def LDL(param, X, pm, Nstep, baryon=True):
fac = 1.0 * pm.Nmesh.prod() / pm.comm.allreduce(len(X), op=MPI.SUM)
X = Displacement(param, X, pm, Nstep)
#paint particle overdensity field
layout = fastpm.decompose(X, pm)
Xl = fastpm.exchange(X, layout)
delta = fac * fastpm.paint(Xl, 1., None, pm)
if baryon:
#take parameters
mu = linalg.take(param, 5*Nstep, axis=0)
b1 = linalg.take(param, 5*Nstep+1, axis=0)
b0 = linalg.take(param, 5*Nstep+2, axis=0)
mu = mpi.allbcast(mu, comm=pm.comm)
mu = linalg.broadcast_to(mu, eval(delta, lambda x : x.shape))
b1 = mpi.allbcast(b1, comm=pm.comm)
b1 = linalg.broadcast_to(b1, eval(delta, lambda x : x.shape))
b0 = mpi.allbcast(b0, comm=pm.comm)
b0 = linalg.broadcast_to(b0, eval(delta, lambda x : x.shape))
#Field transformation
F = ReLU(b1 * (delta+1e-8) ** mu + b0) #definition of b0 is different from the paper
else:
F = delta
return F
def model(self, x):
layout = fastpm.decompose(x, pm=self.pm)
x1 = fastpm.exchange(x, layout)
y1 = fastpm.paint(x1, mass=1.0, layout=None, pm=self.pm)
y = linalg.add(y1,
self.mesh) # biasing a bit to get non-zero derivatives.
return y
def LDL(param, X, pm, Nstep, baryon=True):
fac = 1.0 * pm.Nmesh.prod() / pm.comm.allreduce(len(X), op=MPI.SUM)
X = Displacement(param, X, pm, Nstep)
#paint particle overdensity field
layout = fastpm.decompose(X, pm)
Xl = fastpm.exchange(X, layout)
delta = fac * fastpm.paint(Xl, 1., None, pm)
if baryon:
#take parameters
gamma = linalg.take(param, 5*Nstep, axis=0)
bias0 = linalg.take(param, 5*Nstep+1, axis=0)
bias1 = linalg.take(param, 5*Nstep+2, axis=0)
gamma = mpi.allbcast(gamma, comm=pm.comm)
gamma = linalg.broadcast_to(gamma, eval(delta, lambda x : x.shape))
bias0 = mpi.allbcast(bias0, comm=pm.comm)
bias0 = linalg.broadcast_to(bias0, eval(delta, lambda x : x.shape))
bias1 = mpi.allbcast(bias1, comm=pm.comm)
bias1 = linalg.broadcast_to(bias1, eval(delta, lambda x : x.shape))
#Field transformation
F = ReLU(bias0 * (delta+1e-8) ** gamma + bias1)
else:
F = delta
return F
def PGD_correction(X, alpha, kl, ks, pm, q):
layout = fastpm.decompose(X, pm)
xl = fastpm.exchange(X, layout)
rho = fastpm.paint(xl, 1.0, None, pm)
fac = 1.0 * pm.Nmesh.prod() / pm.comm.allreduce(len(q))
rho = rho * fac
rhok = fastpm.r2c(rho)
p = fastpm.apply_transfer(rhok, PGDkernel(kl, ks))
r1 = []
for d in range(pm.ndim):
dx1_c = fastpm.apply_transfer(
p, fastpm.fourier_space_neg_gradient(d, pm, order=1))
dx1_r = fastpm.c2r(dx1_c)
dx1l = fastpm.readout(dx1_r, xl, None)
dx1 = fastpm.gather(dx1l, layout)
r1.append(dx1)
S = linalg.stack(r1, axis=-1)
S = S * alpha
return S
def model(self, x):
compensation = self.pm.resampler.get_compensation()
layout = vmadfastpm.decompose(self.w, self.pm)
map = vmadfastpm.paint(self.w, x, layout, self.pm)
y = map + self.xx # bias needed to avoid zero derivative
# compensation for cic window
c = vmadfastpm.r2c(y)
c = vmadfastpm.apply_transfer(c,
lambda k: compensation(k, 1.0),
kind='circular')
map = vmadfastpm.c2r(c)
return map
def makemap(self, xy, w):
"""
paint projected particles to 2D mesh
xy: particle positions in radians
w: weighting = projection kernel
"""
if (self.mappm.affine.period != 0).any():
raise RuntimeError("The ParticeMesh object must be non-periodic")
if self.mappm.ndim != 2:
raise RuntimeError(
"The ParticeMesh object must be 2 dimensional. ")
compensation = self.mappm.resampler.get_compensation()
layout = fastpm.decompose(xy, self.mappm)
map = fastpm.paint(xy, w, layout, self.mappm)
# compensation for cic window
c = fastpm.r2c(map)
c = fastpm.apply_transfer(c,
lambda k: compensation(k, 1.0),
kind='circular')
map = fastpm.c2r(c)
return map
def Displacement(param, X, pm, Nstep):
#Lagrangian displacement
#normalization constant for overdensity
fac = 1.0 * pm.Nmesh.prod() / pm.comm.allreduce(len(X), op=MPI.SUM)
for i in range(Nstep):
#move the particles across different MPI ranks
layout = fastpm.decompose(X, pm)
xl = fastpm.exchange(X, layout)
delta = fac * fastpm.paint(xl, 1.0, None, pm)
#take parameters
alpha = linalg.take(param, 5*i, axis=0)
gamma = linalg.take(param, 5*i+1, axis=0)
kh = linalg.take(param, 5*i+2, axis=0)
kl = linalg.take(param, 5*i+3, axis=0)
n = linalg.take(param, 5*i+4, axis=0)
#delta**gamma
gamma = mpi.allbcast(gamma, comm=pm.comm)
gamma = linalg.broadcast_to(gamma, eval(delta, lambda x : x.shape))
delta = (delta+1e-8) ** gamma
#Fourier transform
deltak = fastpm.r2c(delta)
#Green's operator in Fourier space
Filter = Literal(pm.create(type='complex', value=1).apply(lambda k, v: k.normp(2, zeromode=1e-8) ** 0.5))
kh = mpi.allbcast(kh, comm=pm.comm)
kh = linalg.broadcast_to(kh, eval(Filter, lambda x : x.shape))
kl = mpi.allbcast(kl, comm=pm.comm)
kl = linalg.broadcast_to(kl, eval(Filter, lambda x : x.shape))
n = mpi.allbcast(n, comm=pm.comm)
n = linalg.broadcast_to(n, eval(Filter, lambda x : x.shape))
Filter = - unary.exp(-Filter**2/kl**2) * unary.exp(-kh**2/Filter**2) * Filter**n
Filter = compensate2factor(Filter)
p = complex_mul(deltak, Filter)
#gradient of potential
r1 = []
for d in range(pm.ndim):
dx1_c = fastpm.apply_transfer(p, fastpm.fourier_space_neg_gradient(d, pm, order=1))
dx1_r = fastpm.c2r(dx1_c)
dx1l = fastpm.readout(dx1_r, xl, None)
dx1 = fastpm.gather(dx1l, layout)
r1.append(dx1)
#displacement
S = linalg.stack(r1, axis=-1)
alpha = mpi.allbcast(alpha, comm=pm.comm)
alpha = linalg.broadcast_to(alpha, eval(S, lambda x : x.shape))
S = S * alpha
X = X+S
return X
def model(self, x):
y = fastpm.paint(self.pos, layout=None, mass=x, pm=self.pm)
return y
def model(self, x):
layout = fastpm.decompose(x, pm=self.pm)
y = fastpm.paint(x, layout=layout, mass=1.0, pm=self.pm)
y = linalg.add(y,
self.mesh) # biasing a bit to get non-zero derivatives.
return y