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allow HW pixelisations with both even and odd number of rings

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This commit is contained in:
Martin Reinecke 2012-11-20 15:00:54 +01:00
parent 41062aa64a
commit 329f08b7b4
2 changed files with 11 additions and 15 deletions
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25
libsharp/sharp_geomhelpers.c
View file

@ -100,6 +100,9 @@ void sharp_make_weighted_healpix_geom_info (int nside, int stride,
DEALLOC(stride_); 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 /* Function adapted from GNU GSL file glfixed.c
Original author: Pavel Holoborodko (http://www.holoborodko.com) Original author: Pavel Holoborodko (http://www.holoborodko.com)
@ -137,8 +140,7 @@ static void gauss_legendre_tbl(int n, double* x, double* w)
P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2); P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2);
} }
// dpdx = ((x0*P0 - P_1) * n) / ((x0-1.)*(x0+1.)); dpdx = (P_1 - x0*P0) * n / one_minus_x2(x0);
dpdx = (x0*P0 - P_1) * n / (x0*x0-1.);
/* Newton step */ /* Newton step */
x1 = x0 - P0/dpdx; x1 = x0 - P0/dpdx;
@ -152,8 +154,7 @@ static void gauss_legendre_tbl(int n, double* x, double* w)
x[i-1] = -x0; x[i-1] = -x0;
x[n-i] = x0; x[n-i] = x0;
// w[i-1] = w[n-i] = 2. / (((1.-x0)*(1.+x0)) * dpdx * dpdx); w[i-1] = w[n-i] = 2. / (one_minus_x2(x0) * dpdx * dpdx);
w[i-1] = w[n-i] = 2. / ((1.-x0*x0) * dpdx * dpdx);
} }
} }
@ -249,9 +250,7 @@ static inline double eps(int j, int J)
return 0.; return 0.;
} }
/* Weights from Keiner & Potts: "Fast evaluation of quadrature formulae /* Weights from Waldvogel 2006: BIT Numerical Mathematics 46, p. 195 */
on the sphere", 2008 */
/* nrings MUST be odd */
void sharp_make_hw_geom_info (int nrings, int ppring, double phi0, void sharp_make_hw_geom_info (int nrings, int ppring, double phi0,
int stride_lon, int stride_lat, sharp_geom_info **geom_info) int stride_lon, int stride_lat, sharp_geom_info **geom_info)
{ {
@ -264,9 +263,6 @@ void sharp_make_hw_geom_info (int nrings, int ppring, double phi0,
ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings); ptrdiff_t *ofs=RALLOC(ptrdiff_t,nrings);
int *stride_=RALLOC(int,nrings); int *stride_=RALLOC(int,nrings);
UTIL_ASSERT((nrings&1)==1,"nrings must be an odd number");
int lmax=(nrings-1)/2;
for (int m=0; m<=nrings/2; ++m) for (int m=0; m<=nrings/2; ++m)
{ {
theta[m]=pi*m/(nrings-1.); theta[m]=pi*m/(nrings-1.);
@ -278,10 +274,11 @@ void sharp_make_hw_geom_info (int nrings, int ppring, double phi0,
ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat); ofs[nrings-1-m]=(ptrdiff_t)((nrings-1-m)*stride_lat);
stride_[m]=stride_[nrings-1-m]=stride_lon; stride_[m]=stride_[nrings-1-m]=stride_lon;
double wgt=0; double wgt=0;
double prefac=4*pi*eps(m,2*lmax)/lmax; int n=nrings-1;
for (int l=0; l<=lmax; ++l) for (int j=1; j<=n/2; ++j)
wgt+=eps(l,lmax)/(1-4*l*l)*cos((pi*((m*l)%(2*lmax)))/lmax); wgt += ((2*j==n)?1.:2.)/(4.*j*j-1.)*cos(2*j*theta[m]);
weight[m]=weight[nrings-1-m]=prefac*wgt/nph[m]; wgt = ((m%n==0)?1.:2.)/n*(1.-wgt)*2*pi/nph[m];
weight[m]=weight[nrings-1-m]=wgt;
} }
sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, NULL, weight, sharp_make_geom_info (nrings, nph, ofs, stride_, phi0_, theta, NULL, weight,

1
libsharp/sharp_geomhelpers.h
View file

@ -84,7 +84,6 @@ void sharp_make_ecp_geom_info (int nrings, int nphi, double phi0,
is \a stride_lat. is \a stride_lat.
\note The spacing of pixel centers is equidistant in colatitude and \note The spacing of pixel centers is equidistant in colatitude and
longitude. longitude.
\note \a nrings must be an odd number.
\note The sphere is pixelized in a way that the colatitude of the first ring \note The sphere is pixelized in a way that the colatitude of the first ring
is \a 0 and that of the last ring is \a pi. is \a 0 and that of the last ring is \a pi.
\note This is the grid used by Huffenberger & Wandelt 2010 \note This is the grid used by Huffenberger & Wandelt 2010