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alm2allmaps_transpose_mpi.c
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alm2allmaps_transpose_mpi.c
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/*
map synthesis HEALPix function w/ MPI - does MPI parallel alm -> map and all gradient maps up to second order
This is a complete rewrite in C of the HEALPix synthesis function. Parts of these routines were
taken from the public HEALPix package. See copyright and GPL info below.
-Matthew R. Becker, UofC 2011
*/
/*
!-----------------------------------------------------------------------------
!
! Copyright (C) 1997-2008 Krzysztof M. Gorski, Eric Hivon,
! Benjamin D. Wandelt, Anthony J. Banday,
! Matthias Bartelmann, Hans K. Eriksen,
! Frode K. Hansen, Martin Reinecke
!
!
! This file is part of HEALPix.
!
! HEALPix is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 2 of the License, or
! (at your option) any later version.
!
! HEALPix is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with HEALPix; if not, write to the Free Software
! Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
!
! For more information about HEALPix see http://healpix.jpl.nasa.gov
!
!-----------------------------------------------------------------------------
! Written by Hans Kristian Eriksen and Snorre Boasson,
! but copying large parts from the serial HEALPix code.
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <fftw3.h>
#include <mpi.h>
#include <assert.h>
#include "healpix_utils.h"
#include "healpix_shtrans.h"
void alm2allmaps_mpi(double *alm_real, double *alm_imag, float *mapvec, float *mapvec_gt, float *mapvec_gp,
float *mapvec_gtt, float *mapvec_gtp, float *mapvec_gpp,
HEALPixSHTPlan plan)
{
int NTasks,ThisTask;
int *sendcnts,*sdispls,*rdispls,*recvcnts;
double *transDataRealRecv,*transDataImagRecv;
long NrTDR,NmTDR;
long mapNum,Nmaps;
long nring,j,i,lmind,l,m,mp,k,lmin,ringpix_complex;
double sfact,skfact;
double rval,ival;
long nstartpix,ringpix,shifted;
double nsintheta,ncostheta;
long Nside,lmax;
long Nrings;
long firstRing,lastRing,lastLoopRing;
long NringsThisTask,NringsLoop;
const long NringChunkBase = 20;
long ringChunkStart,ringChunkStop,*ringpixRingChunk,*shiftedRingChunk,NringChunk;
double *nsinthetaRingChunk,*ncosthetaRingChunk;
double **qmn_real[6],**qmn_imag[6],**qms_real[6],**qms_imag[6];
long Nqm,firstChunkRing,lastChunkRing;
double *plm;
plmgen_data *plmdata;
double plmeps;
long firstl;
long firstM,lastM,NMThisTask;
double runTime;
#ifdef OUTPUT_SHT_LOADBALANCE
double mintm,maxtm,avgtm;
#endif
long memTot = 0;
double transTime,fftTime,sumTime,pixTime,plmTime;
fftwf_complex *mapvec_complex[6];
double *mTime;
long Nchunks,chunkInd;
long lmaxp1;
double gradquantn,gradquants,gradfact,*svec;
double gradplmn,gradplms,gradplm_lm1_n,gradplm_lm1_s;
double ncos_nsin,ncos_nsin2,ncos2_nsin2,fac1,fac2,fac3;
long task,start,NmT,nind,sind;
double *transDataReal;
double *transDataImag;
long NmTD,NrTD;
long mind;
//init timing and basic data for plan
runTime = -MPI_Wtime();
MPI_Comm_size(MPI_COMM_WORLD,&NTasks);
MPI_Comm_rank(MPI_COMM_WORLD,&ThisTask);
transTime = 0.0;
fftTime = 0.0;
sumTime = 0.0;
pixTime = 0.0;
plmTime = 0.0;
Nmaps = 6;
Nside = order2nside(plan.order);
Nrings = 2*Nside;
plmeps = 1e-30;
lmax = plan.lmax;
mapvec_complex[0] = (fftwf_complex*) mapvec;
mapvec_complex[1] = (fftwf_complex*) mapvec_gt;
mapvec_complex[2] = (fftwf_complex*) mapvec_gp;
mapvec_complex[3] = (fftwf_complex*) mapvec_gtt;
mapvec_complex[4] = (fftwf_complex*) mapvec_gtp;
mapvec_complex[5] = (fftwf_complex*) mapvec_gpp;
//get rings for this task
firstRing = plan.firstRingTasks[ThisTask];
lastRing = plan.lastRingTasks[ThisTask];
firstM = plan.firstMTasks[ThisTask];
