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pNbody/pNbody/libgrid.py
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libgrid.py
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##########################################################
# grid functions
##########################################################
from numpy import *
from numpy import clip as numclip
import mapping
import libutil
import treelib
import myNumeric
import sys
'''
definition of indexes and corresponding physical values
ix = int( (x-xmin)/(xmax-xmin)* nx )
x = ix*(xmax-xmin)/(nx) + xmin
center of cell
xc = (ix+0.5)*(xmax-xmin)/(nx) + xmin
physical size of cells
dx = ((arange(nx)+1)*(xmax-xmin)/(nx) + xmin )
- ((arange(nx) )*(xmax-xmin)/(nx) + xmin )
= (xmax-xmin)/nx * ones(nx)
# linear density of spherical density
lambda(r) = 4*pi*r**2*rho(r)
here we may deal the following grids :
- carthesian 2d
- carthesian 3d
- cylindrical 2d
- cylindrical 3d
- spherical 3d
!!! when computing the potential, in some 1d/2d grid,
!!! we do not take into account the fact that the model
!!! may be assymetric
!!! We should better compute potential on 3d grid
!!! and take the mean.
!!! the cylindrical grid is not symetric in z
'''
####################################################################################################################################
#
# GENERIC 1D GRID
#
####################################################################################################################################
class Generic_1d_Grid:
def __init__(self,rmin,rmax,nr,g=None,gm=None):
'''
f(rmin) = f(rmin)
f(rmax) = f(rmax)
'''
self.nr = int(nr)
self.rmin = float(rmin)
self.rmax = float(rmax)
self.g = g
self.gm = gm
self.f = lambda r:r # by default, identity
self.fm = lambda r:r # by default, identity
if self.g != None and self.gm != None:
self.f = lambda r: ( self.g(r)-self.g(self.rmin) )/( self.g(self.rmax)-self.g(self.rmin) ) *(self.rmax-self.rmin) + self.rmin
self.fm = lambda f: self.gm( (f-self.rmin)*( self.g(self.rmax)-self.g(self.rmin) )/( self.rmax-self.rmin ) + self.g(self.rmin) )
def get_r(self,offr=0):
ir = arange(self.nr)
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
return self.fm(r)
def get_Points(self,offr=0):
'''
Return an array of points corresponding to the nodes of
a 1d spherical grid
To get a nt X nr array from the returned vector (pos), do
x = pos[:,0]
y = pos[:,0]
z = pos[:,0]
x.shape = (nr,np,nt)
y.shape = (nr,np,nt)
z.shape = (nr,np,nt)
'''
ir = indices((self.nr,))
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
r = ravel(r)
r = self.fm(r)
x = r
y = zeros(len(x))
z = zeros(len(x))
return transpose(array([x,y,z])).astype(float32)
def get_MassMap(self,r,mass):
'''
Return an array of points containing mass of particles
'''
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = ones(pos.shape).astype(float32)
mass= mass.astype(float32)
shape = (self.nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_GenericMap(self,r,mass,val):
'''
Return an array of points containing mass of particles
'''
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = val.astype(float32)
mass= mass.astype(float32)
shape = (self.nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_MeanMap(self,r,mass,val):
'''
Return an array of points containing mean of val
'''
mv = self.get_GenericMap(r,mass,val)
m = self.get_MassMap(r,mass)
# compute mean
mv = where(mv ==0,0,mv)
m = where(m==0,1,m)
mean = mv/m
return mean,m,mv
def get_SigmaMap(self,r,mass,val):
'''
Return an array of points containing sigma of val
'''
mv = self.get_GenericMap(r,mass,val)
mv2 = self.get_GenericMap(r,mass,val*val)
m = self.get_MassMap(r,mass)
# compute sigma
mv = where(mv ==0,0,mv)
mv2 = where(mv2==0,0,mv2)
m = where(m==0,1,m)
sigma = mv2/m - (mv/m)**2
sigma = sqrt(numclip(sigma,0,1e10))
return sigma,m,mv,mv2
####################################################################################################################################
#
# SPHERICAL 1D GRID
#
####################################################################################################################################
class Spherical_1d_Grid:
def __init__(self,rmin,rmax,nr,g=None,gm=None):
'''
f(rmin) = f(rmin)
f(rmax) = f(rmax)
'''
self.nr = int(nr)
self.rmin = float(rmin)
self.rmax = float(rmax)
self.g = g
self.gm = gm
self.f = lambda r:r # by default, identity
self.fm = lambda r:r # by default, identity
if self.g != None and self.gm != None:
self.f = lambda r: ( self.g(r)-self.g(self.rmin) )/( self.g(self.rmax)-self.g(self.rmin) ) *(self.rmax-self.rmin) + self.rmin
self.fm = lambda f: self.gm( (f-self.rmin)*( self.g(self.rmax)-self.g(self.rmin) )/( self.rmax-self.rmin ) + self.g(self.rmin) )
def get_r(self,offr=0):
ir = arange(self.nr)
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
return self.fm(r)
def get_Points(self,offr=0):
'''
Return an array of points corresponding to the nodes of
a 1d spherical grid
To get a nt X nr array from the returned vector (pos), do
x = pos[:,0]
y = pos[:,0]
z = pos[:,0]
x.shape = (nr,np,nt)
y.shape = (nr,np,nt)
z.shape = (nr,np,nt)
'''
ir = indices((self.nr,))
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
r = ravel(r)
r = self.fm(r)
x = r
y = zeros(len(x))
z = zeros(len(x))
return transpose(array([x,y,z])).astype(float32)
def get_MassMap(self,nb):
'''
Return an array of points containing mass of particles
'''
r = nb.rxyz()
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (self.nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_NumberMap(self,nb):
'''
Return an array of points containing number of particles
'''
r = nb.rxyz()
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (self.nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_ValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing val of particles
'''
r = nb.rxyz()
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_MeanValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing mean val of particles
'''
r = nb.rxyz()
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,)
# compute zero momentum
m0 = mapping.mkmap1d(pos,mass,ones(len(pos),float32),shape)
# compute first momentum
m1 = mapping.mkmap1d(pos,mass,val,shape)
return libutil.GetMeanMap(m0,m1)
def get_SigmaValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing sigma val of particles
'''
r = nb.rxyz()
r = self.f(r)
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin)
# compute values
pos = transpose(array(r)).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,)
# compute zero momentum
m0 = mapping.mkmap1d(pos,mass,ones(len(pos),float32),shape)
# compute first momentum
m1 = mapping.mkmap1d(pos,mass,val,shape)
# compute second momentum
m2 = mapping.mkmap1d(pos,mass,val*val,shape)
return libutil.GetSigmaMap(m0,m1,m2)
def get_PotentialMap(self,nb,eps,UseTree=True,Tree=None):
'''
Return an array of points containing potential
'''
pos = self.get_Points()
if UseTree:
pot = nb.TreePot(pos,eps,Tree)
else:
pot = nb.Pot(pos,eps)
# transform back into array
pot.shape = (self.nr,)
return pot
def get_SurfaceMap(self):
'''
Return an array of points containing surface (volume)
of each cell.
