Merge branch '31-rewrite-unitloggauss' into 'NIFTy_5'

Resolve "Rewrite UnitLogGauss"

Closes #31

See merge request ift/nifty-dev!21

demos/Wiener_Filter.ipynb

@@ -172,7 +172,7 @@
     "                                    tol_abs_gradnorm=0.1)\n",
     "    # WienerFilterCurvature is (R.adjoint*N.inverse*R + Sh.inverse) plus some handy\n",
     "    # helper methods.\n",
-    "    return ift.library.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)"
+    "    return ift.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)"
    ]
   },
   {
 %% Cell type:markdown id: tags:
 
 # A NIFTy demonstration
 
 %% Cell type:markdown id: tags:
 
 ## IFT: Big Picture
 IFT starting point:
 
 $$d = Rs+n$$
 
 Typically, $s$ is a continuous field, $d$ a discrete data vector. Particularly, $R$ is not invertible.
 
 IFT aims at **inverting** the above uninvertible problem in the **best possible way** using Bayesian statistics.
 
 
 ## NIFTy
 
 NIFTy (Numerical Information Field Theory) is a Python framework in which IFT problems can be tackled easily.
 
 Main Interfaces:
 
 - **Spaces**: Cartesian, 2-Spheres (Healpix, Gauss-Legendre) and their respective harmonic spaces.
 - **Fields**: Defined on spaces.
 - **Operators**: Acting on fields.
 
 %% Cell type:markdown id: tags:
 
 ## Wiener Filter: Formulae
 
 ### Assumptions
 
 - $d=Rs+n$, $R$ linear operator.
 - $\mathcal P (s) = \mathcal G (s,S)$, $\mathcal P (n) = \mathcal G (n,N)$ where $S, N$ are positive definite matrices.
 
 ### Posterior
 The Posterior is given by:
 
 $$\mathcal P (s|d) \propto P(s,d) = \mathcal G(d-Rs,N) \,\mathcal G(s,S) \propto \mathcal G (m,D) $$
 
 where
 $$\begin{align}
 m &= Dj \\
 D^{-1}&= (S^{-1} +R^\dagger N^{-1} R )\\
 j &= R^\dagger N^{-1} d
 \end{align}$$
 
 Let us implement this in NIFTy!
 
 %% Cell type:markdown id: tags:
 
 ## Wiener Filter: Example
 
 - We assume statistical homogeneity and isotropy. Therefore the signal covariance $S$ is diagonal in harmonic space, and is described by a one-dimensional power spectrum, assumed here as $$P(k) = P_0\,\left(1+\left(\frac{k}{k_0}\right)^2\right)^{-\gamma /2},$$
 with $P_0 = 0.2, k_0 = 5, \gamma = 4$.
 - $N = 0.2 \cdot \mathbb{1}$.
 - Number of data points $N_{pix} = 512$.
 - reconstruction in harmonic space.
 - Response operator:
 $$R = FFT_{\text{harmonic} \rightarrow \text{position}}$$
 
 %% Cell type:code id: tags:
 
 ``` python
 N_pixels = 512     # Number of pixels
 
 def pow_spec(k):
     P0, k0, gamma = [.2, 5, 4]
     return P0 / ((1. + (k/k0)**2)**(gamma / 2))
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Wiener Filter: Implementation
 
 %% Cell type:markdown id: tags:
 
 ### Import Modules
 
 %% Cell type:code id: tags:
 
 ``` python
 import numpy as np
 np.random.seed(40)
 import nifty5 as ift
 import matplotlib.pyplot as plt
 %matplotlib inline
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Implement Propagator
 