lastM = plan.lastMTasks[ThisTask];
if(firstRing == -1 || lastRing == -1 || firstM == -1 || lastM == -1)
{
fprintf(stderr,"problem with assigning rings/ms to tasks! (Did you ask for more tasks than rings?)\n");
for(i=0;i<NTasks;++i)
fprintf(stderr,"\t%ld: firstRing,lastRing,Nrings = %ld|%ld,%ld, firstM,lastM,NM = %ld|%ld|%ld\n",i,
plan.firstRingTasks[i],plan.lastRingTasks[i],2*Nside,
plan.firstMTasks[i],plan.lastMTasks[i],plan.lmax+1);
MPI_Abort(MPI_COMM_WORLD,123);
}
#ifdef DEBUG_IO
if(ThisTask == 0)
for(i=0;i<NTasks;++i)
fprintf(stderr,"\t%ld: firstRing,lastRing,Nrings = %ld|%ld,%ld, firstM,lastM,NM = %ld|%ld|%ld\n",i,
plan.firstRingTasks[i],plan.lastRingTasks[i],2*Nside,
plan.firstMTasks[i],plan.lastMTasks[i],plan.lmax+1);
#endif
NMThisTask = lastM-firstM+1;
NringsThisTask = lastRing - firstRing + 1;
NringsLoop = NringsThisTask;
lastLoopRing = lastRing;
if(lastRing == Nrings)
{
--NringsLoop;
--lastLoopRing;
}
Nqm = NMThisTask;
//init plm generator
plm = (double*)malloc(sizeof(double)*(lmax + 1));
assert(plm != NULL);
memTot += sizeof(double)*(lmax + 1);
plmTime -= MPI_Wtime();
plmdata = plmgen_init(lmax,plmeps);
plmTime += MPI_Wtime();
//compute layout for transposed data
NmTD = NMThisTask;
NrTD = 4*Nside-1;
//memory buffers
transDataReal = (double*)malloc(sizeof(double)*NrTD*Nmaps*NmTD);
assert(transDataReal != NULL);
memTot += sizeof(double)*NrTD*Nmaps*NmTD;
transDataImag = (double*)malloc(sizeof(double)*NrTD*Nmaps*NmTD);
assert(transDataImag != NULL);
memTot += sizeof(double)*NrTD*Nmaps*NmTD;
for(i=0;i<NrTD;++i)
for(j=0;j<Nmaps;++j)
for(k=0;k<NmTD;++k)
{
transDataReal[(i*Nmaps + j)*NmTD + k] = 0.0;
transDataImag[(i*Nmaps + j)*NmTD + k] = 0.0;
}
ringpixRingChunk = (long*)malloc(sizeof(long)*NringChunkBase);
assert(ringpixRingChunk != NULL);
memTot += sizeof(long)*NringChunkBase;
shiftedRingChunk = (long*)malloc(sizeof(long)*NringChunkBase);
assert(shiftedRingChunk != NULL);
memTot += sizeof(long)*NringChunkBase;
nsinthetaRingChunk = (double*)malloc(sizeof(double)*NringChunkBase);
assert(nsinthetaRingChunk !=NULL);
memTot += sizeof(double)*NringChunkBase;
ncosthetaRingChunk = (double*)malloc(sizeof(double)*NringChunkBase);
assert(ncosthetaRingChunk !=NULL);
memTot += sizeof(double)*NringChunkBase;
for(j=0;j<6;++j)
{
qmn_real[j] = (double**)malloc(sizeof(double*)*NringChunkBase);
assert(qmn_real[j] != NULL);
memTot += sizeof(double*)*NringChunkBase;
qmn_imag[j] = (double**)malloc(sizeof(double*)*NringChunkBase);
assert(qmn_imag[j] != NULL);
memTot += sizeof(double*)*NringChunkBase;
qms_real[j] = (double**)malloc(sizeof(double*)*NringChunkBase);
assert(qms_real[j] != NULL);
memTot += sizeof(double*)*NringChunkBase;
qms_imag[j] = (double**)malloc(sizeof(double*)*NringChunkBase);
assert(qms_imag[j] != NULL);
memTot += sizeof(double*)*NringChunkBase;
for(i=0;i<NringChunkBase;++i)
{
qmn_real[j][i] = (double*)malloc(sizeof(double)*Nqm);
assert(qmn_real[j][i] != NULL);
memTot += sizeof(double)*Nqm;
qmn_imag[j][i] = (double*)malloc(sizeof(double)*Nqm);
assert(qmn_imag[j][i] != NULL);
memTot += sizeof(double)*Nqm;
qms_real[j][i] = (double*)malloc(sizeof(double)*Nqm);
assert(qms_real[j][i] != NULL);
memTot += sizeof(double)*Nqm;
qms_imag[j][i] = (double*)malloc(sizeof(double)*Nqm);
assert(qms_imag[j][i] != NULL);
memTot += sizeof(double)*Nqm;
}
}
lmaxp1 = lmax+1;
svec = (double*)malloc(sizeof(double)*(lmax + 1)*NMThisTask);
assert(svec != NULL);
memTot += sizeof(double)*(lmax + 1)*NMThisTask;
for(m=firstM;m<=lastM;++m)
for(l=m;l<=lmax;++l)
svec[l+lmaxp1*(m-firstM)] = sqrt((2.0*l+1.0)/(2.0*l-1.0)*((double) (l*l-m*m)));
//time each m value to get load balance correct
mTime = (double*)malloc(sizeof(double)*NMThisTask);
assert(mTime != NULL);
memTot += sizeof(double)*NMThisTask;
