/
sh_exp.c
2356 lines (2141 loc) · 54 KB
/
sh_exp.c
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/*
lower level routines to handle spherical harmonics expansions
the higher level routines that operate on single (or triple)
sets of expansions are in sh_model.c
$Id: sh_exp.c,v 1.15 2006/03/20 05:32:48 becker Exp becker $
*/
#include "hc.h"
/*
allocates and initializes spherical harmonics structure
*/
void
sh_allocate_and_init (exp, n, lmax, type, ivec, verbose, regular)
struct sh_lms **exp;
int n;
int lmax;
int type;
int ivec;
hc_boolean verbose;
hc_boolean regular;
{
int i;
/* init as zeroes! (but this won't necessarily set the logic flags!) */
*exp = (struct sh_lms *)calloc(n,sizeof(struct sh_lms));
if(!(*exp))
HC_MEMERROR("sh_allocate_and_init");
for(i=0;i < n;i++){
sh_init_expansion((*exp+i),lmax,type,ivec,verbose,regular);
}
}
/*
compute the parameters needed for a single expansion of order lmax and
allocate initial array for spectral coefficients. the type of array
depends on the type of expansion.
if you want vector harmonics at any point during a computation, set
ivec to unity initially
coefficients are initialized as zero
if regular is set, will not use Gauss points
*/
void
sh_init_expansion (exp, lmax, type, ivec, verbose, regular)
struct sh_lms *exp;
int lmax;
int type;
int ivec;
hc_boolean verbose;
hc_boolean regular;
{
/*
initialize logic flags
*/
exp->spectral_init = FALSE;
/* type of expansion, e.g. SH_HEALPIX or SH_RICK, this will be checked later */
exp->type = type;
#ifdef HC_DEBUG
/*
l and m bounds
*/
if(lmax < 1){
fprintf(stderr,"sh_init_expansion: error: lmax out of bounds: %i\n",
lmax);
exit(-1);
}
#endif
exp->lmax = lmax;
/* same as above, plus one */
exp->lmaxp1 = exp->lmax+1;
/*
size of one set of coefficients (l,m) if stored by wasting space
(assuming we are using complex numbers)
*/
exp->lmbig = exp->lmaxp1 * exp->lmaxp1;
/*
size of coefficients when stored compactly like
(l+1)*l/2 + m, times two for A and B
*/
exp->lmsmall2 = (exp->lmaxp1)*(exp->lmaxp1+1); /* for A and B */
/*
*/
exp->plm_computed = FALSE;
/*
allocate the spectral (coefficients) storage and initialize possibly
other arrays
*/
switch(exp->type){
#ifdef HC_USE_HEALPIX
case SH_HEALPIX: /* SH_HEALPIX part */
if(regular)
HC_ERROR("regular init not implemented for healpix");
/*
get single precision complex array which holds A and B
*/
exp->n_lm = exp->lmbig;
hc_scmplx_vecalloc(&exp->alm_c,exp->n_lm,"init_expansion");
sh_clear_alm(exp);
/*
init the Healpix parameters and determine the number of points
in the spatial domain
*/
heal_init_parameters(&exp->heal,(lmax/2)+2,SH_HEALPIX_RING,
ivec,exp->lmax,&exp->npoints,
&exp->n_plm,&exp->tn_plm);
break;
#endif
case SH_RICK: /* SH_RICK PART */
exp->rick.was_called = FALSE; /* this used to work via a calloc
call, but because not int, make
sure to work */
exp->rick.computed_legendre =
exp->rick.initialized =
exp->rick.vector_sh_fac_init =
exp->rick.sin_cos_saved = FALSE;
/*
make room for the coefficients A and B in compact storage
*/
exp->n_lm = exp->lmsmall2;