 %% Cell type:code id: tags:
 
 ``` python
 def Curvature(R, N, Sh):
     IC = ift.GradientNormController(iteration_limit=50000,
                                     tol_abs_gradnorm=0.1)
     # WienerFilterCurvature is (R.adjoint*N.inverse*R + Sh.inverse) plus some handy
     # helper methods.
-    return ift.library.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)
+    return ift.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Conjugate Gradient Preconditioning
 
 - $D$ is defined via:
 $$D^{-1} = \mathcal S_h^{-1} + R^\dagger N^{-1} R.$$
 In the end, we want to apply $D$ to $j$, i.e. we need the inverse action of $D^{-1}$. This is done numerically (algorithm: *Conjugate Gradient*).
 
 <!--
 - One can define the *condition number* of a non-singular and normal matrix $A$:
 $$\kappa (A) := \frac{|\lambda_{\text{max}}|}{|\lambda_{\text{min}}|},$$
 where $\lambda_{\text{max}}$ and $\lambda_{\text{min}}$ are the largest and smallest eigenvalue of $A$, respectively.
 
 - The larger $\kappa$ the slower Conjugate Gradient.
 
 - By default, conjugate gradient solves: $D^{-1} m = j$ for $m$, where $D^{-1}$ can be badly conditioned. If one knows a non-singular matrix $T$ for which $TD^{-1}$ is better conditioned, one can solve the equivalent problem:
 $$\tilde A m = \tilde j,$$
 where $\tilde A = T D^{-1}$ and $\tilde j = Tj$.
 
 - In our case $S^{-1}$ is responsible for the bad conditioning of $D$ depending on the chosen power spectrum. Thus, we choose
 
 $$T = \mathcal F^\dagger S_h^{-1} \mathcal F.$$
 -->
 
 %% Cell type:markdown id: tags:
 
 ### Generate Mock data
 
 - Generate a field $s$ and $n$ with given covariances.
 - Calculate $d$.
 
 %% Cell type:code id: tags:
 
 ``` python
 s_space = ift.RGSpace(N_pixels)
 h_space = s_space.get_default_codomain()
 HT = ift.HarmonicTransformOperator(h_space, target=s_space)
 
 # Operators
 Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
 R = HT #*ift.create_harmonic_smoothing_operator((h_space,), 0, 0.02)
 
 # Fields and data
 sh = Sh.draw_sample()
 noiseless_data=R(sh)
 noise_amplitude = np.sqrt(0.2)
 N = ift.ScalingOperator(noise_amplitude**2, s_space)
 
 n = ift.Field.from_random(domain=s_space, random_type='normal',
                           std=noise_amplitude, mean=0)
 d = noiseless_data + n
 j = R.adjoint_times(N.inverse_times(d))
 curv = Curvature(R=R, N=N, Sh=Sh)
 D = curv.inverse
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Run Wiener Filter
 
 %% Cell type:code id: tags:
 
 ``` python
 m = D(j)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Signal Reconstruction
 
 %% Cell type:code id: tags:
 
 ``` python
 # Get signal data and reconstruction data
 s_data = HT(sh).to_global_data()
 m_data = HT(m).to_global_data()
 d_data = d.to_global_data()
 
 plt.figure(figsize=(15,10))
 plt.plot(s_data, 'r', label="Signal", linewidth=3)
 plt.plot(d_data, 'k.', label="Data")
 plt.plot(m_data, 'k', label="Reconstruction",linewidth=3)
 plt.title("Reconstruction")
 plt.legend()
 plt.show()
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 plt.figure(figsize=(15,10))
 plt.plot(s_data - s_data, 'r', label="Signal", linewidth=3)
 plt.plot(d_data - s_data, 'k.', label="Data")
 plt.plot(m_data - s_data, 'k', label="Reconstruction",linewidth=3)
 plt.axhspan(-noise_amplitude,noise_amplitude, facecolor='0.9', alpha=.5)
 plt.title("Residuals")
 plt.legend()
 plt.show()
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Power Spectrum
 
 %% Cell type:code id: tags:
 
 ``` python
 s_power_data = ift.power_analyze(sh).to_global_data()
 m_power_data = ift.power_analyze(m).to_global_data()
 plt.figure(figsize=(15,10))
 plt.loglog()
 plt.xlim(1, int(N_pixels/2))
 ymin = min(m_power_data)
 plt.ylim(ymin, 1)
 xs = np.arange(1,int(N_pixels/2),.1)
 plt.plot(xs, pow_spec(xs), label="True Power Spectrum", color='k',alpha=0.5)
 plt.plot(s_power_data, 'r', label="Signal")
 plt.plot(m_power_data, 'k', label="Reconstruction")
 plt.axhline(noise_amplitude**2 / N_pixels, color="k", linestyle='--', label="Noise level", alpha=.5)
 plt.axhspan(noise_amplitude**2 / N_pixels, ymin, facecolor='0.9', alpha=.5)
 plt.title("Power Spectrum")
 plt.legend()
 plt.show()
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Wiener Filter on Incomplete Data
 
 %% Cell type:code id: tags:
 
 ``` python
 # Operators
 Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
 N = ift.ScalingOperator(noise_amplitude**2,s_space)
 # R is defined below
 