for(i=0;i<NMThisTask;++i)
mTime[i] = 0.0;
//setup chunks
firstChunkRing = 1;
lastChunkRing = 2*Nside-1;
Nchunks = (lastChunkRing-firstChunkRing+1)/NringChunkBase;
if(Nchunks*NringChunkBase < lastChunkRing-firstChunkRing+1)
++Nchunks;
sumTime -= MPI_Wtime();
#ifdef DEBUG
#if DEBUG_LEVEL > 0
fprintf(stderr,"%f MB allocated in alm2allmaps_mpi.\n",((double) (sizeof(double)*(memTot)))/1024.0/1024.0);
#endif
#endif
//do sums over plms - store rings in transData for MPI transpose
for(chunkInd=0;chunkInd<Nchunks;++chunkInd)
{
//get index range of subchunks
ringChunkStart = chunkInd*NringChunkBase + firstChunkRing;
ringChunkStop = ringChunkStart + NringChunkBase - 1;
if(ringChunkStop > lastChunkRing)
ringChunkStop = lastChunkRing;
NringChunk = ringChunkStop - ringChunkStart + 1;
//init parms for subchunks
for(i=0;i<NringChunk;++i)
{
nring = i + ringChunkStart;
get_ring_info2(nring,&nstartpix,ringpixRingChunk+i,ncosthetaRingChunk+i,nsinthetaRingChunk+i,shiftedRingChunk+i,plan.order);
for(mapNum=0;mapNum<6;++mapNum)
for(j=0;j<Nqm;++j)
{
qmn_real[mapNum][i][j] = 0.0;
qmn_imag[mapNum][i][j] = 0.0;
qms_real[mapNum][i][j] = 0.0;
qms_imag[mapNum][i][j] = 0.0;
}
}
//sum over l at fixed m for each ring using only alms on ThisTask
for(m=firstM;m<=lastM;++m)
{
mind = m-firstM;
mTime[mind] -= MPI_Wtime();
//sum over rings - lmind tracks alm coefficients for this m
lmind = (lmax+1)*(m-firstM) + ((firstM-2)*(firstM+1))/2 - ((m-2)*(m+1))/2;
for(i=0;i<NringChunk;++i)
{
//do not sum over Ylm which are too small
lmin = get_lmin_ylm(m,(float) (nsinthetaRingChunk[i]));
if(lmin <= lmax)
{
plmTime -= MPI_Wtime();
plmgen(ncosthetaRingChunk[i],nsinthetaRingChunk[i],m,plm,&firstl,plmdata);
plmTime += MPI_Wtime();
//now do sum over l
if(firstl <= lmax)
{
//alm -> map - mapNum = 0
sfact = 1.0 - (((firstl+m)%2) << 1);
for(l=firstl;l<=lmax;++l)
{
//this is always true assert((((l+m)%2 == 0 && sfact == 1.0)) || (((l+m)%2 == 1 && sfact == -1.0)));
//pure synthesis of map
rval = alm_real[lmind + l-m]*plm[l];
ival = alm_imag[lmind + l-m]*plm[l];
qmn_real[0][i][mind] += rval;
qmn_imag[0][i][mind] += ival;
qms_real[0][i][mind] += sfact*rval;
qms_imag[0][i][mind] += sfact*ival;
//gradient w.r.t. phi is i*m/sin(\theta)P_{lm}\exp(i*m*\phi)*a_{lm} \hat{\phi}
rval *= m;
ival *= m;
qmn_real[2][i][mind] -= ival;//+= -1.0*alm_imag[lmind + l-m]*plm[l]*((double) m);
qmn_imag[2][i][mind] += rval;//alm_real[lmind + l-m]*plm[l]*((double) m);
qms_real[2][i][mind] -= sfact*ival;//+= sfact*(-1.0)*alm_imag[lmind + l-m]*plm[l]*((double) m);
qms_imag[2][i][mind] += sfact*rval;//sfact*alm_real[lmind + l-m]*plm[l]*((double) m);
//del2phi_div_sin2theta is -m^2/sin^{2}(\theta)P_{lm}\exp(i*m*\phi)*a_{lm}
rval *= m;
ival *= m;
qmn_real[5][i][mind] -= rval;//+= -1.0*alm_real[lmind + l-m]*plm[l]*((double) (m*m));
qmn_imag[5][i][mind] -= ival;//+= -1.0*alm_imag[lmind + l-m]*plm[l]*((double) (m*m));
qms_real[5][i][mind] -= sfact*rval;//+= sfact*(-1.0)*alm_real[lmind + l-m]*plm[l]*((double) (m*m));
qms_imag[5][i][mind] -= sfact*ival;//+= sfact*(-1.0)*alm_imag[lmind + l-m]*plm[l]*((double) (m*m));
sfact = -sfact;
}
//grad theta, grad2 theta, and gradthetgradphi transforms
sfact = 1.0 - 2.0*((firstl+m)%2);
ncos_nsin = ncosthetaRingChunk[i]/nsinthetaRingChunk[i];
ncos_nsin2 = ncosthetaRingChunk[i]/nsinthetaRingChunk[i]/nsinthetaRingChunk[i];
ncos2_nsin2 = ncos_nsin*ncos_nsin;
//this is the first iteration of the loop
//it is broken out here to avoid branching in the loop
l = firstl;
if(l > 0)
{
//grad theta
gradplmn = ((double) l)*ncos_nsin*plm[l];
gradplms = -sfact*gradplmn; //-1 for cos(pi-nsintheta)
qmn_real[1][i][mind] += alm_real[lmind + l-m]*gradplmn;
qmn_imag[1][i][mind] += alm_imag[lmind + l-m]*gradplmn;
qms_real[1][i][mind] += alm_real[lmind + l-m]*gradplms;
