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ift
NIFTy
Commits
03cb016f
Commit
03cb016f
authored
Feb 19, 2018
by
Martin Reinecke
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more tweaks
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03577165
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#25148
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-23
docs/source/code.rst
docs/source/code.rst
+45
-21
nifty4/domains/unstructured_domain.py
nifty4/domains/unstructured_domain.py
+7
-0
test/test_operators/test_harmonic_transform_operator.py
test/test_operators/test_harmonic_transform_operator.py
+1
-2
No files found.
docs/source/code.rst
View file @
03cb016f
...
@@ -15,15 +15,13 @@ From such a perspective,
...
@@ -15,15 +15,13 @@ From such a perspective,
- IFT problems largely consist of *minimization* problems involving a large
- IFT problems largely consist of *minimization* problems involving a large
number of equations.
number of equations.
- The equations are built mostly from the application of *linear operators*,
but
- The equations are built mostly from the application of *linear operators*,
there may also be nonlinear functions involved.
but
there may also be nonlinear functions involved.
- The unknowns in the equations represent either continuous physical *fields*,
- The unknowns in the equations represent either continuous physical *fields*,
or they are simply individual measured *data* points.
or they are simply individual measured *data points*.
- The locations and volume elements attached to discretized *field* values are
- Discretized *fields* have geometrical information (like locations and volume
supplied by *domain* objects. There are many variants of such discretized
elements) associated with every entry; this information is called the field's
*domains* supported by NIFTy4, including Cartesian and spherical geometries
*domain*.
and their harmonic counterparts. *Fields* can live on arbitrary products of
such *domains*.
In the following sections, the concepts briefly presented here will be
In the following sections, the concepts briefly presented here will be
discussed in more detail; this is done in reversed order of their introduction,
discussed in more detail; this is done in reversed order of their introduction,
...
@@ -67,7 +65,7 @@ NIFTy requires them to provide the volume elements of their grid cells.
...
@@ -67,7 +65,7 @@ NIFTy requires them to provide the volume elements of their grid cells.
The additional methods are specified in the abstract class
The additional methods are specified in the abstract class
:class:`StructuredDomain`:
:class:`StructuredDomain`:
- The
attribut
es :attr:`~StructuredDomain.scalar_dvol`,
- The
properti
es :attr:`~StructuredDomain.scalar_dvol`,
:attr:`~StructuredDomain.dvol`, and :attr:`~StructuredDomain.total_volume`
:attr:`~StructuredDomain.dvol`, and :attr:`~StructuredDomain.total_volume`
provide information about the domain's pixel volume(s) and its total volume.
provide information about the domain's pixel volume(s) and its total volume.
- The property :attr:`~StructuredDomain.harmonic` specifies whether a domain
- The property :attr:`~StructuredDomain.harmonic` specifies whether a domain
...
@@ -105,14 +103,18 @@ Some examples are:
...
@@ -105,14 +103,18 @@ Some examples are:
a product of an :class:`HPSpace` (for location) with an :class:`RGSpace`
a product of an :class:`HPSpace` (for location) with an :class:`RGSpace`
(for energy).
(for energy).
- a polarised field, which could be modeled as a product of any structured
- a polarised field, which could be modeled as a product of any structured
domain representing location with a four-element
:class:`UnstructuredDomain`
domain
(
representing location
)
with a four-element
holding Stokes I, Q, U and V components.
:class:`UnstructuredDomain`
holding Stokes I, Q, U and V components.
Consequently, NIFTy defines a class called :class:`DomainTuple` holding
Consequently, NIFTy defines a class called :class:`DomainTuple` holding
a sequence of :class:`Domain` objects, which is used to specify full field
a sequence of :class:`Domain` objects, which is used to specify full field
domains. In principle, a :class:`DomainTuple` can even be empty, which implies
domains. In principle, a :class:`DomainTuple` can even be empty, which implies
that the field living on it is a scalar.
that the field living on it is a scalar.