'''
r1 = self.get_r(offr=0)
r2 = self.get_r(offr=1)
mat = r2-r1
mat = mat.astype(float32)
return mat
def get_VolumeMap(self):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
r1 = self.get_r(offr=0)
r2 = self.get_r(offr=1)
mat = 4.0/3.0*pi*( (r2)**3 - (r1)**3 )
mat = mat.astype(float32)
return mat
def get_DensityMap(self,nb):
'''
Return an array of points containing density in each cell
'''
m = self.get_MassMap(nb)
v = self.get_VolumeMap()
return m/v
def get_LinearDensityMap(self,nb):
'''
Return an array of points containing the linear density in each cell
'''
m = self.get_MassMap(nb)
s = self.get_SurfaceMap()
return m/s
def get_AccumulatedMassMap(self,nb):
'''
Return an array of points containing M(r) in each cell
'''
m = self.get_MassMap(nb)
mr = get_Accumulation_Along_Axis(m,axis=0)
return mr
def get_Interpolation(self,pos,mat,offr=0):
'''
Interpolates continuous value of pos, using matrix mat
'''
r = sqrt(pos[:,0]**2+pos[:,1]**2+pos[:,2]**2)
r = self.f(r)
ir = (r-self.rmin)/(self.rmax-self.rmin)* self.nr - offr
return myNumeric.Interpolate_From_1d_Array(ir.astype(float32),mat.astype(float32))
####################################################################################################################################
#
# CYLINDRICAL 2D GRID (r-z)
#
####################################################################################################################################
class Cylindrical_2drz_Grid:
def __init__(self,rmin,rmax,nr,zmin,zmax,nz,g=None,gm=None):
'''
f(rmin) = f(rmin)
f(rmax) = f(rmax)
'''
self.nr = int(nr)
self.rmin = float(rmin)
self.rmax = float(rmax)
self.nz = int(nz)
self.zmin = float(zmin)
self.zmax = float(zmax)
self.g = g
self.gm = gm
self.f = lambda r:r # by default, identity
self.fm = lambda r:r # by default, identity
if self.g != None and self.gm != None:
self.f = lambda r: ( self.g(r)-self.g(self.rmin) )/( self.g(self.rmax)-self.g(self.rmin) ) *(self.rmax-self.rmin) + self.rmin
self.fm = lambda f: self.gm( (f-self.rmin)*( self.g(self.rmax)-self.g(self.rmin) )/( self.rmax-self.rmin ) + self.g(self.rmin) )
def get_rz(self,offr=0,offz=0):
ir = arange(self.nr)
iz = arange(self.nz)
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
z = (iz+offz)*(self.zmax-self.zmin)/self.nz + self.zmin
r = self.fm(r)
return r,z
def get_Points(self,offr=0,offz=0):
'''
Return an array of points corresponding to the nodes of
a 2d cylindrical grid
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nr,nt)
y.shape = (nr,nt)
z.shape = (nr,nt)
# to get r and theta
r = sqrt(x**2+y**2+z**2)
t = arctan2(y,x)*180/pi
'''
ir,iz = indices((self.nr,self.nz))
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
z = (iz+offz)*(self.zmax-self.zmin)/self.nz + self.zmin
r = ravel(r)
z = ravel(z)
r = self.fm(r)
x = r
y = zeros(len(x))
z = z
return transpose(array([x,y,z])).astype(float32)
def get_MassMap(self,nb,offr=0,offz=0):
'''
Return an array of points containing mass of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
z = (z-self.zmin)/(self.zmax-self.zmin) - offz/self.nz
# compute values
pos = transpose(array([r,z,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (self.nr,self.nz)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_NumberMap(self,nb,offr=0,offz=0):
'''
Return an array of points containing mass of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
z = (z-self.zmin)/(self.zmax-self.zmin) - offz/self.nz
# compute values
pos = transpose(array([r,z,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (self.nr,self.nz)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_PotentialMap(self,nb,eps,UseTree=True,Tree=None,AdaptativeSoftenning=False):
'''
Return an array of points containing potential
'''
if AdaptativeSoftenning:
pos = self.get_Points()
pot = zeros(len(pos),float)
# define eps
R1,z1 = self.get_rz(offr=0)
R2,z2 = self.get_rz(offr=1)
epss = R2-R1
epss = epss/epss[0]*eps
pos = self.get_Points()
for ir in range(self.nr):
for iz in range(self.nz):
#print ir*self.nz + iz, pos[ir*self.nz + iz], epss[ir]
if UseTree:
pot[ir*self.nz + iz] = nb.TreePot(array([pos[ir*self.nz + iz]]),epss[ir])
else:
pot[ir*self.nz + iz] = nb.Pot( array([pos[ir*self.nz + iz]]),epss[ir])
else:
pos = self.get_Points()
if UseTree:
pot = nb.TreePot(pos,eps)
else:
pot = nb.Pot(pos,eps)
# transform back into array
pot.shape = (self.nr,self.nz)
return pot
def get_AccelerationMap(self,nb,eps,UseTree=True,Tree=None):
'''
Return an array of points containing accelerations
'''
if AdaptativeSoftenning:
pos = self.get_Points()
acc = pos*0
# define eps
R1,z1 = self.get_rz(offr=0)
R2,z2 = self.get_rz(offr=1)
epss = R2-R1
epss = epss/epss[0]*eps
pos = self.get_Points()
for ir in range(self.nr):
for iz in range(self.nz):
#print ir*self.nz + iz, pos[ir*self.nz + iz], epss[ir]
if UseTree:
acc[ir*self.nz + iz] = nb.TreeAccel(array([pos[ir*self.nz + iz]]),epss[ir])
else:
acc[ir*self.nz + iz] = nb.Accel( array([pos[ir*self.nz + iz]]),epss[ir])
else:
pos = self.get_Points()
if UseTree:
acc = nb.TreeAccel(pos,eps)
else:
acc = nb.Accel(pos,eps)
accx = copy(acc[:,0])
accy = copy(acc[:,1])
accz = copy(acc[:,2])
# transform back into array
accx.shape = (self.nr,self.nz)
accy.shape = (self.nr,self.nz)
accz.shape = (self.nr,self.nz)
return accx,accy,accz
def get_VolumeMap(self,offr=0,offz=0):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rs,zs = self.get_rz(offr,offz)
def volume(ir,iz):
if ir==self.nr-1:
r1 = rs[ir-1] # un peu bricolage...
r2 = rs[ir]
else:
r1 = rs[ir]
r2 = rs[ir+1]
if iz==self.nz-1:
z1 = zs[iz-1] # un peu bricolage...
