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Wrapped tex strings to 80-character limit (#19)
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* likelihood: wrapped tex to 80-character limit

* likelihood: some more style improvements

* workflow: appeased pep8 (whitespace only)

* results: more pep8 appeasement

* docs: minor tweak to code block formatting

changed colour of `>>>` prompts

* likelihood: added missing class to __all__
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Duncan Macleod authored and Collin Capano committed Apr 17, 2018
1 parent 3c1a85a commit 0d50dca
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4 changes: 4 additions & 0 deletions docs/_static/css/gwin.css
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Expand Up @@ -19,3 +19,7 @@ code,
background: none;
color: #e74C3c;
}

.gp {
color: #999;
}
145 changes: 100 additions & 45 deletions gwin/likelihood.py
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Expand Up @@ -41,7 +41,7 @@


def _call_global_likelihood(*args, **kwds):
return _global_instance(*args, **kwds) # pylint:disable=not-callable
return _global_instance(*args, **kwds) # pylint:disable=not-callable


class _NoPrior(object):
Expand All @@ -68,17 +68,19 @@ class BaseLikelihoodEvaluator(object):
* the **noise likelihood**: :math:`p(d|n)`
* the **likelihood ratio**: :math:`\mathcal{L}(\Theta) = \frac{p(d|\Theta)}{p(d|n)}`
* the **likelihood ratio**:
:math:`\mathcal{L}(\Theta) = \frac{p(d|\Theta)}{p(d|n)}`
* the **prior**: :math:`p(\Theta)`
* the **posterior**: :math:`p(\Theta|d) \propto p(d|\Theta)p(\Theta)`
* the **prior-weighted likelihood ratio**: :math:`\hat{\mathcal{L}}(\Theta) = \frac{p(d|\Theta)p(\Theta)}{p(d|n)}`
* the **prior-weighted likelihood ratio**:
:math:`\hat{\mathcal{L}}(\Theta) = \frac{p(d|\Theta)p(\Theta)}{p(d|n)}`
* the **SNR**: :math:`\rho(\Theta) = \sqrt{2\log\mathcal{L}(\Theta)}`; for
two detectors, this is approximately the same quantity as the coincident
SNR used in the CBC search.
* the **SNR**: :math:`\rho(\Theta) = \sqrt{2\log\mathcal{L}(\Theta)}`;
for two detectors, this is approximately the same quantity as the
coincident SNR used in the CBC search.
.. note::
Expand All @@ -95,7 +97,8 @@ class BaseLikelihoodEvaluator(object):
.. math::
\log \mathcal{L}(\Theta) = \sum_i \left[\log p(\Theta|d_i) - \log p(n|d_i)\right]
\log \mathcal{L}(\Theta) =
\sum_i \left[\log p(\Theta|d_i) - \log p(n|d_i)\right]
This class provides boiler-plate methods and attributes for evaluating the
log likelihood ratio, log prior, and log likelihood. This class
Expand Down Expand Up @@ -294,7 +297,8 @@ def logjacobian(self, **params):
.. math::
p_y(\mathbf{y}) = p_x(\mathbf{x})\left|\mathrm{det}\,\mathbf{J}_{ij}\right|,
p_y(\mathbf{y}) =
p_x(\mathbf{x})\left|\mathrm{det}\,\mathbf{J}_{ij}\right|,
where :math:`\mathbf{J}_{ij}` is the Jacobian of the inverse transform
:math:`\mathbf{x} = g(\mathbf{y})`. This has elements:
Expand Down Expand Up @@ -556,7 +560,8 @@ class TestEggbox(BaseLikelihoodEvaluator):
.. math::
\log \mathcal{L}(\Theta) = \left[2+\prod_{i=1}^{n}\cos\left(\frac{\theta_{i}}{2}\right)\right]^{5}
\log \mathcal{L}(\Theta) = \left[
2+\prod_{i=1}^{n}\cos\left(\frac{\theta_{i}}{2}\right)\right]^{5}
The number of dimensions is set by the number of ``variable_args`` that are
