/*
derive series expansion from random numbers.
called every timestep, updating the seed
*/
void SCF_calc_from_random(long *seed)
{
int n, l, m;
for (l=0; l<=SCF_LMAX; l++)
for (m=0; m<=l; m++)
for (n=0; n<=SCF_NMAX; n++)
{
sinsum[nlm(n,l,m)]=SCF_Hnml_rand(n,l,m,seed);
cossum[nlm(n,l,m)]=SCF_Gnml_rand(n,l,m,seed);
}
}
/* set the expansion factors back to zero */
void SCF_reset(void)
{
int n, l, m;
for (l=0; l<=SCF_LMAX; l++)
for (m=0; m<=l; m++)
for (n=0; n<=SCF_NMAX; n++)
{
sinsum[nlm(n,l,m)]=0.0;
cossum[nlm(n,l,m)]=0.0;
}
}
/* write out coefficients and check potential + accelerations (note the scaling!) */
void SCF_collect_update(void)
{
int n, l, m;
for (n=0; n<=SCF_NMAX; n++)
{
for (l=0; l<=SCF_LMAX; l++)
{
for (m=0; m<=l; m++)
{
sinsum[nlm(n,l,m)]=sinsum_all[nlm(n,l,m)];
cossum[nlm(n,l,m)]=cossum_all[nlm(n,l,m)];
}
}
}
}
bool YlmRnlSet<GT>::add(int n, int l, int m, int s, value_type occ)
{
if(Restriction == "spin+space")
{
NLIndex nl(n,l);
NL_Map_t::iterator it = NL.find(nl);
///if the orbital is new add it to the end of the list
if(it == NL.end())
{
///assign the orbital a new id
ID.push_back(NumUniqueOrb);
///the id counter is set to 1
IDcount.push_back(1);
///add a new element to the map
NL[nl] = NumUniqueOrb;
///increment the number of unique orbitals
NumUniqueOrb++;
///now add the radial grid orbital
psi.push_back(RadialOrbital_t(m_grid));
///add the quantum numbers to the list
N.push_back(n);
L.push_back(l);
M.push_back(m);
S.push_back(s);
Occ.push_back(occ);
}
else
{
///if an orbital of the same restriction type has already
///been added, add the orbital such that all the
///orbitals with the same restriction type are grouped
///together
///increment the id counter
IDcount[(*it).second]++;
///locate the position in the array where the orbital
///will be added
// IDmap.resize(IDcount.size());
vector<int> IDmap(IDcount.size());
IDmap[0] = 0;
int sum = 0;
for(int i=1; i < IDmap.size(); i++)
{
sum += IDcount[i-1];
IDmap[i] = sum;
}
ID.insert(ID.begin()+IDmap[(*it).second],(*it).second);
psi.insert(psi.begin()+IDmap[(*it).second],RadialOrbital_t(m_grid));
N.insert(N.begin()+IDmap[(*it).second],n);
L.insert(L.begin()+IDmap[(*it).second],l);
M.insert(M.begin()+IDmap[(*it).second],m);
S.insert(S.begin()+IDmap[(*it).second],s);
Occ.insert(Occ.begin()+IDmap[(*it).second],occ);
IDmap.clear();
}
}
if(Restriction == "spin")
{
NLMIndex nlm(n,l,m);
NLM_Map_t::iterator it = NLM.find(nlm);
if(it == NLM.end())
{
ID.push_back(NumUniqueOrb);
IDcount.push_back(1);
NLM[nlm] = NumUniqueOrb;
NumUniqueOrb++;
psi.push_back(RadialOrbital_t(m_grid));
N.push_back(n);
L.push_back(l);
M.push_back(m);
