''' Convert (ra,dec) to cartesian (x,y,z) coordinates '''

sin_ra = np.sin(ra * np.pi / 180.)

cos_ra = np.cos(ra * np.pi / 180.)

sin_dec = np.sin(np.pi / 2 - dec * np.pi / 180.)

cos_dec = np.cos(np.pi / 2 - dec * np.pi / 180.)

''' Convert (ra,dec,reds) to cartesian (x,y,z) coordiantes for a given cosmology '''

ra = np.asarray(ra)

dec = np.asarray(dec)

reds = np.asarray(reds)

sin_ra = np.sin(ra*np.pi/180.)

cos_ra = np.cos(ra*np.pi/180.)

sin_dec = np.sin(np.pi/2 - dec*np.pi/180)

cos_dec = np.cos(np.pi/2 - dec*np.pi/180)

r = cosmo.comoving_distance(reds).value

x = r * cos_ra * sin_dec

y = r * sin_ra * sin_dec

z = r * cos_dec

'''

Generate n random points in a spherical shell of thickness r2-r1, centered

on (xc,yc,zc)

'''

th = np.random.random(n)*(2*np.pi)

z0 = np.random.random(n)*2. + (-1.)

x0 = np.sqrt(1-z0**2)*np.cos(th)

y0 = np.sqrt(1-z0**2)*np.sin(th)

t = np.random.random(n)*(r2**3 - r1**3) + r1**3

r = t**(1./3.)

x = x0*r + xc

y = y0*r + yc

z = z0*r + zc

''' Convert (ra,r) to polar coordinates for 2D cone plot'''

theta = ra * np.pi / 180 # radians

x = r * np.cos(theta)

y = r * np.sin(theta)

''' Draw uniform n points inside a sphere of radius R'''

phi = np.random.random(n)*2*np.pi

costheta = np.random.random(n)*2. - 1.0

h = np.random.random(n)

theta = np.arccos(costheta)

r = R * (h**(1./3.))

x = r * np.sin(theta) * np.cos(phi)

y = r * np.sin(theta) * np.sin(phi)

z = r * np.cos(theta)

m = np.asarray([x,y,z])

m = m.T

'''

Basic 3D scatter plot. Can pass a single xyz array of shape (n,3) or

3 different vectors for x,y,z

'''

from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure(figsize=(10,10))

ax = fig.add_subplot(111, projection='3d')

if xyz.shape[1]==3:

x,y,z = xyz[:,0],xyz[:,1],xyz[:,2]

else :

x,y,z = xyz,y,z

''' Send a 2D array or astropy table to topcat via SAMP '''

from sampc import Client

c = Client()

'''

Randomize a set of (x,y,z) points defined over box of size b, by random

mirroring axes and by randomly rotating coordinates by 90 deg.

This function is useful when a simulated box of points needs to be stacked

multiple times. By randomizing the box, we preserve the inner strucures but

avoid creating artificial patterns.

Parameters

----------

xyz : array

Array of 3D points of shape (n,3)

b : float

Box size

Returns

----------

ranxyz : array

Array of randomized 3D points

'''

# Mirror along a randomly chosen axis

x,y,z = xyz[:,0],xyz[:,1],xyz[:,2]

rn = np.random.random_integers(1,8)

if rn==1 :

x = x

else :

if rn==2 :

x = b-x

else :

if rn==3 :

y = b-y

else :

if rn==4 :

z = b-z

else :

if rn==5 :

x = b-x

y = b-y

else :

if rn==6 :

y = b-y

z = b-z

else :

if rn==7 :

x = b-x

z = b-z

else :

if rn==8 :

x = b-x

y = b-y

# Rotate by 90 deg around a randomly chosen direction

rn = np.random.random_integers(1,6)

if rn==1 :

ranxyz = np.asarray(zip(x,y,z))

else :

if rn==2 :

ranxyz = np.asarray(zip(z,x,y))

else :

if rn==3 :

ranxyz = np.asarray(zip(y,z,x))

else :

if rn==4 :

ranxyz = np.asarray(zip(x,z,y))

else :

if rn==5 :

ranxyz = np.asarray(zip(y,x,z))

else :

if rn==6 :

ranxyz = np.asarray(zip(z,y,x))

