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mgpoissonsolve.c
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mgpoissonsolve.c
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#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <string.h>
#include <fftw3.h>
#include <mpi.h>
#include <hdf5.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_linalg.h>
#include "raytrace.h"
#include "mgpoissonsolve.h"
//macros for debugging
//#define PRINT_MGGRID //prints out all grids used for MG poisson solve
//#define NANCHECK_MGGRID //checks grid values for NaNs
//macros for code
//#define NGP_FILL_U_MGGRID /* controls what kind of interpolation is done for guess at lens pot */
/* the NGP interp is faster, but then MG poisson solver is slower by approx same factor */
#define MGDERIV_METRIC_FAC_AT_END /* define to compute metric factors for derivs on MG grid after interp to ray position */
//#define SCALE_MGDENS /* define to scale the density and potential by a constant factor before poisson solver runs */
//prototypes
static void mgpoissonsolve_bundlecell(long bundleCell, const double densfact, const double backdens);
static void fill_rho_mggrid(MGGrid rho, long bundleCell, const double densfact, const double backdens);
static void fill_bcs_mggrid(MGGrid u);
static void fill_u_mggrid(MGGrid u);
static void fill_uderivs_rays(MGGrid u, long bundleCell);
static void getderiv_mggrid_xtheta(MGGrid u, double *gx);
static void getderiv_mggrid_xtheta_xtheta(MGGrid u, double *gxx);
static void getderiv_mggrid_yphi(MGGrid u, double *gy);
static void getderiv_mggrid_yphi_yphi(MGGrid u, double *gyy);
static void getderiv_mggrid_xtheta_yphi(MGGrid u, double *gxy);
static double getinterpval_healpix_mggrid(double vec[3], double RmatPatchToSphere[3][3]);
static void get_rmats_bundlecell(long bundleCell, double RmatSphereToPatch[3][3], double RmatPatchToSphere[3][3]);
static void rot_tangvectens(double _vec[3], double tvec[2], double ttens[2][2], double Rmat[3][3], double rvec[3], double rtvec[2], double rttens[2][2]);
//static double sphdist_haversine(double t1, double p1, double t2, double p2);
//static void getderiv_mggrid(MGGrid u, double **gx, double **gy, double **gxx, double **gxy, double **gyy);
//timing variables
#define NUMRUNTIMES 11
static double runTimes[NUMRUNTIMES];
/* Timing variables
runTimes[0] - total time to compute density
runTimes[1] - total time to do MG solve
runTimes[2] - time to prep density kernels
runTimes[3] - time to normalize density kernels
runTimes[4] - time to assign density kernels
runTimes[5] - total time to comute BCs for MG solve
runTimes[6] - total time to compute initial guess for MG solve solution
runTimes[7] - total extra time not covered above by 0,1,5,6
runTimes[8] - time to compute derivs of potential
runTimes[9] - time to assign derivs to rays
runTimes[10] - time to rot derivs back to global coords
*/
void mgpoissonsolve(double densfact, double backdens)
{
long i;
for(i=0;i<NUMRUNTIMES;++i)
runTimes[i] = 0.0;
double runTime,mintm,maxtm,avgtm,ptime;
int pstart = 1,numd = 0,numt = lastRestrictedPeanoIndTasks[ThisTask] - firstRestrictedPeanoIndTasks[ThisTask] + 1;
double totTime;
logProfileTag(PROFILETAG_MG);
totTime = -MPI_Wtime();
runTime = -MPI_Wtime();
ptime = -MPI_Wtime();
runTimes[7] -= MPI_Wtime();
//loop through active bundle cells and run MG solver
for(i=0;i<NbundleCells;++i)
{
if(ISSETBITFLAG(bundleCells[i].active,PRIMARY_BUNDLECELL))
{
runTimes[7] += MPI_Wtime();
bundleCells[i].cpuTime -= MPI_Wtime();
mgpoissonsolve_bundlecell(i,densfact,backdens);
bundleCells[i].cpuTime += MPI_Wtime();
runTimes[7] -= MPI_Wtime();
if(ThisTask == 0 && ((ptime + MPI_Wtime()) > 60.0 || pstart))
{