A :class:`DomainTuple` supports iteration and indexing, and also provides the
properties :attr:`~DomainTuple.shape`, :attr:`~DomainTuple.size` in analogy to
the elementary :class:`Domain`.
Fields
Fields
======
======
...
@@ -123,7 +125,28 @@ A :class:`Field` object consists of the following components:
...
@@ -123,7 +125,28 @@ A :class:`Field` object consists of the following components:
- a data type (e.g. numpy.float64)
- a data type (e.g. numpy.float64)
- an array containing the actual values
- an array containing the actual values
Fields support arithmetic operations, contractions, etc.
Usually, the array is stored in the for of a ``numpy.ndarray``, but for very
resource-intensive tasks NIFTy also provides an alternative storage method to
be used with distributed memory processing.
Fields support a wide range of arithmetic operations, either involving two
fields with equal domains, or a field and a scalar.
Contractions (like summation, integration, minimum/maximum, computation of
statistical moments) can be carried out either over an entire field (producing
a scalar result) or over sub-domains (resulting in a field living on a smaller
domain). Scalar products of two fields can also be computed easily.
There is also a set of convenience functions to generate fields with constant
values or fields filled with random numbers according to a user-specified
distribution.
Fields are the only fundamental NIFTy objects which can change state after they
have been constructed: while their data type, domain, and array shape cannot
be modified, the actual data content of the array may be manipulated during the
lifetime of the object. This is a slight deviation from the philosophy that all
NIFTy objects should be immutable, but this choice offers considerable
performance benefits.
Linear Operators
Linear Operators
================
================
...
@@ -162,7 +185,7 @@ four operations. This subset can be queried using the
...
@@ -162,7 +185,7 @@ four operations. This subset can be queried using the
If needed, the set of supported operations can be enhanced by iterative
If needed, the set of supported operations can be enhanced by iterative
inversion methods;
inversion methods;
for example, an operator defining direct and adjoint multiplication could be
for example, an operator defining direct and adjoint multiplication could be
enhanced to support the complete set
by this method
. This functionality is
enhanced
by this approach
to support the complete set. This functionality is
provided by NIFTy's :class:`InversionEnabler` class, which is itself a linear
provided by NIFTy's :class:`InversionEnabler` class, which is itself a linear
operator.
operator.
...
@@ -180,10 +203,10 @@ field with potentially different values.
...
@@ -180,10 +203,10 @@ field with potentially different values.
Further operator classes provided by NIFTy are
Further operator classes provided by NIFTy are
- :class:`HarmonicTransformOperator` for transforms from harmonic domain to
- :class:`HarmonicTransformOperator` for transforms from
a
harmonic domain to
their
counterpart
s
in position space, and their adjoint
its
counterpart in position space, and their adjoint
- :class:`PowerDistributor` for transforms from a :class:`PowerSpace` to
- :class:`PowerDistributor` for transforms from a :class:`PowerSpace` to
the
associated harmonic domain, and their adjoint
an
associated harmonic domain, and their adjoint
- :class:`GeometryRemover`, which transforms from structured domains to
- :class:`GeometryRemover`, which transforms from structured domains to
unstructured ones. This is typically needed when building instrument response
unstructured ones. This is typically needed when building instrument response
operators.
operators.
...
@@ -225,23 +248,24 @@ Energy functionals
...
@@ -225,23 +248,24 @@ Energy functionals
In NIFTy4 such functions are represented by objects of type :class:`Energy`.
In NIFTy4 such functions are represented by objects of type :class:`Energy`.
These hold the prescription how to calculate the function's
These hold the prescription how to calculate the function's
:attr:`~Energy.value`, :attr:`~Energy.gradient` and
:attr:`~Energy.value`, :attr:`~Energy.gradient` and
(optionally) :attr:`~Energy.curvature` at any given position.
