/*** Initialize 2D spline ***/
void Spline::init(double *dom1, double *dom2, double **f, int n1, int n2) {
int i, j;
// Clear previous settings if existent:
if (dim!=0) dealloc();
// Set variables and allocate memory:
dim = 2;
N1 = n1;
N2 = n2;
x1 = vector<double>(splOffset, N1+splOffset-1);
x2 = vector<double>(splOffset, N2+splOffset-1);
f1d = NULL;
f2d = matrix<double>(splOffset, N1+splOffset-1, splOffset, N2+splOffset-1);
d2fdx2 = NULL;
d2fdxdy = matrix<double>(splOffset, N1+splOffset-1, splOffset, N2+splOffset-1);
// Copy function sampled point to internal arrays:
for (i=splOffset; i<N1+splOffset; i++) x1[i] = dom1[i];
for (j=splOffset; j<N2+splOffset; j++) x2[j] = dom2[j];
for (i=splOffset; i<N1+splOffset; i++)
for (j=splOffset; j<N2+splOffset; j++){
f2d[i][j] = f[i][j];
}
// Compute second derivatives that are needed for Spline:
splie2(x1, x2, f2d, N1, N2, d2fdxdy);
}
// Will use the Cov[i][j][l] tensor, you have to specify the field index and
// the multipole l, and the code loops over redshifts.
void Spline::init(const FZdatabase & fieldlist, double ***Cov, int field, int lpos) {
int i, j, z1, z2;
// Clear previous settings if existent:
if (dim!=0) dealloc();
// Set variables and allocate memory:
dim = 2;
N1 = fieldlist.Nz4f(field);
N2 = fieldlist.Nz4f(field);
x1 = vector<double>(splOffset, N1+splOffset-1);
x2 = vector<double>(splOffset, N2+splOffset-1);
f1d = NULL;
f2d = matrix<double>(splOffset, N1+splOffset-1, splOffset, N2+splOffset-1);
d2fdx2 = NULL;
d2fdxdy = matrix<double>(splOffset, N1+splOffset-1, splOffset, N2+splOffset-1);
// Copy function sampled point to internal arrays:
for (z1=0; z1<N1; z1++) {
fieldlist.fFixedIndex(field, z1, &i);
// Will use the mean redshift in the bin as point where Cov was sampled:
x1[splOffset+z1] = (fieldlist.zmin(i)+fieldlist.zmax(i))/2.0;
x2[splOffset+z1] = x1[splOffset+z1];
}
for (z1=splOffset; z1<N1+splOffset; z1++) {
fieldlist.fFixedIndex(field, z1, &i);
for (z2=splOffset; z2<N2+splOffset; z2++) {
fieldlist.fFixedIndex(field, z2, &j);
f2d[z1][z2] = Cov[i][j][lpos];
}
}
// Compute second derivatives that are needed for Spline:
splie2(x1, x2, f2d, N1, N2, d2fdxdy);
}
int main(void)
{
int i,j;
float x1x2,*x1,*x2,**y,**y2;
x1=vector(1,N);
x2=vector(1,N);
y=matrix(1,M,1,N);
y2=matrix(1,M,1,N);
for (i=1;i<=M;i++) x1[i]=0.2*i;
for (i=1;i<=N;i++) x2[i]=0.2*i;
for (i=1;i<=M;i++)
for (j=1;j<=N;j++) {
x1x2=x1[i]*x2[j];
y[i][j]=x1x2*x1x2;
}
splie2(x1,x2,y,M,N,y2);
printf("\nsecond derivatives from SPLIE2\n");
printf("natural spline assumed\n");
for (i=1;i<=5;i++) {
for (j=1;j<=5;j++) printf("%12.6f",y2[i][j]);
printf("\n");
}
printf("\nactual second derivatives\n");
for (i=1;i<=5;i++) {
for (j=1;j<=5;j++) printf("%12.6f",2.0*x1[i]*x1[i]);
printf("\n");
}
free_matrix(y2,1,M,1,N);
free_matrix(y,1,M,1,N);
free_vector(x2,1,N);
free_vector(x1,1,N);
return 0;
}
double xi2d_interp(double rs1, double rp1, double rs2, double rp2)
{
static double **xi2d,rmax,rmin,*rsig,*rpi,**yy2d;
static int flag=1,n,prev;
int i,j,ng=20;
double dx,dy,dlogr,xsum,rs,rp,x;
if(flag || prev!=RESET_COSMOLOGY)
{
two_halo(1,1);
prev=RESET_COSMOLOGY;
n=35;
if(flag)
{
xi2d=dmatrix(1,n,1,n);
yy2d=dmatrix(1,n,1,n);
rsig=dvector(1,n);
rpi=dvector(1,n);
}
flag=0;
rmax=log(40.5);
rmin=log(0.05);
dlogr = (rmax-rmin)/(n-1);
for(i=1;i<=n;++i)
rsig[i]=rpi[i]=exp((i-1)*dlogr+rmin);
calc_xi2d(xi2d,n,rmax,rmin);
splie2(rsig,rpi,xi2d,n,n,yy2d);
}
if(rs2<0 && rp2<0)
{
splin2(rsig,rpi,xi2d,yy2d,n,n,(rs1),(rp1),&x);
return(x);
}
dx=(rs2-rs1)/ng;
dy=(rp2-rp1)/ng;
xsum=0;
for(i=1;i<=ng;++i)
for(j=1;j<=ng;++j)
{
rs=rs1+(i-0.5)*dx;
rp=rp1+(j-0.5)*dy;
splin2(rsig,rpi,xi2d,yy2d,n,n,(rs),(rp),&x);
xsum+=2*dy*rs*dx*(x);
}
xsum/=((rs2*rs2-rs1*rs1)*(rp2-rp1));
return(xsum);
}
/* The angular grid here is set such that
* it's only used for the small-r SDSS multipoles, i<=3, or r<~ 1 Mpc/h
*/
double xi2d_interp_polar(double rs1, double rs2, double phi1, double phi2)
{
static double **xi2d,rmax,rmin,*rsig,*rpi,**yy2d;
static int flag=1,n,prev;
int i,j,ng=20;
double dx,dy,dlogr,xsum,rs,rp,x,vsum,dr,dphi,phi,r;
if(flag || prev!=RESET_COSMOLOGY)
{
two_halo(1,1);
prev=RESET_COSMOLOGY;
n=15;
if(flag)
{
xi2d=dmatrix(1,n,1,n);
yy2d=dmatrix(1,n,1,n);
rsig=dvector(1,n);
rpi=dvector(1,n);
}
flag=0;
rmax=log(2.5);
rmin=log(0.05);
dlogr = (rmax-rmin)/(n-1);
for(i=1;i<=n;++i)
rsig[i]=rpi[i]=exp((i-1)*dlogr+rmin);
calc_xi2d(xi2d,n,rmax,rmin);
splie2(rsig,rpi,xi2d,n,n,yy2d);
}
rs1 = log(rs1);
rs2 = log(rs2);
dr=(rs2-rs1)/ng;
dphi=(phi2-phi1)/ng;
xsum=vsum=0;
for(i=1;i<=ng;++i)
for(j=1;j<=ng;++j)
{
r=exp(rs1+(i-0.5)*dr);
phi=phi1+(j-0.5)*dphi;
rp = r*sin(phi);
rs = r*cos(phi);
splin2(rsig,rpi,xi2d,yy2d,n,n,(rs),(rp),&x);
xsum+=sin(phi)*r*r*r*(x);
vsum+=r*r*r*sin(phi);
}
xsum/=vsum;
return(xsum);
}