fprintf(stderr,"%5d of %5d - multi-grid poisson solve times: dens,BCS+Ufill,solve = %lf|%lf|%lf sec, prep,norm,assign,BCS,Ufill = %lf|%lf|%lf|%lf|%lf\n",
numd+1,numt,runTimes[0],runTimes[5]+runTimes[6],runTimes[1],runTimes[2],runTimes[3],runTimes[4],runTimes[5],runTimes[6]);
ptime = -MPI_Wtime();
pstart = 0;
}
++numd;
}
}
free_mapcells();
runTimes[7] += MPI_Wtime();
runTime += MPI_Wtime();
logProfileTag(PROFILETAG_MG);
MPI_Reduce(&runTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&runTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&runTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
{
//timing info that can be printed if wanted
//print_runtimes_mgsteps();
reset_runtimes_mgsteps();
//fprintf(stderr,"deriv times - comp,interp,rot = %lf|%lf|%lf seconds.\n",runTimes[8],runTimes[9],runTimes[10]);
fprintf(stderr,"dens+BCS+Ufill,solve,deriv+extra = %lf|%lf|%lf seconds.\n",
runTimes[0]+runTimes[5]+runTimes[6],runTimes[1],runTimes[7]);
fprintf(stderr,"multi-grid poisson solve took %lf seconds (max,min,avg = %lf|%lf|%lf seconds, %.2f percent).\n",
runTime,maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
}
}
//# of base grid sizes to test
#define MGGRID_NTEST 4
void mgpoissonsolve_bundlecell(long bundleCell, const double densfact, const double backdens)
{
long N,Nlev,lev,Nmin,j;
double L;
MGGrid u;
MGGridSet *grids;
long NumPreSmooth,NumPostSmooth,NumOuterCycles,NumInnerCycles;
long Nminv[MGGRID_NTEST] = {4,5,7,9};
long Nmaxv[MGGRID_NTEST],Nlevv[MGGRID_NTEST];
#ifdef PRINT_MGGRID
char fname[MAX_FILENAME];
#endif
runTimes[7] -= MPI_Wtime();
//setup
L = MGPATCH_SIZE_FAC*sqrt(4.0*M_PI/order2npix(rayTraceData.bundleOrder));
N = rayTraceData.NumMGPatch;
NumPreSmooth = 1;
NumPostSmooth = NumPreSmooth;
NumOuterCycles = 200;
NumInnerCycles = 2;
//find most efficient grid
for(j=0;j<MGGRID_NTEST;++j)
{
Nmin = Nminv[j];
Nlev = 1;
while(Nmin < N)
{
Nmin *= 2;
++Nlev;
}
Nlevv[j] = Nlev;
Nmaxv[j] = Nmin;
}
N = Nmaxv[0];
Nlev = Nlevv[0];
for(j=1;j<MGGRID_NTEST;++j)
{
if(Nmaxv[j] < N)
{
N = Nmaxv[j];
Nlev = Nlevv[j];
}
}
grids = (MGGridSet*)malloc(sizeof(MGGridSet)*Nlev);
assert(grids != NULL);
for(lev=Nlev-1;lev>=0;--lev)
{
grids[lev].u = alloc_mggrid(N,L);
get_rmats_bundlecell(bundleCell,grids[lev].u->RmatSphereToPatch,grids[lev].u->RmatPatchToSphere);
grids[lev].rho = copy_mggrid(grids[lev].u);
N /= 2;
}
runTimes[7] += MPI_Wtime();
//get dens and BCS
runTimes[0] -= MPI_Wtime();
fill_rho_mggrid(grids[Nlev-1].rho,bundleCell,densfact,backdens);
#ifdef PRINT_MGGRID
sprintf(fname,"%s/mgpatch_rho_bcell%ld.dat",rayTraceData.OutputPath,bundleCell);
write_mggrid(fname,grids[Nlev-1].rho);
#endif
runTimes[0] += MPI_Wtime();
runTimes[5] -= MPI_Wtime();
for(lev=Nlev-1;lev>=0;--lev)
fill_bcs_mggrid(grids[lev].u);
runTimes[5] += MPI_Wtime();
runTimes[6] -= MPI_Wtime();
fill_u_mggrid(grids[Nlev-1].u);
runTimes[6] += MPI_Wtime();
#ifdef SCALE_MGDENS
long i;
double nfact = backdens;
for(lev=Nlev-1;lev>=0;--lev)
{
//scale dens
for(i=0;i<grids[lev].rho->N;++i)
for(j=0;j<grids[lev].rho->N;++j)
grids[lev].rho->grid[j + (grids[lev].rho->N)*i] = (grids[lev].rho->grid[j + (grids[lev].rho->N)*i])/nfact;
//scale pot
for(i=0;i<grids[lev].u->N;++i)
for(j=0;j<grids[lev].u->N;++j)
grids[lev].u->grid[j + (grids[lev].u->N)*i] = (grids[lev].u->grid[j + (grids[lev].u->N)*i])/nfact;
}
#endif
#ifdef PRINT_MGGRID
sprintf(fname,"%s/mgpatch_ustart_bcell%ld.dat",rayTraceData.OutputPath,bundleCell);
write_mggrid(fname,grids[Nlev-1].u);
#endif
//solve poisson equation
double t,L1norm;
t = runTimes[1];
runTimes[1] -= MPI_Wtime();
logProfileTag(PROFILETAG_MG);
logProfileTag(PROFILETAG_MGSOLVE);
/*debugging code for pure relaxation method
lev = Nlev-1;
j = 0;
do
{