S.push_back(s);
Occ.push_back(occ);
}
else
{
IDcount[(*it).second]++;
vector<int> IDmap(IDcount.size());
// IDmap.resize(IDcount.size());
IDmap[0] = 0;
int sum = 0;
for(int i=1; i < IDmap.size(); i++)
{
sum += IDcount[i-1];
IDmap[i] = sum;
}
ID.insert(ID.begin()+IDmap[(*it).second],(*it).second);
psi.insert(psi.begin()+IDmap[(*it).second],RadialOrbital_t(m_grid));
N.insert(N.begin()+IDmap[(*it).second],n);
L.insert(L.begin()+IDmap[(*it).second],l);
M.insert(M.begin()+IDmap[(*it).second],m);
S.insert(S.begin()+IDmap[(*it).second],s);
Occ.insert(Occ.begin()+IDmap[(*it).second],occ);
IDmap.clear();
}
}
if(Restriction == "none")
{
///add the orbital at the end of the list
ID.push_back(NumUniqueOrb);
IDcount.push_back(1);
NumUniqueOrb++;
psi.push_back(RadialOrbital_t(m_grid));
N.push_back(n);
L.push_back(l);
M.push_back(m);
S.push_back(s);
Occ.push_back(occ);
}
return true;
}
/* write out coefficients and check potential + accelerations (note the scaling!) */
void SCF_write(int task)
{
int n, l, m;
/* print selected task */
if (ThisTask == task)
{
for (n=0; n<=SCF_NMAX; n++)
{
for (l=0; l<=SCF_LMAX; l++)
{
for (m=0; m<=l; m++)
{
#ifdef SCF_SCALEFAC
fprintf(FdSCF, "Step %d: Task: %d H[%d,%d,%d] = %g %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, sinsum[nlm(n,l,m)], sinsum[nlm(n,l,m)]*scalefac_nlm[nlm(n,l,m)]);
fprintf(FdSCF, "Step %d: Task: %d G[%d,%d,%d] = %g %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, cossum[nlm(n,l,m)], cossum[nlm(n,l,m)]*scalefac_nlm[nlm(n,l,m)]);
#else
fprintf(FdSCF, "Step %d: Task: %d H[%d,%d,%d] = %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, sinsum[nlm(n,l,m)]);
fprintf(FdSCF, "Step %d: Task: %d G[%d,%d,%d] = %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, cossum[nlm(n,l,m)]);
#endif
fflush(FdSCF);
}
}
}
}
/* print all tasks */
if (-1 == task)
{
for (n=0; n<=SCF_NMAX; n++)
{
for (l=0; l<=SCF_LMAX; l++)
{
for (m=0; m<=l; m++)
{
#ifdef SCF_SCALEFAC
fprintf(FdSCF, "Step %d: Task: %d H[%d,%d,%d] = %g %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, sinsum[nlm(n,l,m)], sinsum[nlm(n,l,m)]*scalefac_nlm[nlm(n,l,m)]);
fprintf(FdSCF, "Step %d: Task: %d G[%d,%d,%d] = %g %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, cossum[nlm(n,l,m)], cossum[nlm(n,l,m)]*scalefac_nlm[nlm(n,l,m)]);
#else
fprintf(FdSCF, "Step %d: Task: %d H[%d,%d,%d] = %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, sinsum[nlm(n,l,m)]);
fprintf(FdSCF, "Step %d: Task: %d G[%d,%d,%d] = %g\n", All.NumCurrentTiStep, ThisTask, n, l, m, cossum[nlm(n,l,m)]);
#endif
fflush(FdSCF);
}
}
}
}
}
/* SCF init routine */
void SCF_init(void)
{
int l, n, m;
MyDouble K_nl, deltam0;
