Commit d0bda184 authored by Torsten Ensslin's avatar Torsten Ensslin
Browse files

merge conflict solved

parents 05ca5466 60d0bba7
......@@ -39,9 +39,9 @@ Installation
- [Python 3](https://www.python.org/) (3.5.x or later)
- [SciPy](https://www.scipy.org/)
- [pyFFTW](https://pypi.python.org/pypi/pyFFTW)
Optional dependencies:
- [pyFFTW](https://pypi.python.org/pypi/pyFFTW) for faster Fourier transforms
- [pyHealpix](https://gitlab.mpcdf.mpg.de/ift/pyHealpix) (for harmonic
transforms involving domains on the sphere)
- [mpi4py](https://mpi4py.scipy.org) (for MPI-parallel execution)
......@@ -61,18 +61,29 @@ distributions, the "apt" lines will need slight changes.
NIFTy5 and its mandatory dependencies can be installed via:
sudo apt-get install git libfftw3-dev python3 python3-pip python3-dev
sudo apt-get install git python3 python3-pip python3-dev
pip3 install --user git+https://gitlab.mpcdf.mpg.de/ift/NIFTy.git@NIFTy_5
Plotting support is added via:
pip3 install --user matplotlib
FFTW support is added via:
sudo apt-get install libfftw3-dev
pip3 install --user pyfftw
To actually use FFTW in your Nifty calculations, you need to call
nifty5.fft.enable_fftw()
at the beginning of your code.
(Note: If you encounter problems related to `pyFFTW`, make sure that you are
using a pip-installed `pyFFTW` package. Unfortunately, some distributions are
shipping an incorrectly configured `pyFFTW` package, which does not cooperate
with the installed `FFTW3` libraries.)
Plotting support is added via:
pip3 install --user matplotlib
Support for spherical harmonic transforms is added via:
pip3 install --user git+https://gitlab.mpcdf.mpg.de/ift/pyHealpix.git
......@@ -86,7 +97,7 @@ MPI support is added via:
To run the tests, additional packages are required:
sudo apt-get install python3-coverage python3-parameterized python3-pytest python3-pytest-cov
sudo apt-get install python3-coverage python3-pytest python3-pytest-cov
Afterwards the tests (including a coverage report) can be run using the
following command in the repository root:
......
......@@ -74,7 +74,7 @@ if __name__ == '__main__':
ic_sampling = ift.GradientNormController(iteration_limit=100)
# Minimize the Hamiltonian
H = ift.Hamiltonian(likelihood, ic_sampling)
H = ift.StandardHamiltonian(likelihood, ic_sampling)
H = ift.EnergyAdapter(position, H, want_metric=True)
# minimizer = ift.L_BFGS(ic_newton)
H, convergence = minimizer(H)
......
......@@ -99,7 +99,7 @@ if __name__ == '__main__':
minimizer = ift.NewtonCG(ic_newton)
# Compute MAP solution by minimizing the information Hamiltonian
H = ift.Hamiltonian(likelihood)
H = ift.StandardHamiltonian(likelihood)
initial_position = ift.from_random('normal', domain)
H = ift.EnergyAdapter(initial_position, H, want_metric=True)
H, convergence = minimizer(H)
......
......@@ -100,10 +100,10 @@ if __name__ == '__main__':
# Set up likelihood and information Hamiltonian
likelihood = ift.GaussianEnergy(mean=data, covariance=N)(signal_response)
H = ift.Hamiltonian(likelihood, ic_sampling)
H = ift.StandardHamiltonian(likelihood, ic_sampling)
initial_position = ift.MultiField.full(H.domain, 0.)
position = initial_position
initial_mean = ift.MultiField.full(H.domain, 0.)
mean = initial_mean
plot = ift.Plot()
plot.add(signal(mock_position), title='Ground Truth')
......@@ -117,9 +117,9 @@ if __name__ == '__main__':
# Draw new samples to approximate the KL five times
for i in range(5):
# Draw new samples and minimize KL
KL = ift.KL_Energy(position, H, N_samples)
KL = ift.MetricGaussianKL(mean, H, N_samples)
KL, convergence = minimizer(KL)
position = KL.position
mean = KL.position
# Plot current reconstruction
plot = ift.Plot()
......@@ -128,7 +128,7 @@ if __name__ == '__main__':
plot.output(ny=1, ysize=6, xsize=16, name="loop-{:02}.png".format(i))
# Draw posterior samples
KL = ift.KL_Energy(position, H, N_samples)
KL = ift.MetricGaussianKL(mean, H, N_samples)
sc = ift.StatCalculator()
for sample in KL.samples:
sc.add(signal(sample + KL.position))
......
