Technical notes¶
lensingGW has a modular structure which allows to import each routine individually.
Detailed package description is available at the lensingGW package
section of the documentation. Here, we provide a few technical notes on the packages that require special attention.
The amplification factor package¶
This package computes the geometrical optics amplification from a set of images and lensing potentials.
Unlike in the light lensing, gravitational waves from compact binaries are transient signals. Thus, only the images
that superimpose into the detectors should be fed to the amplification routine. This amounts to considering groups of
images whose pairwise time delays are shorter than the unlensed signal duration.
The time delay of each image can be checked through the TimeDelay module in the utils package.
The solver package¶
This section contains the complete list of solver settings that can be tuned by the users along with their descriptions and default values. For the sake of clarity, here they are grouped in:
standard settings – specifications that are always considered for the two-step procedure. If users don’t specify input for these settings, default values are assumed
optimization-related settings – settings that are considered only when the \(\texttt{optimization}\) mode is active. Users who wish to use these settings should enable the \(\texttt{optimization}\) mode.
further specifications – additional features.
Standard settings
For most cases, the \(\texttt{optimization}\) mode is not required. The following settings apply the solving algorithm in its standard form.
Option |
Type |
Default |
Description |
|---|---|---|---|
Scaled |
bool |
False |
Specifies if the input is given in arbitrary units. If
\(False\), radians are assumed
|
ScaleFactor |
float |
1 |
Constant factor \(\alpha\) to convert from radians to
arbitrary units, as per \(x_{a.u.} = x_{radians}/\alpha\)
|
MacroIndex |
list |
[0] |
Indices matching the profiles in
lens_model_list that form the macromodel
|
SearchWindowMacro |
float |
needs user input |
Size of the first macromodel grid |
PixelsMacro |
int |
\(10^3\) |
Number of pixels of the first macromodel
grid
|
OverlapDistMacro |
float |
\(10^{-15}\rm{rad}\) |
Distance below which macroimages are
considered overlaps
|
ImgIndex |
list
or
None
|
None |
Indices of the macroimages to be considered for
the two-step procedure. If None,
all macroimages are considered
|
SearchWindow |
float |
needs user input |
Same as SearchWindowMacro, but for
the complete model
|
Pixels |
int |
\(10^3\) |
Same as PixelsMacro, but for
the complete model
|
OverlapDist |
float |
\(10^{-15}\rm{rad}\) |
Same as OverlapDistMacro, but for
the complete model
|
PrecisionLimit |
float |
\(10^{-20}\rm{rad}\) |
Precision of the solutions in the
source plane
|
Optimization |
bool |
False |
Enables the \(\texttt{optimization}\) mode |
Verbose |
bool |
False |
Prints detailed diagnostic |
Optimization-related settings
When the \(\texttt{optimization}\) mode is active, users can tune the following additional parameters
Option |
Type |
Default |
Description |
|---|---|---|---|
OptimizationWindowMacro |
float |
2 |
Multiplying factor \(\gamma\) for the size
of the macromodel iteration grids.
The next window size \(w_s\) is
\(w_s = \gamma p_s\), where \(p_s\) is the pixel size
of the current iteration
|
OptimizationPixelsMacro |
int |
\(30\) |
Number of pixels of the macromodel
iteration grids
|
MinDistMacro |
float
or
None
|
None |
Minimum ray-shooted distance
from the source \(d^s_0\) that pixels of the
first macromodel grid must satisfy
to be iterated over.
If None, all candidate pixels
are iterated over
|
ImprovementMacro |
float
or
None
|
None |
Improvement \(\delta\) on the ray-shooted
distance \(d^s_0\) that pixels of the
macromodel grids must satisfy to be
iterated over.
Pixels are considered for the \(n^{th}\)
iteration if their ray-shooted
distance at the \({n-1}^{th}\) iteration
is \(d^s_{n-1} < d^s_0 \cdot \delta^{n-1}\),
where \(0 < \delta \leq1\).
If None, \(d^s_{n-1}\equiv d^s_0\)
for all the iterations
|
OptimizationPrecisionLimitMacro |
float |
\(10^{-20}\rm{rad}\) |
Precision of the macromodel
solutions in the source plane
|
OptimizationWindow |
float |
2 |
Same as OptimizationWindowMacro,
but for the complete model
|
OptimizationPixels |
int |
\(30\) |
Same as OptimizationPixelsMacro,
but for the complete model
|
MinDist |
float
or
None
|
None |
Same as MinDistMacro, but for the
complete model
|
Improvement |
float
or
None
|
None |
Same as ImprovementMacro,
but for the complete model
|
OptimizationPrecisionLimit |
float |
\(10^{-20}\rm{rad}\) |
Same as
OptimizationPrecisionLimitMacro,
but for the complete model
|
further specifications
In addition to the above-mentioned options, users can specify
Option |
Type |
Default |
Description |
|---|---|---|---|
OnlyMacro |
bool |
False |
Solves for the macromodel only |
NearSource |
bool |
False |
Enables a further screening for
macroimages close to the unlensed
image position, with a customized
window size and number of pixels
|
SearchWindowNearSource |
float
or
None
|
needs user input |
Same as SearchWindowMacro, but for
the inspection near the unlensed
image position.
It requires \(\texttt{NearSource}= True\)
|
PixelsNearSource |
int |
\(10^3\) |
Same as PixelsMacro, but for
the inspection near the unlensed
image position.
It requires \(\texttt{NearSource}= True\)
|
The \(\texttt{NearSource}\) option is compatible with the \(\texttt{optimization}\) mode. When both are active, the \(\texttt{optimization}\) settings applied to the screening near the unlensed image position are the same as the ones specified for the macromodel. The SearchWindowNearSource must necessarily be specified when this option is active.