph);
  DEALLOC(phi0_);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }

/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
void sharp_make_fejer1_geom_info (int nrings, int ppring, double phi0,
  int stride_lon, int stride_lat, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;

  double *theta=RALLOC(double,nrings);
  double *weight=RALLOC(double,nrings);
  int *nph=RALLOC(int,nrings);
  double *phi0_=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);

  weight[0]=2.;
  for (int k=1; k<=(nrings-1)/2; ++k)
    {
    weight[2*k-1]=2./(1.-4.*k*k)*cos((k*pi)/nrings);
    weight[2*k  ]=2./(1.-4.*k*k)*sin((k*pi)/nrings);
    }
  if ((nrings&1)==0) weight[nrings-1]=0.;
  real_plan plan = make_real_plan(nrings);
  real_plan_backward_fftpack(plan,weight);
  kill_real_plan(plan);

  for (int m=0; m<(nrings+1)/2; ++m)
    {
    theta[m]=pi*(m+0.5)/nrings;
    theta[nrings-1-m]=pi-theta[m];
    nph[m]=nph[nrings-1-m]=ppring;
    phi0_[m]=phi0_[nrings-1-m]=phi0;
    ofs[m]=(ptrdiff_t)m*stride_lat;
    ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
    stride_[m]=stride_[nrings-1-m]=stride_lon;
    weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(nrings*nph[m]);
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, weight,
    geom_info);

  DEALLOC(theta);
  DEALLOC(weight);
  DEALLOC(nph);
  DEALLOC(phi0_);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }

/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
void sharp_make_cc_geom_info (int nrings, int ppring, double phi0,
  int stride_lon, int stride_lat, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;

  double *theta=RALLOC(double,nrings);
  double *weight=RALLOC(double,nrings);
  int *nph=RALLOC(int,nrings);
  double *phi0_=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);

  int n=nrings-1;
  SET_ARRAY(weight,0,nrings,0.);
  double dw=-1./(n*n-1.+(n&1));
  weight[0]=2.+dw;
  for (int k=1; k<=(n/2-1); ++k)
    weight[2*k-1]=2./(1.-4.*k*k) + dw;
  weight[2*(n/2)-1]=(n-3.)/(2*(n/2)-1) -1. -dw*((2-(n&1))*n-1);
  real_plan plan = make_real_plan(n);
  real_plan_backward_fftpack(plan,weight);
  kill_real_plan(plan);
  weight[n]=weight[0];

  for (int m=0; m<(nrings+1)/2; ++m)
    {
    theta[m]=pi*m/(nrings-1.);
    if (theta[m]<1e-15) theta[m]=1e-15;
    theta[nrings-1-m]=pi-theta[m];
    nph[m]=nph[nrings-1-m]=ppring;
    phi0_[m]=phi0_[nrings-1-m]=phi0;
    ofs[m]=(ptrdiff_t)m*stride_lat;
    ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
    stride_[m]=stride_[nrings-1-m]=stride_lon;
    weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(n*nph[m]);
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, weight,
    geom_info);

  DEALLOC(theta);
  DEALLOC(weight);
  DEALLOC(nph);
  DEALLOC(phi0_);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }

/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
void sharp_make_fejer2_geom_info (int nrings, int ppring, double phi0,
  int stride_lon, int stride_lat, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;

  double *theta=RALLOC(double,nrings);
  double *weight=RALLOC(double,nrings+1);
  int *nph=RALLOC(int,nrings);
  double *phi0_=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);

  int n=nrings+1;
  SET_ARRAY(weight,0,n,0.);
  weight[0]=2.;
  for (int k=1; k<=(n/2-1); ++k)
    weight[2*k-1]=2./(1.-4.*k*k);
  weight[2*(n/2)-1]=(n-3.)/(2*(n/2)-1) -1.;
  real_plan plan = make_real_plan(n);
  real_plan_backward_fftpack(plan,weight);
  kill_real_plan(plan);
  for (int m=0; m<nrings; ++m)
    weight[m]=weight[m+1];

  for (int m=0; m<(nrings+1)/2; ++m)
    {
    theta[m]=pi*(m+1)/(nrings+1.);
    theta[nrings-1-m]=pi-theta[m];
    nph[m]=nph[nrings-1-m]=ppring;
    phi0_[m]=phi0_[nrings-1-m]=phi0;
    ofs[m]=(ptrdiff_t)m*stride_lat;
    ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
    stride_[m]=stride_[nrings-1-m]=stride_lon;
    weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(n*nph[m]);
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, weight,
    geom_info);

  DEALLOC(theta);
  DEALLOC(weight);
  DEALLOC(nph);
  DEALLOC(phi0_);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }

void sharp_make_mw_geom_info (int nrings, int ppring, double phi0,
  int stride_lon, int stride_lat, sharp_geom_info **geom_info)
  {
  const double pi=3.141592653589793238462643383279502884197;

  double *theta=RALLOC(double,nrings);
  int *nph=RALLOC(int,nrings);
  double *phi0_=RALLOC(double,nrings);
  ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
  int *stride_=RALLOC(int,nrings);

  for (int m=0; m<nrings; ++m)
    {
    theta[m]=pi*(2.*m+1.)/(2.*nrings-1.);
    if (theta[m]>pi-1e-15) theta[m]=pi-1e-15;
    nph[m]=ppring;
    phi0_[m]=phi0;
    ofs[m]=(ptrdiff_t)m*stride_lat;
    stride_[m]=stride_lon;
    }

  sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, NULL,
    geom_info);

  DEALLOC(theta);
  DEALLOC(nph);
  DEALLOC(phi0_);
  DEALLOC(ofs);
  DEALLOC(stride_);
  }