z2 = zs[iz]
else:
z1 = zs[iz]
z2 = zs[iz+1]
return pi*(r2**2 - r1**2 ) * (z2-z1)
# make the map
mat = zeros((self.nr,self.nz))
for ir in range(self.nr):
for iz in range(self.nz):
mat[ir,iz]=volume(ir,iz)
mat = mat.astype(float32)
return mat
def get_SurfaceMap(self,offr=0,offz=0):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rs,zs = self.get_rz(offr,offz)
def surface(ir):
if ir==self.nr-1:
r1 = rs[ir-1] # un peu bricolage...
r2 = rs[ir]
else:
r1 = rs[ir]
r2 = rs[ir+1]
return pi*(r2**2 - r1**2 )
# make the map
mat = zeros(self.nr)
for ir in range(self.nr):
mat[ir]=surface(ir)
mat = mat.astype(float32)
return mat
def get_DensityMap(self,nb,offr=0,offz=0):
'''
Return an array of points containing density in each cell
'''
m = self.get_MassMap(nb,offr=offr,offz=offz)
v = self.get_VolumeMap(offr=offr,offz=offz)
return m/v
def get_SurfaceDensityMap(self,nb,offr=0,offz=0):
'''
Return an array (1d) of points containing the surface density along r
'''
m = self.get_MassMap(nb,offr=offr,offz=offz)
m = get_Sum_Along_Axis(m)
s = self.get_SurfaceMap(offr=offr,offz=offz)
return m/s
def get_Interpolation(self,pos,mat,offr=0,offz=0):
'''
Interpolates continuous value of pos, using matrix mat
'''
r = sqrt(pos[:,0]**2+pos[:,1]**2)
r = self.f(r)
z = pos[:,2]
ir = (r-self.rmin)/(self.rmax-self.rmin)* self.nr - offr
iz = (z-self.zmin)/(self.zmax-self.zmin)* self.nz - offz
return myNumeric.Interpolate_From_2d_Array(ir.astype(float32),iz.astype(float32),mat.astype(float32))
def get_r_Interpolation(self,pos,mat,offr=0):
'''
Interpolates continuous value of pos, using matrix mat
only along first axis.
'''
r = sqrt(pos[:,0]**2+pos[:,1]**2)
r = self.f(r)
ir = (r-self.rmin)/(self.rmax-self.rmin)* self.nr - offr
return myNumeric.Interpolate_From_1d_Array(ir.astype(float32),mat.astype(float32))
####################################################################################################################################
#
# CYLINDRICAL 2D GRID (r-t)
#
####################################################################################################################################
class Cylindrical_2drt_Grid:
def __init__(self,rmin,rmax,nr,nt,z=None,g=None,gm=None):
'''
f(rmin) = f(rmin)
f(rmax) = f(rmax)
'''
tmin = 0
tmax = 2*pi
self.z = z
self.nr = int(nr)
self.rmin = float(rmin)
self.rmax = float(rmax)
self.nt = int(nt)
self.tmin = float(tmin)
self.tmax = float(tmax)
self.g = g
self.gm = gm
self.f = lambda r:r # by default, identity
self.fm = lambda r:r # by default, identity
if self.g != None and self.gm != None:
self.f = lambda r: ( self.g(r)-self.g(self.rmin) )/( self.g(self.rmax)-self.g(self.rmin) ) *(self.rmax-self.rmin) + self.rmin
self.fm = lambda f: self.gm( (f-self.rmin)*( self.g(self.rmax)-self.g(self.rmin) )/( self.rmax-self.rmin ) + self.g(self.rmin) )
def get_rt(self,offr=0,offt=0):
ir = arange(self.nr)
it = arange(self.nt)
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
t = (it+offt)*(self.tmax-self.tmin)/self.nt + self.tmin
r = self.fm(r)
return r,t
def get_Points(self,offr=0,offt=0):
'''
Return an array of points corresponding to the nodes of
a 2d cylindrical grid
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nr,nt)
y.shape = (nr,nt)
z.shape = (nr,nt)
# to get r and theta
r = sqrt(x**2+y**2+z**2)
t = arctan2(y,x)*180/pi
'''
ir,it = indices((self.nr,self.nt))
r = (ir+offr)*(self.rmax-self.rmin)/self.nr + self.rmin
t = (it+offt)*(self.tmax-self.tmin)/self.nt + self.tmin
r = ravel(r)
t = ravel(t)
r = self.fm(r)
x = r*cos(t)
y = r*sin(t)
z = ones(len(x))*self.z
return transpose(array([x,y,z])).astype(float32)
def get_MassMap(self,nb,offr=0,offt=0):
'''
Return an array of points containing mass of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
t = (t-self.tmin)/(self.tmax-self.tmin) - offt/self.nt
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (self.nr,self.nt)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_NumberMap(self,nb,offr=0,offt=0):
'''
Return an array of points containing mass of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
t = (t-self.tmin)/(self.tmax-self.tmin) - offt/self.nt
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (self.nr,self.nt)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_ValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing val of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
t = (t-self.tmin)/(self.tmax-self.tmin) - offt/self.nt
# compute values
pos = transpose(array([r,t,z])).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,self.nt)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_MeanValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing mean val of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
t = (t-self.tmin)/(self.tmax-self.tmin) - offt/self.nt
# compute values
pos = transpose(array([r,t,z])).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,self.nt)
# compute zero momentum
m0 = mapping.mkmap2d(pos,mass,ones(len(pos),float32),shape)
# compute first momentum
m1 = mapping.mkmap2d(pos,mass,val,shape)
return libutil.GetMeanMap(m0,m1)
def get_SigmaValMap(self,nb,val,offr=0,offt=0):
'''
Return an array of points containing sigma val of particles
'''
r = nb.rxy()
r = self.f(r)
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-self.rmin)/(self.rmax-self.rmin) - offr/self.nr
t = (t-self.tmin)/(self.tmax-self.tmin) - offt/self.nt
# compute values
pos = transpose(array([r,t,z])).astype(float32)
mass= nb.mass.astype(float32)
val = val.astype(float32)
shape = (self.nr,self.nt)
# compute zero momentum
m0 = mapping.mkmap2d(pos,mass,ones(len(pos),float32),shape)
# compute first momentum
m1 = mapping.mkmap2d(pos,mass,val,shape)
# compute second momentum
m2 = mapping.mkmap2d(pos,mass,val*val,shape)
return libutil.GetSigmaMap(m0,m1,m2)
def get_PotentialMap(self,nb,eps,UseTree=True,Tree=None,AdaptativeSoftenning=False):
'''
Return an array of points containing potential
'''
if AdaptativeSoftenning:
pos = self.get_Points()
pot = zeros(len(pos),float)
# define eps
R1,t1 = self.get_rt(offr=0)
R2,t2 = self.get_rt(offr=1)
epss = R2-R1
epss = epss/epss[0]*eps
pos = self.get_Points()
for ir in range(self.nr):
for it in range(self.nt):
#print ir*self.nt + it, pos[ir*self.nt + it], epss[ir]
if UseTree:
pot[ir*self.nt + it] = nb.TreePot(array([pos[ir*self.nt + it]]),epss[ir])
else:
pot[ir*self.nt + it] = nb.Pot( array([pos[ir*self.nt + it]]),epss[ir])
else:
pos = self.get_Points()
if UseTree:
pot = nb.TreePot(pos,eps)
else:
pot = nb.Pot(pos,eps)
# transform back into array
pot.shape = (self.nr,self.nt)
return pot
def get_AccelerationMap(self,nb,eps,UseTree=True,Tree=None,AdaptativeSoftenning=False):
'''
Return an array of points containing accelerations
'''
if AdaptativeSoftenning:
pos = self.get_Points()
acc = pos*0
# define eps
R1,t1 = self.get_rt(offr=0)
R2,t2 = self.get_rt(offr=1)
epss = R2-R1
epss = epss/epss[0]*eps
pos = self.get_Points()
for ir in range(self.nr):
for it in range(self.nt):
#print ir*self.nt + it, pos[ir*self.nt + it], epss[ir]
if UseTree:
acc[ir*self.nt + it] = nb.TreeAccel(array([pos[ir*self.nt + it]]),epss[ir])
else:
acc[ir*self.nt + it] = nb.Accel( array([pos[ir*self.nt + it]]),epss[ir])
else:
pos = self.get_Points()
if UseTree:
acc = nb.TreeAccel(pos,eps)
else:
acc = nb.Accel(pos,eps)
accx = copy(acc[:,0])
accy = copy(acc[:,1])
accz = copy(acc[:,2])
# transform back into array
accx.shape = (self.nr,self.nt)
accy.shape = (self.nr,self.nt)
accz.shape = (self.nr,self.nt)
return accx,accy,accz
def get_SurfaceMap(self,nb,offr=0,offt=0):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rs,ts = self.get_rt(offr,offt)
def surface(ir):
if ir==self.nr-1:
r1 = rs[ir-1] # un peu bricolage...
