Commit a0ab986b authored by Philipp Arras's avatar Philipp Arras
Browse files

Merge remote-tracking branch 'nifty-dev/NIFTy_5' into misc_work

parents 0f7cc8c4 73532911
......@@ -96,3 +96,12 @@ run_getting_started_3:
script:
- python demos/getting_started_3.py
- python3 demos/getting_started_3.py
run_bernoulli:
stage: demo_runs
script:
- python demos/bernoulli_demo.py
- python3 demos/bernoulli_demo.py
artifacts:
paths:
- '*.png'
......@@ -58,7 +58,7 @@
"### Posterior\n",
"The Posterior is given by:\n",
"\n",
"$$\\mathcal P (s|d) \\propto P(s,d) = \\mathcal G(d-Rs,N) \\,\\mathcal G(s,S) \\propto \\mathcal G (m,D) $$\n",
"$$\\mathcal P (s|d) \\propto P(s,d) = \\mathcal G(d-Rs,N) \\,\\mathcal G(s,S) \\propto \\mathcal G (s-m,D) $$\n",
"\n",
"where\n",
"$$\\begin{align}\n",
......
%% Cell type:markdown id: tags:
# A NIFTy demonstration
%% Cell type:markdown id: tags:
## IFT: Big Picture
IFT starting point:
$$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) $$
$$\mathcal P (s|d) \propto P(s,d) = \mathcal G(d-Rs,N) \,\mathcal G(s,S) \propto \mathcal G (s-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}}$$
%% Cell type:code id: tags:
``` python
N_pixels = 512 # Number of pixels
def pow_spec(k):
P0, k0, gamma = [.2, 5, 4]
return P0 / ((1. + (k/k0)**2)**(gamma / 2))
```
%% Cell type:markdown id: tags:
## Wiener Filter: Implementation
%% Cell type:markdown id: tags:
### Import Modules
%% Cell type:code id: tags:
``` python
import numpy as np
np.random.seed(40)
import nifty5 as ift
import matplotlib.pyplot as plt
%matplotlib inline
```
%% Cell type:markdown id: tags:
### Implement Propagator
%% Cell type:code id: tags:
``` python
def Curvature(R, N, Sh):
IC = ift.GradientNormController(iteration_limit=50000,
tol_abs_gradnorm=0.1)
# WienerFilterCurvature is (R.adjoint*N.inverse*R + Sh.inverse) plus some handy
# helper methods.
return ift.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)
```
%% Cell type:markdown id: tags:
### Conjugate Gradient Preconditioning
- $D$ is defined via:
$$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().copy()
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().copy()
# 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().copy()
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!**
......
# 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
if __name__ == '__main__':
# ABOUT THIS CODE
# FIXME ABOUT THIS CODE
np.random.seed(41)
# Set up the position space of the signal
......@@ -70,6 +88,6 @@ if __name__ == '__main__':
reconstruction = sky.at(H.position).value
ift.plot(reconstruction, title='reconstruction', name='reconstruction.pdf')
ift.plot(GR.adjoint_times(data), title='data', name='data.pdf')
ift.plot(sky.at(mock_position).value, title='truth', name='truth.pdf')
ift.plot(reconstruction, title='reconstruction', name='reconstruction.png')
ift.plot(GR.adjoint_times(data), title='data', name='data.png')
ift.plot(sky.at(mock_position).value, title='truth', name='truth.png')
# 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 make_chess_mask():
def make_chess_mask(position_space):
mask = np.ones(position_space.shape)
for i in range(4):
for j in range(4):
......@@ -17,27 +35,35 @@ def make_random_mask():
return mask.to_global_data()
if __name__ == '__main__':
# # description of the tutorial ###
# Choose problem geometry and masking
def mask_to_nan(mask, field):
masked_data = field.local_data.copy()
masked_data[mask.local_data == 0] = np.nan
return ift.from_local_data(field.domain, masked_data)
# One dimensional regular grid
position_space = ift.RGSpace([1024])
mask = np.ones(position_space.shape)
# # Two dimensional regular grid with chess mask
# position_space = ift.RGSpace([128,128])
# mask = make_chess_mask()
if __name__ == '__main__':
np.random.seed(42)
# FIXME description of the tutorial
# # Sphere with half of its locations randomly masked
# position_space = ift.HPSpace(128)
# mask = make_random_mask()
# Choose problem geometry and masking
mode = 0
if mode == 0:
# One dimensional regular grid
position_space = ift.RGSpace([1024])
mask = np.ones(position_space.shape)
elif mode == 1:
# Two dimensional regular grid with chess mask
position_space = ift.RGSpace([128, 128])
mask = make_chess_mask(position_space)
else:
# Sphere with half of its locations randomly masked
position_space = ift.HPSpace(128)
mask = make_random_mask()
harmonic_space = position_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(harmonic_space, target=position_space)
# set correlation structure with a power spectrum and build
# Set correlation structure with a power spectrum and build
# prior correlation covariance
def power_spectrum(k):
return 100. / (20.+k**3)
......@@ -47,7 +73,7 @@ if __name__ == '__main__':
S = ift.DiagonalOperator(prior_correlation_structure)
# build instrument response consisting of a discretization, mask
# Build instrument response consisting of a discretization, mask
# and harmonic transformaion
GR = ift.GeometryRemover(position_space)
mask = ift.Field.from_global_data(position_space, mask)
......@@ -56,19 +82,19 @@ if __name__ == '__main__':
data_space = GR.target
# setting the noise covariance
# Set the noise covariance
noise = 5.
N = ift.ScalingOperator(noise, data_space)
# creating mock data
# Create mock data
MOCK_SIGNAL = S.draw_sample()
MOCK_NOISE = N.draw_sample()
data = R(MOCK_SIGNAL) + MOCK_NOISE
# building propagator D and information source j
# Build propagator D and information source j
j = R.adjoint_times(N.inverse_times(data))
D_inv = R.adjoint * N.inverse * R + S.inverse
# make it invertible
# Make it invertible
IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
D = ift.InversionEnabler(D_inv, IC, approximation=S.inverse).inverse
......@@ -76,4 +102,16 @@ if __name__ == '__main__':
m = D(j)
# PLOTTING
# Truth, data, reconstruction, residuals
rg = isinstance(position_space, ift.RGSpace)
if rg and len(position_space.shape) == 1:
ift.plot([HT(MOCK_SIGNAL), GR.adjoint(data), HT(m)],
label=['Mock signal', 'Data', 'Reconstruction'],
alpha=[1, .3, 1],
name='getting_started_1.png')
else:
ift.plot(HT(MOCK_SIGNAL), title='Mock Signal', name='mock_signal.png')
ift.plot(mask_to_nan(mask, (GR*Mask).adjoint(data)),
title='Data', name='data.png')
ift.plot(HT(m), title='Reconstruction', name='reconstruction.png')
ift.plot(mask_to_nan(mask, HT(m-MOCK_SIGNAL)), name='residuals.png')
# 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
......@@ -18,7 +36,7 @@ def get_2D_exposure():
if __name__ == '__main__':
# ABOUT THIS CODE
# FIXME description of the tutorial
np.random.seed(41)
# Set up the position space of the signal
......
# 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
......@@ -9,7 +27,7 @@ def get_random_LOS(n_los):
if __name__ == '__main__':
# ## ABOUT THIS TUTORIAL
# FIXME description of the tutorial
np.random.seed(42)
position_space = ift.RGSpace([128, 128])
......@@ -65,9 +83,9 @@ if __name__ == '__main__':
INITIAL_POSITION = ift.from_random('normal', H.position.domain)
position = INITIAL_POSITION
ift.plot(signal.at(MOCK_POSITION).value, name='truth.pdf')
ift.plot(R.adjoint_times(data), name='data.pdf')
ift.plot([A.at(MOCK_POSITION).value], name='power.pdf')
ift.plot(signal.at(MOCK_POSITION).value, name='truth.png')
ift.plot(R.adjoint_times(data), name='data.png')
ift.plot([A.at(MOCK_POSITION).value], name='power.png')
# number of samples used to estimate the KL
N_samples = 20
......@@ -81,17 +99,17 @@ if __name__ == '__main__':
KL, convergence = minimizer(KL)
position = KL.position
ift.plot(signal.at(position).value, name='reconstruction.pdf')
ift.plot(signal.at(position).value, name='reconstruction.png')
ift.plot([A.at(position).value, A.at(MOCK_POSITION).value],
name='power.pdf')
name='power.png')
sc = ift.StatCalculator()
for sample in samples:
sc.add(signal.at(sample+position).value)
ift.plot(sc.mean, name='avrg.pdf')
ift.plot(ift.sqrt(sc.var), name='std.pdf')
ift.plot(sc.mean, name='avrg.png')
ift.plot(ift.sqrt(sc.var), name='std.png')
powers = [A.at(s+position).value for s in samples]
ift.plot([A.at(position).value, A.at(MOCK_POSITION).value]+powers,
name='power.pdf')
name='power.png')
......@@ -17,11 +17,14 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import sys
import numpy as np
from .random import Random
from mpi4py import MPI
import sys
from ..compat import *
from .random import Random
_comm = MPI.COMM_WORLD
ntask = _comm.Get_size()
......
......@@ -19,9 +19,10 @@
# Data object module for NIFTy that uses simple numpy ndarrays.
import numpy as np
from numpy import empty, empty_like, exp, full, log
from numpy import ndarray as data_object
from numpy import full, empty, empty_like, sqrt, ones, zeros, vdot, \
exp, log, tanh
from numpy import ones, sqrt, tanh, vdot, zeros
from .random import Random
ntask = 1
......
......@@ -17,9 +17,11 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from ..compat import *
class Random(object):
@staticmethod
......
......@@ -17,8 +17,8 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from .compat import *
from .compat import *
try:
from mpi4py import MPI
......
......@@ -17,6 +17,7 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from .compat import *
from .domains.domain import Domain
......
......@@ -17,8 +17,10 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from ..compat import *
from .structured_domain import StructuredDomain
......
......@@ -17,8 +17,10 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import abc
from ..compat import *
from ..utilities import NiftyMetaBase
......
......@@ -17,8 +17,10 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from ..compat import *
from .structured_domain import StructuredDomain
......
......@@ -17,8 +17,10 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from ..compat import *
from .structured_domain import StructuredDomain
......
......@@ -17,10 +17,12 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from .structured_domain import StructuredDomain
from ..compat import *
from ..field import Field
from .structured_domain import StructuredDomain
class LMSpace(StructuredDomain):
......
......@@ -17,11 +17,13 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
from ..sugar import exp
import numpy as np
from .. import dobj
from ..compat import *
from ..field import Field
from ..sugar import exp
from .structured_domain import StructuredDomain
......
......@@ -17,10 +17,12 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from .structured_domain import StructuredDomain
from .. import dobj
from ..compat import *
from .structured_domain import StructuredDomain
class PowerSpace(StructuredDomain):
......
......@@ -17,11 +17,13 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import numpy as np
from .structured_domain import StructuredDomain
from ..field import Field
from .. import dobj
from ..compat import *
from ..field import Field
from .structured_domain import StructuredDomain
class RGSpace(StructuredDomain):
......
......@@ -17,11 +17,14 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from __future__ import absolute_import, division, print_function
from ..compat import *
import abc
from .domain import Domain
import numpy as np
from ..compat import *
from .domain import Domain
class StructuredDomain(Domain):
"""The abstract base class for all structured NIFTy domains.
......