379 lines
11 KiB
C
379 lines
11 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) 2006-2012 Max-Planck-Society<br>
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* Copyright (C) 2007-2008 Pavel Holoborodko (for gauss_legendre_tbl)
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* \author Martin Reinecke \author Pavel Holoborodko
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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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#include "ls_fft.h"
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#include <stdio.h>
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void sharp_make_subset_healpix_geom_info (int nside, int stride, int nrings,
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const int *rings, 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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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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ptrdiff_t curofs=0, checkofs; /* checkofs used for assertion introduced when adding rings arg */
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for (int m=0; m<nrings; ++m)
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{
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int ring = (rings==NULL)? (m+1) : rings[m];
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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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checkofs = 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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checkofs = (ncap + (northring-nside)*nph[m])*stride;
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ofs[m] = curofs;
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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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checkofs = (npix - nph[m])*stride - checkofs;
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ofs[m] = curofs;
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}
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weight_[m]=4.*pi/npix*((weight==NULL) ? 1. : weight[northring-1]);
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if (rings==NULL) {
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UTIL_ASSERT(curofs==checkofs, "Bug in computing ofs[m]");
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}
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ofs[m] = curofs;
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curofs+=nph[m];
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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_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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sharp_make_subset_healpix_geom_info(nside, stride, 4 * nside - 1, NULL, weight, geom_info);
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}
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static inline double one_minus_x2 (double x)
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{ return (fabs(x)>0.1) ? (1.+x)*(1.-x) : 1.-x*x; }
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/* Function adapted from GNU GSL file glfixed.c
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Original author: Pavel Holoborodko (http://www.holoborodko.com)
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Adjustments by M. Reinecke
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- adjusted interface (keep epsilon internal, return full number of points)
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- removed precomputed tables
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- tweaked Newton iteration to obtain higher accuracy */
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static void gauss_legendre_tbl(int n, double *x, double *w)
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{
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const double pi = 3.141592653589793238462643383279502884197;
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const double eps = 3e-14;
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int m = (n+1)>>1;
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double t0 = 1 - (1-1./n) / (8.*n*n);
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double t1 = 1./(4.*n+2.);
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#pragma omp parallel
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{
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int i;
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#pragma omp for schedule(dynamic,100)
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for (i=1; i<=m; ++i)
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{
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double x0 = cos(pi * ((i<<2)-1) * t1) * t0;
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int dobreak=0;
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int j=0;
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double dpdx;
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while(1)
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{
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double P_1 = 1.0;
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double P0 = x0;
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double dx, x1;
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for (int k=2; k<=n; k++)
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{
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double P_2 = P_1;
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P_1 = P0;
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// P0 = ((2*k-1)*x0*P_1-(k-1)*P_2)/k;
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P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2);
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}
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dpdx = (P_1 - x0*P0) * n / one_minus_x2(x0);
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/* Newton step */
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x1 = x0 - P0/dpdx;
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dx = x0-x1;
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x0 = x1;
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if (dobreak) break;
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if (fabs(dx)<=eps) dobreak=1;
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UTIL_ASSERT(++j<100,"convergence problem");
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}
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x[i-1] = -x0;
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x[n-i] = x0;
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w[i-1] = w[n-i] = 2. / (one_minus_x2(x0) * dpdx * dpdx);
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}
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} // end of parallel region
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}
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void sharp_make_gauss_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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gauss_legendre_tbl(nrings,theta,weight);
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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]=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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/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
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void sharp_make_fejer1_geom_info (int nrings, int ppring, 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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weight[0]=2.;
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for (int k=1; k<=(nrings-1)/2; ++k)
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{
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weight[2*k-1]=2./(1.-4.*k*k)*cos((k*pi)/nrings);
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weight[2*k ]=2./(1.-4.*k*k)*sin((k*pi)/nrings);
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}
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if ((nrings&1)==0) weight[nrings-1]=0.;
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real_plan plan = make_real_plan(nrings);
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real_plan_backward_fftpack(plan,weight);
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kill_real_plan(plan);
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for (int m=0; m<(nrings+1)/2; ++m)
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{
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theta[m]=pi*(m+0.5)/nrings;
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theta[nrings-1-m]=pi-theta[m];
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nph[m]=nph[nrings-1-m]=ppring;
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phi0_[m]=phi0_[nrings-1-m]=phi0;
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ofs[m]=(ptrdiff_t)m*stride_lat;
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ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
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stride_[m]=stride_[nrings-1-m]=stride_lon;
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weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(nrings*nph[m]);
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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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/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
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void sharp_make_cc_geom_info (int nrings, int ppring, 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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int n=nrings-1;
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SET_ARRAY(weight,0,nrings,0.);
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double dw=-1./(n*n-1.+(n&1));
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weight[0]=2.+dw;
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for (int k=1; k<=(n/2-1); ++k)
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weight[2*k-1]=2./(1.-4.*k*k) + dw;
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weight[2*(n/2)-1]=(n-3.)/(2*(n/2)-1) -1. -dw*((2-(n&1))*n-1);
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real_plan plan = make_real_plan(n);
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real_plan_backward_fftpack(plan,weight);
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kill_real_plan(plan);
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weight[n]=weight[0];
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for (int m=0; m<(nrings+1)/2; ++m)
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{
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theta[m]=pi*m/(nrings-1.);
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if (theta[m]<1e-15) theta[m]=1e-15;
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theta[nrings-1-m]=pi-theta[m];
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nph[m]=nph[nrings-1-m]=ppring;
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phi0_[m]=phi0_[nrings-1-m]=phi0;
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ofs[m]=(ptrdiff_t)m*stride_lat;
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ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
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stride_[m]=stride_[nrings-1-m]=stride_lon;
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weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(n*nph[m]);
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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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/* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
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void sharp_make_fejer2_geom_info (int nrings, int ppring, 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+1);
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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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int n=nrings+1;
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SET_ARRAY(weight,0,n,0.);
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weight[0]=2.;
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for (int k=1; k<=(n/2-1); ++k)
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weight[2*k-1]=2./(1.-4.*k*k);
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weight[2*(n/2)-1]=(n-3.)/(2*(n/2)-1) -1.;
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real_plan plan = make_real_plan(n);
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real_plan_backward_fftpack(plan,weight);
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kill_real_plan(plan);
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for (int m=0; m<nrings; ++m)
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weight[m]=weight[m+1];
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for (int m=0; m<(nrings+1)/2; ++m)
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{
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theta[m]=pi*(m+1)/(nrings+1.);
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theta[nrings-1-m]=pi-theta[m];
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nph[m]=nph[nrings-1-m]=ppring;
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phi0_[m]=phi0_[nrings-1-m]=phi0;
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ofs[m]=(ptrdiff_t)m*stride_lat;
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ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
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stride_[m]=stride_[nrings-1-m]=stride_lon;
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weight[m]=weight[nrings-1-m]=weight[m]*2*pi/(n*nph[m]);
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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_mw_geom_info (int nrings, int ppring, 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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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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theta[m]=pi*(2.*m+1.)/(2.*nrings-1.);
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if (theta[m]>pi-1e-15) theta[m]=pi-1e-15;
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nph[m]=ppring;
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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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}
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sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, NULL,
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geom_info);
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DEALLOC(theta);
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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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