demo_wf2.py

## 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 steepest descent.

"""
from __future__ import division

#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')
#
#
# comment

from nifty import *                                              # version 0.8.0
from nifty.operators.nifty_minimization import steepest_descent_new


# some signal space; e.g., a two-dimensional regular grid
x_space = rg_space([256, 256])                                   # 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, codomain=x_space, spec=power)                          # define signal covariance
s = S.get_random_field(domain=x_space, codomain=k_space)                           # generate signal

R = response_operator(x_space, codomain=k_space, sigma=0.0, mask=1.0, assign=None) # define response
d_space = R.target                                               # get data space

# 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

d = R(s) + n                                                     # compute data

j = R.adjoint_times(N.inverse_times(d))                          # define information source
D = propagator_operator(S=S, N=N, R=R)                           # define information propagator



def energy(x):
    DIx = D.inverse_times(x)
    H = 0.5 * DIx.dot(x) - j.dot(x)
    return H


def gradient(x):
    DIx = D.inverse_times(x)
    g = DIx - j
    return g


def eggs(x):
    """
        Calculation of the information Hamiltonian and its gradient.

    """
#    DIx = D.inverse_times(x)
#    H = 0.5 * DIx.dot(x) - j.dot(x)                              # compute information Hamiltonian
#    g = DIx - j                                                  # compute its gradient
#    return H, g
    return energy(x), gradient(x)


m = field(x_space, codomain=k_space)                               # reconstruct map

#with PyCallGraph(output=graphviz, config=config):
m, convergence = steepest_descent(eggs=eggs, note=True)(m, tol=1E-3, clevel=3)

m = field(x_space, codomain=k_space)
m, convergence = steepest_descent_new(energy, gradient, note=True)(m, tol=1E-3, clevel=3)
#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