''' Generate n uniform random points (ra,dec) in a given piece of sky'''

zlim = np.sin(np.pi * np.asarray(declim) / 180.)

z = zlim[0] + (zlim[1] - zlim[0]) * np.random.random(n)

dec = (180. / np.pi) * np.arcsin(z)

ra = ralim[0] + (ralim[1] - ralim[0]) * np.random.random(n)

rand_elong=False,fix_nmemb=False,random_state=None,

doplot=False,colorize=False,cosmo=None,oformat='table'):

'''

Generate a mock light cone of random 3D points with added gaussian blobs

or "clusters"

These clusters are distributed randomly over the cone and can have either

fixed or random sizes within a given interval. They can alse be randomly

elongated along xyz axes. The nr. of memebers of each cluster can be either

fixed or proportional to its extension (really?)

The fraction of uniform (non-clustered) points (``ufrac``) can be specified,

leaving (1-ufrac)*n points that are distributed among ``ncen`` clusters

Parameters

----------

ralim : list (ra0, ra1)

RA limits [deg]

declim : list (dec0, dec1)

DEC limits [deg]

zlim : list (z0, z1)

Redshift limits

npts : integer

Total number of points in the cone. Default 20000

ufrac : float

Fraction of uniformly distributed points (i.e. non-clustered objects)

ncen : integer

Number of clusters

cradlim : float or list of form [rmin,rmax]

Size of clusters in Mpc. In reality it corresponds to 2*sigma of the

gaussians. If float, all clusters have the same size. If a list,

sizes are chosen randomly between the given limits. If None, defaults

to [0.5,25]

rand_elong : bool

If True, clusters are randomly deformed along xyz axes by a factor of 3

fix_nmemb : bool

If True, all clusters have the same nr of members

random_state : integer

Seed for random number generator

doplot : bool

If True, generate a plane polar and a ra-dec plot

docolorize : bool

If True, points for centers and cluster members are colored differently

cosmo : astropy cosmology object

If None, defaults to a flat LambdaCDM with H_0=100 and Om=0.3

oformat : string

Select output format as

* 'table' : astropy table. Default

* 'array' : numpy array

Notes

-----

The exact nr of uniform (non-clustered) points is added at the end to

complete ``n`` total points

Returns

----------

kone : astropy.table / array of shape (nobj_in_cone,7)

Table or array of 7 columns [ra,dec,redshift,comdis(redshift),x,y,z]

'''

if random_state is not None: np.random.seed(seed=random_state)

if cradlim is None : cradlim = [0.5,25.]

if cosmo is None:

cosmo = FlatLambdaCDM(H0=100, Om0=0.3)

nunif = np.int(ufrac*n) # Desided nr of uniform sources

nnotunif = n-nunif # Desired nr of sources in clusters

# Randomly pick ncen centers for the clusters -----------------------------

Cra,Cdec = uniform_sky(ralim,declim,n=ncen)

Cred = (zlim[1]-zlim[0])*np.random.random(ncen) + zlim[0]

Cx,Cy,Cz = rdz2xyz(Cra,Cdec,Cred,cosmo)

# Set a fixed or random radius within a the input range ------------------

if isinstance(cradlim,list):

Crad = (cradlim[1]-cradlim[0])*np.random.random_sample(ncen) + cradlim[0]

else:

Crad = np.asarray([cradlim]*ncen)

Crad = Crad/2. # inout radius is 2*std, so get std for multivariate_normal()

# Set the number of members of each cluster ------------------------------

if fix_nmemb:

k = np.int(1.0*nnotunif/ncen) #same nr for all clusters

Cmem = [k]*ncen

else :

uu = np.random.randint(4,nnotunif+1,ncen-1)

tt = np.append(uu,[4,nnotunif+1])

tt.sort()

Cmem = np.diff(tt) # n_members by some proportionality to extension

# Generate clusters -----------------------------------------------------

print 'Generating clusters...'

for i in range(ncen):

print ' |--',i,Cra[i],Cdec[i],Cred[i],Crad[i],Cmem[i]