/*
use single precision vector
*/
rick_vecalloc(&exp->alm,exp->n_lm,"sh_init_expansion");
sh_clear_alm(exp); /* set to zero */
/*
init the parameters for Rick subroutines
*/
#ifdef NO_RICK_FORTRAN
rick_init(exp->lmax,ivec,&exp->npoints,
&exp->n_plm,&exp->tn_plm,&exp->rick,regular);
#else
/* f90 version */
rick_f90_init(&exp->lmax,&ivec,&exp->npoints,
&exp->n_plm,&exp->tn_plm,regular);
#endif
break;
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_GAUSS:
case SH_SPHEREPACK_EVEN:
HC_ERROR("init_expansion","Spherepack not implemented");
/*
make room for coefficients
*/
/*
initialize
*/
break;
#endif
default:
sh_exp_type_error("sh_init_expansion",exp);
break;
}
}
/*
free an expansion structure with n elements
*/
void
sh_free_expansion (exp, n)
struct sh_lms *exp;
int n;
{
int i;
for(i=0;i<n;i++){
switch(exp[i].type){
#ifdef HC_USE_HEALPIX
case SH_HEALPIX: /* SH_HEALPIX part */
heal_free_structure(&exp[i].heal);
free(exp[i].alm_c);
break;
#endif
case SH_RICK:
free(exp[i].alm);
break;
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_GAUSS:
case SH_SPHEREPACK_EVEN:
HC_ERROR("free_expansion","Spherepack not implemented");
break;
#endif
default:
sh_exp_type_error("sh_free_expansion",(exp+i));
break;
}
}
}
/*
zero out all coefficients
*/
void
sh_clear_alm (exp)
struct sh_lms *exp;
{
int i;
switch(exp->type){
#ifdef HC_USE_HEALPIX
case SH_HEALPIX:
/* init with zeroes */
for(i=0;i<exp->n_lm;i++)
exp->alm_c[i].dr = exp->alm_c[i].di = 0.0;
break;
#endif
case SH_RICK:
for(i=0;i<exp->n_lm;i++)
exp->alm[i] = 0.0;
break;
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_GAUSS:
case SH_SPHEREPACK_EVEN:
HC_ERROR("clear_alm","Spherepack not implemented");
break;
#endif
default:
sh_exp_type_error("sh_clear_alm",exp);
break;
}
}
/*
compute | \Psi | ^2 = \sum (2l+1) \sigma^2
kindof RMS^2
*/
HC_CPREC
sh_total_power (exp)
struct sh_lms *exp;
{
HC_PREC *power;
double sum;
int l;
hc_vecalloc(&power,exp->lmaxp1,"sh_total_power");
sh_compute_power_per_degree(exp,power);
for(sum=0.0,l=0;l<=exp->lmax;l++)
sum += (double)(2.0*(HC_CPREC)l+1.0) * (double)power[l];
free(power);
return (HC_CPREC)sum;
}
HC_CPREC sh_total_rms (exp)
struct sh_lms *exp;
{
HC_PREC *power;
HC_PREC sum;
int l;
hc_vecalloc(&power,exp->lmaxp1,"sh_total_power");
sh_compute_power_per_degree(exp,power);
for(sum=0.0,l=1;l<=exp->lmax;l++){
//fprintf(stderr,"%g\n",(double)power[l]);
sum += (double)(2.0*(HC_CPREC)l+1.0) * (double)power[l];
}
free(power);
return sqrt(sum);
}
/*
compute the power (sigma^2) per degree and unit area
power[lmaxp1]
*/
void
sh_compute_power_per_degree (exp, power)
struct sh_lms *exp;
HC_PREC *power;
{
int l,m;
HC_CPREC value[2];
hc_boolean need_b;
for(l=0;l<=exp->lmax;l++){
power[l] = 0.0;
for(m=0;m<=l;m++){
need_b = (hc_boolean) ((m == 0) ? (0) : (2));
sh_get_coeff(exp,l,m,need_b,TRUE,value); /* convert to DT
normalization */
power[l] += value[0] * value[0];
if(need_b)
power[l] += value[1] * value[1];
} /* end m loop */
power[l] /= 2.0*((HC_CPREC)l)+1.0;
} /* end l loop */
}
/* compute total correlation up to llim */