(optionally) :attr:`~Energy.curvature` at any given :attr:`~Energy.position`
in parameter space.
Function values are floating-point scalars, gradients have the form of fields
Function values are floating-point scalars, gradients have the form of fields
living on the energy's position domain, and curvatures are represented by
living on the energy's position domain, and curvatures are represented by
linear operator objects.
linear operator objects.
Energies are classes that typically have to be provided by the user when
tackling new IFT problems.
Some examples of concrete energy classes delivered with NIFTy4 are
Some examples of concrete energy classes delivered with NIFTy4 are
:class:`QuadraticEnergy` (with position-independent curvature, mainly used with
:class:`QuadraticEnergy` (with position-independent curvature, mainly used with
conjugate gradient minimization) and :class:`~nifty4.library.WienerFilterEnergy`.
conjugate gradient minimization) and :class:`~nifty4.library.WienerFilterEnergy`.
Energies are classes that typically have to be provided by the user when
tackling new IFT problems.
Iteration control
Iteration control
-----------------
-----------------
Iterative minimization of an energy reqires some means of
Iterative minimization of an energy reqires some means of
c
ontroll
ing the quality of the current solution estimate and stopping once
c
heck
ing the quality of the current solution estimate and stopping once
it is sufficiently accurate. In case of numerical problems, the iteration needs
it is sufficiently accurate. In case of numerical problems, the iteration needs
to be terminated as well, returning a suitable error description.
to be terminated as well, returning a suitable error description.
...
@@ -275,7 +299,7 @@ choice of algorithm is the :class:`ConjugateGradient` minimizer.
...
@@ -275,7 +299,7 @@ choice of algorithm is the :class:`ConjugateGradient` minimizer.
A similar algorithm suited for nonlinear problems is provided by
A similar algorithm suited for nonlinear problems is provided by
:class:`NonlinearCG`.
:class:`NonlinearCG`.
Many minimizers for nonlinear problems can be
desc
ri
b
ed as
Many minimizers for nonlinear problems can be
characte
ri
z
ed as
- first deciding on a direction for the next step
- first deciding on a direction for the next step
- then finding a suitable step length along this direction, resulting in the
- then finding a suitable step length along this direction, resulting in the
...
...
nifty4/domains/unstructured_domain.py
View file @
03cb016f
...
@@ -25,7 +25,14 @@ class UnstructuredDomain(Domain):
...
@@ -25,7 +25,14 @@ class UnstructuredDomain(Domain):
associated geometry.
associated geometry.
Typically used for data spaces.
Typically used for data spaces.
Parameters
----------
shape : tuple of int
The required shape for an array which can hold the unstructured
domain's data.
"""
"""
_needed_for_hash
=
[
"_shape"
]
_needed_for_hash
=
[
"_shape"
]
def
__init__
(
self
,
shape
):
def
__init__
(
self
,
shape
):
...
...
test/test_operators/test_harmonic_transform_operator.py
View file @
03cb016f
...
@@ -71,6 +71,5 @@ class HarmonicTransformOperatorTests(unittest.TestCase):
...
@@ -71,6 +71,5 @@ class HarmonicTransformOperatorTests(unittest.TestCase):
std
=
1
,
mean
=
2
,
dtype
=
tp
)
std
=
1
,
mean
=
2
,
dtype
=
tp
)
out
=
fft
.
times
(
inp
)
out
=
fft
.
times
(
inp
)
zero_idx
=
tuple
([
0
]
*
len
(
space
.
shape
))
zero_idx
=
tuple
([
0
]
*
len
(
space
.
shape
))
assert_allclose
(
ift
.
dobj
.
to_global_data
(
inp
.
val
)[
zero_idx
],
assert_allclose
(
inp
.
to_global_data
()[
zero_idx
],
out
.
integrate
(),
out
.
integrate
(),
rtol
=
tol
,
atol
=
tol
)
rtol
=
tol
,
atol
=
tol
)
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