 # Fields
 sh = Sh.draw_sample()
 s = HT(sh)
 n = ift.Field.from_random(domain=s_space, random_type='normal',
                       std=noise_amplitude, mean=0)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Partially Lose Data
 
 %% Cell type:code id: tags:
 
 ``` python
 l = int(N_pixels * 0.2)
 h = int(N_pixels * 0.2 * 2)
 
 mask = np.full(s_space.shape, 1.)
 mask[l:h] = 0
 mask = ift.Field.from_global_data(s_space, mask)
 
 R = ift.DiagonalOperator(mask)*HT
 n = n.to_global_data()
 n[l:h] = 0
 n = ift.Field.from_global_data(s_space, n)
 
 d = R(sh) + n
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 curv = Curvature(R=R, N=N, Sh=Sh)
 D = curv.inverse
 j = R.adjoint_times(N.inverse_times(d))
 m = D(j)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Compute Uncertainty
 
 %% Cell type:code id: tags:
 
 ``` python
 m_mean, m_var = ift.probe_with_posterior_samples(curv, HT, 200)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Get data
 
 %% Cell type:code id: tags:
 
 ``` python
 # Get signal data and reconstruction data
 s_data = s.to_global_data()
 m_data = HT(m).to_global_data()
 m_var_data = m_var.to_global_data()
 uncertainty = np.sqrt(m_var_data)
 d_data = d.to_global_data()
 
 # Set lost data to NaN for proper plotting
 d_data[d_data == 0] = np.nan
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 fig = plt.figure(figsize=(15,10))
 plt.axvspan(l, h, facecolor='0.8',alpha=0.5)
 plt.fill_between(range(N_pixels), m_data - uncertainty, m_data + uncertainty, facecolor='0.5', alpha=0.5)
 plt.plot(s_data, 'r', label="Signal", alpha=1, linewidth=3)
 plt.plot(d_data, 'k.', label="Data")
 plt.plot(m_data, 'k', label="Reconstruction", linewidth=3)
 plt.title("Reconstruction of incomplete data")
 plt.legend()
 ```
 
 %% Cell type:markdown id: tags:
 
 # 2d Example
 
 %% Cell type:code id: tags:
 
 ``` python
 N_pixels = 256      # Number of pixels
 sigma2 = 2.         # Noise variance
 
 def pow_spec(k):
     P0, k0, gamma = [.2, 2, 4]
     return P0 * (1. + (k/k0)**2)**(-gamma/2)
 
 s_space = ift.RGSpace([N_pixels, N_pixels])
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 h_space = s_space.get_default_codomain()
 HT = ift.HarmonicTransformOperator(h_space,s_space)
 
 # Operators
 Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
 N = ift.ScalingOperator(sigma2,s_space)
 
 # Fields and data
 sh = Sh.draw_sample()
 n = ift.Field.from_random(domain=s_space, random_type='normal',
                       std=np.sqrt(sigma2), mean=0)
 
 # Lose some data
 
 l = int(N_pixels * 0.33)
 h = int(N_pixels * 0.33 * 2)
 
 mask = np.full(s_space.shape, 1.)
 mask[l:h,l:h] = 0.
 mask = ift.Field.from_global_data(s_space, mask)
 
 R = ift.DiagonalOperator(mask)*HT
 n = n.to_global_data()
 n[l:h, l:h] = 0
 n = ift.Field.from_global_data(s_space, n)
 curv = Curvature(R=R, N=N, Sh=Sh)
 D = curv.inverse
 
 d = R(sh) + n
 j = R.adjoint_times(N.inverse_times(d))
 
 # Run Wiener filter
 m = D(j)
 
 # Uncertainty
 m_mean, m_var = ift.probe_with_posterior_samples(curv, HT, 20)
 
 # Get data
 s_data = HT(sh).to_global_data()
 m_data = HT(m).to_global_data()
 m_var_data = m_var.to_global_data()
 d_data = d.to_global_data()
 uncertainty = np.sqrt(np.abs(m_var_data))
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 cm = ['magma', 'inferno', 'plasma', 'viridis'][1]
 
 mi = np.min(s_data)
 ma = np.max(s_data)
 
 fig, axes = plt.subplots(1, 2, figsize=(15, 7))
 
 data = [s_data, d_data]
 caption = ["Signal", "Data"]
 
 for ax in axes.flat:
     im = ax.imshow(data.pop(0), interpolation='nearest', cmap=cm, vmin=mi,
                    vmax=ma)
     ax.set_title(caption.pop(0))
 
 fig.subplots_adjust(right=0.8)
 cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])
 fig.colorbar(im, cax=cbar_ax)
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 mi = np.min(s_data)
 ma = np.max(s_data)
 
 fig, axes = plt.subplots(3, 2, figsize=(15, 22.5))
 sample = HT(curv.draw_sample(from_inverse=True)+m).to_global_data()
 post_mean = (m_mean + HT(m)).to_global_data()
 
 data = [s_data, m_data, post_mean, sample, s_data - m_data, uncertainty]
 caption = ["Signal", "Reconstruction", "Posterior mean", "Sample", "Residuals", "Uncertainty Map"]
 
 for ax in axes.flat:
     im = ax.imshow(data.pop(0), interpolation='nearest', cmap=cm, vmin=mi, vmax=ma)
     ax.set_title(caption.pop(0))
 
 fig.subplots_adjust(right=0.8)
 cbar_ax = fig.add_axes([.85, 0.15, 0.05, 0.7])
 fig.colorbar(im, cax=cbar_ax)
 ```
 
