Multivariate regression analysis of core-collapse simulations

## Project description

ccsnmultivar companion code

===========================

This `Python <http://www.python.org/>`_ module aids the analysis of

core-collapse supernova gravitational waves. It is the companion code

for `this paper <http://arxiv.org/abs/1406.1164>`_.

- **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

- Approximate waveforms from anywhere within the parameter space

- Includes the `Abdikamalov et. al. <http://arxiv.org/abs/1311.3678>`_

catalog for example use

Details

-------

- A simplified formula language (like in R, or patsy) specific to this

domain

- `Documentation <http://ccsnmultivar.readthedocs.org/en/latest/>`_

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

1. Download github zip file here

2. Unzip

\`\`\`python # cd /CCSNMultivar-master

python setup.py install \`\`\` or

::

pip install ccsnmultivar

Its a good idea to update often because the package is being changed

often. To update, type

::

pip install -U ccsnmultivar

Basic Walkthrough

-----------------

Using the code happens in five steps:

1. Instantiate a Catalog object

2. Instantiate a Basis object.

3. Instantiate a DesignMatrix object.

4. Wrapping them in a Multivar object.

5. Analysis using the Multivar object's methods.

::

# import code

import ccsnmultivar as cc

# load waveforms

path_to_waveforms = "/path/to/Abdika13_waveforms.csv"

# the Abdikamalov waveform file is called "Abdika13_waveforms.csv"

# we want to analyze the waveforms in the time domain, so instantiate

# a Catalog object with the transform_type arguement specified

Y = cc.Catalog(path_to_waveforms,transform_type='time')

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. The directory

Example\_Waveforms isn't included when the package is installed using

pip.

Now we need to make two objects, a Basis object and a DesignMatrix

object

First we instantiate a Basis object. Currently, there are two available

types of Basis objects, with more planned.

1. PCA - using the Singular Value Decompostion (SVD)

2. ICA - Independent Component Ananlysis. A wrapper for skearns

`FastICA <http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.FastICA.html>`_

``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 + beta + A*beta | Dum(A,ref=2), Poly(beta,degree=4)"

The formula contains 5 peices of information that determine how the

design matrix is encoded. Reading the formula from left to right:

1. Include columns for the physical parameter named "A".

2. Include columns for the physical parameter named "beta".

3. Include columns for interaction terms between parameters "A" and

"beta".

The "\|" character seperates instructions for *what* goes into the

design matrix from *how* it goes in.

4. 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".

5. Use a Chebyshev polynomial encoding on parameter "beta". Fit "beta"

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/Abdika13\_params.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.

\`\`\`python # now we do a fit to time domain waveforms (solve for B)

M.fit()

print summary of the hypothesis tests, metadata, and other

==========================================================

facts defined by the particular formula and basis used to make M.

=================================================================

M.summary()

Waveform Domain time Number of Waveforms 92 Catalog Mean Subtracted?

False Catalog Name Abdika13\_waveforms.csv Normalization Factor

2.45651978042e+20 Decomposition PCA num\_components 10 ================

================ =========== Comparison Hotellings T^2 p-value

================ ================ =========== Intercept 1129.44

1.11022e-16 A:[1 - 2] 87.9454 1.11022e-16 A:[3 - 2] 8.06119 5.49626e-08

A:[4 - 2] 1.8598 0.0700502 A:[5 - 2] 0.823121 0.607991 beta^1 257.711

1.11022e-16 beta^2 383.961 1.11022e-16 beta^3 93.1575 1.11022e-16 beta^4

18.3438 1.55431e-14 A:[1 - 2]*beta^1 77.7596 1.11022e-16 A:[1 -

2]*beta^2 14.0067 3.68272e-12 . . . . . . . . .

we can view the waveform reconstructions with the Multivar method .reconstruct()

================================================================================

Y\_reconstructed = M.reconstruct()

and pull out the original catalog waveforms for comparison

==========================================================

Y\_original = M.get\_waveforms()

plot the last waveform in the array with its reconstruction (requires matplotlib)

