demo_wf2.py 3.7 KB
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## 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/>.

"""
    ..                  __   ____   __
    ..                /__/ /   _/ /  /_
    ..      __ ___    __  /  /_  /   _/  __   __
    ..    /   _   | /  / /   _/ /  /   /  / /  /
    ..   /  / /  / /  / /  /   /  /_  /  /_/  /
    ..  /__/ /__/ /__/ /__/    \___/  \___   /  demo
    ..                               /______/

    NIFTY demo applying a Wiener filter using steepest descent.

"""
from __future__ import division
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#from pycallgraph import PyCallGraph
#from pycallgraph import Config
#from pycallgraph import GlobbingFilter
#from pycallgraph.output import GraphvizOutput
#
#config = Config()
#config.trace_filter = GlobbingFilter(exclude=[
#    'pycallgraph.*',
#    #'*.secret_function',
#])
#
#graphviz = GraphvizOutput(output_file='steepest_profiling.png')
#
#


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from nifty import *                                              # version 0.8.0
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# some signal space; e.g., a two-dimensional regular grid
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x_space = rg_space([128, 128])                                   # define signal space
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k_space = x_space.get_codomain()                                 # get conjugate space
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# some power spectrum
power = (lambda k: 42 / (k + 1) ** 3)

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S = power_operator(k_space, codomain=x_space, spec=power)                          # define signal covariance
s = S.get_random_field(domain=x_space, codomain=k_space)                           # generate signal
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R = response_operator(x_space, codomain=k_space, sigma=0.0, mask=1.0, assign=None) # define response
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d_space = R.target                                               # get data space
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# some noise variance; e.g., signal-to-noise ratio of 1
N = diagonal_operator(d_space, diag=s.var(), bare=True)          # define noise covariance
n = N.get_random_field(domain=d_space)                           # generate noise
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d = R(s) + n                                                     # compute data
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j = R.adjoint_times(N.inverse_times(d))                          # define information source
D = propagator_operator(S=S, N=N, R=R)                           # define information propagator
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def eggs(x):
    """
        Calculation of the information Hamiltonian and its gradient.

    """
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    DIx = D.inverse_times(x)
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    H = 0.5 * DIx.dot(x) - j.dot(x)                              # compute information Hamiltonian
    g = DIx - j                                                  # compute its gradient
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    return H, g
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m = field(x_space, codomain=k_space)                               # reconstruct map

#with PyCallGraph(output=graphviz, config=config):
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m, convergence = steepest_descent(eggs=eggs, note=True)(m, tol=1E-3, clevel=3)
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#s.plot(title="signal")                                           # plot signal
#d_ = field(x_space, val=d.val, target=k_space)
#d_.plot(title="data", vmin=s.min(), vmax=s.max())                # plot data
#m.plot(title="reconstructed map", vmin=s.min(), vmax=s.max())    # plot map
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