r2 = rs[ir]
else:
r1 = rs[ir]
r2 = rs[ir+1]
return pi*(r2**2 - r1**2 ) / self.nt
# make the map
mat = zeros(self.nr)
for ir in range(self.nr):
mat[ir]=surface(ir)
mat = mat.astype(float32)
mat = transpose( ones((self.nt,self.nr))*mat )
return mat
def get_SurfaceDensityMap(self,nb,offr=0,offt=0):
'''
Return an array of points containing density in each cell
'''
m = self.get_MassMap(nb,offr=0,offt=0)
s = self.get_SurfaceMap(nb,offr=0,offt=0)
return m/s
def get_ReducedSurfaceDensityMap(self,nb,offr=0,offt=0):
'''
Return an array of points containing density in each cell
'''
m = self.get_MassMap(nb,offr=0,offt=0)
m = sum(m,axis=1)
s = self.get_SurfaceMap(nb,offr=0,offt=0)
s = sum(s,axis=1)
return m/s
####################################################################################################################################
#
# GRID CLASS (not used and not finished)
#
####################################################################################################################################
class Grid:
def __init__(self,dim=1,params={},f=None,fm=None):
"""
Main grid object
parameters
xmin,xmax,nx
ymin,ymax,ny
zmin,zmax,nz
"""
# example : 1d grid
self.xmin = float(params['xmin'])
self.xmax = float(params['xmax'])
self.nx = int(params['nx'])
self.offx = 0.
self.f = f
self.fm= fm
ix = indices((self.nx,))
# apply indx-phys transformation
if self.f!=None:
x = self.f(ix,self.nx,self.xmin,self.xmax)
else:
x = (ix+self.offx)*(self.xmax-self.xmin)/(self.nx-1) + self.xmin
x = ravel(x)
x = x
y = zeros(len(x))
z = zeros(len(x))
self.pos = transpose(array([x,y,z])).astype(float32)
self.shape = (self.nx,)
def GetPoints(self):
return self.pos
def GetNumberMap(self,x):
x = x.astype(float32)
val = ones(x.shape).astype(float32)
# apply phys-indx transformation and tranform between 0 and 1
if self.fm!=None:
x = self.fm(x,self.nx,self.xmin,self.xmax) / (self.nx-1)
else:
x = (x-self.xmin)/(self.xmax-self.xmin)
mat = mapping.mkmap1dw(x,val,val,self.shape)
return mat
def GetMassMap(self,x,mass):
x = x.astype(float32)
mass = mass.astype(float32)
val = ones(x.shape).astype(float32)
# apply phys-indx transformation and tranform between 0 and 1
if self.fm!=None:
x = self.fm(x,self.nx,self.xmin,self.xmax) / (self.nx-1)
else:
x = (x-self.xmin)/(self.xmax-self.xmin)
mat = mapping.mkmap1dw(x,mass,val,self.shape)
return mat
def GetSurfaceMap(self):
# !!!!!!!!!!!! this is for carthesian grid !!!!!!!!!!!!!!!
ix = arange(self.nx-1) + 0.5
ix = concatenate(([0],ix,[self.nx-1]))
# apply indx-phys transformation
if self.f!=None:
ix = self.f(ix,self.nx,self.xmin,self.xmax)
else:
ix = (ix+self.offx)*(self.xmax-self.xmin)/(self.nx-1) + self.xmin
# compute diff.
s = ix[1:] - ix[:-1]
return s
def GetVolumeMap(self):
# !!!!!!!!!!!! this is for spherical grid !!!!!!!!!!!!!!!
ix = arange(self.nx-1) + 0.5
ix = concatenate(([0],ix,[self.nx-1]))
# apply indx-phys transformation
if self.f!=None:
ix = self.f(ix,self.nx,self.xmin,self.xmax)
else:
ix = (ix+self.offx)*(self.xmax-self.xmin)/(self.nx-1) + self.xmin
# compute volume.
v = 4/3.*pi * (ix[1:]**3 - ix[:-1]**3)
return v
def GetSurfaceDensityMap(self,x,mass):
return self.GetMassMap(x,mass)/self.GetSurfaceMap()
def GetDensityMap(self,x,mass):
return self.GetMassMap(x,mass)/self.GetVolumeMap()
def GetPotential(self,nb,eps,force_computation=False,ErrTolTheta=0.8):
Tree = nb.getTree(force_computation=force_computation,ErrTolTheta=ErrTolTheta)
pot = Tree.Potential(self.pos,eps)
# transform back into array
#pot.shape = (nx,ny)
return pot
def write(self,name='grid.dat',ftype='gadget'):
'''
it cant work, because one need pNbody
and pNbody uses libgrid !!!