smooth_mggrid(grids[Nlev-1].u,grids[Nlev-1].rho,10l);
L1norm = L1norm_mggrid(grids[Nlev-1].u,grids[Nlev-1].rho);
fprintf(stderr,"L1norm = %le at %ld\n",L1norm,j);
++j;
}
while(L1norm > 1e-8);
exit(1);
*/
L1norm = solve_fas_mggrid(grids,Nlev,NumPreSmooth,NumPostSmooth,NumOuterCycles,NumInnerCycles,rayTraceData.MGConvFact);
logProfileTag(PROFILETAG_MGSOLVE);
logProfileTag(PROFILETAG_MG);
runTimes[1] += MPI_Wtime();
//fprintf(stderr,"bundle cell %ld took %lf seconds for a %ld cell sized grid with %ld levels w/ L1norm = %le.\n",bundleCell,runTimes[1]-t,N,Nlev,L1norm);
#ifdef PRINT_MGGRID
sprintf(fname,"%s/mgpatch_u_bcell%ld.dat",rayTraceData.OutputPath,bundleCell);
write_mggrid(fname,grids[Nlev-1].u);
#endif
runTimes[7] -= MPI_Wtime();
//free some memory
u = grids[Nlev-1].u;
free_mggrid(grids[Nlev-1].rho);
for(lev=Nlev-2;lev>=0;--lev)
{
free_mggrid(grids[lev].u);
free_mggrid(grids[lev].rho);
}
free(grids);
#ifdef SCALE_MGDENS
//scale pot back
for(i=0;i<u->N;++i)
for(j=0;j<u->N;++j)
u->grid[j + (u->N)*i] = (u->grid[j + (u->N)*i])*nfact;
#endif
//get derivs for rays
fill_uderivs_rays(u,bundleCell);
//clean up
free_mggrid(u);
runTimes[7] += MPI_Wtime();
}
static void fill_rho_mggrid(MGGrid rho, long bundleCell, const double densfact, const double backdens)
{
double L,vecp[3],vec[3],rvec[3],disLim,cosDis,smoothingRad;
long i,j,n,m,k,b;
double thetap,phip,theta,phi,sfac,sfac1,sfac2;
long pmin,pmax,tmin,tmax;
double totmass,r,vol;
struct binData {
long xind;
long yind;
double dens;
double vol;
} *bd;
long Nbd,bdind;
long *listpix,Nlistpix,NlistpixMax;
double z,z0,xa,x,ysq,cosang,dphi;
runTimes[2] -= MPI_Wtime();
listpix = NULL;
NlistpixMax = 0;
//mem for binning
Nbd = 200;
bd = (struct binData*)malloc(sizeof(struct binData)*Nbd);
assert(bd != NULL);
//setup
L = MGPATCH_SIZE_FAC*sqrt(4.0*M_PI/order2npix(rayTraceData.bundleOrder));
zero_mggrid(rho);
disLim = L + rayTraceData.maxSL*2.0;
nest2ang(bundleCell,&theta,&phi,rayTraceData.bundleOrder);
Nlistpix = query_disc_inclusive_nest_fast(theta,phi,disLim,&listpix,&NlistpixMax,rayTraceData.bundleOrder);
runTimes[2] += MPI_Wtime();
//assign dens with parts
for(b=0;b<Nlistpix;++b)
{
i = listpix[b];
if(bundleCells[i].Nparts > 0)
{
for(k=0;k<bundleCells[i].Nparts;++k)
{
runTimes[2] -= MPI_Wtime();
//get part pos in patch coords
vecp[0] = (double) (lensPlaneParts[k+bundleCells[i].firstPart].pos[0]);
vecp[1] = (double) (lensPlaneParts[k+bundleCells[i].firstPart].pos[1]);
vecp[2] = (double) (lensPlaneParts[k+bundleCells[i].firstPart].pos[2]);
rvec[0] = 0.0;
rvec[1] = 0.0;
rvec[2] = 0.0;
for(n=0;n<3;++n)
for(m=0;m<3;++m)
rvec[n] += (rho->RmatSphereToPatch[n][m])*vecp[m];
r = sqrt(rvec[0]*rvec[0] + rvec[1]*rvec[1] + rvec[2]*rvec[2]);
rvec[0] /= r;
rvec[1] /= r;
rvec[2] /= r;
vec2ang(rvec,&thetap,&phip);
while(phip > M_PI)
phip -= 2.0*M_PI;
while(phip < -M_PI)
phip += 2.0*M_PI;
//determine range of cells to add mass to
smoothingRad = lensPlaneParts[k+bundleCells[i].firstPart].smoothingLength;
//code cribbed from healpix
cosang = cos(smoothingRad);
z0 = cos(thetap);
xa = 1.0/sqrt((1-z0)*(1+z0));
//end of code cribbed from healpix
tmin = (thetap - rho->thetaLoc - smoothingRad)/(rho->dL) - 2;
tmax = (thetap - rho->thetaLoc + smoothingRad)/(rho->dL) + 2;
sfac1 = sin(thetap + smoothingRad);
sfac2 = sin(thetap - smoothingRad);
if(sfac1 < sfac2)
sfac = sfac1;
else
sfac = sfac2;
pmin = (phip - rho->phiLoc - smoothingRad/sfac)/(rho->dL) - 2;
pmax = (phip - rho->phiLoc + smoothingRad/sfac)/(rho->dL) + 2;
runTimes[2] += MPI_Wtime();
if(((tmin >= 0 && tmin <= rho->N) || (tmax >= 0 && tmax <= rho->N) ||
(0 >= tmin && 0 <= tmax) || (rho->N >= tmin && rho->N <= tmax))
&&
((pmin >= 0 && pmin <= rho->N) || (pmax >= 0 && pmax <= rho->N) ||