HC_PREC
sh_correlation (exp1, exp2, llim)
struct sh_lms *exp1;
struct sh_lms *exp2;
int llim;
{
return sh_correlation_per_degree(exp1,exp2,1,llim);
}
HC_PREC
sh_correlation_per_degree (exp1, exp2, lmin, lmax)
struct sh_lms *exp1;
struct sh_lms *exp2;
int lmin;
int lmax;
{
int l,m;
HC_CPREC sum[3],tmp,atmp,btmp,ctmp,value1[2],value2[2];
double dtmp;
hc_boolean need_b;
sum[0]=sum[1]=sum[2]=0.0;
if((lmax > exp1->lmax)||(lmax > exp2->lmax)||(lmax < 1)||(lmin < 1)){
fprintf(stderr,"sh_compute_correlation_per_degree: error: L1 %i L2 %i lmin %i lmax %i\n",
exp1->lmax,exp2->lmax,lmin,lmax);
exit(-1);
}
for(l=lmin;l <= lmax;l++){
for(m=0;m<=l;m++){
need_b = (hc_boolean) ((m == 0) ? (0) : (2));
sh_get_coeff(exp1,l,m,need_b,TRUE,value1); /* convert to DT normalization */
sh_get_coeff(exp2,l,m,need_b,TRUE,value2); /* convert to DT normalization */
atmp = value1[0];
ctmp = value2[0];
sum[0] += atmp * ctmp;
sum[1] += atmp * atmp;
sum[2] += ctmp * ctmp;
if(need_b){
btmp = value1[1];
dtmp = value2[1];
sum[0] += btmp* dtmp;
sum[1] += btmp * btmp;
sum[2] += dtmp * dtmp;
}
} /* end m loop */
} /* end l loop */
tmp = sqrt(sum[1]*sum[2]);
return sum[0]/tmp;
}
void
sh_single_par_and_exp_to_file (exp, name, binary, verbose)
struct sh_lms *exp;
char *name;
hc_boolean binary;
hc_boolean verbose;
{
FILE *out;
out = fopen(name,"w");
if(!out){
fprintf(stderr,"sh_single_par_and_exp_to_file: ERROR: problem openeing %s\n",name);
exit(-1);
}
sh_single_par_and_exp_to_stream(exp,out,binary,verbose);
fclose(out);
if(verbose)
fprintf(stderr,"sh_single_par_and_exp_to_file: written to %s\n",name);
}
void
sh_single_par_and_exp_to_stream (exp, out, binary, verbose)
struct sh_lms *exp;
FILE *out;
hc_boolean binary;
hc_boolean verbose;
{
HC_PREC fac[1]={1.0};
const hc_boolean short_format = FALSE;
sh_print_parameters_to_stream(exp,1,0,1,0,out,short_format,binary,verbose);
sh_print_coefficients_to_stream(exp,1,out,fac,binary,verbose);
}
/*
print one line with all parameters needed to identify a spherical
harmonics expansion for a scalar (shps == 1), poloidal/toroidal (shps
== 2), or a vector field (shps == 3)
exp[shps]
ilayer: the layer index (0...nset-1) for nset layers
zlabel: label for layer ilayer
if short_format is selected, will only print
lmax
*/
void
sh_print_parameters_to_stream (exp, shps, ilayer, nset, zlabel, out, short_format, binary, verbose)
struct sh_lms *exp;
int shps;
int ilayer;
int nset;
HC_CPREC zlabel;
FILE *out;
hc_boolean short_format;
hc_boolean binary;
hc_boolean verbose;
{
HC_PREC fz;
/*
print
lmax i z[i] nset shps expansion_type
*/
if(binary){
fz = (HC_PREC)zlabel;
fwrite(&exp[0].lmax,sizeof(int),1,out);
if(!short_format){
fwrite(&ilayer,sizeof(int),1,out);
hc_print_float(&fz,1,out);
fwrite(&nset,sizeof(int),1,out);
fwrite(&shps,sizeof(int),1,out);
fwrite(&exp[0].type,sizeof(int),1,out);
}
}else{
if(!short_format)
fprintf(out,"%6i %6i %.8e %6i %2i %2i ",
exp[0].lmax,ilayer,
(double)zlabel,nset,
shps,exp[0].type);
else
fprintf(out,"%6i ",
exp[0].lmax);
}
/*
additional parameters?