# Real space center for the 3D gaussian (center of cluster)

mm = np.array([Cx[i],Cy[i],Cz[i]])

# Real space std for the 3D gaussian (sort of size of cluster)

if rand_elong :

efac = np.random.random(3)*3.

else :

efac = np.ones(3)

stdx = Crad[i]*efac[0]

stdy = Crad[i]*efac[1]

stdz = Crad[i]*efac[2]

cv = np.array([[stdx,0.,0.],[0.,stdy,0.],[0.,0.,stdz]])

# Number of members of the cluster

#nmem = np.int(1.0*nnotunif/ncen) #same nr for all clusters

nmem = Cmem[i]

# Finally generate the cluster

if Cmem[i] > 0:

m=np.random.multivariate_normal(mm,cv,nmem)

if i == 0 :

abc = m

else:

abc = np.concatenate((abc,m),axis=0)

x1,y1,z1 = abc[:,0],abc[:,1],abc[:,2]

# Convert clusters from (x,y,z) to (ra,dec,redshift) ---------------------

ttt = cartesian_to_spherical(x1,y1,z1)

comd1,dec1,ra1 = ttt[0].value,ttt[1].value*180./np.pi,ttt[2].value*180./np.pi

tmpz = np.linspace(0.,zlim[1]+7.,500)

tmpd = cosmo.comoving_distance(tmpz).value

reds1 = np.interp(comd1,tmpd,tmpz,left=-1., right=-1.)

if (reds1<0).any(): raise Exception('Problem with redshifts!')

# Cut clusters to desired ra,dec,redshift window ------------------------

idx,=np.where( (ra1>ralim[0]) & (ra1<ralim[1]) & (dec1>declim[0]) & (dec1<declim[1]) & (reds1>zlim[0]) & (reds1<zlim[1]) )

ra1,dec1,reds1=ra1[idx],dec1[idx],reds1[idx]

ncpop=len(ra1) # this is the effective nr of clustered objects in the cone

# Add uniform background points to complete n objects --------------------

nback = n-ncen-ncpop

ra2,dec2 = uniform_sky(ralim,declim,n=nback)

reds2 = (zlim[1]-zlim[0])*np.random.random(nback) + zlim[0]

x2,y2,z2 = rdz2xyz(ra2,dec2,reds2,cosmo)

#print 'n,nunif,nnotunif,ncen,ncpop,nback',n,nunif,nnotunif,ncen,ncpop,nback

print 'Results'

print ' |--Nr of clusters :',ncen

print ' |--Nr of cluster members :',ncpop

print ' |--Nr of non-cluster objects :',nback

print ' |--Total nr of objects in cone :',n

# Join everything and do plot --------------------------------------------

ra = np.concatenate([Cra,ra1,ra2])

dec = np.concatenate([Cdec,dec1,dec2])

reds = np.concatenate([Cred,reds1,reds2])

distC = cosmo.comoving_distance(Cred).value

dist1 = cosmo.comoving_distance(reds1).value

dist2 = cosmo.comoving_distance(reds2).value

dist = np.concatenate([distC,dist1,dist2])

x = np.concatenate([Cx,x1,x2])

y = np.concatenate([Cy,y1,y2])

z = np.concatenate([Cz,z1,z2])

if colorize:

c2,c1,cc = 'k','b','r'

spts, scen = 0.2, 20

else:

c2,c1,cc = 'k','k','k'

spts, scen = 0.2, 0.2

if doplot:

#x,y=raz2xy(ra,z)

#plt.scatter(x,y,s=0.4) #c=z,cmap='jet'

#plt.scatter(ra,dec,s=spts,c=z)

x2,y2=raz2xy(ra2,reds2)

x1,y1=raz2xy(ra1,reds1)

xC,yC=raz2xy(Cra,Cred)

plt.scatter(x2,y2,s=spts,color=c2)

plt.scatter(x1,y1,s=spts,color=c1)

plt.scatter(xC,yC,s=scen,color=cc)

plt.figure()

plt.scatter(ra2,dec2,s=spts,color=c2)

plt.scatter(ra1,dec1,s=spts,color=c1)

plt.scatter(Cra,Cdec,s=scen,color=cc)

plt.axis('equal')

# Choose ouput format ----------------------------------------------------

kone = np.asarray(zip(ra,dec,reds,dist,x,y,z))

if oformat == 'table' :

cols = ['ra','dec','z','comd','px','py','pz']

kone = Table(data=kone, names=cols)

'''

Generate random 3D points emulating filamentary structure over a box

To create filaments, the algorithm evolves a set of random points over a

sphere, pushing them away in small steps from a random set of void centers.