......@@ -103,7 +103,7 @@ N = ift.DiagonalOperator(ift.from_global_data(d_space, var))
IC = ift.DeltaEnergyController(tol_rel_deltaE=1e-12, iteration_limit=200)
likelihood = ift.GaussianEnergy(d, N)(R)
Ham = ift.Hamiltonian(likelihood, IC)
Ham = ift.StandardHamiltonian(likelihood, IC)
H = ift.EnergyAdapter(params, Ham, want_metric=True)
# Minimize
......
......@@ -264,13 +264,13 @@ This functionality is provided by NIFTy's
:class:`~inversion_enabler.InversionEnabler` class, which is itself a linear
operator.
.. currentmodule:: nifty5.operators.linear_operator
.. currentmodule:: nifty5.operators.operator
Direct multiplication and adjoint inverse multiplication transform a field
defined on the operator's :attr:`~LinearOperator.domain` to one defined on the
operator's :attr:`~LinearOperator.target`, whereas adjoint multiplication and
inverse multiplication transform from :attr:`~LinearOperator.target` to
:attr:`~LinearOperator.domain`.
defined on the operator's :attr:`~Operator.domain` to one defined on the
operator's :attr:`~Operator.target`, whereas adjoint multiplication and inverse
multiplication transform from :attr:`~Operator.target` to
:attr:`~Operator.domain`.
.. currentmodule:: nifty5.operators
......@@ -379,7 +379,7 @@ Minimization algorithms
All minimization algorithms in NIFTy inherit from the abstract
:class:`~minimizer.Minimizer` class, which presents a minimalistic interface
consisting only of a :meth:`~minimizer.Minimizer.__call__()` method taking an
consisting only of a :meth:`~minimizer.Minimizer.__call__` method taking an
:class:`~energy.Energy` object and optionally a preconditioning operator, and
returning the energy at the discovered minimum and a status code.
......@@ -399,17 +399,16 @@ Many minimizers for nonlinear problems can be characterized as
This family of algorithms is encapsulated in NIFTy's
:class:`~descent_minimizers.DescentMinimizer` class, which currently has three
concrete implementations: :class:`~descent_minimizers.SteepestDescent`,
:class:`~descent_minimizers.RelaxedNewton`,
:class:`~descent_minimizers.NewtonCG`, :class:`~descent_minimizers.L_BFGS` and
:class:`~descent_minimizers.VL_BFGS`. Of these algorithms, only
:class:`~descent_minimizers.RelaxedNewton` requires the energy object to provide
:class:`~descent_minimizers.NewtonCG` requires the energy object to provide
a :attr:`~energy.Energy.metric` property, the others only need energy values and
gradients.
The flexibility of NIFTy's design allows using externally provided minimizers.
With only small effort, adapters for two SciPy minimizers were written; they are
available under the names :class:`~scipy_minimizer.ScipyCG` and
:class:`L_BFGS_B`.
:class:`~scipy_minimizer.L_BFGS_B`.
Application to operator inversion
......@@ -432,4 +431,4 @@ performs a minimization of a
:class:`~minimization.quadratic_energy.QuadraticEnergy` by means of the
:class:`~minimization.conjugate_gradient.ConjugateGradient` algorithm. An
example is provided in
:func:`~ļibrary.wiener_filter_curvature.WienerFilterCurvature`.
:func:`~library.wiener_filter_curvature.WienerFilterCurvature`.
......@@ -13,6 +13,7 @@ napoleon_use_ivar = True
napoleon_use_admonition_for_notes = True
napoleon_use_admonition_for_examples = True
napoleon_use_admonition_for_references = True
napoleon_include_special_with_doc = True
project = u'NIFTy5'
copyright = u'2013-2019, Max-Planck-Society'
......@@ -27,3 +28,5 @@ add_module_names = False
html_theme = "sphinx_rtd_theme"
html_logo = 'nifty_logo_black.png'
exclude_patterns = ['mod/modules.rst']
......@@ -9,19 +9,20 @@ Theoretical Background
IFT is fully Bayesian. How else could infinitely many field degrees of freedom be constrained by finite data?