 %% Cell type:markdown id: tags:
 
 ### Is the uncertainty map reliable?
 
 %% Cell type:code id: tags:
 
 ``` python
 precise = (np.abs(s_data-m_data) < uncertainty)
 print("Error within uncertainty map bounds: " + str(np.sum(precise) * 100 / N_pixels**2) + "%")
 
 plt.figure(figsize=(15,10))
 plt.imshow(precise.astype(float), cmap="brg")
 plt.colorbar()
 ```
 
 %% Cell type:markdown id: tags:
 
 # Start Coding
 ## NIFTy Repository + Installation guide
 
 https://gitlab.mpcdf.mpg.de/ift/NIFTy
 
 NIFTy v5 **more or less stable!**

demos/getting_started_1.py

@@ -2,7 +2,9 @@ import nifty5 as ift
 import numpy as np
 from global_newton.models_other.apply_data import ApplyData
 from global_newton.models_energy.hamiltonian import Hamiltonian
-from nifty5.library.unit_log_gauss import UnitLogGauss
+from nifty5 import GaussianEnergy
+
+
 if __name__ == '__main__':
     # s_space = ift.RGSpace([1024])
     s_space = ift.RGSpace([128,128])
@@ -45,7 +47,7 @@ if __name__ == '__main__':
     NWR = ApplyData(data, ift.Field(d_space,val=noise), Rs)
 
     INITIAL_POSITION = ift.from_random('normal',total_domain)
-    likelihood = UnitLogGauss(INITIAL_POSITION, NWR)
+    likelihood = GaussianEnergy(INITIAL_POSITION, NWR)
 
     IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
     inverter = ift.ConjugateGradient(controller=IC)

nifty5/__init__.py

@@ -16,7 +16,7 @@ from .minimization import *
 from .sugar import *
 from .plotting.plot import plot
 
-from . import library
+from .library import *
 from . import extra
 
 from .utilities import memo

nifty5/energies/hamiltonian.py

+# 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.
+
+from ..library.gaussian_energy import GaussianEnergy
 from ..minimization.energy import Energy
-from ..operators import InversionEnabler, SamplingEnabler
 from ..models.variable import Variable
+from ..operators import InversionEnabler, SamplingEnabler
 from ..utilities import memo
-from ..library.unit_log_gauss import UnitLogGauss
 
 
 class Hamiltonian(Energy):
@@ -15,11 +33,8 @@ class Hamiltonian(Energy):
         super(Hamiltonian, self).__init__(lh.position)
         self._lh = lh
         self._ic = iteration_controller
-        if iteration_controller_sampling is None:
-            self._ic_samp = iteration_controller
-        else:
-            self._ic_samp = iteration_controller_sampling
-        self._prior = UnitLogGauss(Variable(self.position))
+        self._ic_samp = iteration_controller_sampling
+        self._prior = GaussianEnergy(Variable(self.position))
         self._precond = self._prior.curvature
 