In each step, the coordinates are contracted a bit towards the origin. Then,

the sphere is chopped into a cube.

Optionally, the box can be stacked in 3D as desired to cover a larger

volume (but each box is uniquely random)

Parameters

----------

npts : integer

Number of points in the initial unit sphere. Default 80000

nvoids : integer

Number of voids in the initial unit sphere. Default 2000

nsteps : integer

Number of steps that points move away from void. In general, less steps

means softer and weaker filaments. Default 100

rmin : float

After box is created, remove 1 member of each pair closer than rmin [Mpc]

rep : list [nx,ny,nz]

Generate nx*ny*nz unique random boxes and stack them. Default [1,1,1]

b : float

Box size in Mpc. Default 150

Notes

-----

The box is always unit size, which is then scaled to any meaningfull size

by ``b``. The units depend on your intepretation. A choice of ``nvoids=2000``

and ``b=150`` gets a box of 150 Mpc with voids and filaments of size similar

to real ones. In general :

* For a fixed ``b``, the larger ``nsteps`` the stronger the features

* For a fixed ``b``, The larger ``nvoids`` the smaller the structure

* Smaller structure means more points can be included to trace small scales

without getting unrealistic features.

It is hard to estimate a priori how many points will fall inside the box.

Just give a try and change ``npts`` accordingly.

Returns

----------

xyz : array

Array of 3D points of shape (npts,3)

'''

print '-------------------------------------------------------------'

print 'Building cube'

if rep is None : rep = [1,1,1]

b = 1.0*b

# Loop over each stacked box that is desired

ptsa = np.zeros([1,3])

for i in range(rep[0]):

for j in range(rep[1]):

for k in range(rep[2]):

# Get random points and void centers inside unit sphere

voidpts = uniform_sphere(nvoids,1)

pts = uniform_sphere(npts,1)

tree = cKDTree(voidpts)

# Displace points to simulate filaments

for q in range(nstep):

idx = tree.query(pts,n_jobs=-1)[1]

nv = voidpts[idx]

# 0.01 == move pts 1% away from nearest void

# 0.9975 == move pts 0.25% towards the origin

npk = 0.9975*(pts + 0.01*(pts - nv))

pts = npk

# Get unit cube inside sphere and shift origin to [0,0,0]

# Note initial unit sphere has contracted a bit according to nsteps

x,y,z = pts[:,0],pts[:,1],pts[:,2]

idx, = np.where((x>-0.5) & (x<0.5) & (y>-0.5) & (y<0.5) & (z>-0.5) & (z<0.5) )

pts = pts[idx] + [0.5,0.5,0.5]

# Shift unit cube to cover the desired cubic lattice

pts = pts + [1.0*i,1.0*j,1.0*k]

# Accumulate points of cube

ptsa = np.vstack([ptsa,pts])

# Scale points by scale factor

ptsa = ptsa * [b,b,b]

# Find pairs closer than rmin and keep only one member of each pair

if rmin is not None:

tree = cKDTree(ptsa)

cp = tree.query_pairs(rmin)

npairs = len(cp)

if len(cp)>0:

cp = np.asarray(list(cp))

todel = cp[:,1]

ptsa = np.delete(ptsa,todel,axis=0)

print ' |-- Pairs below rmin :',npairs

print ' |-- Total objects in cube :',len(ptsa)

print '-------------------------------------------------------------'

npts=80000,nvoids=2000,nstep=100,rmin=None,cosmo=None):

'''

Fill the volume of an observation light cone with small cubes of 3D points.