*/
switch(exp[0].type){
case SH_RICK:
break;
#ifdef HC_USE_HEALPIX
case SH_HEALPIX:
break;
#endif
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_GAUSS:
case SH_SPHEREPACK_EVEN:
break;
#endif
default:
sh_exp_type_error("sh_print_parameters",exp);
break;
}
if(!binary)
fprintf(out,"\n"); /* finish header line */
}
/*
read parameters needed to initialize an expansion
can be used to read several layers of a model
will return TRUE, if success
default (long format) input is
type lmax shps ilayer nset zlabel ivec
short format is just
lmax
explanations:
type: type of spherical harmonics expansion
lmax: max degree
shps: 1 or 3 for different sets of expansions, scalar or scalar + vector
ilayer: 0..nset
nset: number of sets
zlabel: float label of this set
ivec: scalar/vector flag. 0 for shps==1, 1 else
*/
hc_boolean
sh_read_parameters_from_stream (type, lmax, shps, ilayer, nset, zlabel, ivec, in, short_format, binary, verbose)
int *type;
int *lmax;
int *shps;
int *ilayer;
int *nset;
HC_CPREC *zlabel;
int *ivec;
FILE *in;
hc_boolean short_format;
hc_boolean binary;
hc_boolean verbose;
{
int input1[2],input2[3];
HC_PREC fz;
double dtmp;
/*
read
lmax i+1 z[i] nset shps expansion_type
*/
if(binary){
if(short_format){
if(fread(input1,sizeof(int),1,in) != 1)
return FALSE;
*lmax = input1[0];
}else{
if(fread(input1,sizeof(int),2,in)+
hc_read_float(&fz,1,in) +
fread(input2,sizeof(int),3,in) != 6)
return FALSE;
*lmax = input1[0];
*ilayer=input1[1];
*zlabel = (HC_CPREC) fz;
*nset = input2[0];
*shps = input2[1];
*type = input2[2];
}
}else{
if(short_format){
if(fscanf(in,"%i",lmax)!=1){
return FALSE;
}
}else{
if(fscanf(in,"%i %i %lf %i %i %i",
lmax,ilayer,&dtmp,nset,shps,type)!=6){
return FALSE;
}
*zlabel = (HC_PREC)dtmp;
}
}
if(short_format){
/* default settings for short format */
*zlabel = 0.0;
*ilayer = 0;
*nset=1;
*shps = 1;
*type = HC_DEFAULT_INTERNAL_FORMAT;
}
if(*shps == 1)
*ivec = 0;
else
*ivec = 1;
/*
additional parameters?
*/
switch(*type){
case SH_RICK:
break;
#ifdef HC_USE_HEALPIX
case SH_HEALPIX:
break;
#endif
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_EVEN:
case SH_SPHEREPACK_GAUSS:
break;
#endif
default:
fprintf(stderr,"sh_read_parameters: type %i undefined\n",
*type);
exit(-1);
break;
}
return TRUE;
}
/*
write the coefficients of a spherical harmonic expansion to out stream
output will be real spherical harmonics coefficients as in Dahlen and
Tromp p. 859
for shps = 1
A00 B00
A10 B10
A11 B11
A20 ...
for shps = 2
A00_p B00_p A00_t B00_t
A10_p B10_p A10_t B10_t
....