=================================================================================

import matplotlib.pyplot as plt

plt.plot(Y\_original[-1,8000:9000],label='original')

plt.plot(Y\_reconstructed[-1,8000:9000],label='reconstruction')

plt.legend() \`\`\` Using the Abdikamalov catalog, this is what you

should see:

|alt tag| \`\`\`python # look at a summary of the overlaps between the

waveforms and their reconstructions M.overlap\_summary()

============ ============== Percentile Overlap ============

============== 5%: 0.64866522524 25%: 0.809185728124 50%: 0.879262580569

75%: 0.949587383571 95%: 0.97311500202

Min: 0.518678320514 Mean: 0.858585006085 Max: 0.98214781409 ============

==============

\`\`\` One of the main goals of this method is to predict new waveforms,

given a set of physical parameters that wasn't originally used in the

catalog. For instance:

::

# make a dictionary of the new parameters

new_parameters = {}

# quickly generate two waveforms, one with A = 1, beta = .1, another with

# A = 3, beta = 0.05 (using the abdikamalov example)

new_parameters['A'] = [str(1), str(3)]

new_parameters['beta'] = [.1, .05]

# use the predict method of the multivar object

Y_new = M.predict(new_parameters)

# plot the two waveform predictions (requires matplotlib)

import matplotlib.pyplot as plt

plt.plot(Y_new[0,8000:9000],label='A = 1, beta = .1')

plt.plot(Y_new[1,8000:9000],label='A = 3, beta = .05')

plt.legend()

With the Abdikamalov catalog, this is what you should see:

.. figure:: Example_Catalogs/example_prediction.png

:align: center

:alt: alt tag

alt tag

This allows one to rapidly interpolate the parameter space for

core-collapse waveforms

Dependencies

------------

- numpy

- scipy

- scikits-learn

- tabulate

Planned

-------

- Hotellings T2 with more than one GW detector

- Catalog objects

- amplitude/phase decomposition, spectrograms

- other PC basis methods

- sparse basis decompositions, kmeans, etc.

- other design matrix fitting methods

- splines, rbfs, etc.

- different types of crossvalidation methods

- Gaussian Process (or other interpolation/machine learning method)

classes

.. |alt tag| image:: Example_Catalogs/example_reconstruction.png

===========================

This `Python <http://www.python.org/>`_ module aids the analysis of

core-collapse supernova gravitational waves. It is the companion code

for `this paper <http://arxiv.org/abs/1406.1164>`_.

- **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

- Approximate waveforms from anywhere within the parameter space

- Includes the `Abdikamalov et. al. <http://arxiv.org/abs/1311.3678>`_

catalog for example use

Details

-------

- A simplified formula language (like in R, or patsy) specific to this

domain

- `Documentation <http://ccsnmultivar.readthedocs.org/en/latest/>`_

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

1. Download github zip file here

2. Unzip

\`\`\`python # cd /CCSNMultivar-master

python setup.py install \`\`\` or

::

pip install ccsnmultivar

Its a good idea to update often because the package is being changed

often. To update, type

::

pip install -U ccsnmultivar

Basic Walkthrough

-----------------

Using the code happens in five steps:

1. Instantiate a Catalog object

2. Instantiate a Basis object.

3. Instantiate a DesignMatrix object.

4. Wrapping them in a Multivar object.

5. Analysis using the Multivar object's methods.

::

# import code

import ccsnmultivar as cc

# load waveforms

path_to_waveforms = "/path/to/Abdika13_waveforms.csv"

# the Abdikamalov waveform file is called "Abdika13_waveforms.csv"

# we want to analyze the waveforms in the time domain, so instantiate

# a Catalog object with the transform_type arguement specified

Y = cc.Catalog(path_to_waveforms,transform_type='time')

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. The directory

Example\_Waveforms isn't included when the package is installed using

pip.

Now we need to make two objects, a Basis object and a DesignMatrix

object

First we instantiate a Basis object. Currently, there are two available

types of Basis objects, with more planned.

1. PCA - using the Singular Value Decompostion (SVD)

2. ICA - Independent Component Ananlysis. A wrapper for skearns

`FastICA <http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.FastICA.html>`_

``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 + beta + A*beta | Dum(A,ref=2), Poly(beta,degree=4)"

The formula contains 5 peices of information that determine how the

design matrix is encoded. Reading the formula from left to right:

1. Include columns for the physical parameter named "A".

2. Include columns for the physical parameter named "beta".

3. Include columns for interaction terms between parameters "A" and

"beta".