'''
# create an Nbody object
#nb = Nbody(status='new',p_name=name,pos=self.pos,ftype=ftype)
# and save it
#nb.write()
pass
#######################################
# general functions
#######################################
def get_First_Derivative(f,x,s=None,k=2):
'''
First derivative of f(x)
'''
#if s!=None:
# tck = interpolate.fitpack.splrep(x,f,s=s,k=k)
# f = interpolate.fitpack.splev(x,tck)
fp = zeros(len(x),x.dtype)
fp[0 ] = (f[ 1]-f[ 0])/(x[ 1]-x[ 0])
fp[-1] = (f[-1]-f[-2])/(x[-1]-x[-2])
f1 = f[2:]
f2 = f[:-2]
x1 = x[2:]
x2 = x[:-2]
fp[1:-1] = (f1-f2)/(x1-x2)
return fp
def get_Mean_Along_Axis(mat,axis=0):
if len(mat.shape) == 1:
return mat
elif len(mat.shape) == 2:
a = fmod((axis+1),2)
n = mat.shape[a]
s = mat
s = sum(s,axis=a)/n
elif len(mat.shape) == 3:
a = array([fmod((axis+1),3),fmod((axis+2),3)])
a.sort()
a1 = a[0]
a2 = a[1]
n1 = mat.shape[a1]
n2 = mat.shape[a2]
s = mat
s = sum(s,axis=a2)/n2
s = sum(s,axis=a1)/n1
return s
def get_Sum_Along_Axis(mat,axis=0):
if len(mat.shape) == 1:
return mat
elif len(mat.shape) == 2:
a = fmod((axis+1),2)
s = mat
s = sum(s,axis=a)
elif len(mat.shape) == 3:
a = array([fmod((axis+1),3),fmod((axis+2),3)])
a.sort()
a1 = a[0]
a2 = a[1]
s = mat
s = sum(s,axis=a2)
s = sum(s,axis=a1)
return s
def get_Accumulation_Along_Axis(mat,axis=0):
'''
Accumulate values along an axis
'''
v = get_Sum_Along_Axis(mat,axis=axis)
return add.accumulate(v)
def get_Integral(v,dr,ia,ib):
'''
Integrate the vector v, between ia and ib.
v : values of cells (must be 1 dimensional)
dr : corresponding physical size of cells
ia : lower real indice
ib : higher real indice
'''
print "WARNING : libgrid.get_Integral : you should not use this function !!!"
ia = max(0,ia)
ib = min(len(v),ib)
if ia==ib:
return 0.0
if ia>ib:
raise "ia must be < ib"
iap = int(ceil(ia))
ibp = int(floor(ib))
dra = iap-ia
drb = ib-ibp
Ia = 0.0
if dra != 0:
Ia = v[iap-1] * dra
Ib = 0.0
if drb != 0:
Ib = v[ibp] * drb
I = v[iap:ibp]*dr[iap:ibp]
return sum(I)+Ia+Ib
def get_Symetrisation_Along_Axis(mat,axis=1):
'''
Return an array where the two half are symetrized
'''
nx,ny = mat.shape
odd = fmod(ny,2)
if odd:
mat1 = mat[:,1:(ny/2)+1]
mat2 = mat[:,(ny/2)+1:]
else:
mat1 = mat[:,1:ny/2]
mat2 = mat[:,ny/2+1:]
#mat2 = myNumeric.turnup(mat2,0)
mat2 = fliplr(mat2)
# take the mean
matm = (mat1+mat2) /2
#mat = ones(mat.shape,mat.dtype)
if odd:
mat[:,1:(ny/2)+1] = matm
mat[:,(ny/2)+1:] = fliplr(matm) # myNumeric.turnup(matm,0)
else:
mat[:,1:ny/2] = matm
mat[:,ny/2+1:] = fliplr(matm) # myNumeric.turnup(matm,0)
return mat
def get_Symetrisation_Along_Axis_Old(mat,axis=1):
'''
Return an array where the two half are symetrized
Old but more correct than new one
'''
nx,ny = mat.shape
odd = fmod(ny,2)
if odd:
mat1 = mat[:,0:(ny-1)/2]
mat2 = mat[:,(ny-1)/2+1:]
mat3 = mat[:,(ny-1)/2]
else:
mat1 = mat[:,0:ny/2]
mat2 = mat[:,ny/2:]
#mat2 = myNumeric.turnup(mat2,0)
mat2 = fliplr(mat2)
# take the mean
matm = (mat1+mat2) /2
mat = ones(mat.shape,mat.dtype)
if odd:
mat[:,0:(ny-1)/2] = matm
mat[:,(ny-1)/2+1:] = fliplr(matm) # myNumeric.turnup(matm,0)
mat[:,(ny-1)/2] = mat3
else:
mat[:,0:ny/2] = matm
mat[:,ny/2:] = fliplr(matm) # myNumeric.turnup(matm,0)
return mat
#######################################
# carthesian grid
#######################################
##############
# 2 dimensions
##############
def get_xy_Of_Carthesian_2d_Grid(nx,ny,xmin,xmax,ymin,ymax,offx=0,offy=0):
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
ix = arange(nx)
iy = arange(ny)
x = (ix+offx)*(xmax-xmin)/nx + xmin
y = (iy+offy)*(ymax-ymin)/ny + ymin
return x,y
def get_Points_On_Carthesian_2d_Grid(nx,ny,xmin,xmax,ymin,ymax,offx=0,offy=0):
'''
Return an array of points corresponding to the center of cells
af a 2d carthesian grid.
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nx,ny)
y.shape = (nx,ny)
z.shape = (nx,ny)
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
nx = int(nx)
ny = int(ny)
ix,iy = indices((nx,ny))
x = (ix+offx)*(xmax-xmin)/nx + xmin
y = (iy+offy)*(ymax-ymin)/ny + ymin
x = ravel(x)
y = ravel(y)
z = zeros(len(x))
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax):
'''
Return an array of points containing mass of particles
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
x = nb.pos[:,0]
y = nb.pos[:,1]
z = nb.pos[:,2]
# scale between 0 and 1
x = (x-xmin)/(xmax-xmin)
y = (y-ymin)/(ymax-ymin)
# compute values
pos = transpose(array([x,y,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nx,ny)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax):
'''
Return an array of points containing mass of particles
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
x = nb.pos[:,0]
y = nb.pos[:,1]
z = nb.pos[:,2]
# scale between 0 and 1
x = (x-xmin)/(xmax-xmin)
y = (y-ymin)/(ymax-ymin)
# compute values
pos = transpose(array([x,y,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nx,ny)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Carthesian_2d_Grid(nx,ny,xmin,xmax,ymin,ymax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nx,ny)
return pot
def get_SurfaceMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
# compute volume (surface)
dx = (xmax-xmin)/nx
dy = (ymax-ymin)/ny
v = dx*dy
# make the map
mat = ones((nx,ny)) * v
mat = mat.astype(float32)
return mat
def get_SurfaceDensityMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax)
s = get_SurfaceMap_On_Carthesian_2d_Grid(nb,nx,ny,xmin,xmax,ymin,ymax)
return m/s
##############
# 3 dimensions
##############
def get_xyz_Of_Carthesian_3d_Grid(nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax,offx=0,offy=0,offz=0):
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
zmax = float(zmax)
zmin = float(zmin)
ix = arange(nx)
iy = arange(ny)
iz = arange(nz)
x = (ix+offx)*(xmax-xmin)/nx + xmin
y = (iy+offy)*(ymax-ymin)/ny + ymin
z = (iz+offz)*(zmax-zmin)/nz + zmin
return x,y,z
def get_Points_On_Carthesian_3d_Grid(nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax,offx=0,offy=0,offz=0):
'''
Return an array of points corresponding to the center of cells
af a 3d carthesian grid.
