Commit db9c8667 authored by Marco Selig's avatar Marco Selig

explicit 'demo_wf3.py' added.

parent fb06eff7
## NIFTY (Numerical Information Field Theory) has been developed at the
## Max-Planck-Institute for Astrophysics.
##
## Copyright (C) 2013 Max-Planck-Society
##
## Author: Marco Selig
## Project homepage: <http://www.mpa-garching.mpg.de/ift/nifty/>
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
## See the GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
.. __ ____ __
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.. / / / / / / / / / /_ / /_/ /
.. /__/ /__/ /__/ /__/ \___/ \___ / demo
.. /______/
NIFTY demo applying a Wiener filter using explicit matrices.
"""
from __future__ import division
from nifty import * # version 0.7.0
from nifty.nifty_explicit import *
# some signal space; e.g., a one-dimensional regular grid
x_space = rg_space(128) # define signal space
k_space = x_space.get_codomain() # get conjugate space
# some power spectrum
power = (lambda k: 42 / (k + 1) ** 3)
S = power_operator(k_space, spec=power) # define signal covariance
s = S.get_random_field(domain=x_space) # generate signal
s -= s.val.mean()
R = response_operator(x_space, sigma=0.0, mask=1.0, assign=None) # define response
d_space = R.target # get data space
# some noise variance
delta = 1000 * (np.arange(1, x_space.dim() + 1) / x_space.dim()) ** 5
N = diagonal_operator(d_space, diag=delta, bare=True) # define noise covariance
n = N.get_random_field(domain=d_space) # generate noise
d = R(s) + n # compute data
j = R.adjoint_times(N.inverse_times(d)) # define information source
class M_operator(operator):
def _multiply(self,x):
N,R = self.para
return R.adjoint_times(N.inverse_times(R.times(x)))
C = explicify(S, newdomain=x_space, newtarget=x_space) # explicify S
M = M_operator(x_space,sym=True,uni=False,imp=True,para=(N,R))
M = explicify(M) # explicify M
D = (C.inverse()+M).inverse() # define information propagator
m = D(j) # reconstruct map
vminmax = {"vmin":1.5 * s.val.min(), "vmax":1.5 * s.val.max()}
s.plot(title="signal", **vminmax) # plot signal
d_ = field(x_space, val=d.val, target=k_space)
d_.plot(title="data", **vminmax) # plot data
m.plot(title="reconstructed map", error=D.diag(bare=True), **vminmax) # plot map
D.plot(title="information propagator", bare=True) # plot information propagator
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