qms_imag[1][i][mind] += alm_imag[lmind + l-m]*gradplms;
//we need grad^2\theta which is l*cos\theta/sin\theta\gradplm[l] - l*plm[l]
// - l*cos^{2}\theta/sin^{2}\theta*plm[l]
// + (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*plm[l-1]*cos\theta/sin^{2}\theta
// - (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*\gradplm[l-1]/sin\theta
fac1 = ((double) l)*ncos_nsin;
fac2 = ((double) l)*plm[l]*(1.0 + ncos2_nsin2);
gradquantn = fac1*gradplmn - fac2;
gradquants = -fac1*gradplms - sfact*fac2;
qmn_real[3][i][mind] += alm_real[lmind + l-m]*gradquantn;
qmn_imag[3][i][mind] += alm_imag[lmind + l-m]*gradquantn;
qms_real[3][i][mind] += alm_real[lmind + l-m]*gradquants;
qms_imag[3][i][mind] += alm_imag[lmind + l-m]*gradquants;
gradplm_lm1_n = gradplmn;
gradplm_lm1_s = gradplms;
//grad theta grad phi gives factor of i*m/sintheta
gradplmn *= m;
gradplms *= m;
qmn_real[4][i][mind] -= alm_imag[lmind + l-m]*gradplmn;
qmn_imag[4][i][mind] += alm_real[lmind + l-m]*gradplmn;
qms_real[4][i][mind] -= alm_imag[lmind + l-m]*gradplms; //sfact is over all sign of plm(pi-ncostheta) at l
qms_imag[4][i][mind] += alm_real[lmind + l-m]*gradplms;
}
else
{
gradplm_lm1_n = 0.0;
gradplm_lm1_s = 0.0;
}
sfact = -sfact;
++firstl;
for(l=firstl;l<=lmax;++l)
{
//gradient w.r.t. theta is l*cos\theta/sin\theta*plm[l] - (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*plm[l-1] \hat{\theta}
gradplmn = ((double) l)*ncos_nsin*plm[l]
- svec[l+lmaxp1*(m-firstM)]*plm[l-1]/nsinthetaRingChunk[i];
gradplms = -sfact*gradplmn; //-1 for cos(pi-nsintheta) and also -1 because plm of l-1 differs by -1 from plm of l for pi-theta
qmn_real[1][i][mind] += alm_real[lmind + l-m]*gradplmn;
qmn_imag[1][i][mind] += alm_imag[lmind + l-m]*gradplmn;
qms_real[1][i][mind] += alm_real[lmind + l-m]*gradplms;
qms_imag[1][i][mind] += alm_imag[lmind + l-m]*gradplms;
//we need grad^2\theta which is l*cos\theta/sin\theta\gradplm[l] - l*plm[l]
// - l*cos^{2}\theta/sin^{2}\theta*plm[l]
// + (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*plm[l-1]*cos\theta/sin^{2}\theta
// - (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*\gradplm[l-1]/sin\theta
fac1 = ((double) l)*ncos_nsin;
fac2 = ((double) l)*plm[l]*(1.0 + ncos2_nsin2);
fac3 = svec[l+lmaxp1*(m-firstM)]/nsinthetaRingChunk[i];
gradquantn = fac1*gradplmn - fac2 - fac3*gradplm_lm1_n;
gradquants = -fac1*gradplms - sfact*fac2 - fac3*gradplm_lm1_s;
gradfact = svec[l+lmaxp1*(m-firstM)]*plm[l-1]*ncos_nsin2;
gradquantn += gradfact;
gradquants += gradfact*sfact;
qmn_real[3][i][mind] += alm_real[lmind + l-m]*gradquantn;
qmn_imag[3][i][mind] += alm_imag[lmind + l-m]*gradquantn;
qms_real[3][i][mind] += alm_real[lmind + l-m]*gradquants;
qms_imag[3][i][mind] += alm_imag[lmind + l-m]*gradquants;
gradplm_lm1_n = gradplmn;
gradplm_lm1_s = gradplms;
//grad theta grad phi gives factor of i*m/sintheta
gradplmn *= m;
gradplms *= m;
qmn_real[4][i][mind] -= alm_imag[lmind + l-m]*gradplmn;
qmn_imag[4][i][mind] += alm_real[lmind + l-m]*gradplmn;
qms_real[4][i][mind] -= alm_imag[lmind + l-m]*gradplms; //sfact is over all sign of plm(pi-ncostheta) at l
qms_imag[4][i][mind] += alm_real[lmind + l-m]*gradplms;
sfact = -sfact;
} //for(l=firstl;l<=lmax;++l)
} //if(firstl <= lmax)
} //if(lmax >= lmin)
} //for(i=0;i<NringChunk;++i)
mTime[mind] += MPI_Wtime();
} //for(m=firstM;m<=lastM;++m)
//put data in array for transpose
for(i=0;i<NringChunk;++i)
{
nring = i + ringChunkStart - 1;
for(j=0;j<Nmaps;++j)
for(k=0;k<NmTD;++k)
{
//north ring
transDataReal[((2*nring)*Nmaps + j)*NmTD + k] = qmn_real[j][i][k];
transDataImag[((2*nring)*Nmaps + j)*NmTD + k] = qmn_imag[j][i][k];
//south ring
transDataReal[((2*nring+1)*Nmaps + j)*NmTD + k] = qms_real[j][i][k];
transDataImag[((2*nring+1)*Nmaps + j)*NmTD + k] = qms_imag[j][i][k];
}
}
}//for(chunkInd=0;chunkInd<Nchunks;++chunkInd)
///do last ring on equator as a special case to avoid branching in loops
get_ring_info2(2*Nside,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
//sum over l at fixed m for each ring using only alms on ThisTask
for(m=firstM;m<=lastM;++m)
{
mind = m-firstM;
mTime[mind] -= MPI_Wtime();
for(mapNum=0;mapNum<6;++mapNum)
{
qmn_real[mapNum][0][mind] = 0.0;
qmn_imag[mapNum][0][mind] = 0.0;
}
//lmind tracks alm coefficients for this m
lmind = (lmax+1)*(m-firstM) + ((firstM-2)*(firstM+1))/2 - ((m-2)*(m+1))/2;
//do not sum over Ylm which are too small
lmin = get_lmin_ylm(m,(float) (nsintheta));
if(lmin <= lmax)
{
plmTime -= MPI_Wtime();
plmgen(ncostheta,nsintheta,m,plm,&firstl,plmdata);
plmTime += MPI_Wtime();
//now do sum over l
if(firstl <= lmax)
{
for(l=firstl;l<=lmax;++l)
{
//alm -> map
rval = alm_real[lmind + l-m]*plm[l];
ival = alm_imag[lmind + l-m]*plm[l];
qmn_real[0][0][mind] += rval;//alm_real[lmind + l-m]*plm[l];
qmn_imag[0][0][mind] += ival;//alm_imag[lmind + l-m]*plm[l];
//gradient w.r.t. phi is i*m/sin(\theta)P_{lm}\exp(i*m*\phi)*a_{lm} \hat{\phi}
rval *= m;
ival *= m;
qmn_real[2][0][mind] -= ival;//+= -1.0*alm_imag[lmind + l-m]*plm[l]*((double) m);
qmn_imag[2][0][mind] += rval;//alm_real[lmind + l-m]*plm[l]*((double) m);
//del2phi_div_sin2theta is -m^2/sin^{2}(\theta)P_{lm}\exp(i*m*\phi)*a_{lm}
rval *= m;
ival *= m;
qmn_real[5][0][mind] -= rval;//+= -1.0*alm_real[lmind + l-m]*plm[l]*((double) (m*m));
qmn_imag[5][0][mind] -= ival;//+= -1.0*alm_imag[lmind + l-m]*plm[l]*((double) (m*m));
}
l = firstl;
gradfact = ncostheta/nsintheta;
if(l > 0)
{
//grad theta
gradplmn = ((double) l)*gradfact*plm[l];
qmn_real[1][0][mind] += alm_real[lmind + l-m]*gradplmn;
qmn_imag[1][0][mind] += alm_imag[lmind + l-m]*gradplmn;
//we need grad^2\theta which is l*cos\theta/sin\theta\gradplm[l] - l*plm[l]
// - l*cos^{2}\theta/sin^{2}\theta*plm[l]
// + (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*plm[l-1]*cos\theta/sin^{2}\theta
// - (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*\gradplm[l-1]/sin\theta
gradquantn = ((double) l)*gradfact*gradplmn - ((double) l)*plm[l]*(1.0 + gradfact*gradfact);
qmn_real[3][0][mind] += alm_real[lmind + l-m]*gradquantn;
qmn_imag[3][0][mind] += alm_imag[lmind + l-m]*gradquantn;
gradplm_lm1_n = gradplmn;
//grad theta grad phi
gradplmn *= m;
qmn_real[4][0][mind] -= alm_imag[lmind + l-m]*gradplmn;
qmn_imag[4][0][mind] += alm_real[lmind + l-m]*gradplmn;
}
else
gradplm_lm1_n = 0.0;
++firstl;
for(l=firstl;l<=lmax;++l)
{
//grad theta
gradplmn = ((double) l)*gradfact*plm[l] - svec[l+lmaxp1*(m-firstM)]*plm[l-1]/nsintheta;
qmn_real[1][0][mind] += alm_real[lmind + l-m]*gradplmn;
qmn_imag[1][0][mind] += alm_imag[lmind + l-m]*gradplmn;
//we need grad^2\theta which is l*cos\theta/sin\theta\gradplm[l] - l*plm[l]
// - l*cos^{2}\theta/sin^{2}\theta*plm[l]
// + (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*plm[l-1]*cos\theta/sin^{2}\theta
// - (l+m)*sqrt((2*l+1)/(2*l-1)*(l-m)/(l+m))*\gradplm[l-1]/sin\theta
gradquantn = ((double) l)*gradfact*gradplmn - ((double) l)*plm[l]*(1.0 + gradfact*gradfact)
+ svec[l+lmaxp1*(m-firstM)]/nsintheta*(plm[l-1]*gradfact - gradplm_lm1_n);
qmn_real[3][0][mind] += alm_real[lmind + l-m]*gradquantn;
qmn_imag[3][0][mind] += alm_imag[lmind + l-m]*gradquantn;
gradplm_lm1_n = gradplmn;
//grad theta grad phi
gradplmn *= m;
qmn_real[4][0][mind] -= alm_imag[lmind + l-m]*gradplmn;
qmn_imag[4][0][mind] += alm_real[lmind + l-m]*gradplmn;
}//for(l=firstl;l<=lmax;++l)
}//if(firstl <= lmax)
}//if(lmax >= lmin)
mTime[mind] += MPI_Wtime();
}//for(m=firstM;m<=lastM;++m)
nring = 2*Nside - 1;
for(j=0;j<Nmaps;++j)
{
for(k=0;k<NmTD;++k)
{
//north ring
transDataReal[((2*nring)*Nmaps + j)*NmTD + k] = qmn_real[j][0][k];
transDataImag[((2*nring)*Nmaps + j)*NmTD + k] = qmn_imag[j][0][k];
}//for(k=0;k<NmTD;++k)
}//for(j=0;j<Nmaps;++j)
//free some mem
free(plm);
memTot -= sizeof(double)*(lmax+1);
plmgen_destroy(plmdata);
free(svec);
memTot -= sizeof(double)*(lmax+1)*NMThisTask;
for(mapNum=0;mapNum<6;++mapNum)
{
for(i=0;i<NringChunkBase;++i)
{
free(qmn_real[mapNum][i]);
memTot -= sizeof(double)*Nqm;
free(qmn_imag[mapNum][i]);
memTot -= sizeof(double)*Nqm;
free(qms_real[mapNum][i]);
memTot -= sizeof(double)*Nqm;
free(qms_imag[mapNum][i]);
memTot -= sizeof(double)*Nqm;
}
free(qmn_real[mapNum]);
memTot -= sizeof(double*)*NringChunkBase;
free(qmn_imag[mapNum]);
memTot -= sizeof(double*)*NringChunkBase;
free(qms_real[mapNum]);
memTot -= sizeof(double*)*NringChunkBase;
free(qms_imag[mapNum]);
memTot -= sizeof(double*)*NringChunkBase;
}
free(ringpixRingChunk);
memTot -= sizeof(long)*NringChunkBase;
free(shiftedRingChunk);
memTot -= sizeof(long)*NringChunkBase;
free(nsinthetaRingChunk);
memTot -= sizeof(double)*NringChunkBase;
free(ncosthetaRingChunk);
memTot -= sizeof(double)*NringChunkBase;
sumTime += MPI_Wtime();
/* now do transpose step
done with MPI_Alltoallv
1) compute displacements and counts
2) transpose real map
3) transpose imag map
*/
transTime -= MPI_Wtime();
sendcnts = (int*)malloc(sizeof(int)*NTasks);
assert(sendcnts != NULL);
sdispls = (int*)malloc(sizeof(int)*NTasks);
assert(sdispls != NULL);
recvcnts = (int*)malloc(sizeof(int)*NTasks);
assert(recvcnts != NULL);
rdispls = (int*)malloc(sizeof(int)*NTasks);
assert(rdispls != NULL);
memTot += 4*sizeof(int)*NTasks;
for(i=0;i<NTasks;++i)
{
//compute number of rings on task i
j = 2*(plan.lastRingTasks[i] - plan.firstRingTasks[i] + 1);
if(plan.lastRingTasks[i] == 2*Nside)
--j;
sendcnts[i] = NMThisTask*Nmaps*j;
}
sdispls[0] = 0;
for(i=1;i<NTasks;++i)
sdispls[i] = sdispls[i-1] + sendcnts[i-1];
MPI_Alltoall(sendcnts,1,MPI_INT,recvcnts,1,MPI_INT,MPI_COMM_WORLD);
rdispls[0] = 0;
for(i=1;i<NTasks;++i)
rdispls[i] = rdispls[i-1] + recvcnts[i-1];
NrTDR = 2*(plan.lastRingTasks[ThisTask] - plan.firstRingTasks[ThisTask] + 1);
if(plan.lastRingTasks[ThisTask] == 2*Nside)
--NrTDR;
NmTDR = plan.lmax+1;
transDataRealRecv = (double*)malloc(sizeof(double)*NrTDR*Nmaps*NmTDR);
assert(transDataRealRecv != NULL);
memTot += sizeof(double)*NrTDR*Nmaps*NmTDR;
transDataImagRecv = (double*)malloc(sizeof(double)*NrTDR*Nmaps*NmTDR);
assert(transDataImagRecv != NULL);
memTot += sizeof(double)*NrTDR*Nmaps*NmTDR;
int log2NTasks = 0;
while(NTasks > (1 << log2NTasks))
++log2NTasks;
int level;
int sendTask,recvTask;
MPI_Status Stat;
//algorithm to loop through pairs of tasks linearly
// -lifted from Gadget-2 under GPL (http://www.gnu.org/copyleft/gpl.html)
// -see pm_periodic.c from Gadget-2 at http://www.mpa-garching.mpg.de/gadget/
//
for(level = 0; level < (1 << log2NTasks); level++) // note: for level=0, target is the same task
{
sendTask = ThisTask;
recvTask = ThisTask ^ level;
if(recvTask < NTasks)
{
if(sendTask != recvTask)
{
MPI_Sendrecv(transDataReal+sdispls[recvTask],sendcnts[recvTask],MPI_DOUBLE,recvTask,13,
transDataRealRecv+rdispls[recvTask],recvcnts[recvTask],MPI_DOUBLE,recvTask,13,
MPI_COMM_WORLD,&Stat);
MPI_Sendrecv(transDataImag+sdispls[recvTask],sendcnts[recvTask],MPI_DOUBLE,recvTask,14,
transDataImagRecv+rdispls[recvTask],recvcnts[recvTask],MPI_DOUBLE,recvTask,14,
MPI_COMM_WORLD,&Stat);
}
else // just move cells into workspace since sendTask == recvTask and Nsend == Nrecv
{
for(i=0;i<recvcnts[recvTask];++i)
transDataRealRecv[rdispls[recvTask]+i] = transDataReal[sdispls[recvTask]+i];
for(i=0;i<recvcnts[recvTask];++i)
transDataImagRecv[rdispls[recvTask]+i] = transDataImag[sdispls[recvTask]+i];
}
}
}
free(transDataReal);
memTot -= sizeof(double)*NrTD*Nmaps*NmTD;
free(transDataImag);
memTot -= sizeof(double)*NrTD*Nmaps*NmTD;
/* this version uses MPI_Alltoallv - the version above seems to be faster
transDataRealRecv = (double*)malloc(sizeof(double)*NrTDR*Nmaps*NmTDR);
assert(transDataRealRecv != NULL);
memTot += sizeof(double)*NrTDR*Nmaps*NmTDR;
#ifdef DEBUG //mem high water for this part happens here
#if DEBUG_LEVEL > 0
fprintf(stderr,"%f MB allocated in alm2allmaps_mpi.\n",((double) (sizeof(double)*(memTot)))/1024.0/1024.0);
#endif
#endif
MPI_Alltoallv(transDataReal,sendcnts,sdispls,MPI_DOUBLE,transDataRealRecv,recvcnts,rdispls,MPI_DOUBLE,MPI_COMM_WORLD);
free(transDataReal);
memTot -= sizeof(double)*NrTD*Nmaps*NmTD;
transDataImagRecv = (double*)malloc(sizeof(double)*NrTDR*Nmaps*NmTDR);
assert(transDataImagRecv != NULL);
memTot += sizeof(double)*NrTDR*Nmaps*NmTDR;
MPI_Alltoallv(transDataImag,sendcnts,sdispls,MPI_DOUBLE,transDataImagRecv,recvcnts,rdispls,MPI_DOUBLE,MPI_COMM_WORLD);
free(transDataImag);
memTot -= sizeof(double)*NrTD*Nmaps*NmTD;
*/
free(sendcnts);
free(sdispls);
free(recvcnts);
memTot -= 3*sizeof(int)*NTasks;
transTime += MPI_Wtime();
//now sort rings into their proper pixels
pixTime -= MPI_Wtime();
double *ringTime;
ringTime = (double*)malloc(sizeof(double)*NringsThisTask);
memTot += sizeof(double)*NringsThisTask;
assert(ringTime != NULL);
for(i=0;i<NringsThisTask;++i)
ringTime[i] = 0.0;
#ifdef DEBUG
#if DEBUG_LEVEL > 0
fprintf(stderr,"%f MB allocated in alm2allmaps_mpi.\n",((double) (sizeof(double)*(memTot)))/1024.0/1024.0);
#endif
#endif
//zero mapvecs
for(nring=firstRing;nring<=lastLoopRing;++nring)
{
ringTime[nring-firstRing] -= MPI_Wtime();
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ringpix_complex = ringpix/2+1;
for(mapNum=0;mapNum<6;++mapNum)
for(i=0;i<ringpix_complex;++i)
{
//north rings
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+i][0] = 0.0;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+i][1] = 0.0;
//south rings
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+i][0] = 0.0;
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+i][1] = 0.0;
}
ringTime[nring-firstRing] += MPI_Wtime();
}
if(lastRing == Nrings)
{
ringTime[lastRing-firstRing] -= MPI_Wtime();
get_ring_info2(lastRing,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ringpix_complex = ringpix/2+1;
for(mapNum=0;mapNum<6;++mapNum)
for(i=0;i<ringpix_complex;++i)
{
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+i][0] = 0.0;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+i][1] = 0.0;
}
ringTime[lastRing-firstRing] += MPI_Wtime();
}
//unpack map rings
for(task=0;task<NTasks;++task)
{
start = rdispls[task];
NmT = plan.lastMTasks[task] - plan.firstMTasks[task] + 1;
for(i=0;i<NringsLoop;++i)
{
nring = i + firstRing;
ringTime[nring-firstRing] -= MPI_Wtime();
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ringpix_complex = ringpix/2+1;
for(k=0;k<NmT;++k)
{
m = k + plan.firstMTasks[task];
//positive m
mp = m%ringpix;
if(mp < ringpix_complex)
{
l = (m-mp)/ringpix;
if(shifted && (l%2))
skfact = -1.0;
else
skfact = 1.0;
for(mapNum=0;mapNum<6;++mapNum)
{
nind = start + ((2*(nring-firstRing))*Nmaps + mapNum)*NmT;
sind = start + ((2*(nring-firstRing)+1)*Nmaps + mapNum)*NmT;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][1] += transDataImagRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[sind+k]*skfact;
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+mp][1] += transDataImagRecv[sind+k]*skfact;
}
}
//negative m
if(m > 0)
{
mp = ringpix - 1 - ((m-1)%(ringpix));
//assert(mp >= 0 && mp < ringpixRingChunk[i]); //this is true
if(mp < ringpix_complex)
{
//assert(mp < ringpix_complex) //this needs to be true and should be