(0 >= pmin && 0 <= pmax) || (rho->N >= pmin && rho->N <= pmax)))
{
runTimes[3] -= MPI_Wtime();
bdind = (tmax-tmin+1)*(pmax-pmin+1);
if(bdind >= Nbd)
{
Nbd = bdind;
bd = (struct binData*)realloc(bd,sizeof(struct binData)*Nbd);
if(bd == NULL)
{
fprintf(stderr,"%d: Nbd = %ld, t = %ld|%ld, p = %ld|%ld\n",ThisTask,Nbd,tmin,tmax,pmin,pmax);
assert(bd != NULL);
}
}
//get total mass by summing over all cells, even if not in grid
bdind = 0;
totmass = 0.0;
for(n=tmin;n<=tmax;++n)
{
theta = n*(rho->dL) + rho->thetaLoc;
if(n >= 0 && n < rho->N)
{
vol = (rho->dL)*(rho->cosfacs[n]);
z = rho->costheta[n];
}
else
{
vol = (rho->dL)*(cos(n*(rho->dL) + rho->thetaLoc - (rho->dL)/2.0) - cos(n*(rho->dL) + rho->thetaLoc + (rho->dL)/2.0));
z = cos(theta);
}
//code cribbed from healpix
//z = cos(theta); - computed above
x = (cosang-z*z0)*xa;
ysq = 1-z*z-x*x;
if(ysq < 0.0)
continue;
//not needed - just continue assert(ysq>=0);
dphi=atan2(sqrt(ysq),x);
//end of code cribbed from healpix
pmin = (phip - rho->phiLoc - dphi)/(rho->dL) - 2;
pmax = (phip - rho->phiLoc + dphi)/(rho->dL) + 2;
for(m=pmin;m<=pmax;++m)
{
phi = m*(rho->dL) + rho->phiLoc;
if(n >= 0 && n < rho->N && m >= 0 && m < rho->N)
{
vecp[0] = (rho->sintheta[n])*(rho->cosphi[m]);
vecp[1] = (rho->sintheta[n])*(rho->sinphi[m]);
vecp[2] = rho->costheta[n];
}
else
ang2vec(vecp,theta,phi);
cosDis = rvec[0]*vecp[0] + rvec[1]*vecp[1] + rvec[2]*vecp[2];
r = spline_part_dens(cosDis,smoothingRad)*vol;
#ifdef NANCHECK_MGGRID ///////////////////////////////////////////////////////////////////////////////
if(!(gsl_finite(r)))
{
fprintf(stderr,"bcell = %ld, tp,pp = %le|%le, t,p = %le|%le, rvec = %le|%le|%le, vecp = %le|%le|%le, cosDis = %le, vol = %le, sr = %le, dens = %le\n",
bundleCell,thetap,phip,theta,phi,rvec[0],rvec[1],rvec[2],vecp[0],vecp[1],vecp[2],cosDis,vol,smoothingRad,spline_part_dens(cosDis,smoothingRad));
MPI_Abort(MPI_COMM_WORLD,999);
}
#endif ///////////////////////////////////////////////////////////////////////////////
if(n >= 0 && n < rho->N && m >= 0 && m < rho->N && r > 0.0)
{
bd[bdind].xind = n;
bd[bdind].yind = m;
bd[bdind].dens = r;
bd[bdind].vol = vol;
++bdind;
assert(bdind <= Nbd);
}
totmass += r;
}
}
runTimes[3] += MPI_Wtime();
runTimes[4] -= MPI_Wtime();
//assign mass using only cells in grid
if(totmass == 0.0) //make sure smoothing rad is not smaller than cell size
{
n = (thetap - rho->thetaLoc)/(rho->dL);
m = (phip - rho->phiLoc)/(rho->dL);
if(n >= 0 && n < rho->N && m >= 0 && m < rho->N)
{
rho->grid[n*(rho->N)+m] += lensPlaneParts[k+bundleCells[i].firstPart].mass;
#ifdef NANCHECK_MGGRID ///////////////////////////////////////////////////////////////////////////////
if(!(gsl_finite(rho->grid[n*(rho->N)+m])))
{
fprintf(stderr,"bcell = %ld, n,m = %ld|%ld, mass = %le\n",
bundleCell,n,m,lensPlaneParts[k+bundleCells[i].firstPart].mass);
MPI_Abort(MPI_COMM_WORLD,999);
}
#endif ///////////////////////////////////////////////////////////////////////////////
}
}
else
{
r = lensPlaneParts[k+bundleCells[i].firstPart].mass/totmass;
for(j=0;j<bdind;++j)
{
rho->grid[(bd[j].xind)*(rho->N)+(bd[j].yind)] += bd[j].dens*r;
#ifdef NANCHECK_MGGRID ///////////////////////////////////////////////////////////////////////////////
if(!(gsl_finite(rho->grid[(bd[j].xind)*(rho->N)+(bd[j].yind)])))
{
fprintf(stderr,"bcell = %ld, ifn,jfn,N = %ld|%ld|%ld, dens,r,totmass,vol,sinf = %le|%le|%le\n",
bundleCell,bd[j].xind,bd[j].yind,rho->N,bd[j].dens,r,totmass);
fflush(stderr);
MPI_Abort(MPI_COMM_WORLD,999);
}
#endif ///////////////////////////////////////////////////////////////////////////////
}//for(j=0;j<bdind;++j)
}//else ...
runTimes[4] += MPI_Wtime();
}//if((tmin >= 0 && tmin <= rho->N) || ...