There is a full toolbox of methods that can be used, like the classical approximation (= Maximum a posteriori = MAP), effective action (= Variational Bayes = VI), Feynman diagrams, renormalitation, and more. IFT reproduces many known well working algorithms. This should be reassuring. And, there were certainly previous works in a similar spirit. Anyhow, in many cases IFT provides novel rigorous ways to extract information from data. NIFTy comes with reimplemented MAP and VI estimators. It also provides a Hamiltonian Monte Carlo sampler for Fields (HMCF).
There is a full toolbox of methods that can be used, like the classical approximation (= Maximum a posteriori = MAP), effective action (= Variational Bayes = VI), Feynman diagrams, renormalitation, and more. IFT reproduces many known well working algorithms. This should be reassuring. And, there were certainly previous works in a similar spirit. Anyhow, in many cases IFT provides novel rigorous ways to extract information from data. NIFTy comes with reimplemented MAP and VI estimators.
.. tip:: *In-a-nutshell introductions to information field theory* can be found in [2]_, [3]_, [4]_, and [5]_, with the latter probably being the most didactically.
.. tip:: *In-a-nutshell introductions to information field theory* can be found in [2]_, [3]_, [4]_, and [5]_, with the latter probably being the most didactical.
.. [1] T.A. Enßlin et al. (2009), "Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis", PhysRevD.80.105005, 09/2009; `arXiv:0806.3474 <http://www.arxiv.org/abs/0806.3474>`_
.. [1] T.A. Enßlin et al. (2009), "Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis", PhysRevD.80.105005, 09/2009; `[arXiv:0806.3474] <http://www.arxiv.org/abs/0806.3474>`_
.. [2] T.A. Enßlin (2013), "Information field theory", proceedings of MaxEnt 2012 -- the 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering; AIP Conference Proceedings, Volume 1553, Issue 1, p.184; `arXiv:1301.2556 <http://arxiv.org/abs/1301.2556>`_
.. [2] T.A. Enßlin (2013), "Information field theory", proceedings of MaxEnt 2012 -- the 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering; AIP Conference Proceedings, Volume 1553, Issue 1, p.184; `[arXiv:1301.2556] <http://arxiv.org/abs/1301.2556>`_
.. [3] T.A. Enßlin (2014), "Astrophysical data analysis with information field theory", AIP Conference Proceedings, Volume 1636, Issue 1, p.49; `arXiv:1405.7701 <http://arxiv.org/abs/1405.7701>`_
.. [3] T.A. Enßlin (2014), "Astrophysical data analysis with information field theory", AIP Conference Proceedings, Volume 1636, Issue 1, p.49; `[arXiv:1405.7701] <http://arxiv.org/abs/1405.7701>`_
.. [4] Wikipedia contributors (2018), `"Information field theory" <https://en.wikipedia.org/w/index.php?title=Information_field_theory&oldid=876731720>`_, Wikipedia, The Free Encyclopedia.
.. [5] T.A. Enßlin (2019), "Information theory for fields", accepted by Annalen der Physik; `arXiv:1804.03350 <http://arxiv.org/abs/1804.03350>`_
.. [5] T.A. Enßlin (2019), "Information theory for fields", accepted by Annalen der Physik; `[DOI] <https://doi.org/10.1002/andp.201800127>`_, `[arXiv:1804.03350] <http://arxiv.org/abs/1804.03350>`_
Discretized continuum
---------------------
......@@ -83,7 +84,7 @@ The above line of argumentation analogously applies to the discretization of ope
A(x \in \Omega_p, y \in \Omega_q) \quad\mapsto\quad A_{pq} \quad=\quad \frac{\iint_{\Omega_p \Omega_q} \mathrm{d}x \, \mathrm{d}y \; A(x,y)}{\iint_{\Omega_p \Omega_q} \mathrm{d}x \, \mathrm{d}y} \quad=\quad \big< \big< A(x,y) \big>_{\Omega_p} \big>_{\Omega_q}
.
The proper discretization of spaces, fields, and operators, as well as the normalization of position integrals, is essential for the conservation of the continuum limit. Their consistent implementation in NIFTY allows a pixelization independent coding of algorithms.
The proper discretization of spaces, fields, and operators, as well as the normalization of position integrals, is essential for the conservation of the continuum limit. Their consistent implementation in NIFTy allows a pixelization independent coding of algorithms.