Anltilde=(MyDouble*)mymalloc("Anltilde",(SCF_NMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
coeflm=(MyDouble*)mymalloc("coeflm",(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
cosmphi=(MyDouble*)mymalloc("cosmphi",(SCF_LMAX+1)*sizeof(MyDouble));
sinmphi=(MyDouble*)mymalloc("sinmphi",(SCF_LMAX+1)*sizeof(MyDouble));
ultrasp=(MyDouble*)mymalloc("ultrasp",(SCF_NMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
ultraspt=(MyDouble*)mymalloc("ultraspt",(SCF_NMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
ultrasp1=(MyDouble*)mymalloc("ultrasp1",(SCF_NMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
plm=(MyDouble*)mymalloc("plm",(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
dplm=(MyDouble*)mymalloc("dplm",(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
dblfact=(MyDouble*)mymalloc("dblfact",(SCF_LMAX+1)*sizeof(MyDouble));
sinsum=(MyDouble*)mymalloc("sinsum",(SCF_NMAX+1)*(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
cossum=(MyDouble*)mymalloc("cossum",(SCF_NMAX+1)*(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
#ifdef SCF_HYBRID
sinsum_all=(MyDouble*)mymalloc("sinsum_all",(SCF_NMAX+1)*(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
cossum_all=(MyDouble*)mymalloc("cossum_all", (SCF_NMAX+1)*(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
int i;
/* store masses in backup field */
for (i = 0; i < NumPart; i++)
P[i].MassBackup = P[i].Mass;
#endif
#ifdef SCF_SCALEFAC
scalefac_nlm=(float*)mymalloc("sinsum_all",(SCF_NMAX+1)*(SCF_LMAX+1)*(SCF_LMAX+1)*sizeof(MyDouble));
FILE *fd;
if(!(fd = fopen("scf_scalefac.dat", "r")))
{
printf("Cannot read SCF scaling file `scf_scalefac.dat'\n");
endrun(10121);
}
for (n=0; n<=SCF_NMAX; n++)
for (l=0; l<=SCF_LMAX; l++)
for (m=0; m<=l; m++)
fscanf(fd, "%g", (float*)&scalefac_nlm[nlm(n,l,m)]);
fclose(fd);
#ifdef DEBUG
if (ThisTask == 0)
for (n=0; n<=SCF_NMAX; n++)
for (l=0; l<=SCF_LMAX; l++)
for (m=0; m<=l; m++)
printf("(%d,%d,%d) = %g\n", n,l,m,scalefac_nlm[nlm(n,l,m)]);
#endif
#endif
Anltilde[0]=0.0;
coeflm[0]=0.0;
cosmphi[0]=0.0;
sinmphi[0]=0.0;
ultrasp[0]=0.0;
ultraspt[0]=0.0;
plm[0]=0.0;
ultrasp1[0]=0.0;
dplm[0]=0.0;
dblfact[1]=1.;
/* set initial random number seed (global variable, so that all processors generate the same potential */
scf_seed=42;
for (l=2; l<=SCF_LMAX; l++)
dblfact[l]=dblfact[l-1]*(2.*l-1.);
for (n=0; n<=SCF_NMAX; n++)
for (l=0; l<=SCF_LMAX; l++)
Anltilde[nl(n,l)]=0.0;
for (l=0; l<=SCF_LMAX; l++)
for (m=0; m<=l; m++)
coeflm[lm(l,m)]=0.0;
for (n=0; n<=SCF_NMAX; n++)
for (l=0; l<=SCF_LMAX; l++)
{
K_nl = 0.5*n*(n+4.*l+3.)+(l+1.)*(2.*l+1.); /* eq.(2.23) */