}//for(k=0;k<bundleCells[i].Nparts;++k)
}//if(bundleCells[i].Nparts > 0 && cosDis > cosDisLim)
}//for(b=0;b<Nlistpix;++b)
runTimes[2] -= MPI_Wtime();
if(bd != NULL)
free(bd);
if(NlistpixMax > 0)
free(listpix);
//factors for kappa
double nfact;
for(i=0;i<rho->N;++i)
{
nfact = 1.0/(rho->dL)/(rho->cosfacs[i])*densfact;
for(j=0;j<rho->N;++j)
{
rho->grid[j + (rho->N)*i] = (rho->grid[j + (rho->N)*i])*nfact; // /(rho->dL)/(rho->cosfacs[i])*densfact;
rho->grid[j + (rho->N)*i] = rho->grid[j + (rho->N)*i] - backdens;
}
}
//check if on boundary if needed
#ifndef USE_FULLSKY_PARTDIST
double ra,dec;
long checkVacCells;
nest2ang(bundleCell,&theta,&phi,rayTraceData.bundleOrder);
ang2radec(theta,phi,&ra,&dec);
checkVacCells = test_vaccell_boundary(ra,dec,(rho->L)*2.0);
if(checkVacCells)
{
for(i=0;i<rho->N;++i)
for(j=0;j<rho->N;++j)
{
//theta = i*(rho->dL) + rho->thetaLoc;
//phi = j*(rho->dL) + rho->phiLoc;
//ang2vec(vec,theta,phi);
vec[0] = (rho->sintheta[i])*(rho->cosphi[j]);
vec[1] = (rho->sintheta[i])*(rho->sinphi[j]);
vec[2] = rho->costheta[i];
/* unrolled this
rvec[0] = 0.0;
rvec[1] = 0.0;
rvec[2] = 0.0;
for(n=0;n<3;++n)
for(m=0;m<3;++m)
rvec[n] += (rho->RmatPatchToSphere[n][m])*vec[m];
*/
rvec[0] = (rho->RmatPatchToSphere[0][0])*vec[0] + (rho->RmatPatchToSphere[0][1])*vec[1] + (rho->RmatPatchToSphere[0][2])*vec[2];
rvec[1] = (rho->RmatPatchToSphere[1][0])*vec[0] + (rho->RmatPatchToSphere[1][1])*vec[1] + (rho->RmatPatchToSphere[1][2])*vec[2];
rvec[2] = (rho->RmatPatchToSphere[2][0])*vec[0] + (rho->RmatPatchToSphere[2][1])*vec[1] + (rho->RmatPatchToSphere[2][2])*vec[2];
vec2ang(rvec,&theta,&phi);
ang2radec(theta,phi,&ra,&dec);
if(test_vaccell(ra,dec))
rho->grid[j + (rho->N)*i] = 0.0;
}
}
#endif
runTimes[2] += MPI_Wtime();
}
static void fill_u_mggrid(MGGrid u)
{
long i,j;
double vec[3],rvec[3],phiv;
long bnest,offset,nest;
long bundleMapShift = 2*(rayTraceData.poissonOrder - rayTraceData.bundleOrder);
#ifndef NGP_FILL_U_MGGRID
double wgt[4],phi,theta;
long n,pix[4];
#endif
//not using this option - allows one to do fewer interps, but slows down MG convergence by same factor
//long numg = 1;
//for(i=1;i<u->N-1;i+=numg)
//for(j=1;j<u->N-1;j+=numg)
for(i=1;i<u->N-1;++i)
{
for(j=1;j<u->N-1;++j)
{
//thetag = i*(u->dL) + u->thetaLoc + (numg - 1.0)*(u->dL)/2.0;
//phig = j*(u->dL) + u->phiLoc + (numg - 1.0)*(u->dL)/2.0;
//thetag = i*(u->dL) + u->thetaLoc;
//phig = j*(u->dL) + u->phiLoc;
//ang2vec(vec,thetag,phig);
vec[0] = (u->sintheta[i])*(u->cosphi[j]);
vec[1] = (u->sintheta[i])*(u->sinphi[j]);
vec[2] = u->costheta[i];
/* unrolled this
rvec[0] = 0.0;
rvec[1] = 0.0;
rvec[2] = 0.0;
for(n=0;n<3;++n)
for(m=0;m<3;++m)
rvec[n] += (u->RmatPatchToSphere[n][m])*vec[m];
*/
rvec[0] = (u->RmatPatchToSphere[0][0])*vec[0] + (u->RmatPatchToSphere[0][1])*vec[1] + (u->RmatPatchToSphere[0][2])*vec[2];
rvec[1] = (u->RmatPatchToSphere[1][0])*vec[0] + (u->RmatPatchToSphere[1][1])*vec[1] + (u->RmatPatchToSphere[1][2])*vec[2];
rvec[2] = (u->RmatPatchToSphere[2][0])*vec[0] + (u->RmatPatchToSphere[2][1])*vec[1] + (u->RmatPatchToSphere[2][2])*vec[2];
#ifdef NGP_FILL_U_MGGRID
nest = vec2nest(rvec,rayTraceData.poissonOrder);
bnest = nest >> bundleMapShift;
offset = nest - (bnest << bundleMapShift);