The cube is stacked in 3D along the desired volume with as many cubes as

needed. This can generate artificial strucure so each cube can be :

(1) Copied as is (``repmethod='copy'``). This will likely introduce artificial patterns.

(2) Randomly rotated and mirrored (``repmethod='rotation'``)

(3) Generated randomly, so each box is uniquely random (``repmethod='fullrandom'``). Naturally this is slower

In case (3), the routine ``filament_box()`` is used to generate boxes

with filamentary structure

Parameters

----------

ralim : list (ra0, ra1)

RA limits [deg]

declim : list (dec0, dec1)

DEC limits [deg]

zlim : list (z0, z1)

Redshift limits

xyz : array of shape (:,3)

The building block of points to be stacked. This is **not used** when

``repmethod=fullrandom``, as then each box is generated uniquely

b : float

Box size in Mpc. Default 150

repmethod : string

* 'copy' : the same box is repeated

* 'rotation' : the same box is repeated but rotated and mirrored. Default

* 'fullrandom' : generate unique random boxes each time

npts : integer

Number of points in the initial unit sphere. Default 80000. Used only

if ``repmethod='fullrandom'``

nvoids : integer

Number of voids in the initial unit sphere. Default 2000. Used only

if ``repmethod='fullrandom'``

nsteps : integer

Number of steps that points move away from void. In general, less steps

means softer and weaker filaments. Default 100. Used only if

``repmethod='fullrandom'``

rmin : float

After box is created, remove 1 member of each pair closer than rmin [Mpc].

Used only if ``repmethod='fullrandom'``

cosmo : astropy cosmology object

If not given, defaults to a flat LambdaCDM with H_0=100 and Om=0.3

Notes

-----

The box is always unit size, which is then scaled to any meaningfull size

by ``b``. The units depend on your intepretation. A choice of ``nvoids=2000``

and ``b=150`` gets a box of 300 Mpc with voids and filaments of size similar

to real ones. In general :

* For a fixed ``b``, the larger ``nsteps`` the stronger the features

* For a fixed ``b``, The larger ``nvoids`` the smaller the structure

* Smaller structure means more points can be included to trace small scales

without getting unrealistic features.

It is hard to estimate a priori how many points will fall inside the

observation cone. Just give a try and change ``npts`` accordingly.

Returns

----------

kone : array of shape (n,7)

Array of 7 columns [ra,dec,redshift,comdis(redshift),x,y,z]

'''

print '-------------------------------------------------------------'

print 'Filling light cone with cubes'

if cosmo is None: cosmo = FlatLambdaCDM(H0=100, Om0=0.3)

# Get (ra/dec/z) into units of radians and comov_Mpc ---------------------

torad = np.pi/180

ra0, ra1 = ralim[0]*torad, ralim[1]*torad

dec0,dec1 = declim[0]*torad, declim[1]*torad

d0 = cosmo.comoving_distance(zlim[0]).value

d1 = cosmo.comoving_distance(zlim[1]).value

d_max = np.floor(1 + d1/b)*b # maximum comov distance in box lengths

xyza = np.zeros([1,3]) # accumulation array with dummy zero element

# Loop for a 3d grid of cubes coverting the cone length ------------------

nb = 0

for x0 in np.arange(-1*d_max,d_max,b):

for y0 in np.arange(-1*d_max,d_max,b):

for z0 in np.arange(-1*d_max,d_max,b):

x1 = x0 + b

y1 = y0 + b

z1 = z0 + b

# For each cube find corners (0 and 1) in ra/dec/dist/x/y/z space

if (x0>=0) and (y0>=0):

tra0 = np.arctan2(y0,x1)

tra1 = np.arctan2(y1,x0)

if (z0>=0):

tdec0 = np.arctan2(z0,np.sqrt(x1**2+y1**2))

tdec1 = np.arctan2(z1,np.sqrt(x0**2+y0**2))

else:

tdec0 = np.arctan2(z0,np.sqrt(x0**2+y0**2))

tdec1 = np.arctan2(z1,np.sqrt(x1**2+y1**2))

if (x0<0) and (y0>=0):

tra0 = np.arctan2(y1,x1)

tra1 = np.arctan2(y0,x0)