Anltilde[nl(n,l)]=-pow(2.,8.*l+6.)*factrl(n)*(n+2.*l+1.5)*tgamma(2.*l+1.5)*tgamma(2.*l+1.5)/(4.*M_PI*K_nl*factrl(n+4*l+2));
}
for (l=0; l<=SCF_LMAX; l++)
{
for (m=0; m<=l; ++m)
{
deltam0=2.;
if (m==0) deltam0=1.;
coeflm[lm(l,m)]=(2.*l+1.)*deltam0*factrl(l-m)/factrl(l+m); /* N_lm eq. (3.15) */
}
}
}
/* Calculate SCF coefficients based on particle distribution */
void SCF_calc_from_particles(void)
{
double r, un, unm1, costh, sinth, phi, xi;
double plm1m,plm2m,temp1,temp2,temp3;
int n,l,m;
int i;
double x, y, z, mass;
for(i = 0; i < NumPart; i++)
{
/* consider only DM particles of SCF coefficients */
if (P[i].Type != 1)
continue;
/* scale to unit hernquist sphere */
to_unit(P[i].Pos[0], P[i].Pos[1], P[i].Pos[2], &x, &y, &z);
mass = P[i].Mass /SCF_HQ_MASS;
/* OR: not */
//x = P[i].Pos[0]; y = P[i].Pos[1]; z = P[i].Pos[2];
//mass = P[i].Mass;
/* particle coordinate transformation */
r = sqrt(x * x + y * y + z * z);
costh=z/r;
phi=atan2(y,x);
xi=(r-1.)/(r+1.);
sinth=sqrt(1.-costh*costh);
for (m=0; m<=SCF_LMAX; m++)
{
cosmphi[m]=cos(m*phi);
sinmphi[m]=sin(m*phi);
}
/* Ultraspherical polynomials */
for (l=0; l<=SCF_LMAX; l++)
{
ultrasp[nl(0,l)]=1.0;
if (SCF_NMAX>0)
{
ultrasp[nl(1,l)]=(2.0*(2.*l+1.5))*xi;
un=ultrasp[nl(1,l)];
unm1=1.0;
/* recursion */
for(n=1; n<=SCF_NMAX-1; n++)
{
ultrasp[nl(n+1,l)]=((2.0*n+(2.0*(2.*l+1.5)))*xi*un-(1.0*n-1.0+(2.0*(2.*l+1.5)))*unm1)*1.0/(n+1.0);
unm1=un;
un=ultrasp[nl(n+1,l)];
}
}
for (n=0; n<=SCF_NMAX; n++)
{
ultraspt[nl(n,l)]=ultrasp[nl(n,l)]*Anltilde[nl(n,l)];
}
}
/* Legendre polynomials */
for (m=0; m<=SCF_LMAX; m++)
{
plm[lm(m,m)]=1.0;
if (m>0)
plm[lm(m,m)]=-pow(1,m)*dblfact[m]*pow(sinth,m);
plm1m=plm[lm(m,m)];
plm2m=0.0;
/* recursion */
for (l=m+1; l<=SCF_LMAX; l++)
{
plm[lm(l,m)]=(costh*(2.*l-1.)*plm1m-(l+m-1.)*plm2m)/(l-m);
plm2m=plm1m;
plm1m=plm[lm(l,m)];
}
}
for (l=0; l<=SCF_LMAX; l++)
{
temp1=pow(r,l)/pow(1.+r,2*l+1)*mass;
for (m=0; m<=l; m++)
{
temp2=temp1*plm[lm(l,m)]*coeflm[lm(l,m)]*sinmphi[m];
temp3=temp1*plm[lm(l,m)]*coeflm[lm(l,m)]*cosmphi[m];
for (n=0; n<=SCF_NMAX; n++)
{
sinsum[nlm(n,l,m)]+=temp2*ultraspt[nl(n,l)];
cossum[nlm(n,l,m)]+=temp3*ultraspt[nl(n,l)];
}
}
}
}
}
/* get force and potential based on SCF expansion of (unit!) sphere */
void SCF_evaluate(MyDouble x, MyDouble y, MyDouble z, MyDouble *potential, MyDouble *ax, MyDouble *ay, MyDouble *az)
{
int n,l,m;
MyDouble r,rl, costh,sinth,phi,xi;
MyDouble ar,ath,aphi,poten;
MyDouble un,unm1,unplusr,phinltil;
MyDouble plm1m,plm2m;
MyDouble temp1,temp2,temp3,temp4;
MyDouble Clm,Dlm,Elm,Flm;
/* particle coordinate transformation */
r = sqrt(x * x + y * y + z * z);
costh=z/r;
phi=atan2(y,x);
xi=(r-1.)/(r+1.);
