getting_started_3.py 4.24 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
# 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/>.
#
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

Jakob Knollmueller's avatar
Jakob Knollmueller committed
19 20 21 22 23
import nifty5 as ift
import numpy as np


def get_random_LOS(n_los):
24 25
    starts = list(np.random.uniform(0, 1, (n_los, 2)).T)
    ends = list(np.random.uniform(0, 1, (n_los, 2)).T)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
26 27
    return starts, ends

Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
28

Jakob Knollmueller's avatar
Jakob Knollmueller committed
29
if __name__ == '__main__':
Philipp Arras's avatar
Philipp Arras committed
30
    # FIXME description of the tutorial
31
    np.random.seed(42)
Philipp Arras's avatar
Philipp Arras committed
32
    np.seterr(all='raise')
33
    position_space = ift.RGSpace([128, 128])
Jakob Knollmueller's avatar
Jakob Knollmueller committed
34

Jakob Knollmueller's avatar
Jakob Knollmueller committed
35
    # Setting up an amplitude model
36
    A = ift.AmplitudeModel(position_space, 64, 3, 0.4, -4., 1, 1., 1.)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
37 38 39 40

    # Building the model for a correlated signal
    harmonic_space = position_space.get_default_codomain()
    ht = ift.HarmonicTransformOperator(harmonic_space, position_space)
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
41
    power_space = A.target[0]
Jakob Knollmueller's avatar
Jakob Knollmueller committed
42 43
    power_distributor = ift.PowerDistributor(harmonic_space, power_space)

44
    vol = harmonic_space.scalar_dvol
Martin Reinecke's avatar
Martin Reinecke committed
45
    vol = ift.ScalingOperator(vol**(-0.5), harmonic_space)
Martin Reinecke's avatar
Martin Reinecke committed
46 47
    correlated_field = ht(
        vol(power_distributor(A))*ift.ducktape(harmonic_space, None, 'xi'))
48
    # alternatively to the block above one can do:
49
    #correlated_field = ift.CorrelatedField(position_space, A)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
50 51

    # apply some nonlinearity
Martin Reinecke's avatar
Martin Reinecke committed
52
    signal = ift.positive_tanh(correlated_field)
Martin Reinecke's avatar
Martin Reinecke committed
53

Jakob Knollmueller's avatar
Jakob Knollmueller committed
54
    # Building the Line of Sight response
55
    LOS_starts, LOS_ends = get_random_LOS(100)
Philipp Arras's avatar
Philipp Arras committed
56
    R = ift.LOSResponse(position_space, starts=LOS_starts, ends=LOS_ends)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
57
    # build signal response model and model likelihood
Martin Reinecke's avatar
Martin Reinecke committed
58
    signal_response = R(signal)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
59 60
    # specify noise
    data_space = R.target
Jakob Knollmueller's avatar
Jakob Knollmueller committed
61
    noise = .001
62
    N = ift.ScalingOperator(noise, data_space)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
63 64

    # generate mock data
Philipp Arras's avatar
Philipp Arras committed
65
    MOCK_POSITION = ift.from_random('normal', signal_response.domain)
Martin Reinecke's avatar
cleanup  
Martin Reinecke committed
66
    data = signal_response(MOCK_POSITION) + N.draw_sample()
Jakob Knollmueller's avatar
Jakob Knollmueller committed
67 68

    # set up model likelihood
Philipp Arras's avatar
Philipp Arras committed
69
    likelihood = ift.GaussianEnergy(mean=data, covariance=N)(signal_response)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
70 71

    # set up minimization and inversion schemes
Jakob Knollmueller's avatar
Jakob Knollmueller committed
72
    ic_sampling = ift.GradientNormController(iteration_limit=100)
Martin Reinecke's avatar
Martin Reinecke committed
73
    ic_newton = ift.GradInfNormController(
74
        name='Newton', tol=1e-7, iteration_limit=35)
75
    minimizer = ift.NewtonCG(ic_newton)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
76

Jakob Knollmueller's avatar
Jakob Knollmueller committed
77
    # build model Hamiltonian
Martin Reinecke's avatar
Martin Reinecke committed
78
    H = ift.Hamiltonian(likelihood, ic_sampling)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
79

80
    INITIAL_POSITION = ift.MultiField.full(H.domain, 0.)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
81
    position = INITIAL_POSITION
Jakob Knollmueller's avatar
Jakob Knollmueller committed
82

83
    plot = ift.Plot()
Martin Reinecke's avatar
merge  
Martin Reinecke committed
84 85
    plot.add(signal(MOCK_POSITION), title='Ground Truth')
    plot.add(R.adjoint_times(data), title='Data')
Philipp Arras's avatar
Philipp Arras committed
86
    plot.add([A.force(MOCK_POSITION)], title='Power Spectrum')
Martin Reinecke's avatar
merge  
Martin Reinecke committed
87
    plot.output(ny=1, nx=3, xsize=24, ysize=6, name="setup.png")
Jakob Knollmueller's avatar
Jakob Knollmueller committed
88

Jakob Knollmueller's avatar
Jakob Knollmueller committed
89
    # number of samples used to estimate the KL
90
    N_samples = 20
91
    for i in range(5):
Martin Reinecke's avatar
Martin Reinecke committed
92
        KL = ift.KL_Energy(position, H, N_samples)
Jakob Knollmueller's avatar
Jakob Knollmueller committed
93 94 95
        KL, convergence = minimizer(KL)
        position = KL.position

96
        plot = ift.Plot()
Martin Reinecke's avatar
merge  
Martin Reinecke committed
97
        plot.add(signal(KL.position), title="reconstruction")
Philipp Arras's avatar
Philipp Arras committed
98
        plot.add([A.force(KL.position), A.force(MOCK_POSITION)], title="power")
Lukas Platz's avatar
Lukas Platz committed
99
        plot.output(ny=1, ysize=6, xsize=16, name="loop-{:02}.png".format(i))
Jakob Knollmueller's avatar
Jakob Knollmueller committed
100

Philipp Arras's avatar
Philipp Arras committed
101
    KL = ift.KL_Energy(position, H, N_samples)
102
    plot = ift.Plot()
Martin Reinecke's avatar
Martin Reinecke committed
103
    sc = ift.StatCalculator()
104
    for sample in KL.samples:
Philipp Arras's avatar
Philipp Arras committed
105
        sc.add(signal(sample + KL.position))
Martin Reinecke's avatar
merge  
Martin Reinecke committed
106 107
    plot.add(sc.mean, title="Posterior Mean")
    plot.add(ift.sqrt(sc.var), title="Posterior Standard Deviation")
Martin Reinecke's avatar
Martin Reinecke committed
108

Philipp Arras's avatar
Philipp Arras committed
109
    powers = [A.force(s + KL.position) for s in KL.samples]
Martin Reinecke's avatar
merge  
Martin Reinecke committed
110
    plot.add(
Lukas Platz's avatar
Lukas Platz committed
111 112 113
        powers + [A.force(KL.position), A.force(MOCK_POSITION)],
        title="Sampled Posterior Power Spectrum",
        linewidth=[1.]*len(powers) + [3., 3.])
Martin Reinecke's avatar
merge  
Martin Reinecke committed
114
    plot.output(ny=1, nx=3, xsize=24, ysize=6, name="results.png")