222 lines
5.9 KiB
C
222 lines
5.9 KiB
C
/*
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* This file is part of libsharp.
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*
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* libsharp is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* libsharp is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with libsharp; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/*
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* libsharp is being developed at the Max-Planck-Institut fuer Astrophysik
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* and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
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* (DLR).
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*/
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/*! \file sharp_geomhelpers.c
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* Spherical transform library
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*
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* Copyright (C) 2006-2011 Max-Planck-Society
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* \author Martin Reinecke
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*/
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#include <math.h>
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#include "sharp_geomhelpers.h"
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#include "c_utils.h"
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void sharp_make_healpix_geom_info (int nside, int stride,
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sharp_geom_info **geom_info)
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{
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double *weight=RALLOC(double,2*nside);
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SET_ARRAY(weight,0,2*nside,1);
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sharp_make_weighted_healpix_geom_info (nside, stride, weight, geom_info);
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DEALLOC(weight);
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}
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void sharp_make_weighted_healpix_geom_info (int nside, int stride,
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const double *weight, sharp_geom_info **geom_info)
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{
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const double pi=3.141592653589793238462643383279502884197;
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ptrdiff_t npix=(ptrdiff_t)nside*nside*12;
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ptrdiff_t ncap=2*(ptrdiff_t)nside*(nside-1);
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int nrings=4*nside-1;
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double *theta=RALLOC(double,nrings);
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double *weight_=RALLOC(double,nrings);
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int *nph=RALLOC(int,nrings);
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double *phi0=RALLOC(double,nrings);
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ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
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int *stride_=RALLOC(int,nrings);
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for (int m=0; m<nrings; ++m)
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{
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int ring=m+1;
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ptrdiff_t northring = (ring>2*nside) ? 4*nside-ring : ring;
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stride_[m] = stride;
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if (northring < nside)
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{
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theta[m] = 2*asin(northring/(sqrt(6.)*nside));
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nph[m] = 4*northring;
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phi0[m] = pi/nph[m];
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ofs[m] = 2*northring*(northring-1)*stride;
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}
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else
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{
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double fact1 = (8.*nside)/npix;
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double costheta = (2*nside-northring)*fact1;
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theta[m] = acos(costheta);
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nph[m] = 4*nside;
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if ((northring-nside) & 1)
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phi0[m] = 0;
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else
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phi0[m] = pi/nph[m];
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ofs[m] = (ncap + (northring-nside)*nph[m])*stride;
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}
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if (northring != ring) /* southern hemisphere */
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{
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theta[m] = pi-theta[m];
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ofs[m] = (npix - nph[m])*stride - ofs[m];
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}
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weight_[m]=4.*pi/npix*weight[northring-1];
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}
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sharp_make_geom_info (nrings, nph, ofs, stride_, phi0, theta, weight_,
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geom_info);
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DEALLOC(theta);
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DEALLOC(weight_);
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DEALLOC(nph);
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DEALLOC(phi0);
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DEALLOC(ofs);
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DEALLOC(stride_);
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}
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static void gauleg (double x1, double x2, double *x, double *w, int n)
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{
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const double pi = 3.141592653589793238462643383279502884197;
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const double eps = 3.0E-14;
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int m = (n+1)/2;
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double xm = 0.5*(x2+x1);
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double xl = 0.5*(x2-x1);
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for(int i=1; i<=m; ++i)
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{
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double z = cos(pi*(i-0.25)/(n+0.5));
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double pp;
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int dobreak=0;
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while(1)
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{
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double p1 = 1.0, p2 = 0.0;
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double z1 = z;
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int j;
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for(j=1; j<=n; ++j)
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{
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double p3 = p2;
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p2 = p1;
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p1 = ((2*j-1)*z*p2-(j-1)*p3)/j;
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}
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pp = n*(z*p1-p2)/(z*z-1);
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z = z1 - p1/pp;
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if (dobreak) break;
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if (fabs(z-z1) <= eps) dobreak=1;
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}
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x[i-1] = xm - xl*z;
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x[n-i] = xm + xl*z;
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w[i-1] = w[n-i] = 2*xl/((1-z*z)*pp*pp);
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}
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}
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static void makeweights (int bw, double *weights)
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{
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const double pi = 3.141592653589793238462643383279502884197;
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const double fudge = pi/(4*bw);
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for (int j=0; j<2*bw; ++j)
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{
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double tmpsum = 0;
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for (int k=0; k<bw; ++k)
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tmpsum += 1./(2*k+1) * sin((2*j+1)*(2*k+1)*fudge);
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tmpsum *= sin((2*j+1)*fudge);
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tmpsum *= 2./bw;
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weights[j] = tmpsum;
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/* weights[j + 2*bw] = tmpsum * sin((2*j+1)*fudge); */
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}
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}
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void sharp_make_gauss_geom_info (int nrings, int nphi, int stride_lon,
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int stride_lat, sharp_geom_info **geom_info)
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{
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const double pi=3.141592653589793238462643383279502884197;
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double *theta=RALLOC(double,nrings);
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double *weight=RALLOC(double,nrings);
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int *nph=RALLOC(int,nrings);
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double *phi0=RALLOC(double,nrings);
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ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
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int *stride_=RALLOC(int,nrings);
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gauleg(-1,1,theta,weight,nrings);
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for (int m=0; m<nrings; ++m)
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{
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theta[m] = acos(-theta[m]);
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nph[m]=nphi;
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phi0[m]=0;
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ofs[m]=(ptrdiff_t)m*stride_lat;
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stride_[m]=stride_lon;
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weight[m]*=2*pi/nphi;
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}
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sharp_make_geom_info (nrings, nph, ofs, stride_, phi0, theta, weight,
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geom_info);
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DEALLOC(theta);
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DEALLOC(weight);
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DEALLOC(nph);
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DEALLOC(phi0);
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DEALLOC(ofs);
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DEALLOC(stride_);
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}
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void sharp_make_ecp_geom_info (int nrings, int nphi, double phi0,
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int stride_lon, int stride_lat, sharp_geom_info **geom_info)
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{
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const double pi=3.141592653589793238462643383279502884197;
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double *theta=RALLOC(double,nrings);
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double *weight=RALLOC(double,nrings);
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int *nph=RALLOC(int,nrings);
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double *phi0_=RALLOC(double,nrings);
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ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
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int *stride_=RALLOC(int,nrings);
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UTIL_ASSERT((nrings&1)==0,
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"Even number of rings needed for equidistant grid!");
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makeweights(nrings/2,weight);
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for (int m=0; m<nrings; ++m)
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{
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theta[m] = (m+0.5)*pi/nrings;
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nph[m]=nphi;
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phi0_[m]=phi0;
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ofs[m]=(ptrdiff_t)m*stride_lat;
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stride_[m]=stride_lon;
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weight[m]*=2*pi/nphi;
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}
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sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, weight,
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geom_info);
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DEALLOC(theta);
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DEALLOC(weight);
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DEALLOC(nph);
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DEALLOC(phi0_);
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DEALLOC(ofs);
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DEALLOC(stride_);
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}
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