     def at(self, position):
@@ -39,8 +54,11 @@ class Hamiltonian(Energy):
     @memo
     def curvature(self):
         prior_curv = self._prior.curvature
-        c = SamplingEnabler(self._lh.curvature, prior_curv.inverse,
-                            self._ic_samp, prior_curv.inverse)
+        if self._ic_samp is None:
+            c = self._lh.curvature + prior_curv
+        else:
+            c = SamplingEnabler(self._lh.curvature, prior_curv.inverse,
+                                self._ic_samp, prior_curv.inverse)
         return InversionEnabler(c, self._ic, self._precond)
 
     def __str__(self):

nifty5/library/__init__.py

 from .amplitude_model import make_amplitude_model
 from .apply_data import ApplyData
+from .gaussian_energy import GaussianEnergy
 from .los_response import LOSResponse
-from .nonlinear_wiener_filter_energy import NonlinearWienerFilterEnergy
-from .unit_log_gauss import UnitLogGauss
 from .point_sources import PointSources
-from .poisson_log_likelihood import PoissonLogLikelihood
+from .poissonian_energy import PoissonianEnergy
 from .smooth_sky import make_smooth_mf_sky_model, make_smooth_sky_model
 from .wiener_filter_curvature import WienerFilterCurvature
 from .wiener_filter_energy import WienerFilterEnergy

nifty5/library/apply_data.py

 def ApplyData(data, var, model_data):
-    from .. import DiagonalOperator, Constant, sqrt
+    # TODO This is rather confusing. Delete that eventually.
+    from ..operators.diagonal_operator import DiagonalOperator
+    from ..models.constant import Constant
+    from ..sugar import sqrt
     sqrt_n = DiagonalOperator(sqrt(var))
     data = Constant(model_data.position, data)
     return sqrt_n.inverse(model_data - data)

nifty5/library/unit_log_gauss.py → nifty5/library/gaussian_energy.py

@@ -17,45 +17,50 @@
 # and financially supported by the Studienstiftung des deutschen Volkes.
 
 from ..minimization.energy import Energy
-from ..operators.inversion_enabler import InversionEnabler
 from ..operators.sandwich_operator import SandwichOperator
 from ..utilities import memo
 
 
-class UnitLogGauss(Energy):
-    def __init__(self, s, inverter=None):
+class GaussianEnergy(Energy):
+    def __init__(self, inp, mean=None, covariance=None):
         """
-        s: Sky model object
+        inp: Model object
 
         value = 0.5 * s.vdot(s), i.e. a log-Gauss distribution with unit
         covariance
         """
-        super(UnitLogGauss, self).__init__(s.position)
-        self._s = s
-        self._inverter = inverter
+        super(GaussianEnergy, self).__init__(inp.position)
+        self._inp = inp
+        self._mean = mean
+        self._cov = covariance
 
     def at(self, position):
-        return self.__class__(self._s.at(position), self._inverter)
+        return self.__class__(self._inp.at(position), self._mean, self._cov)
 
     @property
     @memo
-    def _gradient_helper(self):
-        return self._s.gradient
+    def residual(self):
+        if self._mean is not None:
+            return self._inp.value - self._mean
+        return self._inp.value
 
     @property
     @memo
     def value(self):
-        return .5 * self._s.value.squared_norm()
+        if self._cov is None:
+            return .5 * self.residual.vdot(self.residual).real
+        return .5 * self.residual.vdot(self._cov.inverse(self.residual)).real
 
     @property
     @memo
     def gradient(self):
-        return self._gradient_helper.adjoint(self._s.value)
+        if self._cov is None:
+            return self._inp.gradient.adjoint(self.residual)
+        return self._inp.gradient.adjoint(self._cov.inverse(self.residual))
 
     @property
     @memo
     def curvature(self):
-        c = SandwichOperator.make(self._gradient_helper)
-        if self._inverter is None:
-            return c
-        return InversionEnabler(c, self._inverter)
+        if self._cov is None:
+            return SandwichOperator.make(self._inp.gradient, None)
+        return SandwichOperator.make(self._inp.gradient, self._cov.inverse)

nifty5/library/nonlinear_wiener_filter_energy.py

-# 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.
-
-from ..models.constant import Constant
-from .unit_log_gauss import UnitLogGauss
-from ..energies.hamiltonian import Hamiltonian
-
-
-def NonlinearWienerFilterEnergy(measured_data, data_model, sqrtN, iteration_controller):
-        d = measured_data.lock()
-        residual = Constant(data_model.position, d) - data_model
-        lh = UnitLogGauss(sqrtN.inverse(residual))
-        return Hamiltonian(lh, iteration_controller)

nifty5/library/poisson_log_likelihood.py → nifty5/library/poissonian_energy.py

@@ -23,7 +23,7 @@ from ..operators.sandwich_operator import SandwichOperator
 from ..sugar import log, makeOp
 