if (z0>=0):

tdec0 = np.arctan2(z0,np.sqrt(x0**2+y1**2))

tdec1 = np.arctan2(z1,np.sqrt(x1**2+y0**2))

else:

tdec0 = np.arctan2(z0,np.sqrt(x1**2+y0**2))

tdec1 = np.arctan2(z1,np.sqrt(x0**2+y1**2))

if (x0<0) and (y0<0):

tra0 = np.arctan2(-1*y1,-1*x0) + np.pi

tra1 = np.arctan2(-1*y0,-1*x1) + np.pi

if (z0>=0):

tdec0 = np.arctan2(z0,np.sqrt(x0**2+y0**2))

tdec1 = np.arctan2(z1,np.sqrt(x1**2+y1**2))

else:

tdec0 = np.arctan2(z0,np.sqrt(x1**2+y1**2))

tdec1 = np.arctan2(z1,np.sqrt(x0**2+y0**2))

if (x0>=0) and (y0<0):

tra0 = np.arctan2(-1*y0,-1*x0) + np.pi

tra1 = np.arctan2(-1*y1,-1*x1) + np.pi

if (z0>=0):

tdec0 = np.arctan2(z0,np.sqrt(x1**2+y0**2))

tdec1 = np.arctan2(z1,np.sqrt(x0**2+y1**2))

else:

tdec0 = np.arctan2(z0,np.sqrt(x0**2+y1**2))

tdec1 = np.arctan2(z1,np.sqrt(x1**2+y0**2))

x00 = (x0 if x0>=0 else x1)

y00 = (y0 if y0>=0 else y1)

z00 = (z0 if z0>=0 else z1)

x11 = (x1 if x0>=0 else x0)

y11 = (y1 if y0>=0 else y0)

z11 = (z1 if z0>=0 else z0)

td0 = np.sqrt(x00**2+y00**2+z00**2)

td1 = np.sqrt(x11**2+y11**2+z11**2)

# Check if cube corners fall inside the cone -----------------

if ((td1>d0) and (td0<d1) and (tra0<ra1) and (tra1>ra0) and (tdec0<dec1) and (tdec1>dec0)) :

print ' Cube',nb,'inside cone'

print ' |--- ','(x0,y0,z0,d0) = ',(x00,y00,z00,td0)

print ' |--- ','(x1,y1,z1,d1) = ',(x11,y11,z11,td1)

# Choose how to replicate the box

if repmethod == 'copy':

xyz = xyz

if repmethod == 'rotation':

xyz = randomize(xyz,b)

if repmethod == 'fullrandom':

xyz = filament_box(npts=npts,nvoids=nvoids,nstep=nstep,rmin=rmin,b=b)

# Shift the cube and accumulate its xyz points -----------

xyza = np.vstack([xyza, xyz + [x0,y0,z0] ])

nb = nb + 1

# Since replication can reusult in new close pairs along the edges,

# find those closer than rmin and keep only one member of these pairs

if rmin is not None:

tree = cKDTree(xyza)

cp = tree.query_pairs(rmin)

npairs = len(cp)

if len(cp)>0:

cp = np.asarray(list(cp))

todel = cp[:,1]

xyza = np.delete(xyza,todel,axis=0)

print ' |-- Pairs below rmin (along edges of cubes):',npairs

print ' |-- Nr of intersecting cubes :',nb

print ' |-- Objects inside all intersecting cubes :',len(xyza)

print '-------------------------------------------------------------'

b=150.,repmethod='rotation',cosmo=None,oformat='table'):

'''

Generate a mock light cone of random 3D points emulating filamentary structure

To create filaments, the algorithm evolves a set of random points over a

sphere, pushing them away in small steps from a random set of void centers.

In each step, the coordinates are contracted a bit towards the origin. Then,

the sphere is chopped into a cube.

This cube is then stacked in 3D along the desired observation cone with

as many cubes as needed. This can generate artificial strucure so each cube

can be :

(1) Copied as is (``repmethod='copy'``). This will likely introduce artificial patterns.