sinth=sqrt(1.-costh*costh);
for (m=0; m<=SCF_LMAX; m++)
{
cosmphi[m]=cos(m*phi);
sinmphi[m]=sin(m*phi);
}
ar=0.0;
ath=0.0;
aphi=0.0;
poten=0.0;
/* Ultraspherical polynomials */
for (l=0; l<=SCF_LMAX; l++)
{
ultrasp[nl(0,l)]=1.0;
ultrasp1[nl(0,l)]=0.0;
if (SCF_NMAX>0)
{
ultrasp[nl(1,l)]=(2.0*(2.*l+1.5))*xi;
ultrasp1[nl(1,l)]=1.0;
un=ultrasp[nl(1,l)];
unm1=1.0;
/* recursion */
for(n=1; n<=SCF_NMAX-1; n++)
{
ultrasp[nl(n+1,l)]=((2.0*n+(2.0*(2.*l+1.5)))*xi*un-(1.0*n-1.0+(2.0*(2.*l+1.5)))*unm1)*1.0/(n+1.0);
unm1=un;
un=ultrasp[nl(n+1,l)];
ultrasp1[nl(n+1,l)]=(((2.0*(2.*l+1.5))+(n+1)-1.)*unm1-(n+1)*xi*ultrasp[nl(n+1,l)])/((2.0*(2.*l+1.5))*(1.-xi*xi));
}
}
}
/* Legendre polynomials */
for (m=0; m<=SCF_LMAX; m++)
{
plm[lm(m,m)]=1.0;
if(m>0)
plm[lm(m,m)]=pow(-1,m)*dblfact[m]*pow(sinth,m);
plm1m=plm[lm(m,m)];
plm2m=0.0;
/* recursion */
for(l=m+1; l<=SCF_LMAX; l++)
{
plm[lm(l,m)]=(costh*(2.*l-1.)*plm1m-(l+m-1.)*plm2m)/(l-m);
plm2m=plm1m;
plm1m=plm[lm(l,m)];
}
}
/* derivatives of Legendre polynomials */
dplm[0]=0.0;
for(l=1; l<=SCF_LMAX; l++)
{
for(m=0; m<=l; m++)
{
if(l==m)
dplm[lm(l,m)]=l*costh*plm[lm(l,m)]/(costh*costh-1.0);
else
dplm[lm(l,m)]=(l*costh*plm[lm(l,m)]-(l+m)*plm[lm(l-1,m)])/(costh*costh-1.0);
}
}
for (l=0; l<=SCF_LMAX; l++)
{
temp1=0.0;
temp2=0.0;
temp3=0.0;
temp4=0.0;
for(m=0; m<=l; m++)
{
Clm=0.0;
Dlm=0.0;
Elm=0.0;
Flm=0.0;
for(n=0; n<=SCF_NMAX; n++)
{
#ifdef SCF_SCALEFAC
Clm += ultrasp[nl(n,l)]*cossum[nlm(n,l,m)] * scalefac_nlm[nlm(n,l,m)];
Dlm += ultrasp[nl(n,l)]*sinsum[nlm(n,l,m)] * scalefac_nlm[nlm(n,l,m)];
Elm += ultrasp1[nl(n,l)]*cossum[nlm(n,l,m)] * scalefac_nlm[nlm(n,l,m)];
Flm += ultrasp1[nl(n,l)]*sinsum[nlm(n,l,m)] * scalefac_nlm[nlm(n,l,m)];
#else
Clm += ultrasp[nl(n,l)]*cossum[nlm(n,l,m)];
Dlm += ultrasp[nl(n,l)]*sinsum[nlm(n,l,m)];
Elm += ultrasp1[nl(n,l)]*cossum[nlm(n,l,m)];
Flm += ultrasp1[nl(n,l)]*sinsum[nlm(n,l,m)];
#endif
}
temp1 += plm[lm(l,m)]*(Clm*cosmphi[m]+Dlm*sinmphi[m]);
temp2 += -plm[lm(l,m)]*(Elm*cosmphi[m]+Flm*sinmphi[m]);
temp3 += -dplm[lm(l,m)]*(Clm*cosmphi[m]+Dlm*sinmphi[m]);
temp4 += -m*plm[lm(l,m)]*(Dlm*cosmphi[m]-Clm*sinmphi[m]);
}
rl=pow(r,l);
unplusr=pow(1.+r,2*l+1);
phinltil=rl/unplusr;
/* add contributions to potential */
poten += temp1*phinltil;
/* add contributions to accelerations in spherical coordinates */
ar += phinltil*(-temp1*(l/r-(2.*l+1.)/(1.+r))+temp2*4.*(2.*l+1.5)/(pow(1.+r,2)));
ath += temp3*phinltil;
aphi += temp4*phinltil;
}
/* convert to cartesian coordinates */
*ax=(sinth*cos(phi)*ar+costh*cos(phi)*ath-sin(phi)*aphi);
*ay=(sinth*sin(phi)*ar+costh*sin(phi)*ath+cos(phi)*aphi);
*az=(costh*ar-sinth*ath);
*potential = poten;
}