for shps = 3
A00_s B00_s A00_p B00_p A00_t B00_t
A10_s B10_s A10_p B10_p A10_t B10_t
....
where s, p, and t are the scalar (radial), poloidal, and toroidal expansions,
respectively
pass shps as unity, if scalar, as 2 if pol/tor part of field, and
as 3 if u_r pol tor components with three expansions for velocity
field
basically, all values of shps can be passed, as long as exp[shps]
fac[3] scales the coefficients
*/
void
sh_print_coefficients_to_stream (exp, shps, out, fac, binary, verbose)
struct sh_lms *exp;
int shps;
FILE *out;
HC_CPREC *fac;
hc_boolean binary;
hc_boolean verbose;
{
int j,l,m;
HC_PREC value[2];
HC_PREC fvalue[2];
/*
test other expansions this set
*/
for(j=0;j < shps;j++){ /* check the lmax */
if(exp[j].lmax != exp[0].lmax){
fprintf(stderr,"sh_print_coefficients: error: lmax(%i):%i != lmax(0):%i\n",
j+1,exp[j].lmax,exp[0].lmax);
exit(-1);
}
if(exp[j].type != exp[0].type ){
fprintf(stderr,"sh_print_coefficients: error: type(%i):%i != type(0):%i\n",
j+1,exp[j].type,exp[0].type);
exit(-1);
}
} /* end test */
if(binary){
for(l=0;l <= exp[0].lmax;l++)
for(m=0;m <= l;m++)
for(j=0;j < shps;j++){
/*
output is in physical convention, convert from whatever
we are using internally
*/
sh_get_coeff((exp+j),l,m,2,TRUE,value);
fvalue[0] = value[0]*fac[j];
fvalue[1] = value[1]*fac[j];
hc_print_float(fvalue, 2, out);
}
}else{
for(l=0;l <= exp[0].lmax;l++){
for(m=0;m <= l;m++){
for(j=0;j < shps;j++){
/* output in physical convention, convert from internal
convention */
sh_get_coeff((exp+j),l,m,2,TRUE,value);
fprintf(out,"%15.7e %15.7e\t",
(double)(value[0]*fac[j]),
(double)(value[1]*fac[j]));
}
fprintf(out,"\n");
} /* end m loop */
} /* end l loop */
//fprintf(out,"\n");
}
}
/*
read in spherical harmonic coefficients in real, physics convention of
Dahlen and Tromp p. 859, and convert to whatever internal format may
be used
shps: number of spherical harmonics sets
scale coefficients with factor fac[shps]
lmax: -1: use lmax from expansion
else: read up to lmax
*/
void
sh_read_coefficients_from_stream (exp, shps, lmax, in, binary, fac, verbose)
struct sh_lms *exp;
int shps;
int lmax;
FILE *in;
hc_boolean binary;
HC_CPREC *fac;
hc_boolean verbose;
{
int j,k,l,m,lmax_loc;
HC_CPREC value[2]={0,0};
HC_PREC fvalue[2]={0,0};
if(lmax < 0)
lmax_loc = exp[0].lmax;
else
lmax_loc = lmax;
/*
test other expansions of this set
*/
for(j=1;j < shps;j++){ /* check the lmax */
if(exp[j].lmax != exp[0].lmax){
fprintf(stderr,"sh_read_coefficients_from_stream: error: lmax(%i):%i != lmax(0):%i\n",
j+1,exp[j].lmax,exp[0].lmax);
exit(-1);
}
if(exp[j].type != exp[0].type ){
fprintf(stderr,"sh_read_coefficients_from_stream: error: type(%i):%i != type(0):%i\n",
j+1,exp[j].type,exp[0].type);
exit(-1);
}
} /* end test */
if(binary){
