amplitude_model.py 5.84 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) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

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from __future__ import absolute_import, division, print_function
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import numpy as np
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from ..compat import *
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from ..domains.power_space import PowerSpace
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from ..field import Field
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from ..operators.operator import Operator
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from ..sugar import makeOp, sqrt
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def _ceps_kernel(dof_space, k, a, k0):
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    return a**2/(1 + (k/k0)**2)**2
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def create_cepstrum_amplitude_field(domain, cepstrum):
    """Creates a ...
    Writes the sum of all modes into the zero-mode.

    Parameters
    ----------
    domain: ???
        ???
    cepstrum: Callable
        ???
    """

    dim = len(domain.shape)
    shape = domain.shape

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    q_array = domain.get_k_array()
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    # Fill cepstrum field (all non-zero modes)
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    no_zero_modes = (slice(1, None),)*dim
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    ks = q_array[(slice(None),) + no_zero_modes]
    cepstrum_field = np.zeros(shape)
    cepstrum_field[no_zero_modes] = cepstrum(ks)

    # Fill cepstrum field (zero-mode subspaces)
    for i in range(dim):
        # Prepare indices
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        fst_dims = (slice(None),)*i
        sl = fst_dims + (slice(1, None),)
        sl2 = fst_dims + (0,)
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        # Do summation
        cepstrum_field[sl2] = np.sum(cepstrum_field[sl], axis=i)

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    return Field.from_global_data(domain, cepstrum_field)
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class CepstrumModel(Operator):
    '''
    Parameters
    ----------
    ceps_a, ceps_k0 : Smoothness parameters in ceps_kernel
                        eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2
                        a = ceps_a,  k0 = ceps_k0
    '''

    def __init__(self, logk_space, ceps_a, ceps_k):
        from ..operators.qht_operator import QHTOperator
        from ..operators.symmetrizing_operator import SymmetrizingOperator
        qht = QHTOperator(target=logk_space)
        dof_space = qht.domain[0]
        sym = SymmetrizingOperator(logk_space)
        kern = lambda k: _ceps_kernel(dof_space, k, ceps_a, ceps_k)
        cepstrum = create_cepstrum_amplitude_field(dof_space, kern)
        self._qht = qht
        self._ceps = makeOp(sqrt(cepstrum))
        self._op = sym(qht(makeOp(sqrt(cepstrum))))
        self._domain, self._target = self._op.domain, self._op.target

    def apply(self, x):
        self._check_input(x)
        return self._op(x)

    @property
    def qht(self):
        return self._qht

    @property
    def ceps(self):
        return self._ceps


class SlopeModel(Operator):
    '''
    Parameters
    ----------

    sm, sv : slope_mean = expected exponent of power law (e.g. -4),
                slope_variance (default=1)

    im, iv : y-intercept_mean, y-intercept_variance  of power_slope
    '''

    def __init__(self, logk_space, sm, sv, im, iv):
        from ..operators.slope_operator import SlopeOperator

        phi_mean = np.array([sm, im + sm*logk_space.t_0[0]])
        phi_sig = np.array([sv, iv])

        self._slope = SlopeOperator(logk_space)
        self._slope = self._slope(
            makeOp(Field.from_global_data(self._slope.domain, phi_sig)))
        self._norm_phi_mean = Field.from_global_data(self._slope.domain,
                                                     phi_mean/phi_sig)

        self._domain = self._slope.domain
        self._target = self._slope.target

    def apply(self, x):
        self._check_input(x)
        return self._slope(x + self._norm_phi_mean)

    @property
    def norm_phi_mean(self):
        return self._norm_phi_mean


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class AmplitudeModel(Operator):
    '''
    Computes a smooth power spectrum.
    Output lives in PowerSpace.

    Parameters
    ----------

    Npixdof : #pix in dof_space

    ceps_a, ceps_k0 : Smoothness parameters in ceps_kernel
                        eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2
                        a = ceps_a,  k0 = ceps_k0

    sm, sv : slope_mean = expected exponent of power law (e.g. -4),
                slope_variance (default=1)

    im, iv : y-intercept_mean, y-intercept_variance  of power_slope
    '''
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    def __init__(self, s_space, Npixdof, ceps_a, ceps_k, sm, sv, im, iv, keys=['tau', 'phi']):
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        from ..operators.exp_transform import ExpTransform
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        from ..operators.simple_linear_operators import FieldAdapter
        from ..operators.scaling_operator import ScalingOperator
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        h_space = s_space.get_default_codomain()
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        et = ExpTransform(PowerSpace(h_space), Npixdof)
        logk_space = et.domain[0]
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        smooth = CepstrumModel(logk_space, ceps_a, ceps_k)
        linear = SlopeModel(logk_space, sm, sv, im, iv)
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        self._qht, self._ceps = smooth.qht, smooth.ceps
        self._norm_phi_mean = linear.norm_phi_mean
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        fa_smooth = FieldAdapter(smooth.domain, keys[0])
        fa_linear = FieldAdapter(linear.domain, keys[1])
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        fac = ScalingOperator(0.5, smooth.target)
        self._op = et((fac(smooth(fa_smooth) + linear(fa_linear))).exp())
        self._domain, self._target = self._op.domain, self._op.target
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    def apply(self, x):
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        self._check_input(x)
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        return self._op(x)
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    @property
    def qht(self):
        return self._qht

    @property
    def ceps(self):
        return self._ceps
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    @property
    def norm_phi_mean(self):
        return self._norm_phi_mean