if((ISSETBITFLAG(bundleCells[bnest].active,PRIMARY_BUNDLECELL) || ISSETBITFLAG(bundleCells[bnest].active,MAPBUFF_BUNDLECELL))
&& bundleCells[bnest].firstMapCell >= 0)
{
phiv = mapCells[bundleCells[bnest].firstMapCell + offset].val;
assert(nest == mapCells[bundleCells[bnest].firstMapCell + offset].index);
}
else
{
fprintf(stderr,"%d: could not get map cell value in MG poisson solve Ufill!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
#else
vec2ang(rvec,&theta,&phi);
get_interpol(theta,phi,pix,wgt,rayTraceData.poissonOrder);
phiv = 0.0;
for(n=0;n<4;++n)
{
nest = ring2nest(pix[n],rayTraceData.poissonOrder);
bnest = nest >> bundleMapShift;
offset = nest - (bnest << bundleMapShift);
if((ISSETBITFLAG(bundleCells[bnest].active,PRIMARY_BUNDLECELL) || ISSETBITFLAG(bundleCells[bnest].active,MAPBUFF_BUNDLECELL))
&& bundleCells[bnest].firstMapCell >= 0)
{
phiv += mapCells[bundleCells[bnest].firstMapCell + offset].val*wgt[n];
assert(nest == mapCells[bundleCells[bnest].firstMapCell + offset].index);
}
else
{
fprintf(stderr,"%d: could not get map cell value in MG poisson solve Ufill!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
}
#endif
//for(n=0;n<numg;++n)
//for(m=0;m<numg;++m)
//u->grid[(i+n)*(u->N)+j+m] = phiv;
u->grid[i*(u->N)+j] = phiv;
//u->grid[i*(u->N)+j] = getinterpval_healpix_mggrid(vec,u->RmatPatchToSphere);
}
}
}
static void fill_bcs_mggrid(MGGrid u)
{
long i,j;
double vec[3];
i = 0;
for(j=0;j<u->N;++j)
{
vec[0] = (u->sintheta[i])*(u->cosphi[j]);
vec[1] = (u->sintheta[i])*(u->sinphi[j]);
vec[2] = u->costheta[i];
u->grid[i*(u->N)+j] = getinterpval_healpix_mggrid(vec,u->RmatPatchToSphere);
}
i = u->N-1;
for(j=0;j<u->N;++j)
{
vec[0] = (u->sintheta[i])*(u->cosphi[j]);
vec[1] = (u->sintheta[i])*(u->sinphi[j]);
vec[2] = u->costheta[i];
u->grid[i*(u->N)+j] = getinterpval_healpix_mggrid(vec,u->RmatPatchToSphere);
}
j = 0;
for(i=1;i<u->N-1;++i)
{
vec[0] = (u->sintheta[i])*(u->cosphi[j]);
vec[1] = (u->sintheta[i])*(u->sinphi[j]);
vec[2] = u->costheta[i];
u->grid[i*(u->N)+j] = getinterpval_healpix_mggrid(vec,u->RmatPatchToSphere);
}
j = u->N-1;
for(i=1;i<u->N-1;++i)
{
vec[0] = (u->sintheta[i])*(u->cosphi[j]);
vec[1] = (u->sintheta[i])*(u->sinphi[j]);
vec[2] = u->costheta[i];
u->grid[i*(u->N)+j] = getinterpval_healpix_mggrid(vec,u->RmatPatchToSphere);
}
}
static double getinterpval_healpix_mggrid(double vec[3], double RmatPatchToSphere[3][3])
{
double theta,phi,rvec[3],phiv,wgt[4];
long n,pix[4],bnest,offset,nest;
long bundleMapShift = 2*(rayTraceData.poissonOrder - rayTraceData.bundleOrder);
/* unrolled this
rvec[0] = 0.0;
rvec[1] = 0.0;
rvec[2] = 0.0;
for(n=0;n<3;++n)
for(m=0;m<3;++m)
rvec[n] += RmatPatchToSphere[n][m]*vec[m];
*/
rvec[0] = RmatPatchToSphere[0][0]*vec[0] + RmatPatchToSphere[0][1]*vec[1] + RmatPatchToSphere[0][2]*vec[2];
rvec[1] = RmatPatchToSphere[1][0]*vec[0] + RmatPatchToSphere[1][1]*vec[1] + RmatPatchToSphere[1][2]*vec[2];
rvec[2] = RmatPatchToSphere[2][0]*vec[0] + RmatPatchToSphere[2][1]*vec[1] + RmatPatchToSphere[2][2]*vec[2];
vec2ang(rvec,&theta,&phi);
get_interpol(theta,phi,pix,wgt,rayTraceData.poissonOrder);
phiv = 0.0;
for(n=0;n<4;++n)
{
nest = ring2nest(pix[n],rayTraceData.poissonOrder);
bnest = nest >> bundleMapShift;