for(l=0;l <= lmax_loc;l++)
for(m=0;m <= l;m++)
for(j=0;j < shps;j++){
if(hc_read_float(fvalue,2,in)!=2){
fprintf(stderr,"sh_read_coefficients_from_stream: read error: set %i l %i m %i\n",
j+1,l,m);
exit(-1);
}
for(k=0;k<2;k++)
value[k] = (HC_CPREC)fvalue[k];
/* read in real, Dahlen & Tromp normalized coefficients and
convert to whatever format we are using internally */
sh_write_coeff((exp+j),l,m,(m==0)?(0):(2),TRUE,value);
}
}else{
for(l=0;l <= lmax_loc;l++)
for(m=0;m <= l;m++)
for(j=0;j < shps;j++){
if(fscanf(in,HC_TWO_FLT_FORMAT,value,(value+1))!=2){
fprintf(stderr,"sh_read_coefficients_from_stream: read error: set %i l %i m %i, last val: %g %g\n",
j+1,l,m,(double)value[0],(double)value[1]);
exit(-1);
}
/* read in real, Dahlen & Tromp normalized coefficients and
convert to whatever format we are using internally */
sh_write_coeff((exp+j),l,m,(m==0)?(0):(2),TRUE,value);
}
}
/* fill up rest with zeroes, if we are limiting to lmax_loc */
if(lmax_loc < exp[0].lmax){
value[0] = value[1] = 0.0;
for(l=lmax_loc+1;l <= exp[0].lmax;l++)
for(m=0;m <= l;m++)
for(j=0;j < shps;j++)
sh_write_coeff((exp+j),l,m,(m==0)?(0):(2),TRUE,value);
}
for(j=0;j < shps;j++){
//sh_print_nonzero_coeff((exp+j),stderr);
sh_scale_expansion((exp+j),fac[j]);
//sh_print_nonzero_coeff((exp+j),stderr);
exp[j].spectral_init = TRUE;
}
}
/* print a raw set of coefficients to out if nonzero, for
debugging */
void
sh_print_nonzero_coeff (exp, out)
struct sh_lms *exp;
FILE *out;
{
int l,m;
HC_CPREC value[2];
for(l=0;l <= exp->lmax;l++){
for(m=0;m <= l;m++){
sh_get_coeff(exp,l,m,2,FALSE,value);
if(fabs(value[0])+fabs(value[1]) > 1e-8)
fprintf(out,"%5i %5i %15.7e %15.7e\n",l,m,
(double)value[0],(double)value[1]);
}
}
}
/*
given an initializez expansion structure, read the corresponding spatial data in
lon lat data
format from FILE *in
the output is in the data array, which has to be passed
data[shps * exp->npoints]
if use_3d is set, will read in
lon lat z data
instead
*/
void
sh_read_spatial_data_from_stream (exp, in, use_3d, shps, data, z)
struct sh_lms *exp;
FILE *in;
my_boolean use_3d;
int shps;
HC_PREC *data;
HC_PREC *z;
{
sh_read_spatial_data(exp,in,use_3d,shps,data,z);
}
/*
generic function
*/
void
sh_read_spatial_data (exp, in, use_3d, shps, data, z)
struct sh_lms *exp;
FILE *in;
my_boolean use_3d;
int shps;
HC_PREC *data;
HC_PREC *z;
{
HC_PREC lon,lat,xp[3];
int j,k;
/*
read in data for each layer
*/
for(j=0;j < exp->npoints;j++){
/*
get expected coordinates to check if the input is OK
*/
switch(exp->type){
#ifdef HC_USE_HEALPIX
case SH_HEALPIX:
switch(exp->heal.ordering){
case SH_HEALPIX_RING:
pix2ang_ring((long)exp->heal.nside,(long)j,
(xp+HC_THETA),(xp+HC_PHI));
break;
case SH_HEALPIX_NEST:
pix2ang_nest((long)exp->heal.nside,(long)j,
(xp+HC_THETA),(xp+HC_PHI));
