test_map.py 10.1 KB
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# 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) 2013-2017 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

import unittest
import nifty4 as ift
import numpy as np
from itertools import product
from test.common import expand
from numpy.testing import assert_allclose


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def _flat_PS(k):
    return np.ones_like(k)


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class Energy_Tests(unittest.TestCase):
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    @expand(product([ift.RGSpace(64, distances=.789),
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                     ift.RGSpace([32, 32], distances=.789)],
                    [4, 78, 23]))
    def testLinearMap(self, space, seed):
        np.random.seed(seed)
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        dim = len(space.shape)
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        hspace = space.get_default_codomain()
        ht = ift.HarmonicTransformOperator(hspace, target=space)
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        binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
        pspace = ift.PowerSpace(hspace, binbounds=binbounds)
        P = ift.PowerProjectionOperator(domain=hspace, power_space=pspace)
        xi0 = ift.Field.from_random(domain=hspace, random_type='normal')

        def pspec(k): return 1 / (1 + k**2)**dim
        pspec = ift.PS_field(pspace, pspec)
        A = P.adjoint_times(ift.sqrt(pspec))
        n = ift.Field.from_random(domain=space, random_type='normal')
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        s0 = xi0 * A
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        Instrument = ift.ScalingOperator(10., space)
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        R = Instrument * ht
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        N = ift.ScalingOperator(1., space)
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        d = R(s0) + n
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        direction = ift.Field.from_random('normal', hspace)
        direction /= np.sqrt(direction.var())
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        eps = 1e-7
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        s1 = s0 + eps * direction

        IC = ift.GradientNormController(
            iteration_limit=100,
            tol_abs_gradnorm=1e-5)
        inverter = ift.ConjugateGradient(IC)
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        S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
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        energy0 = ift.library.WienerFilterEnergy(
            position=s0, d=d, R=R, N=N, S=S, inverter=inverter)
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        energy1 = energy0.at(s1)
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        a = (energy1.value - energy0.value) / eps
        b = energy0.gradient.vdot(direction)
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        tol = 1e-5
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        assert_allclose(a, b, rtol=tol, atol=tol)

    @expand(product([ift.RGSpace(64, distances=.789),
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                     ift.RGSpace([32, 32], distances=.789)],
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                    [4, 78, 23]))
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    def testLognormalMap(self, space, seed):
        np.random.seed(seed)
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        dim = len(space.shape)
        hspace = space.get_default_codomain()
        ht = ift.HarmonicTransformOperator(hspace, target=space)
        binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
        pspace = ift.PowerSpace(hspace, binbounds=binbounds)
        P = ift.PowerProjectionOperator(domain=hspace, power_space=pspace)
        xi0 = ift.Field.from_random(domain=hspace, random_type='normal')

        def pspec(k): return 1 / (1 + k**2)**dim
        pspec = ift.PS_field(pspace, pspec)
        A = P.adjoint_times(ift.sqrt(pspec))
        n = ift.Field.from_random(domain=space, random_type='normal')
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        sh0 = xi0 * A
        s = ht(sh0)
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        Instrument = ift.ScalingOperator(10., space)
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        R = Instrument * ht
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        N = ift.ScalingOperator(1., space)
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        d = Instrument(ift.exp(s)) + n
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        direction = ift.Field.from_random('normal', hspace)
        direction /= np.sqrt(direction.var())
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        eps = 1e-6
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        sh1 = sh0 + eps * direction
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        IC = ift.GradientNormController(
            iteration_limit=100,
            tol_abs_gradnorm=1e-5)
        inverter = ift.ConjugateGradient(IC)

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        S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
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        energy0 = ift.library.LogNormalWienerFilterEnergy(
            position=sh0, d=d, R=R, N=N, S=S, inverter=inverter)
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        energy1 = energy0.at(sh1)
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        a = (energy1.value - energy0.value) / eps
        b = energy0.gradient.vdot(direction)
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        tol = 1e-3
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        assert_allclose(a, b, rtol=tol, atol=tol)

    @expand(product([ift.RGSpace(64, distances=.789),
                     ift.RGSpace([32, 32], distances=.789)],
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                    [ift.library.Exponential, ift.library.Linear],
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                    [4, 78, 23]))
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    def testNonlinearMap(self, space, nonlinearity, seed):
        np.random.seed(seed)
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        f = nonlinearity()
        dim = len(space.shape)
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        hspace = space.get_default_codomain()
        ht = ift.HarmonicTransformOperator(hspace, target=space)
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        binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
        pspace = ift.PowerSpace(hspace, binbounds=binbounds)
        P = ift.PowerProjectionOperator(domain=hspace, power_space=pspace)
        xi0 = ift.Field.from_random(domain=hspace, random_type='normal')

        def pspec(k): return 1 / (1 + k**2)**dim
        pspec = ift.PS_field(pspace, pspec)
        A = P.adjoint_times(ift.sqrt(pspec))
        n = ift.Field.from_random(domain=space, random_type='normal')
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        s = ht(xi0 * A)
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        R = ift.ScalingOperator(10., space)
        N = ift.ScalingOperator(1., space)
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        d = R(f(s)) + n

        direction = ift.Field.from_random('normal', hspace)
        direction /= np.sqrt(direction.var())
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        eps = 1e-7
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        xi1 = xi0 + eps * direction