Free Theory & Implicit Operators
--------------------------------
......@@ -100,10 +101,9 @@ and the measurement equation is linear in both signal and noise,
d= R\, s + n,
with :math:`{R}` the measurement response, which maps the continous signal field into the discrete data space.
with :math:`{R}` being the measurement response, which maps the continous signal field into the discrete data space.
This is called a free theory, as the information Hamiltonian
associate professor
.. math::
......@@ -135,9 +135,9 @@ the posterior covariance operator, and
j = R^\dagger N^{-1} d
the information source. The operation in :math:`{d= D\,R^\dagger N^{-1} d}` is also called the generalized Wiener filter.
the information source. The operation in :math:`{m = D\,R^\dagger N^{-1} d}` is also called the generalized Wiener filter.
NIFTy permits to define the involved operators :math:`{R}`, :math:`{R^\dagger}`, :math:`{S}`, and :math:`{N}` implicitely, as routines that can be applied to vectors, but which do not require the explicit storage of the matrix elements of the operators.
NIFTy permits to define the involved operators :math:`{R}`, :math:`{R^\dagger}`, :math:`{S}`, and :math:`{N}` implicitly, as routines that can be applied to vectors, but which do not require the explicit storage of the matrix elements of the operators.
Some of these operators are diagonal in harmonic (Fourier) basis, and therefore only require the specification of a (power) spectrum and :math:`{S= F\,\widehat{P_s} F^\dagger}`. Here :math:`{F = \mathrm{HarmonicTransformOperator}}`, :math:`{\widehat{P_s} = \mathrm{DiagonalOperator}(P_s)}`, and :math:`{P_s(k)}` is the power spectrum of the process that generated :math:`{s}` as a function of the (absolute value of the) harmonic (Fourier) space koordinate :math:`{k}`. For those, NIFTy can easily also provide inverse operators, as :math:`{S^{-1}= F\,\widehat{\frac{1}{P_s}} F^\dagger}` in case :math:`{F}` is unitary, :math:`{F^\dagger=F^{-1}}`.
......@@ -175,23 +175,23 @@ NIFTy takes advantage of this formulation in several ways:
1) All prior degrees of freedom have unit covariance which improves the condition number of operators which need to be inverted.
2) The amplitude operator can be regarded as part of the response, :math:`{R'=R\,A}`. In general, more sophisticated responses can be constructed out of the composition of simpler operators.
3) The response can be non-linear, e.g. :math:`{R'(s)=R \exp(A\,\xi)}`, see demos/getting_started_2.py.
4) The amplitude operator can be made dependent on unknowns as well, e.g. :math:`A=A(\tau)= F\, \widehat{e^\tau}` represents an amplitude operator with a positive definite, unknown spectrum defined in Fourier domain. The amplitude field :math:`{\tau}` would get its own amplitude operator, with a cepstrum (spectrum of a log spectrum) defined in quefrency space (harmonic space of a logarithmically binned harmonic space) to regularize its degrees of freedom by imposing some (user-defined level of) spectral smoothness.
5) NIFTy can calculate the gradient of the information Hamiltonian and the Fischer information metric with respect to all unknown parameters, here :math:`{\xi}` and :math:`{\tau}`, by automatic differentiation. The gradients are used for MAP and HMCF estimates, and the Fischer matrix is required in addition to the gradient by Metric Gaussian Variational Inference (MGVI), which is available in NIFTy as well. MGVI is an implicit operator extension of Automatic Differentiation Variational Inference (ADVI).
4) The amplitude operator can be made dependent on unknowns as well, e.g. :math:`A=A(\tau)= F\, \widehat{e^\tau}` represents an amplitude operator with a positive definite, unknown spectrum defined in the Fourier domain. The amplitude field :math:`{\tau}` would get its own amplitude operator, with a cepstrum (spectrum of a log spectrum) defined in quefrency space (harmonic space of a logarithmically binned harmonic space) to regularize its degrees of freedom by imposing some (user-defined degree of) spectral smoothness.
5) NIFTy can calculate the gradient of the information Hamiltonian and the Fisher information metric with respect to all unknown parameters, here :math:`{\xi}` and :math:`{\tau}`, by automatic differentiation. The gradients are used for MAP and HMCF estimates, and the Fisher matrix is required in addition to the gradient by Metric Gaussian Variational Inference (MGVI), which is available in NIFTy as well. MGVI is an implicit operator extension of Automatic Differentiation Variational Inference (ADVI).
The reconstruction of a non-Gaussian signal with unknown covarinance from a non-trivial (tomographic) response is demonstrated in demos/getting_started_3.py. Here, the uncertainty of the field and the power spectrum of its generating process are probed via posterior samples provided by the MGVI algorithm.
The reconstruction of a non-Gaussian signal with unknown covariance from a non-trivial (tomographic) response is demonstrated in demos/getting_started_3.py. Here, the uncertainty of the field and the power spectrum of its generating process are probed via posterior samples provided by the MGVI algorithm.
+----------------------------------------------------+
| **Output of tomography demo getting_started_3.py** |
+----------------------------------------------------+
| .. image:: images/getting_started_3_setup.png |
| |
| :width: 50 % |
+----------------------------------------------------+
| Non-Gaussian signal field, |
| data backprojected into the image domain, power |
| spectrum of underlying Gausssian process. |
+----------------------------------------------------+
| .. image:: images/getting_started_3_results.png |
| |
| :width: 50 % |
+----------------------------------------------------+
| Posterior mean field signal |
| reconstruction, its uncertainty, and the power |
......@@ -199,3 +199,54 @@ The reconstruction of a non-Gaussian signal with unknown covarinance from a non-
| samples in comparison to the correct one (thick |
| orange line). |
+----------------------------------------------------+
Variational Inference
---------------------
One popular field estimation method is MAP.
It only requires to minimize the information Hamiltonian, e.g by a gradient descent method that stops when
.. math::
\frac{\partial \mathcal{H}(d,\xi)}{\partial \xi} = 0.
NIFTy5 is able to calculate the necessary gradient from a generative model of the signal and the data and to minimize the Hamiltonian.
However, MAP provides often unsatisfactory result in case a deep hirachical Bayesian networks describes the singal and data generation.
The reason for this is that MAP ignores the volume factors in parameter space, which are not to be neglected in deciding whether a solution is reasonable or not.
In the high dimensional setting of field inference these volume factors can differ by large ratios.
A MAP estimate, which is only representative for a tiny fraction of the parameter space, might be a poorer choice (with respect to an error norm) compared to a slightly worse location with slightly lower posterior probability, which, however, is associated with a much larger volume (of nearby locations with similar probability).
This causes MAP signal estimates to be more prone to overfitting the noise as well as to perception thresholds than methods that take volume effects into account.
One such method is VI. In VI, the posterior :math:`\mathcal{P}(\xi|d)` is approximated by a simpler distribution, often a Gaussian :math:`\mathcal{Q}(\xi)=\mathcal{G}(\xi-m,D)`.
The parameters of :math:`\mathcal{Q}`, the mean :math:`m` and its uncertainty dispersion :math:`D` are obtained by minimization of an appropriate information distance measure between :math:`\mathcal{Q}` and :math:`\mathcal{P}`.
As a compromise between being optimal and being computational affordable the (reverse) Kullbach Leiberler (KL) divergence is used in VI:
.. math::
\mathrm{KL}(m,D|d)= \mathcal{D}_\mathrm{KL}(\mathcal{Q}||\mathcal{P})=
\int \mathcal{D}\xi \,\mathcal{Q}(\xi) \log \left( \frac{\mathcal{Q}(\xi)}{\mathcal{P}(\xi)} \right)
Minimizing this with respect to all entries of the covariance :math:`D` is unfeasible for fields.
Therefore, MGVI makes the Ansatz to approximate the precision matrix :math:`M=D^{-1}` by the Bayesian Fisher information metric,
.. math::
M \approx \left\langle \frac{\partial \mathcal{H}(d,\xi)}{\partial \xi} \, \frac{\partial \mathcal{H}(d,\xi)}{\partial \xi}^\dagger \right\rangle_{(d,\xi)},
where in the MGVI practice the average is performed over :math:`\mathcal{Q}` by evaluating the expression at samples drawn from this Gaussian.
With this approximation, the KL becomes effectively a function of the mean :math:`m`, as :math:`D= D(m) \approx M^{-1}`. Thus, only the gradient of the KL is needed with respect to this, which can be expressed as
.. math::
\frac{\partial \mathrm{KL}(m|d)}{\partial m} = \left\langle \frac{\partial \mathcal{H}(d,\xi)}{\partial \xi} \right\rangle_{\mathcal{G}(\xi-m,D)}.
The advantage of this Ansatz is that the averages can be represented by sample averages, and all the gradients are represented by operators that NIFTy5 can calculate and that do not need the storage of full matrices. Therefore, NIFTy5 is able to draw samples according to a Gaussian with a covariance given by the inverse information metric, and to minimize the KL correspondingly.
As this requires stochastic optimization, the parameters governing the numerics might need problem specific tuning.
The demo getting_started_3.py for example infers this way not only a field, but also the power spectrum of the process that has generated the field.
The cross-correlation of field and power spectum is taken care of thereby.
Posterior samples can be obtained to study this cross-correlation.
It should be noted that MGVI as any VI method typically underestimates uncertainties due to the fact that :math:`\mathcal{D}_\mathrm{KL}(\mathcal{Q}||\mathcal{P})`, the reverse KL, is used, whereas :math:`\mathcal{D}_\mathrm{KL}(\mathcal{P}||\mathcal{Q})` would be optimal to approximate :math:`\mathcal{P}` by :math:`\mathcal{Q}` from an information theoretical perspective.
This, however, would require that one is able to integrate the posterior, in wich case one can calculate the desired posterior mean and its uncertainty covariance directly.
NIFTy -- Numerical Information Field Theory
===========================================
**NIFTy** [1]_, "\ **N**\umerical **I**\nformation **F**\ield **T**\heor\ **y**\ ", is a versatile library designed to enable the development of signal inference algorithms that are independent of the underlying spatial grid and its resolution.
**NIFTy** [1]_, [2]_, "\ **N**\umerical **I**\nformation **F**\ield **T**\heor\ **y**\ ", is a versatile library designed to enable the development of signal inference algorithms that are independent of the underlying spatial grid and its resolution.
Its object-oriented framework is written in Python, although it accesses libraries written in C++ and C for efficiency.
NIFTy offers a toolkit that abstracts discretized representations of continuous spaces, fields in these spaces, and operators acting on fields into classes.
......@@ -13,22 +13,18 @@ The set of spaces on which NIFTy operates comprises point sets, *n*-dimensional
References
----------
.. [1] Steininger et al., "NIFTy 3 - Numerical Information Field Theory - A Python framework for multicomponent signal inference on HPC clusters", 2017, submitted to PLOS One; `[arXiv:1708.01073] <https://arxiv.org/abs/1708.01073>`_
.. [1] Selig et al., "NIFTY - Numerical Information Field Theory. A versatile PYTHON library for signal inference ", 2013, Astronmy and Astrophysics 554, 26; `[DOI] <https://ui.adsabs.harvard.edu/link_gateway/2013A&A...554A..26S/doi:10.1051/0004-6361/201321236>`_, `[arXiv:1301.4499] <https://arxiv.org/abs/1301.4499>`_
.. [2] Steininger et al., "NIFTy 3 - Numerical Information Field Theory - A Python framework for multicomponent signal inference on HPC clusters", 2017, accepted by Annalen der Physik; `[arXiv:1708.01073] <https://arxiv.org/abs/1708.01073>`_
Contents
........
.. toctree::
:maxdepth: 2
ift
Gallery <http://wwwmpa.mpa-garching.mpg.de/ift/nifty/gallery/>
installation
code
citations
Indices and tables
..................
* :any:`Module Index <mod/modules>`
* :ref:`search`
Package Documentation <mod/nifty5>
......@@ -7,18 +7,29 @@ distributions, the "apt" lines will need slight changes.
NIFTy5 and its mandatory dependencies can be installed via::
sudo apt-get install git libfftw3-dev python3 python3-pip python3-dev
sudo apt-get install git python3 python3-pip python3-dev
pip3 install --user git+https://gitlab.mpcdf.mpg.de/ift/NIFTy.git@NIFTy_5
Plotting support is added via::
pip3 install --user matplotlib
FFTW support is added via:
sudo apt-get install libfftw3-dev
pip3 install --user pyfftw
To actually use FFTW in your Nifty calculations, you need to call
nifty5.fft.enable_fftw()
at the beginning of your code.
(Note: If you encounter problems related to `pyFFTW`, make sure that you are
using a pip-installed `pyFFTW` package. Unfortunately, some distributions are
shipping an incorrectly configured `pyFFTW` package, which does not cooperate
with the installed `FFTW3` libraries.)
Plotting support is added via::
pip3 install --user matplotlib
Support for spherical harmonic transforms is added via::
pip3 install --user git+https://gitlab.mpcdf.mpg.de/ift/pyHealpix.git
......
......@@ -19,6 +19,7 @@ from .field import Field
from .multi_field import MultiField
from .operators.operator import Operator
from .operators.adder import Adder
from .operators.diagonal_operator import DiagonalOperator
from .operators.distributors import DOFDistributor, PowerDistributor
from .operators.domain_tuple_field_inserter import DomainTupleFieldInserter
......@@ -33,7 +34,6 @@ from .operators.field_zero_padder import FieldZeroPadder
from .operators.inversion_enabler import InversionEnabler
from .operators.linear_operator import LinearOperator
from .operators.mask_operator import MaskOperator
from .operators.offset_operator import OffsetOperator
from .operators.qht_operator import QHTOperator
from .operators.regridding_operator import RegriddingOperator
from .operators.sampling_enabler import SamplingEnabler
......@@ -49,7 +49,7 @@ from .operators.simple_linear_operators import (
from .operators.value_inserter import ValueInserter
from .operators.energy_operators import (
EnergyOperator, GaussianEnergy, PoissonianEnergy, InverseGammaLikelihood,
BernoulliEnergy, Hamiltonian, AveragedEnergy)
BernoulliEnergy, StandardHamiltonian, AveragedEnergy)
from .probing import probe_with_posterior_samples, probe_diagonal, \
StatCalculator
......@@ -68,7 +68,7 @@ from .minimization.scipy_minimizer import (ScipyMinimizer, L_BFGS_B, ScipyCG)
from .minimization.energy import Energy
from .minimization.quadratic_energy import QuadraticEnergy
from .minimization.energy_adapter import EnergyAdapter
from .minimization.kl_energy import KL_Energy
from .minimization.metric_gaussian_kl import MetricGaussianKL
from .sugar import *
from .plot import Plot
......
......@@ -16,10 +16,10 @@
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from functools import reduce
from ..utilities import NiftyMetaBase
from ..utilities import NiftyMeta
class Domain(NiftyMetaBase()):
class Domain(metaclass=NiftyMeta):
"""The abstract class repesenting a (structured or unstructured) domain.
"""
def __repr__(self):
......
......@@ -19,23 +19,63 @@ from .utilities import iscomplextype
import numpy as np
_use_fftw = True
_use_fftw = False
_fftw_prepped = False
_fft_extra_args = {}
if _use_fftw:
import pyfftw
from pyfftw.interfaces.numpy_fft import fftn, rfftn, ifftn
pyfftw.interfaces.cache.enable()
pyfftw.interfaces.cache.set_keepalive_time(1000.)
# Optional extra arguments for the FFT calls
# if exact reproducibility is needed,
# set "planner_effort" to "FFTW_ESTIMATE"
import os
nthreads = int(os.getenv("OMP_NUM_THREADS", "1"))
_fft_extra_args = dict(planner_effort='FFTW_ESTIMATE', threads=nthreads)
else:
from numpy.fft import fftn, rfftn, ifftn
_fft_extra_args = {}
def enable_fftw():
global _use_fftw
_use_fftw = True
def disable_fftw():
global _use_fftw
_use_fftw = False
def _init_pyfftw():
global _fft_extra_args, _fftw_prepped
if not _fftw_prepped:
import pyfftw
from pyfftw.interfaces.numpy_fft import fftn, rfftn, ifftn
pyfftw.interfaces.cache.enable()
pyfftw.interfaces.cache.set_keepalive_time(1000.)
# Optional extra arguments for the FFT calls
# if exact reproducibility is needed,
# set "planner_effort" to "FFTW_ESTIMATE"
import os
nthreads = int(os.getenv("OMP_NUM_THREADS", "1"))
_fft_extra_args = dict(planner_effort='FFTW_ESTIMATE',
threads=nthreads)
_fftw_prepped = True
def fftn(a, axes=None):
if _use_fftw:
from pyfftw.interfaces.numpy_fft import fftn
_init_pyfftw()
return fftn(a, axes=axes, **_fft_extra_args)
else:
return np.fft.fftn(a, axes=axes)
def rfftn(a, axes=None):
if _use_fftw:
from pyfftw.interfaces.numpy_fft import rfftn
_init_pyfftw()
return rfftn(a, axes=axes, **_fft_extra_args)
else:
return np.fft.rfftn(a, axes=axes)
def ifftn(a, axes=None):
if _use_fftw:
from pyfftw.interfaces.numpy_fft import ifftn
_init_pyfftw()
return ifftn(a, axes=axes, **_fft_extra_args)
else:
return np.fft.ifftn(a, axes=axes)
def hartley(a, axes=None):
......@@ -46,7 +86,7 @@ def hartley(a, axes=None):
if iscomplextype(a.dtype):
raise TypeError("Hartley transform requires real-valued arrays.")
tmp = rfftn(a, axes=axes, **_fft_extra_args)
tmp = rfftn(a, axes=axes)
def _fill_array(tmp, res, axes):
if axes is None:
......@@ -89,7 +129,7 @@ def my_fftn_r2c(a, axes=None):
if iscomplextype(a.dtype):
raise TypeError("Transform requires real-valued input arrays.")
tmp = rfftn(a, axes=axes, **_fft_extra_args)
tmp = rfftn(a, axes=axes)
def _fill_complex_array(tmp, res, axes):
if axes is None:
......@@ -123,4 +163,4 @@ def my_fftn_r2c(a, axes=None):
def my_fftn(a, axes=None):
return fftn(a, axes=axes, **_fft_extra_args)
return fftn(a, axes=axes)
......@@ -25,7 +25,7 @@ from .domain_tuple import DomainTuple
class Field(object):
"""The discrete representation of a continuous field over multiple spaces.
Stores data arrays and carries all the needed metainformation (i.e. the
Stores data arrays and carries all the needed meta-information (i.e. the
domain) for operators to be able to operate on them.
Parameters
......
......@@ -16,10 +16,9 @@
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from ..minimization.energy_adapter import EnergyAdapter
from ..multi_domain import MultiDomain
from ..multi_field import MultiField
from ..operators.distributors import PowerDistributor
from ..operators.energy_operators import Hamiltonian, InverseGammaLikelihood
from ..operators.energy_operators import StandardHamiltonian, InverseGammaLikelihood
from ..operators.scaling_operator import ScalingOperator
from ..operators.simple_linear_operators import ducktape
......@@ -35,25 +34,27 @@ def make_adjust_variances(a,
Constructs a Hamiltonian to solve constant likelihood optimizations of the
form phi = a * xi under the constraint that phi remains constant.
FIXME xi is white.
Parameters
----------
a : Operator
Operator which gives the amplitude when evaluated at a position
Gives the amplitude when evaluated at a position.
xi : Operator
Operator which gives the excitation when evaluated at a position
postion : Field, MultiField
Position of the whole problem
Gives the excitation when evaluated at a position.
position : Field, MultiField
Position of the entire problem.
samples : Field, MultiField
Residual samples of the whole problem
Residual samples of the whole problem.
scaling : Float
Optional rescaling of the Likelihood
Optional rescaling of the Likelihood.
ic_samp : Controller
Iteration Controller for Hamiltonian
Iteration Controller for Hamiltonian.
Returns
-------
Hamiltonian
A Hamiltonian that can be used for further minimization
StandardHamiltonian
A Hamiltonian that can be used for further minimization.
"""
d = a*xi
......@@ -71,7 +72,7 @@ def make_adjust_variances(a,
if scaling is not None:
x = ScalingOperator(scaling, x.target)(x)
return Hamiltonian(InverseGammaLikelihood(d_eval)(x), ic_samp=ic_samp)
return StandardHamiltonian(InverseGammaLikelihood(d_eval)(x), ic_samp=ic_samp)
def do_adjust_variances(position,
......@@ -79,6 +80,9 @@ def do_adjust_variances(position,
minimizer,
xi_key='xi',
samples=[]):
'''
FIXME
'''
h_space = position[xi_key].domain[0]
pd = PowerDistributor(h_space, amplitude_operator.target[0])
......
......@@ -25,15 +25,15 @@ from ..operators.simple_linear_operators import ducktape
def CorrelatedField(target, amplitude_operator, name='xi'):
'''Constructs an operator which turns a white Gaussian excitation field
"""Constructs an operator which turns a white Gaussian excitation field
into a correlated field.