passed.
Expand Down Expand Up @@ -590,7 +595,8 @@ class TestRosenbrock(BaseLikelihoodEvaluator):
.. math::
\log \mathcal{L}(\Theta) = -\sum_{i=1}^{n-1}[(1-\theta_{i})^{2}+100(\theta_{i+1} - \theta_{i}^{2})^{2}]
\log \mathcal{L}(\Theta) = -\sum_{i=1}^{n-1}[
(1-\theta_{i})^{2}+100(\theta_{i+1} - \theta_{i}^{2})^{2}]
The number of dimensions is set by the number of ``variable_args`` that are
passed.
Expand Down Expand Up @@ -626,8 +632,10 @@ class TestVolcano(BaseLikelihoodEvaluator):
r"""The test distribution is a two-dimensional 'volcano' function:
.. math::
\Theta = \sqrt{\theta_{1}^{2} + \theta_{2}^{2}}
\log \mathcal{L}(\Theta) = 25(e^{\frac{-\Theta}{35}} + \frac{1}{2\sqrt{2\pi}} e^{-\frac{(\Theta-5)^{2}}{8}})
\Theta =
\sqrt{\theta_{1}^{2} + \theta_{2}^{2}} \log \mathcal{L}(\Theta) =
25\left(e^{\frac{-\Theta}{35}} +
\frac{1}{2\sqrt{2\pi}} e^{-\frac{(\Theta-5)^{2}}{8}}\right)
Parameters
----------
Expand Down Expand Up @@ -678,7 +686,8 @@ class GaussianLikelihood(BaseLikelihoodEvaluator):
.. math::
\log p(d|\Theta) &= -\frac{1}{2} \sum_i \left<h_i(\Theta) - d_i | h_i(\Theta) - d_i\right> \\
\log p(d|\Theta) &= -\frac{1}{2} \sum_i
\left< h_i(\Theta) - d_i | h_i(\Theta) - d_i \right> \\
\log p(d|n) &= -\frac{1}{2} \sum_i \left<d_i | d_i\right>
where the sum is over the number of detectors, :math:`d_i` is the data in
Expand All @@ -687,7 +696,8 @@ class GaussianLikelihood(BaseLikelihoodEvaluator):
.. math::
\left<a | b\right> = 4\Re \int_{0}^{\infty} \frac{\tilde{a}(f) \tilde{b}(f)}{S_n(f)} \mathrm{d}f,
\left<a | b\right> = 4\Re \int_{0}^{\infty}
\frac{\tilde{a}(f) \tilde{b}(f)}{S_n(f)} \mathrm{d}f,
where :math:`S_n(f)` is the PSD in the given detector.
Expand All @@ -697,7 +707,9 @@ class GaussianLikelihood(BaseLikelihoodEvaluator):
.. math::
\log \hat{\mathcal{L}} = \log p(\Theta) + \sum_i \left[ \left<h_i(\Theta)|d_i\right> - \frac{1}{2} \left<h_i(\Theta)|h_i(\Theta)\right> \right]
\log \hat{\mathcal{L}} = \log p(\Theta) + \sum_i \left[
\left<h_i(\Theta)|d_i\right> -
\frac{1}{2} \left<h_i(\Theta)|h_i(\Theta)\right> \right]
For this reason, by default this class returns ``logplr`` when called as a
function instead of ``logposterior``. This can be changed via the
Expand Down Expand Up @@ -758,35 +770,48 @@ class GaussianLikelihood(BaseLikelihoodEvaluator):
Create a signal, and set up the likelihood evaluator on that signal:
>>> from pycbc import psd as pypsd
>>> from pycbc.waveform.generator import FDomainDetFrameGenerator, FDomainCBCGenerator
>>> from pycbc.waveform.generator import (FDomainDetFrameGenerator,
FDomainCBCGenerator)
>>> import gwin
>>> seglen = 4
>>> sample_rate = 2048
>>> N = seglen*sample_rate/2+1
>>> fmin = 30.
>>> m1, m2, s1z, s2z, tsig, ra, dec, pol, dist = 38.6, 29.3, 0., 0., 3.1, 1.37, -1.26, 2.76, 3*500.
>>> generator = FDomainDetFrameGenerator(FDomainCBCGenerator, 0., variable_args=['tc'], detectors=['H1', 'L1'], delta_f=1./seglen, f_lower=fmin, approximant='SEOBNRv2_ROM_DoubleSpin', mass1=m1, mass2=m2, spin1z=s1z, spin2z=s2z, ra=ra, dec=dec, polarization=pol, distance=dist)
>>> m1, m2, s1z, s2z, tsig, ra, dec, pol, dist = (
38.6, 29.3, 0., 0., 3.1, 1.37, -1.26, 2.76, 3*500.)
>>> generator = FDomainDetFrameGenerator(
FDomainCBCGenerator, 0.,
variable_args=['tc'], detectors=['H1', 'L1'],
delta_f=1./seglen, f_lower=fmin,
approximant='SEOBNRv2_ROM_DoubleSpin',
mass1=m1, mass2=m2, spin1z=s1z, spin2z=s2z,
ra=ra, dec=dec, polarization=pol, distance=dist)
>>> signal = generator.generate(tc=tsig)
>>> psd = pypsd.aLIGOZeroDetHighPower(N, 1./seglen, 20.)
>>> psds = {'H1': psd, 'L1': psd}
>>> likelihood_eval = gwin.GaussianLikelihood(['tc'], generator, signal, fmin, psds=psds, return_meta=False)
>>> likelihood_eval = gwin.GaussianLikelihood(
['tc'], generator, signal, fmin, psds=psds, return_meta=False)
Now compute the log likelihood ratio and prior-weighted likelihood ratio;
since we have not provided a prior, these should be equal to each other:
>>> likelihood_eval.loglr(tc=tsig), likelihood_eval.logplr(tc=tsig)
(ArrayWithAligned(277.92945279883855), ArrayWithAligned(277.92945279883855))
>>> likelihood_eval.loglr(tc=tsig)
ArrayWithAligned(277.92945279883855)
>>> likelihood_eval.logplr(tc=tsig)
ArrayWithAligned(277.92945279883855)
Compute the log likelihood and log posterior; since we have not
provided a prior, these should both be equal to zero:
>>> likelihood_eval.loglikelihood(tc=tsig), likelihood_eval.logposterior(tc=tsig)
(ArrayWithAligned(0.0), ArrayWithAligned(0.0))
>>> likelihood_eval.loglikelihood(tc=tsig)
ArrayWithAligned(0.0)
>>> likelihood_eval.logposterior(tc=tsig)
ArrayWithAligned(0.0)
Compute the SNR; for this system and PSD, this should be approximately 24:
>>> likelihood_eval.snr([tsig])
ArrayWithAligned(23.576660187517593)
ArrayWithAligned(23.576660187517593)
Using the same likelihood evaluator, evaluate the log prior-weighted
likelihood ratio at several points in time, check that the max is at tsig,
Expand All @@ -797,21 +822,24 @@ class GaussianLikelihood(BaseLikelihoodEvaluator):
>>> times = numpy.arange(seglen*sample_rate)/float(sample_rate)
>>> lls = numpy.array([likelihood_eval([t]) for t in times])
>>> times[lls.argmax()]
3.10009765625
3.10009765625
>>> fig = pyplot.figure(); ax = fig.add_subplot(111)
>>> ax.plot(times, lls)
[<matplotlib.lines.Line2D at 0x1274b5c50>]
[<matplotlib.lines.Line2D at 0x1274b5c50>]
>>> fig.show()
Create a prior and use it (see distributions module for more details):
>>> from pycbc import distributions
>>> uniform_prior = distributions.Uniform(tc=(tsig-0.2,tsig+0.2))
>>> prior_eval = gwin.JointDistribution(['tc'], uniform_prior)
>>> likelihood_eval = gwin.GaussianLikelihood(generator, signal, 20., psds=psds, prior=prior_eval, return_meta=False)
>>> likelihood_eval.logplr([tsig]), likelihood_eval.logposterior([tsig])
(ArrayWithAligned(278.84574353071264), ArrayWithAligned(0.9162907318741418))
>>> likelihood_eval = gwin.GaussianLikelihood(
generator, signal, 20., psds=psds, prior=prior_eval,
return_meta=False)
>>> likelihood_eval.logplr([tsig])
ArrayWithAligned(278.84574353071264)
>>> likelihood_eval.logposterior([tsig])
ArrayWithAligned(0.9162907318741418)
"""
name = 'gaussian'
required_kwargs = ['waveform_generator', 'data', 'f_lower']
Expand Down Expand Up @@ -883,7 +911,9 @@ def loglr(self, **params):
.. math::
\log \mathcal{L}(\Theta) = \sum_i \left<h_i(\Theta)|d_i\right> - \frac{1}{2}\left<h_i(\Theta)|h_i(\Theta)\right>,
\log \mathcal{L}(\Theta) = \sum_i
\left<h_i(\Theta)|d_i\right> -
\frac{1}{2}\left<h_i(\Theta)|h_i(\Theta)\right>,