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nx,ny,nz)
y.shape = (nx,ny,nz)
z.shape = (nx,ny,nz)
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
zmax = float(zmax)
zmin = float(zmin)
nx = int(nx)
ny = int(ny)
nz = int(nz)
ix,iy,iz = indices((nx,ny,nz))
x = (ix+offx)*(xmax-xmin)/nx + xmin
y = (iy+offy)*(ymax-ymin)/ny + ymin
z = (iz+offz)*(zmax-zmin)/nz + zmin
x = ravel(x)
y = ravel(y)
z = ravel(z)
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
zmax = float(zmax)
zmin = float(zmin)
x = nb.pos[:,0]
y = nb.pos[:,1]
z = nb.pos[:,2]
# scale between 0 and 1
x = (x-xmin)/(xmax-xmin)
y = (y-ymin)/(ymax-ymin)
z = (z-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([x,y,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nx,ny,nz)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
zmax = float(zmax)
zmin = float(zmin)
x = nb.pos[:,0]
y = nb.pos[:,1]
z = nb.pos[:,2]
# scale between 0 and 1
x = (x-xmin)/(xmax-xmin)
y = (y-ymin)/(ymax-ymin)
z = (z-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([x,y,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nx,ny,nz)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nx,ny,nz)
return pot
def get_VolumeMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
xmax = float(xmax)
xmin = float(xmin)
ymax = float(ymax)
ymin = float(ymin)
zmax = float(zmax)
zmin = float(zmin)
# compute volume (surface)
dx = (xmax-xmin)/nx
dy = (ymax-ymin)/ny
dz = (zmax-zmin)/nz
v = dx*dy*dz
# make the map
mat = ones((nx,ny,nz)) * v
mat = mat.astype(float32)
return mat
def get_DensityMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax)
v = get_VolumeMap_On_Carthesian_3d_Grid(nb,nx,ny,nz,xmin,xmax,ymin,ymax,zmin,zmax)
return m/v
#######################################
# cylindrical grid
#######################################
######################
# 2 dimensions r,t (h)
######################
def get_rt_Of_Cylindrical_2dh_Grid(nr,nt,rmax,offr=0,offt=0):
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
ir = arange(nr)
it = arange(nt)
r = (ir+offr)*(rmax-rmin)/nr + rmin
t = (it+offt)*(tmax-tmin)/nt + tmin
return r,t
def get_Points_On_Cylindrical_2dh_Grid(nr,nt,rmax,offr=0,offt=0):
'''
Return an array of points corresponding to the nodes of
a 2d cylindrical grid
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nr,nt)
y.shape = (nr,nt)
z.shape = (nr,nt)
# to get r and theta
r = sqrt(x**2+y**2+z**2)
t = arctan2(y,x)*180/pi
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
nr = int(nr)
nt = int(nt)
ir,it = indices((nr,nt))
r = (ir+offr)*(rmax-rmin)/nr + rmin
t = (it+offt)*(tmax-tmin)/nt + tmin
r = ravel(r)
t = ravel(t)
x = r*cos(t)
y = r*sin(t)
z = zeros(len(x))
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
t = (t-tmin)/(tmax-tmin)
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,nt)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
t = (t-tmin)/(tmax-tmin)
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nr,nt)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Cylindrical_2dh_Grid(nr,nt,rmax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nr,nt)
return pot
def get_SurfaceMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rmax = float(rmax)
# compute volume (surface)
#dr = rmax/nr
#rs = arange(nr+1)*dr
#v = (pi*rs[1:]**2 - pi*rs[:-1]**2 )/nt
def volume(ir,it):
dr = (rmax/nr)
r = ir*dr
return pi*((r+dr)**2 - (r)**2 )/nt
# make the map
mat = fromfunction(volume,(nr,nt))
mat = mat.astype(float32)
return mat
def get_SurfaceDensityMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax)
s = get_SurfaceMap_On_Cylindrical_2dh_Grid(nb,nr,nt,rmax)
return m/s
######################
# 2 dimensions r,z (v)
######################
def get_rz_Of_Cylindrical_2dv_Grid(nr,nz,rmax,zmin,zmax):
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
ir = arange(nr)
iz = arange(nz)
r = (ir+0.0)*(rmax-rmin)/nr + rmin
z = (iz+0.0)*(zmax-zmin)/nz + zmin
return r,z
def get_Points_On_Cylindrical_2dv_Grid(nr,nz,rmax,zmin,zmax,offr=0,offz=0):
'''
Return an array of points corresponding to the nodes of
a 2d cylindrical grid
To get a nt X nr array from the returned vector (pos), do
x = copy(pos[:,0])
y = copy(pos[:,1])
z = copy(pos[:,2])
x.shape = (nr,nt)
y.shape = (nr,nt)
z.shape = (nr,nt)
# to get r and theta
r = sqrt(x**2+y**2+z**2)
t = arctan2(y,x)*180/pi
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
ir,iz = indices((nr,nz))
r = (ir+offr)*(rmax-rmin)/nr + rmin
z = (iz+offz)*(zmax-zmin)/nz + zmin
r = ravel(r)
z = ravel(z)
x = r
y = zeros(len(x))
z = z
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
z = (z-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([r,z,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,nz)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
z = (z-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([r,z,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nr,nz)
# make the map
mat = mapping.mkmap2d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Cylindrical_2dv_Grid(nr,nz,rmax,zmin,zmax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nr,nz)
return pot
def get_AccelerationMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax,eps,Tree=None):
'''
Return an array of points containing accelerations
'''
pos = get_Points_On_Cylindrical_2dv_Grid(nr,nz,rmax,zmin,zmax)
Tree = nb.getTree()
acc = Tree.Acceleration(pos,eps)
accx = copy(acc[:,0])
accy = copy(acc[:,1])
accz = copy(acc[:,2])
# transform back into array
accx.shape = (nr,nz)
accy.shape = (nr,nz)
accz.shape = (nr,nz)
return accx,accy,accz
def get_VolumeMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
# compute volume (surface)
#dr = rmax/nr
#rs = arange(nr+1)*dr
#v = (pi*rs[1:]**2 - pi*rs[:-1]**2 )/nt
def volume(ir,iz):
dr = (rmax-rmin)/nr
dz = (zmax-zmin)/nz
r = ir*dr
return pi*((r+dr)**2 - (r)**2 ) * dz
# make the map
mat = fromfunction(volume,(nr,nz))
mat = mat.astype(float32)
return mat
def get_DensityMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax)
v = get_VolumeMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax)
return m/v
def get_SurfaceDensityMap_From_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax):
'''
Return an array of points containing the surface density along r
'''
m = get_MassMap_On_Cylindrical_2dv_Grid(nb,nr,nz,rmax,zmin,zmax)
m = get_Sum_Along_Axis(m)
def surface(ir):
dr = (rmax)/nr
r = ir*dr
return pi*((r+dr)**2 - (r)**2 )
s = fromfunction(surface,(nr,))
return m/s
def get_Interpolation_On_Cylindrical_2dv_Grid(pos,mat,nr,nz,rmax,zmin,zmax,offr=0,offz=0):
'''
Interpolates continuous value of pos, using matrix mat
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
r = sqrt(pos[:,0]**2+pos[:,1]**2)
z = pos[:,2]
ir = (r-rmin)/(rmax-rmin)* nr - offr
iz = (z-zmin)/(zmax-zmin)* nz - offz
return myNumeric.Interpolate_From_2d_Array(ir.astype(float32),iz.astype(float32),mat.astype(float32))
def get_r_Interpolation_On_Cylindrical_2dv_Grid(pos,mat,nr,nz,rmax,zmin,zmax,offr=0):
'''
Interpolates continuous value of pos, using matrix mat
only along first axis.