 
-class PoissonLogLikelihood(Energy):
+class PoissonianEnergy(Energy):
     def __init__(self, lamb, d):
         """
         lamb: Sky model object
@@ -31,7 +31,7 @@ class PoissonLogLikelihood(Energy):
         value = 0.5 * s.vdot(s), i.e. a log-Gauss distribution with unit
         covariance
         """
-        super(PoissonLogLikelihood, self).__init__(lamb.position)
+        super(PoissonianEnergy, self).__init__(lamb.position)
         self._lamb = lamb
         self._d = d
 

nifty5/multi/multi_field.py

@@ -164,10 +164,25 @@ class MultiField(object):
     def __neg__(self):
         return MultiField({key: -val for key, val in self.items()})
 
+    def __abs__(self):
+        return MultiField({key: abs(val) for key, val in self.items()})
+
     def conjugate(self):
         return MultiField({key: sub_field.conjugate()
                            for key, sub_field in self.items()})
 
+    def all(self):
+        for v in self.values():
+            if not v.all():
+                return False
+        return True
+
+    def any(self):
+        for v in self.values():
+            if v.any():
+                return True
+        return False
+
     def isEquivalentTo(self, other):
         """Determines (as quickly as possible) whether `self`'s content is
         identical to `other`'s content."""

test/test_energies/test_map.py

@@ -57,7 +57,7 @@ class Energy_Tests(unittest.TestCase):
             tol_abs_gradnorm=1e-5)
 
         S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
-        energy = ift.library.WienerFilterEnergy(
+        energy = ift.WienerFilterEnergy(
             position=s0, d=d, R=R, N=N, S=S, iteration_controller=IC)
         ift.extra.check_value_gradient_curvature_consistency(
             energy, ntries=10)
@@ -66,10 +66,10 @@ class Energy_Tests(unittest.TestCase):
                      ift.RGSpace(64, distances=.789),
                      ift.RGSpace([32, 32], distances=.789)],
                     [ift.Tanh, ift.Exponential, ift.Linear],
+                    [1, 1e-2, 1e2],
                     [4, 78, 23]))
-    def testNonlinearMap(self, space, nonlinearity, seed):
+    def testGaussianEnergy(self, space, nonlinearity, noise, seed):
         np.random.seed(seed)
-        f = nonlinearity()
         dim = len(space.shape)
         hspace = space.get_default_codomain()
         ht = ift.HarmonicTransformOperator(hspace, target=space)
@@ -77,23 +77,23 @@ class Energy_Tests(unittest.TestCase):
         pspace = ift.PowerSpace(hspace, binbounds=binbounds)
         Dist = ift.PowerDistributor(target=hspace, power_space=pspace)
         xi0 = ift.Field.from_random(domain=hspace, random_type='normal')
-        xi0_var = ift.Variable(ift.MultiField({'xi':xi0}))['xi']
+        xi0_var = ift.Variable(ift.MultiField({'xi': xi0}))['xi']
 
         def pspec(k): return 1 / (1 + k**2)**dim
         pspec = ift.PS_field(pspace, pspec)
         A = Dist(ift.sqrt(pspec))
-        n = ift.Field.from_random(domain=space, random_type='normal')
+        N = ift.ScalingOperator(noise, space)
+        n = N.draw_sample()
         s = ht(ift.makeOp(A)(xi0_var))
         R = ift.ScalingOperator(10., space)
-        sqrtN = ift.ScalingOperator(1., space)
         d_model = R(ift.LocalModel(s, nonlinearity()))
         d = d_model.value + n
 
-        IC = ift.GradientNormController(iteration_limit=100,
-                tol_abs_gradnorm=1e-5)
-        energy = ift.library.NonlinearWienerFilterEnergy(
-            d, d_model, sqrtN, IC)
-        if isinstance(nonlinearity, ift.Linear):
+        if noise == 1:
+            N = None
+
+        energy = ift.GaussianEnergy(d_model, d, N)
+        if isinstance(nonlinearity(), ift.Linear):
             ift.extra.check_value_gradient_curvature_consistency(
                 energy, ntries=10)
         else: