from nifty import *
#import plotly.offline as pl
#import plotly.graph_objs as go
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.rank
if __name__ == "__main__":
distribution_strategy = 'not'
#Setting up physical constants
#total length of Interval or Volume the field lives on, e.g. in meters
L = 2.
#typical distance over which the field is correlated (in same unit as L)
correlation_length = 0.1
#variance of field in position space sqrt(<|s_x|^2>) (in unit of s)
field_variance = 2.
#smoothing length of response (in same unit as L)
response_sigma = 0.1
#defining resolution (pixels per dimension)
N_pixels = 512
#Setting up derived constants
k_0 = 1./correlation_length
#note that field_variance**2 = a*k_0/4. for this analytic form of power
#spectrum
a = field_variance**2/k_0*4.
pow_spec = (lambda k: a / (1 + k/k_0) ** 4)
pixel_width = L/N_pixels
# Setting up the geometry
s_space = RGSpace([N_pixels, N_pixels], distances = pixel_width)
fft = FFTOperator(s_space)
h_space = fft.target[0]
p_space = PowerSpace(h_space, distribution_strategy=distribution_strategy)
# Creating the mock data
S = create_power_operator(h_space, power_spectrum=pow_spec,
distribution_strategy=distribution_strategy)
sp = Field(p_space, val=pow_spec,
distribution_strategy=distribution_strategy)
sh = sp.power_synthesize(real_signal=True)
ss = fft.inverse_times(sh)
R = SmoothingOperator(s_space, sigma=response_sigma)
signal_to_noise = 1
N = DiagonalOperator(s_space, diagonal=ss.var()/signal_to_noise, bare=True)
n = Field.from_random(domain=s_space,
random_type='normal',
std=ss.std()/np.sqrt(signal_to_noise),
mean=0)
d = R(ss) + n
# Wiener filter
j = R.adjoint_times(N.inverse_times(d))
D = PropagatorOperator(S=S, N=N, R=R)
m = D(j)