The "\|" character seperates instructions for *what* goes into the

design matrix from *how* it goes in.

4. 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".

5. Use a Chebyshev polynomial encoding on parameter "beta". Fit "beta"

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/Abdika13\_params.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.

\`\`\`python # now we do a fit to time domain waveforms (solve for B)

M.fit()

print summary of the hypothesis tests, metadata, and other

==========================================================

facts defined by the particular formula and basis used to make M.

=================================================================

M.summary()

Waveform Domain time Number of Waveforms 92 Catalog Mean Subtracted?

False Catalog Name Abdika13\_waveforms.csv Normalization Factor

2.45651978042e+20 Decomposition PCA num\_components 10 ================

================ =========== Comparison Hotellings T^2 p-value

================ ================ =========== Intercept 1129.44

1.11022e-16 A:[1 - 2] 87.9454 1.11022e-16 A:[3 - 2] 8.06119 5.49626e-08

A:[4 - 2] 1.8598 0.0700502 A:[5 - 2] 0.823121 0.607991 beta^1 257.711

1.11022e-16 beta^2 383.961 1.11022e-16 beta^3 93.1575 1.11022e-16 beta^4

18.3438 1.55431e-14 A:[1 - 2]*beta^1 77.7596 1.11022e-16 A:[1 -

2]*beta^2 14.0067 3.68272e-12 . . . . . . . . .

we can view the waveform reconstructions with the Multivar method .reconstruct()

================================================================================

Y\_reconstructed = M.reconstruct()

and pull out the original catalog waveforms for comparison

==========================================================

Y\_original = M.get\_waveforms()

plot the last waveform in the array with its reconstruction (requires matplotlib)

=================================================================================

import matplotlib.pyplot as plt

plt.plot(Y\_original[-1,8000:9000],label='original')

plt.plot(Y\_reconstructed[-1,8000:9000],label='reconstruction')

plt.legend() \`\`\` Using the Abdikamalov catalog, this is what you

should see:

|alt tag| \`\`\`python # look at a summary of the overlaps between the

waveforms and their reconstructions M.overlap\_summary()

============ ============== Percentile Overlap ============

============== 5%: 0.64866522524 25%: 0.809185728124 50%: 0.879262580569

75%: 0.949587383571 95%: 0.97311500202

Min: 0.518678320514 Mean: 0.858585006085 Max: 0.98214781409 ============

==============

\`\`\` One of the main goals of this method is to predict new waveforms,

given a set of physical parameters that wasn't originally used in the

catalog. For instance:

::

# make a dictionary of the new parameters

new_parameters = {}

# quickly generate two waveforms, one with A = 1, beta = .1, another with

# A = 3, beta = 0.05 (using the abdikamalov example)

new_parameters['A'] = [str(1), str(3)]

new_parameters['beta'] = [.1, .05]

# use the predict method of the multivar object

Y_new = M.predict(new_parameters)

# plot the two waveform predictions (requires matplotlib)

import matplotlib.pyplot as plt

plt.plot(Y_new[0,8000:9000],label='A = 1, beta = .1')

plt.plot(Y_new[1,8000:9000],label='A = 3, beta = .05')

plt.legend()

With the Abdikamalov catalog, this is what you should see:

.. figure:: Example_Catalogs/example_prediction.png

:align: center

:alt: alt tag

alt tag

This allows one to rapidly interpolate the parameter space for

core-collapse waveforms

Dependencies

------------

- numpy

- scipy

- scikits-learn

- tabulate

Planned

-------

- Hotellings T2 with more than one GW detector

- Catalog objects

- amplitude/phase decomposition, spectrograms

- other PC basis methods

- sparse basis decompositions, kmeans, etc.

- other design matrix fitting methods

- splines, rbfs, etc.

- different types of crossvalidation methods

- Gaussian Process (or other interpolation/machine learning method)

classes

.. |alt tag| image:: Example_Catalogs/example_reconstruction.png

## Project details

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