(2) Randomly rotated and mirrored (``repmethod='rotation'``)

(3) Generated randomly, so each box is uniquely random (``repmethod='fullrandom'``). Naturally this is slower

Parameters

----------

ralim : list (ra0, ra1)

RA limits [deg]

declim : list (dec0, dec1)

DEC limits [deg]

zlim : list (z0, z1)

Redshift limits

npts : integer

Number of points in the initial unit sphere. Default 20000

nvoids : integer

Number of voids in the initial unit sphere. Default 1000

nsteps : integer

Number of steps that points move away from void. In general, less steps

means softer and weaker filaments. Default 100

rmin : float

After box is created, remove 1 member of each pair closer than rmin [Mpc]

b : float

Box size in Mpc. Default 300

repmethod : string

Repetition method for the boxes along the cone volume

* 'copy' : the same box is repeated

* 'rotation' : the same box is repeated but rotated and mirrored. Default

* 'fullrandom' : generate unique random boxes each time

cosmo : astropy cosmology object

If not given, defaults to a flat LambdaCDM with H_0=100 and Om=0.3

oformat : string

Select output format as

* 'table' : astropy table. Default

* 'array' : numpy array

Notes

-----

The box is always unit size, which is then scaled to any meaningfull size

by ``b``. The units depend on your intepretation. A choice of ``nvoids=2000``

and ``b=150`` gets a box of 150 Mpc with voids and filaments of size similar

to real ones. In general :

* For a fixed ``b``, the larger ``nsteps`` the stronger the features

* For a fixed ``b``, The larger ``nvoids`` the smaller the structure

* Smaller structure means more points can be included to trace small scales

without getting unrealistic features.

It is hard to estimate a priori how many points will fall inside the

observation cone. Just give a try and change ``npts`` accordingly.

Returns

----------

kone : astropy.table / array of shape (nobj_in_cone,7)

Table or array of 7 columns [ra,dec,redshift,comdis(redshift),x,y,z]

'''

if cosmo is None: cosmo = FlatLambdaCDM(H0=100, Om0=0.3)

# Get (ra/dec/z) into units of radians and comov_Mpc ---------------------

#torad = np.pi/180

#ra0, ra1 = ralim[0]*torad, ralim[1]*torad

#dec0,dec1 = declim[0]*torad, declim[1]*torad

d0 = cosmo.comoving_distance(zlim[0]).value

d1 = cosmo.comoving_distance(zlim[1]).value

# Build unit cube with filaments, scaled by b ----------------------------

xyz = filament_box(npts=npts,nvoids=nvoids,nstep=nstep,rmin=rmin,b=b)

# Fill observation cone with cubes ---------------------------------------

xyza = fill_cone(ralim,declim,zlim,xyz=xyz,b=b,repmethod=repmethod,

npts=npts,nvoids=nvoids,nstep=nstep,rmin=rmin,cosmo=cosmo)

# Prune points outside the exact observation cone ------------------------

x,y,z = xyza[:,0],xyza[:,1],xyza[:,2]

ttt = cartesian_to_spherical(x,y,z)

comd = ttt[0].value

dec = ttt[1].value*180./np.pi

ra = ttt[2].value*180./np.pi

idx, = np.where( (ra>ralim[0]) & (ra<ralim[1]) & (dec>declim[0]) & (dec<declim[1]) & (comd>d0) & (comd<d1))

nobj = len(idx)

print 'Results'

print ' |-- Prunned objects outside intersecting cubes :',len(ra)-nobj

print ' |-- Total points inside light cone :',nobj

print '-------------------------------------------------------------'

# Transform comdis to redshift interpolating over a list -----------------

tmpz = np.linspace(0.,zlim[1]+7.,500)

tmpd = cosmo.comoving_distance(tmpz).value

redsh = np.interp(comd[idx],tmpd,tmpz,left=-1., right=-1.)

if (redsh<0).any(): raise Exception('Problem with redshifts!')

# Choose ouput format ----------------------------------------------------

kone = np.asarray(zip(ra[idx],dec[idx],redsh,comd[idx],x[idx],y[idx],z[idx]))

if oformat == 'table' :

cols = ['ra','dec','z','comd','px','py','pz']

kone = Table(data=kone, names=cols)