offset = nest - (bnest << bundleMapShift);
if((ISSETBITFLAG(bundleCells[bnest].active,PRIMARY_BUNDLECELL) || ISSETBITFLAG(bundleCells[bnest].active,MAPBUFF_BUNDLECELL))
&& bundleCells[bnest].firstMapCell >= 0)
{
phiv += mapCells[bundleCells[bnest].firstMapCell + offset].val*wgt[n];
assert(nest == mapCells[bundleCells[bnest].firstMapCell + offset].index);
}
else
{
fprintf(stderr,"%d: could not get map cell value in MG poisson solve BCs!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
}
return phiv;
}
static void fill_uderivs_rays(MGGrid u, long bundleCell)
{
long j,n,m,xind,yind,xindp,yindp;
double *deriv,wgtx,wgty;
double vecp[3],norm,rvec[3],thetap,phip,vec[3],phiv;
double tvec[2],rtvec[2],ttens[2][2],rttens[2][2];
long notFinite = 0;
double *thetap_vec,*phip_vec;
#ifdef MGDERIV_METRIC_FAC_AT_END
double sint,cost;
#endif
/*
Each deriv is computed one at a time
then transform to global coords at the end
*/
if(bundleCells[bundleCell].Nrays > 0)
{
runTimes[8] -= MPI_Wtime();
thetap_vec = (double*)malloc(sizeof(double)*bundleCells[bundleCell].Nrays);
assert(thetap_vec != NULL);
phip_vec = (double*)malloc(sizeof(double)*bundleCells[bundleCell].Nrays);
assert(phip_vec != NULL);
deriv = (double*)malloc(sizeof(double)*(u->N)*(u->N));
assert(deriv != NULL);
//theta deriv and phi value
getderiv_mggrid_xtheta(u,deriv);
runTimes[8] += MPI_Wtime();
runTimes[9] -= MPI_Wtime();
for(j=0;j<bundleCells[bundleCell].Nrays;++j)
{
vecp[0] = bundleCells[bundleCell].rays[j].n[0];
vecp[1] = bundleCells[bundleCell].rays[j].n[1];
vecp[2] = bundleCells[bundleCell].rays[j].n[2];
norm = sqrt(vecp[0]*vecp[0] + vecp[1]*vecp[1] + vecp[2]*vecp[2]);
vecp[0] /= norm;
vecp[1] /= norm;
vecp[2] /= norm;
rvec[0] = 0.0;
rvec[1] = 0.0;
rvec[2] = 0.0;
for(n=0;n<3;++n)
for(m=0;m<3;++m)
rvec[n] += (u->RmatSphereToPatch[n][m])*vecp[m];
vec2ang(rvec,&thetap,&phip);
while(phip > M_PI)
phip -= 2.0*M_PI;
while(phip < -M_PI)
phip += 2.0*M_PI;
thetap_vec[j] = thetap;
phip_vec[j] = phip;
xind = (thetap - u->thetaLoc)/(u->dL);
yind = (phip - u->phiLoc)/(u->dL);
if(xind >= 0 && xind < u->N-1 && yind >= 0 && yind < u->N-1)
{
wgtx = 1.0 - (thetap - (xind*(u->dL) + u->thetaLoc))/(u->dL);
wgty = 1.0 - (phip - (yind*(u->dL) + u->phiLoc))/(u->dL);
xindp = xind + 1;
yindp = yind + 1;
phiv = (u->grid[yind + (u->N)*xind])*wgtx*wgty;
phiv += (u->grid[yind + (u->N)*xindp])*(1.0-wgtx)*wgty;
phiv += (u->grid[yindp + (u->N)*xind ])*wgtx*(1.0-wgty);
phiv += (u->grid[yindp + (u->N)*xindp])*(1.0-wgtx)*(1.0-wgty);
tvec[0] = deriv[yind + (u->N)*xind ]*wgtx*wgty;
tvec[0] += deriv[yind + (u->N)*xindp]*(1.0-wgtx)*wgty;
tvec[0] += deriv[yindp + (u->N)*xind ]*wgtx*(1.0-wgty);
tvec[0] += deriv[yindp + (u->N)*xindp]*(1.0-wgtx)*(1.0-wgty);
//error check
if(!(gsl_finite(phiv)))
{
fprintf(stderr,"phi is not finite! bcell = %ld, phi = %le, wx,wy = %lf|%lf, phi = %le|%le|%le|%le\n",
bundleCell,phiv,wgtx,wgty,
u->grid[yind + (u->N)*xind],u->grid[yind + (u->N)*xindp],u->grid[yindp + (u->N)*xind ],u->grid[yindp + (u->N)*xindp]);
fflush(stderr);
notFinite = 1;
}
if(!(gsl_finite(tvec[0])))
{
fprintf(stderr,"defl. ang. is not finite! bcell = %ld, tv[0] = %le, wx,wy = %lf|%lf, gx = %le|%le|%le|%le\n",
bundleCell,tvec[0],wgtx,wgty,