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        S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
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        energy0 = ift.library.NonlinearWienerFilterEnergy(
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            position=xi0, d=d, Instrument=R, nonlinearity=f, ht=ht, power=A, N=N, S=S)
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        energy1 = energy0.at(xi1)
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        a = (energy1.value - energy0.value) / eps
        b = energy0.gradient.vdot(direction)
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        tol = 1e-5
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        assert_allclose(a, b, rtol=tol, atol=tol)
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class Curvature_Tests(unittest.TestCase):
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    @expand(product([ift.RGSpace(64, distances=.789),
                     ift.RGSpace([32, 32], distances=.789)],
                    [4, 78, 23]))
    def testLinearMapCurvature(self, space, seed):
        np.random.seed(seed)
        dim = len(space.shape)
        hspace = space.get_default_codomain()
        ht = ift.HarmonicTransformOperator(hspace, target=space)
        binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
        pspace = ift.PowerSpace(hspace, binbounds=binbounds)
        P = ift.PowerProjectionOperator(domain=hspace, power_space=pspace)
        xi0 = ift.Field.from_random(domain=hspace, random_type='normal')

        def pspec(k): return 1 / (1 + k**2)**dim
        pspec = ift.PS_field(pspace, pspec)
        A = P.adjoint_times(ift.sqrt(pspec))
        n = ift.Field.from_random(domain=space, random_type='normal')
        s0 = xi0 * A
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        Instrument = ift.ScalingOperator(10., space)
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        R = Instrument * ht
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        N = ift.ScalingOperator(1., space)
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        d = R(s0) + n

        direction = ift.Field.from_random('normal', hspace)
        direction /= np.sqrt(direction.var())
        eps = 1e-7
        s1 = s0 + eps * direction

        IC = ift.GradientNormController(
            iteration_limit=100,
            tol_abs_gradnorm=1e-5)
        inverter = ift.ConjugateGradient(IC)

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        S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
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        energy0 = ift.library.WienerFilterEnergy(
            position=s0, d=d, R=R, N=N, S=S, inverter=inverter)
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        gradient0 = energy0.gradient
        gradient1 = energy0.at(s1).gradient

        a = (gradient1 - gradient0) / eps
        b = energy0.curvature(direction)
        tol = 1e-7
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        assert_allclose(ift.dobj.to_global_data(a.val),
                        ift.dobj.to_global_data(b.val), rtol=tol, atol=tol)
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    @expand(product([ift.RGSpace(64, distances=.789),
                     ift.RGSpace([32, 32], distances=.789)],
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                    [ift.library.Linear],  # Only linear case due to approximation of Hessian in the case of nontrivial nonlinearities.
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                    [4, 78, 23]))
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    def testNonlinearMapCurvature(self, space, nonlinearity, seed):
        np.random.seed(seed)
        f = nonlinearity()
        dim = len(space.shape)
        hspace = space.get_default_codomain()
        ht = ift.HarmonicTransformOperator(hspace, target=space)
        binbounds = ift.PowerSpace.useful_binbounds(hspace, logarithmic=False)
        pspace = ift.PowerSpace(hspace, binbounds=binbounds)
        P = ift.PowerProjectionOperator(domain=hspace, power_space=pspace)
        xi0 = ift.Field.from_random(domain=hspace, random_type='normal')

        def pspec(k): return 1 / (1 + k**2)**dim
        pspec = ift.PS_field(pspace, pspec)
        A = P.adjoint_times(ift.sqrt(pspec))
        n = ift.Field.from_random(domain=space, random_type='normal')
        s = ht(xi0 * A)
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        R = ift.ScalingOperator(10., space)
        N = ift.ScalingOperator(1., space)
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        d = R(f(s)) + n

        direction = ift.Field.from_random('normal', hspace)
        direction /= np.sqrt(direction.var())
        eps = 1e-7
        xi1 = xi0 + eps * direction

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        S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
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        IC = ift.GradientNormController(
            iteration_limit=500,
            tol_abs_gradnorm=1e-7)
        inverter = ift.ConjugateGradient(IC)
        energy0 = ift.library.NonlinearWienerFilterEnergy(
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            position=xi0,
            d=d,
            Instrument=R,
            nonlinearity=f,
            ht=ht,
            power=A,
            N=N,
            S=S,
            inverter=inverter)
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        gradient0 = energy0.gradient
        gradient1 = energy0.at(xi1).gradient

        a = (gradient1 - gradient0) / eps
        b = energy0.curvature(direction)
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        print(a.vdot(a))
        print(b.vdot(b))
        tol = 1e-7
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        assert_allclose(ift.dobj.to_global_data(a.val),
                        ift.dobj.to_global_data(b.val), rtol=tol, atol=tol)