'''
rmin = 0.0
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nz = int(nz)
r = sqrt(pos[:,0]**2+pos[:,1]**2)
ir = (r-rmin)/(rmax-rmin)* nr - offr
return myNumeric.Interpolate_From_1d_Array(ir.astype(float32),mat.astype(float32))
##############
# 3 dimensions
##############
def get_rtz_Of_Cylindrical_3d_Grid(nr,nt,nz,rmax,zmin,zmax,offr=0,offt=0,offz=0):
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
zmin = float(zmin)
zmax = float(zmax)
ir = arange(nr)
it = arange(nt)
iz = arange(nz)
r = (ir+offr)*(rmax-rmin)/nr + rmin
t = (it+offt)*(tmax-tmin)/nt + tmin
z = (iz+offz)*(zmax-zmin)/nz + zmin
return r,t,z
def get_Points_On_Cylindrical_3d_Grid(nr,nt,nz,rmax,zmin,zmax,offr=0,offt=0,offz=0):
'''
Return an array of points corresponding to the nodes of
a 2d cylindrical grid
To get a nt X nr array from the returned vector (pos), do
x = pos[:,0]
y = pos[:,0]
z = pos[:,0]
x.shape = (nr,nt,nz)
y.shape = (nr,nt,nz)
z.shape = (nr,nt,nz)
# to get r and theta
r = sqrt(x**2+y**2+z**2)
t = arctan2(y,x)*180/pi
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
zmin = float(zmin)
zmax = float(zmax)
nr = int(nr)
nt = int(nt)
nz = int(nz)
ir,it,iz = indices((nr,nt,nz))
r = (ir+offr)*(rmax-rmin)/nr + rmin
t = (it+offt)*(tmax-tmin)/nt + tmin
z = (iz+offz)*(zmax-zmin)/nz + zmin
r = ravel(r)
t = ravel(t)
z = ravel(z)
x = r*cos(t)
y = r*sin(t)
z = z
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
zmin = float(zmin)
zmax = float(zmax)
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
t = (t-tmin)/(tmax-tmin)
z = (t-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,nt,nz)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
tmin = 0.0
tmax = 2*pi
zmin = float(zmin)
zmax = float(zmax)
r = nb.rxy()
t = nb.phi_xy() + pi
z = nb.pos[:,2]
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
t = (t-tmin)/(tmax-tmin)
z = (t-zmin)/(zmax-zmin)
# compute values
pos = transpose(array([r,t,z])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nr,nt,nz)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Cylindrical_3d_Grid(nr,nt,nz,rmax,zmin,zmax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nr,nt,nz)
return pot
def get_VolumeMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rmax = float(rmax)
zmin = float(zmin)
zmax = float(zmax)
# compute volume (surface)
#dr = rmax/nr
#rs = arange(nr+1)*dr
#v = (pi*rs[1:]**2 - pi*rs[:-1]**2 )/nt
def volume(ir,it,iz):
dr = (rmax/nr)
dz = (zmax-zmin)/nz
r = ir*dr
return pi*((r+dr)**2 - (r)**2 )/nt * dz
# make the map
mat = fromfunction(volume,(nr,nt,nz))
mat = mat.astype(float32)
return mat
def get_DensityMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax)
v = get_VolumeMap_On_Cylindrical_3d_Grid(nb,nr,nt,nz,rmax,zmin,zmax)
return m/v
#######################################
# spherical grid
#######################################
##############
# 1 dimension
##############
def get_r_Of_Spherical_1d_Grid(nr,rmax,offr=0,f=None,fm=None):
rmin = 0.0
rmax = float(rmax)
if f!=None:
rmin=f(rmin)
rmax=f(rmax)
ir = arange(nr)
r = (ir+offr)*(rmax-rmin)/nr + rmin
if fm!=None:
r = fm(r)
return r
def get_Points_On_Spherical_1d_Grid(nr,rmax,offr=0,f=None,fm=None):
'''
Return an array of points corresponding to the nodes of
a 1d spherical grid
To get a nt X nr array from the returned vector (pos), do
x = pos[:,0]
y = pos[:,0]
z = pos[:,0]
x.shape = (nr,np,nt)
y.shape = (nr,np,nt)
z.shape = (nr,np,nt)
'''
rmin = 0.0
rmax = float(rmax)
nr = int(nr)
if f!=None:
rmin=f(rmin)
rmax=f(rmax)
ir = indices((nr,))
r = (ir+offr)*(rmax-rmin)/nr + rmin
r = ravel(r)
if fm!=None:
r = fm(r)
x = r
y = zeros(len(x))
z = zeros(len(x))
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
r = nb.rxyz() # 0 -> rmax
# here, we scale
if f!=None:
rmin = f(rmin)
rmax = f(rmax)
r = f(r)
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_GenericMap_On_Spherical_1d_Grid(nb,nr,rmax,val,f=None,fm=None):
'''
Return an array of points containing mass*val
'''
rmin = 0.0
rmax = float(rmax)
r = nb.rxyz() # 0 -> rmax
# here, we scale
if f!=None:
rmin = f(rmin)
rmax = f(rmax)
r = f(r)
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = val.astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing number of particles
'''
rmin = 0.0
rmax = float(rmax)
r = nb.rxyz() # 0 -> rmax
# here, we scale
if f!=None:
rmin = f(rmin)
rmax = f(rmax)
r = f(r)
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
# compute values
pos = transpose(array(r)).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nr,)
# make the map
mat = mapping.mkmap1d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Spherical_1d_Grid(nb,nr,rmax,eps,Tree=None,f=None,fm=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Spherical_1d_Grid(nr,rmax,f=f,fm=fm)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nr,)
return pot
def get_SurfaceMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing surface (volume)
of each cell.