deriv[yind + (u->N)*xind ],deriv[yind + (u->N)*xindp],deriv[yindp + (u->N)*xind ],deriv[yindp + (u->N)*xindp]);
fflush(stderr);
notFinite = 1;
}
if(notFinite)
MPI_Abort(MPI_COMM_WORLD,999);
bundleCells[bundleCell].rays[j].phi = phiv;
bundleCells[bundleCell].rays[j].alpha[0] = tvec[0];
}
else
{
fprintf(stderr,"%d: ray not in MG patch!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
}
runTimes[9] += MPI_Wtime();
//phi deriv
runTimes[8] -= MPI_Wtime();
getderiv_mggrid_yphi(u,deriv);
runTimes[8] += MPI_Wtime();
runTimes[9] -= MPI_Wtime();
for(j=0;j<bundleCells[bundleCell].Nrays;++j)
{
thetap = thetap_vec[j];
phip = phip_vec[j];
xind = (thetap - u->thetaLoc)/(u->dL);
yind = (phip - u->phiLoc)/(u->dL);
if(xind >= 0 && xind < u->N-1 && yind >= 0 && yind < u->N-1)
{
wgtx = 1.0 - (thetap - (xind*(u->dL) + u->thetaLoc))/(u->dL);
wgty = 1.0 - (phip - (yind*(u->dL) + u->phiLoc))/(u->dL);
xindp = xind + 1;
yindp = yind + 1;
tvec[1] = deriv[yind + (u->N)*xind ]*wgtx*wgty;
tvec[1] += deriv[yind + (u->N)*xindp]*(1.0-wgtx)*wgty;
tvec[1] += deriv[yindp + (u->N)*xind ]*wgtx*(1.0-wgty);
tvec[1] += deriv[yindp + (u->N)*xindp]*(1.0-wgtx)*(1.0-wgty);
if(!(gsl_finite(tvec[1])))
{
fprintf(stderr,"defl. ang. is not finite! bcell = %ld, tv[1] = %le, wx,wy = %lf|%lf, gy = %le|%le|%le|%le\n",
bundleCell,tvec[1],wgtx,wgty,
deriv[yind + (u->N)*xind ],deriv[yind + (u->N)*xindp],deriv[yindp + (u->N)*xind ],deriv[yindp + (u->N)*xindp]);
fflush(stderr);
notFinite = 1;
}
if(notFinite)
MPI_Abort(MPI_COMM_WORLD,999);
bundleCells[bundleCell].rays[j].alpha[1] = tvec[1];
}
else
{
fprintf(stderr,"%d: ray not in MG patch!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
}
runTimes[9] += MPI_Wtime();
//theta-theta deriv
runTimes[8] -= MPI_Wtime();
getderiv_mggrid_xtheta_xtheta(u,deriv);
runTimes[8] += MPI_Wtime();
runTimes[9] -= MPI_Wtime();
for(j=0;j<bundleCells[bundleCell].Nrays;++j)
{
thetap = thetap_vec[j];
phip = phip_vec[j];
xind = (thetap - u->thetaLoc)/(u->dL);
yind = (phip - u->phiLoc)/(u->dL);
if(xind >= 0 && xind < u->N-1 && yind >= 0 && yind < u->N-1)
{
wgtx = 1.0 - (thetap - (xind*(u->dL) + u->thetaLoc))/(u->dL);
wgty = 1.0 - (phip - (yind*(u->dL) + u->phiLoc))/(u->dL);
xindp = xind + 1;
yindp = yind + 1;
ttens[0][0] = deriv[yind + (u->N)*xind ]*wgtx*wgty;
ttens[0][0] += deriv[yind + (u->N)*xindp]*(1.0-wgtx)*wgty;
ttens[0][0] += deriv[yindp + (u->N)*xind ]*wgtx*(1.0-wgty);
ttens[0][0] += deriv[yindp + (u->N)*xindp]*(1.0-wgtx)*(1.0-wgty);
if(!(gsl_finite(ttens[0][0])))
{
fprintf(stderr,"shear is not finite! bcell = %ld, tt[0][0] = %le, wx,wy = %lf|%lf\n\tgxx = %le|%le|%le|%le\n",
bundleCell,ttens[0][0],wgtx,wgty,
deriv[yind + (u->N)*xind ],deriv[yind + (u->N)*xindp],deriv[yindp + (u->N)*xind ],deriv[yindp + (u->N)*xindp]);
fflush(stderr);
notFinite = 1;
}
if(notFinite)
MPI_Abort(MPI_COMM_WORLD,999);
bundleCells[bundleCell].rays[j].U[0] = ttens[0][0];
}
else
{
fprintf(stderr,"%d: ray not in MG patch!\n",ThisTask);
MPI_Abort(MPI_COMM_WORLD,987);
}
}
runTimes[9] += MPI_Wtime();
//phi-phi deriv
runTimes[8] -= MPI_Wtime();
getderiv_mggrid_yphi_yphi(u,deriv);
runTimes[8] += MPI_Wtime();
runTimes[9] -= MPI_Wtime();
for(j=0;j<bundleCells[bundleCell].Nrays;++j)
{