l = (-m - mp)/ringpix;
if(shifted && (l%2))
skfact = -1.0;
else
skfact = 1.0;
for(mapNum=0;mapNum<6;++mapNum)
{
nind = start + ((2*(nring-firstRing))*Nmaps + mapNum)*NmT;
sind = start + ((2*(nring-firstRing)+1)*Nmaps + mapNum)*NmT;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][1] -= transDataImagRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[sind+k]*skfact;
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]+mp][1] -= transDataImagRecv[sind+k]*skfact;
}
}
}
}//for(k=0;k<NmT;++k)
ringTime[nring-firstRing] += MPI_Wtime();
}//for(i=0;i<NringsLoop;++i)
//do last ring if needed
if(lastRing == 2*Nside)
{
nring = lastRing;
ringTime[nring-firstRing] -= MPI_Wtime();
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ringpix_complex = ringpix/2+1;
for(k=0;k<NmT;++k)
{
m = k + plan.firstMTasks[task];
//positive m
mp = m%ringpix;
if(mp < ringpix_complex)
{
l = (m-mp)/ringpix;
if(shifted && (l%2))
skfact = -1.0;
else
skfact = 1.0;
for(mapNum=0;mapNum<6;++mapNum)
{
nind = start + ((2*(nring-firstRing))*Nmaps + mapNum)*NmT;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][1] += transDataImagRecv[nind+k]*skfact;
}
}
//negative m
if(m > 0)
{
mp = ringpix - 1 - ((m-1)%(ringpix));
//assert(mp >= 0 && mp < ringpixRingChunk[i]); //this is true
if(mp < ringpix_complex)
{
//assert(mp < ringpix_complex) //this needs to be true and should be
l = (-m - mp)/ringpix;
if(shifted && (l%2))
skfact = -1.0;
else
skfact = 1.0;
for(mapNum=0;mapNum<6;++mapNum)
{
nind = start + ((2*(nring-firstRing))*Nmaps + mapNum)*NmT;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][0] += transDataRealRecv[nind+k]*skfact;
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]+mp][1] -= transDataImagRecv[nind+k]*skfact;
}
}
}
}//for(k=0;k<NmT;++k)
ringTime[nring-firstRing] += MPI_Wtime();
}//if(lastRing == 2*Nside)
}//for(task=0;task<NTasks;++task)
free(transDataRealRecv);
memTot -= sizeof(double)*NrTDR*Nmaps*NmTDR;
free(transDataImagRecv);
memTot -= sizeof(double)*NrTDR*Nmaps*NmTDR;
free(rdispls);
memTot -= sizeof(int)*NTasks;
pixTime += MPI_Wtime();
/* debugging code
i = 0;
for(m=plan.firstMTasks[ThisTask];m<=plan.lastMTasks[ThisTask];++m)
for(l=m;l<=plan.lmax;++l)
{
if(isinf(alm_real[i]) || isnan(alm_real[i]) ||
isinf(alm_imag[i]) || isnan(alm_imag[i]))
{
fprintf(stderr,"alm is nan or inf: l,m = %ld|%ld, value = %lg|%lg\n",l,m,alm_real[i],alm_imag[i]);
assert(0);
}
++i;
}
for(nring=firstRing;nring<=lastLoopRing;++nring)
{
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ringpix = ringpix/2+1;
for(mapNum=0;mapNum<6;++mapNum)
for(i=0;i<ringpix;++i)
if(isnan(mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][0]) ||
isinf(mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][0]) ||
isnan(mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][1]) ||
isinf(mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][1]))
{
fprintf(stderr,"complex mapvec is nan or inf: mapNum = %ld, north ring,ind = %ld|%ld, value = %lg|%lg\n",mapNum,nring,i,
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][0],
mapvec_complex[mapNum][plan.northStartIndMapvec[nring-firstRing]][1]);
assert(0);
}
for(mapNum=0;mapNum<6;++mapNum)
for(i=0;i<ringpix;++i)
if(isnan(mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][0]) ||
isinf(mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][0]) ||
isnan(mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][1]) ||
isinf(mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][1]))
{
fprintf(stderr,"complex mapvec is nan or inf: mapNum = %ld, south ring,ind = %ld|%ld, value = %lg|%lg\n",mapNum,nring,i,
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][0],
mapvec_complex[mapNum][plan.southStartIndMapvec[nring-firstRing]][1]);
assert(0);