Multivariate regression analysis of core-collapse simulations
Project description
ccsnmultivar companion code
This Python module aids the analysis of core-collapse supernova gravitational waves. It is the companion code for this paper.
Multivariate Regression of Fourier Transformed or Time Domain waveforms
Hypothesis testing for measuring the influence of physical parameters
Optionally incorporate additional uncertainty due to detector noise
Waveform reconstruction and prediction
Fit and analyze waveforms in Principal Component space
Includes the Abdikamalov et. al. for use examples
Details
Uses pandas for data handling
A simplified formula language specific to this domain
Installation
Make sure that the python packages numpy, scipy, pandas, and patsy are already installed. pip installer will install patsy, pandas and tabular if they aren’t installed already.
cd /path/to/ccsnmultivar
Download github zip file here
Unzip
```python # cd /CCSNMultivar-master
python setup.py install ``` or
pip install -U ccsnmultivar
Basic Walkthrough
Using the code happens in five steps:
Instantiate a Catalog object
Instantiate a Basis object.
Instantiate a DesignMatrix object.
Wrapping them in a Multivar object.
Analysis using the Multivar object’s methods.
# import code import ccsnmultivar as cc # load waveforms path_to_waveforms = "/path/to/waveforms.dat" # the Abdikamalov waveform file is called "Abdika13_waveforms.csv" # instantiate Catalog object Y = cc.Catalog(path_to_waveforms)
Note that Abdikamalov et al’s 2013 waveform catalog and parameter file are included in the Example_Waveforms directory of the GitHub repo as an example of how to format the raw files for input. To access these for the walkthrough, look at the right side of the GitHub page, there is a toolbar with a Download button. Download, then unzip.
Now we need to make two objects, a Basis object and a DesignMatrix object
First we instantiate a Basis object. Currently, there are three available types of Basis objects.
PCA - using the Singular Value Decompostion (SVD)
KCPA - Kernel PCA. A wrapper for sklearns Kernel PCA
ICA - Independent Component Ananlysis. A wrapper for skearns FastICA
python # use a PCA basis keeping the first 10 Principal Components pca = cc.PCA(num_components=10) Next we instantiate a DesignMatrix object.
# first, define a formula string describing how the physical parameters # need to be translated to the design matrix. Say we only want to use # encodings of the parameters A and B (A is discrete, B is continuous) formula = "A + B + A*B | Dum(A,omit=2), Poly(B,degree=4)"
The formula contains 5 peices of information that determine how the design matrix is encoded. Reading the formula from left to right:
Include columns for the physical parameter named “A”.
Include columns for the physical parameter named “B”.
Include columns for interaction terms between parameters “A” and “B”. The “|” character seperates instructions for what goes into the design matrix from how it goes in.
Use a dummy variable encoding on parameter “A”. One value of “A” needs to be used as a reference in a dummy variable encoding, we chose value “2”.
Use a chebyshev polynomial encoding on parameter “B”. Fit “B” with a 4th degree polynomial.
Now we instantiate the DesignMatrix object with two arguments: the formula, and the path to the parameter file. ```python
note that the provided Abdikamalov+ parameterfile is called “Abdika13_params.csv”
path_to_parameterfile = “/path/to/parameterfile.csv”
note that we dont need to load the paramfile, just supply the path.
X = cc.DesignMatrix(path_to_parameterfile, formula) ```
Now with the waveforms in the Catalog object Y, the Basis object pca, and DesignMatrix object X on hand, we instantiate a Multivar object with these three arguements.
# instantiate Multivar object M = cc.Multivar(Y,X, pca)
This makes it easy to create many different Catalog, DesignMatrix, Basis, and Multivar objects to test different fits and parameter influences very quickly.
# now we do a fit to time domain waveforms (solve for B)
M.fit('time')
# print/save summary of the hypothesis tests, fit metadata, and other
# facts defined by the particular formula and basis used to make M.
M.summary()
================= ================ =========
Comparison Hotellings T^2 p-value
================= ================ =========
[A1 - A2] 3.59 0.1
[A3 - A2] 6.88 0.52
[A4 - A2] 0.4 0.99
B^1 10.6 0.012
B^2 50.9 0.000
B^3 4.3 0.3
[A1 - A2]*B^1 1.1 0.78
[A1 - A2]*B^2 12.99 0.044
. . .
. . .
. . .
# we can view the waveform reconstructions with the Multivar method .reconstruct()
Y_reconstructed = M.reconstruct()
Dependencies
numpy
scipy
scikits-learn
tabulate
Planned
More than one detector (the GW detector network)
Catalog objects
amplitude/phase decomposition, spectrograms, metadata
other PC basis methods
kmeans, fix KernelPCA, etc.
other design matrix fitting methods
splines, rbfs, etc.
cross validation with printed summary()
Gaussian Process (or other interpolation/machine learning method) reconstructions
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
