getting_started_3b.py 4.4 KB
Newer Older
Martin Reinecke's avatar
Martin Reinecke committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
# 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.

import nifty5 as ift
import numpy as np


def get_random_LOS(n_los):
    starts = list(np.random.uniform(0, 1, (n_los, 2)).T)
    ends = list(np.random.uniform(0, 1, (n_los, 2)).T)
    return starts, ends
Martin Reinecke's avatar
Martin Reinecke committed
27

Martin Reinecke's avatar
Martin Reinecke committed
28
29
30
31
32
33
34
35
36
37
38
39
40
41
if __name__ == '__main__':
    # FIXME description of the tutorial
    np.random.seed(42)
    position_space = ift.RGSpace([128, 128])

    # Setting up an amplitude model
    A = ift.AmplitudeModel(position_space, 16, 1, 10, -4., 1, 0., 1.)
    dummy = ift.from_random('normal', A.domain)

    # Building the model for a correlated signal
    harmonic_space = position_space.get_default_codomain()
    ht = ift.HarmonicTransformOperator(harmonic_space, position_space)
    power_space = A.target[0]
    power_distributor = ift.PowerDistributor(harmonic_space, power_space)
Martin Reinecke's avatar
Martin Reinecke committed
42
    dummy = ift.Field.from_random('normal', harmonic_space)
Martin Reinecke's avatar
Martin Reinecke committed
43
44
45
46
47
48

    correlated_field = lambda inp: ht(power_distributor(A(inp))*inp["xi"])
    # alternatively to the block above one can do:
    # correlated_field,_ = ift.make_correlated_field(position_space, A)

    # apply some nonlinearity
Martin Reinecke's avatar
Martin Reinecke committed
49
    signal = lambda inp: correlated_field(inp).positive_tanh()
Martin Reinecke's avatar
Martin Reinecke committed
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67

    # Building the Line of Sight response
    LOS_starts, LOS_ends = get_random_LOS(100)
    R = ift.LOSResponse(position_space, starts=LOS_starts,
                        ends=LOS_ends)
    # build signal response model and model likelihood
    signal_response = lambda inp: R(signal(inp))
    # specify noise
    data_space = R.target
    noise = .001
    N = ift.ScalingOperator(noise, data_space)

    # generate mock data
    domain = ift.MultiDomain.union((A.domain, ift.MultiDomain.make({'xi': harmonic_space})))
    MOCK_POSITION = ift.from_random('normal', domain)
    data = signal_response(MOCK_POSITION) + N.draw_sample()

    # set up model likelihood
Martin Reinecke's avatar
Martin Reinecke committed
68
    likelihood = lambda inp: ift.GaussianEnergy(mean=data, covariance=N)(signal_response(inp))
Martin Reinecke's avatar
Martin Reinecke committed
69
70
71
72
73
74
75
76

    # set up minimization and inversion schemes
    ic_cg = ift.GradientNormController(iteration_limit=10)
    ic_sampling = ift.GradientNormController(iteration_limit=100)
    ic_newton = ift.GradientNormController(name='Newton', iteration_limit=100)
    minimizer = ift.RelaxedNewton(ic_newton)

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

Martin Reinecke's avatar
Martin Reinecke committed
79
    INITIAL_POSITION = ift.from_random('normal', domain)
Martin Reinecke's avatar
Martin Reinecke committed
80
81
82
83
84
85
86
87
88
89
    position = INITIAL_POSITION

    ift.plot(signal(MOCK_POSITION), title='ground truth')
    ift.plot(R.adjoint_times(data), title='data')
    ift.plot([A(MOCK_POSITION)], title='power')
    ift.plot_finish(nx=3, xsize=16, ysize=5, title="setup", name="setup.png")

    # number of samples used to estimate the KL
    N_samples = 20
    for i in range(2):
Martin Reinecke's avatar
Martin Reinecke committed
90
91
        metric = H(ift.Linearization.make_var(position)).metric
        samples = [metric.draw_sample(from_inverse=True)
Martin Reinecke's avatar
Martin Reinecke committed
92
93
94
                   for _ in range(N_samples)]

        KL = ift.SampledKullbachLeiblerDivergence(H, samples)
Martin Reinecke's avatar
Martin Reinecke committed
95
        KL = ift.EnergyAdapter(position, KL)
Martin Reinecke's avatar
Martin Reinecke committed
96
97
98
99
100
        KL = KL.make_invertible(ic_cg)
        KL, convergence = minimizer(KL)
        position = KL.position

        ift.plot(signal(position), title="reconstruction")
Martin Reinecke's avatar
Martin Reinecke committed
101
        ift.plot([A(position), A(MOCK_POSITION)], title="power")
Martin Reinecke's avatar
Martin Reinecke committed
102
103
104
105
106
107
108
109
110
        ift.plot_finish(nx=2, xsize=12, ysize=6, title="loop", name="loop.png")

    sc = ift.StatCalculator()
    for sample in samples:
        sc.add(signal(sample+position))
    ift.plot(sc.mean, title="mean")
    ift.plot(ift.sqrt(sc.var), title="std deviation")

    powers = [A(s+position) for s in samples]
Martin Reinecke's avatar
Martin Reinecke committed
111
    ift.plot([A(position), A(MOCK_POSITION)]+powers, title="power")
Martin Reinecke's avatar
Martin Reinecke committed
112
113
    ift.plot_finish(nx=3, xsize=16, ysize=5, title="results",
                    name="results.png")