'''
rmin = 0.0
rmax = float(rmax)
# compute volume (surface)
#def volume(ir):
# dr = (rmax/nr) + (ir-ir)
# return dr
#
## make the map
#mat = fromfunction(volume,(nr,))
#mat = mat.astype(float32)
r1 = get_r_Of_Spherical_1d_Grid(nr,rmax,offr=0,f=f,fm=fm)
r2 = get_r_Of_Spherical_1d_Grid(nr,rmax,offr=1,f=f,fm=fm)
mat = r2-r1
mat = mat.astype(float32)
return mat
def get_VolumeMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
rmin = 0.0
rmax = float(rmax)
# compute volume (surface)
#def volume(ir):
# dr = (rmax/nr)
# r = ir*dr
# return 4.0/3.0*pi*( (r+dr)**3 - (r)**3 )
#
# make the map
#mat = fromfunction(volume,(nr,))
#mat = mat.astype(float32)
r1 = get_r_Of_Spherical_1d_Grid(nr,rmax,offr=0,f=f,fm=fm)
r2 = get_r_Of_Spherical_1d_Grid(nr,rmax,offr=1,f=f,fm=fm)
mat = 4.0/3.0*pi*( (r2)**3 - (r1)**3 )
mat = mat.astype(float32)
return mat
def get_DensityMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Spherical_1d_Grid(nb,nr,rmax,f=f,fm=fm)
v = get_VolumeMap_On_Spherical_1d_Grid(nb,nr,rmax,f=f,fm=fm)
return m/v
def get_LinearDensityMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing the linear density in each cell
'''
m = get_MassMap_On_Spherical_1d_Grid(nb,nr,rmax,f=f,fm=fm)
s = get_SurfaceMap_On_Spherical_1d_Grid(nb,nr,rmax,f=f,fm=fm)
return m/s
def get_AccumulatedMassMap_On_Spherical_1d_Grid(nb,nr,rmax,f=None,fm=None):
'''
Return an array of points containing M(r) in each cell
'''
m = get_MassMap_On_Spherical_1d_Grid(nb,nr,rmax,f=f,fm=fm)
mr = get_Accumulation_Along_Axis(m,axis=0)
return mr
def get_Interpolation_On_Spherical_1d_Grid(pos,mat,nr,rmax,offr=0,f=None,fm=None):
'''
Interpolates continuous value of pos, using matrix mat
'''
rmin = 0.0
rmax = float(rmax)
nr = int(nr)
r = sqrt(pos[:,0]**2+pos[:,1]**2+pos[:,2]**2)
# here, we scale
if f!=None:
rmin = f(rmin)
rmax = f(rmax)
r = f(r)
ir = (r-rmin)/(rmax-rmin)* nr - offr
return myNumeric.Interpolate_From_1d_Array(ir.astype(float32),mat.astype(float32))
##############
# 3 dimensions
##############
def get_rpt_Of_Spherical_3d_Grid(nr,np,nt,rmax,offr=0,offp=0,offt=0):
rmin = 0.0
rmax = float(rmax)
pmin = 0.0
pmax = 2*pi
tmin = -pi/2
tmax = pi/2
ir = arange(nr)
ip = arange(np)
it = arange(nt)
r = (ir+offr)*(rmax-rmin)/nr + rmin
p = (ip+offp)*(pmax-pmin)/np + pmin
t = (it+offt)*(tmax-tmin)/nt + tmin
return r,p,t
def get_Points_On_Spherical_3d_Grid(nr,np,nt,rmax,offr=0,offp=0,offt=0):
'''
Return an array of points corresponding to the nodes of
a 3d spherical grid
To get a nt X nr array from the returned vector (pos), do
x = pos[:,0]
y = pos[:,0]
z = pos[:,0]
x.shape = (nr,np,nt)
y.shape = (nr,np,nt)
z.shape = (nr,np,nt)
'''
rmin = 0.0
rmax = float(rmax)
pmin = 0.0
pmax = 2*pi
tmin = -pi/2
tmax = pi/2
nr = int(nr)
np = int(np)
nt = int(nt)
ir,ip,it = indices((nr,np,nt))
r = (ir+offr)*(rmax-rmin)/nr + rmin
p = (ip+offp)*(pmax-pmin)/np + pmin
t = (it+offt)*(tmax-tmin)/nt + tmin
r = ravel(r)
p = ravel(p)
t = ravel(t)
x = r*cos(p)*cos(t)
y = r*sin(p)*cos(t)
z = r *sin(t)
return transpose(array([x,y,z])).astype(float32)
def get_MassMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
pmin = 0.0
pmax = 2*pi
tmin = -pi/2
tmax = pi/2
r = nb.rxyz() # 0 -> rmax
p = nb.phi_xyz() + pi # 0 -> pi
t = nb.theta_xyz() # -pi/2 -> pi/2
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
p = (p-pmin)/(pmax-pmin)
t = (t-tmin)/(tmax-tmin)
# compute values
pos = transpose(array([r,p,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= nb.mass.astype(float32)
shape = (nr,np,nt)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_NumberMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax):
'''
Return an array of points containing mass of particles
'''
rmin = 0.0
rmax = float(rmax)
pmin = 0.0
pmax = 2*pi
tmin = -pi/2
tmax = pi/2
r = nb.rxyz() # 0 -> rmax
p = nb.phi_xyz() + pi # 0 -> pi
t = nb.theta_xyz() # -pi/2 -> pi/2
# scale between 0 and 1
r = (r-rmin)/(rmax-rmin)
p = (p-pmin)/(pmax-pmin)
t = (t-tmin)/(tmax-tmin)
# compute values
pos = transpose(array([r,p,t])).astype(float32)
val = ones(pos.shape).astype(float32)
mass= ones(pos.shape).astype(float32)
shape = (nr,np,nt)
# make the map
mat = mapping.mkmap3d(pos,mass,val,shape)
return mat
def get_PotentialMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax,eps,Tree=None):
'''
Return an array of points containing potential
'''
pos = get_Points_On_Spherical_3d_Grid(nr,np,nt,rmax)
Tree = nb.getTree()
pot = Tree.Potential(pos,eps)
# transform back into array
pot.shape = (nr,np,nt)
return pot
def get_VolumeMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax):
'''
Return an array of points containing corresponding physical
volumes of each cell (usefull to compute density)
'''
print "get_VolumeMap_On_Spherical_3d_Grid is probably wrong"
print "we should add a cos(t) or somthing similar"
sys.exit()
rmin = 0.0
rmax = float(rmax)
pmin = 0.0
pmax = 2*pi
tmin = -pi/2
tmax = pi/2
# compute volume (surface)
def volume(ir,ip,it):
dr = (rmax/nr)
r = ir*dr
return 4.0/3.0*pi*( (r+dr)**3 - (r)**3 ) / np / nt
# make the map
mat = fromfunction(volume,(nr,np,nt))
mat = mat.astype(float32)
return mat
def get_DensityMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax):
'''
Return an array of points containing density in each cell
'''
m = get_MassMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax)
v = get_VolumeMap_On_Spherical_3d_Grid(nb,nr,np,nt,rmax)
return m/v
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