break;
default:
fprintf(stderr,"sh_read_spatial_data: error: ordering %i undefined\n",
exp->heal.ordering);
exit(-1);
break;
}
break; /* end Healpix branch */
#endif
case SH_RICK:
/* for Rick's type routine */
#ifdef NO_RICK_FORTRAN
rick_pix2ang(j,exp->lmax,(xp+HC_THETA),(xp+HC_PHI),
&exp->rick);
#else
rick_f90_pix2ang(&j,&exp->lmax,(SH_RICK_PREC)(xp+HC_THETA),
(SH_RICK_PREC)(xp+HC_PHI));
#endif
break;
#ifdef HC_USE_SPHEREPACK
case SH_SPHEREPACK_GAUSS:
case SH_SPHEREPACK_EVEN:
break;
#endif
default:
sh_exp_type_error("sh_read_model_spatial_data",exp);
break;
} /* end type branch */
/*
read coordinates
*/
if(!use_3d){
/*
read in lon lat
*/
if(fscanf(in,HC_TWO_FLT_FORMAT,&lon,&lat) != 2){
fprintf(stderr,"sh_read_spatial_data: error: lon lat format: pixel %i: read error\n",
(int)j);
exit(-1);
}
}else{
/*
read in lon lat z[i]
*/
if(fscanf(in,HC_THREE_FLT_FORMAT,&lon,&lat,z) != 3){
fprintf(stderr,"sh_read_spatial_data: error: lon lat z format: pixel %i: read error\n",
(int)j);
exit(-1);
}
}
/*
read data
*/
for(k=0;k < shps;k++){
if(fscanf(in,HC_FLT_FORMAT,(data+k*exp[0].npoints+j))!=1){
fprintf(stderr,"sh_read_spatial_data: error: scalar format: pixel %i: read error\n",
(int)j);
exit(-1);
}
}
/*
adjust longitude range
*/
if(lon < 0)
lon += 360.0;
/*
check if location is OK (we don't know about z defaults)
*/
if(((fabs(PHI2LON(xp[HC_PHI])-lon) > 1e-3)&&(fabs(fabs(PHI2LON(xp[HC_PHI])-lon)-360) > 1e-3))||
(fabs(THETA2LAT(xp[HC_THETA])-lat) > 1e-3)){
fprintf(stderr,"sh_read_model_spatial_data: error: pixel %i coordinate mismatch:\n",
(int)j);
fprintf(stderr,"sh_read_model_spatial_data: orig: %g, %g file: %g, %g\n",
(double)PHI2LON(xp[HC_PHI]),(double)THETA2LAT(xp[HC_THETA]),
(double)lon,(double)lat);
exit(-1);
}
} /* end points in layer loop */
}
/*
print the spatial basis coordinates of a single spherical
harmonics expansion
for show_z_label is FALSE, the format is
lon lat
for all the npoints of an expansion
for show_z_label is TRUE, the format is
lon lat z
as passed
if out_mode == 0, will write to file *out,
else will use x[] and store the values
*/
void
sh_compute_spatial_basis (exp, out, use_3d, z, x, out_mode, verbose)
struct sh_lms *exp;
FILE *out;
hc_boolean use_3d;
HC_PREC z;
HC_PREC **x;
int out_mode;
hc_boolean verbose;
{
int j,os,inc;
HC_PREC xp[3];
if(out_mode) /* make room for storing x,y,z */
hc_vecrealloc(x,exp->npoints*(2+((use_3d)?(1):(0))),"sh_compute_spatial_basis");
inc = (use_3d)?(3):(2);
for(j=os=0;j < exp->npoints;j++,os+=inc){
/*
get coordinates
*/
switch(exp->type){
#ifdef HC_USE_HEALPIX
case SH_HEALPIX:
switch(exp->heal.ordering){
case SH_HEALPIX_RING:
pix2ang_ring((long)exp->heal.nside,(long)j,
(xp+HC_THETA),(xp+HC_PHI));
break;
case SH_HEALPIX_NEST:
pix2ang_nest((long)exp->heal.nside,(long)j,