at the given point in parameter space :math:`\Theta`.
Expand Down Expand Up @@ -927,7 +957,8 @@ def loglikelihood(self, **params):
.. math::
p(d|\Theta) = -\frac{1}{2}\sum_i \left<h_i(\Theta) - d_i | h_i(\Theta) - d_i\right>
p(d|\Theta) = -\frac{1}{2}\sum_i
\left<h_i(\Theta) - d_i | h_i(\Theta) - d_i\right>
Parameters
----------
Expand Down Expand Up @@ -990,47 +1021,68 @@ class MarginalizedPhaseGaussianLikelihood(GaussianLikelihood):
.. math::
p(\Theta,\phi|d) &\propto p(\Theta)p(\phi)p(d|\Theta,\phi) \\
&\propto p(\Theta)\frac{1}{2\pi}\exp\left[-\frac{1}{2}\sum_{i}^{N_D} \left<h_i(\Theta,\phi) - d_i, h_i(\Theta,\phi) - d_i\right>\right].
p(\Theta,\phi|d)
&\propto p(\Theta)p(\phi)p(d|\Theta,\phi) \\
&\propto p(\Theta)\frac{1}{2\pi}\exp\left[
-\frac{1}{2}\sum_{i}^{N_D} \left<
h_i(\Theta,\phi) - d_i, h_i(\Theta,\phi) - d_i
\right>\right].
Here, the sum is over the number of detectors :math:`N_D`, :math:`d_i`
and :math:`h_i` are the data and signal in the :math:`i`th detector,
and :math:`h_i` are the data and signal in detector :math:`i`,
respectively, and we have assumed a uniform prior on :math:`phi \in [0,
2\pi)`. With the form of the signal model given above, the inner product
in the exponent can be written as:
.. math::
-\frac{1}{2}\left<h_i - d_i, h_i- d_i\right> &= \left<h_i, d_i\right> - \frac{1}{2}\left<h_i, h_i\right> - \frac{1}{2}\left<d_i, d_i\right> \\
&= \Re\left\{O(h^0_i, d_i)e^{-i\phi}\right\} - \frac{1}{2}\left<h^0_i, h^0_i\right> - \frac{1}{2}\left<d_i, d_i\right>,
-\frac{1}{2}\left<h_i - d_i, h_i- d_i\right>
&= \left<h_i, d_i\right> -
\frac{1}{2}\left<h_i, h_i\right> -
\frac{1}{2}\left<d_i, d_i\right> \\
&= \Re\left\{O(h^0_i, d_i)e^{-i\phi}\right\} -
\frac{1}{2}\left<h^0_i, h^0_i\right> -
\frac{1}{2}\left<d_i, d_i\right>,
where:
.. math::
h_i^0 &\equiv \tilde{h}_i(f; \Theta, \phi=0); \\
O(h^0_i, d_i) &\equiv 4 \int_0^\infty \frac{\tilde{h}_i^*(f; \Theta,0) \tilde{d}_i(f)}{S_n(f)}\mathrm{d}f.
O(h^0_i, d_i) &\equiv 4 \int_0^\infty
\frac{\tilde{h}_i^*(f; \Theta,0)\tilde{d}_i(f)}{S_n(f)}\mathrm{d}f.
Gathering all of the terms that are not dependent on :math:`\phi` together:
.. math::
\alpha(\Theta, d) \equiv \exp\left[-\frac{1}{2}\sum_i \left<h^0_i, h^0_i\right> + <d_i, d_i\right>\right],
\alpha(\Theta, d) \equiv \exp\left[-\frac{1}{2}\sum_i
\left<h^0_i, h^0_i\right> + \left<d_i, d_i\right>\right],
we can marginalize the posterior over :math:`\phi`:
.. math::
p(\Theta|d) &\propto p(\Theta)\alpha(\Theta,d)\frac{1}{2\pi}\int_{0}^{2\pi}\exp\left[\Re \left\{ e^{-i\phi} \sum_i O(h^0_i, d_i)\right\}\right]\mathrm{d}\phi \\
&\propto p(\Theta)\alpha(\Theta, d)\frac{1}{2\pi} \int_{0}^{2\pi}\exp\left[x(\Theta,d)\cos(\phi) + y(\Theta, d)\sin(\phi)\right]\mathrm{d}\phi.
p(\Theta|d)
&\propto p(\Theta)\alpha(\Theta,d)\frac{1}{2\pi}
\int_{0}^{2\pi}\exp\left[\Re \left\{
e^{-i\phi} \sum_i O(h^0_i, d_i)
\right\}\right]\mathrm{d}\phi \\
&\propto p(\Theta)\alpha(\Theta, d)\frac{1}{2\pi}
\int_{0}^{2\pi}\exp\left[
x(\Theta,d)\cos(\phi) + y(\Theta, d)\sin(\phi)
\right]\mathrm{d}\phi.
The integral in the last line is equal to :math:`2\pi I_0(\sqrt{x^2+y^2})`,
where :math:`I_0` is the modified Bessel function of the first kind. Thus
the marginalized log posterior is:
.. math::
\log p(\Theta|d) \propto \log p(\Theta) + I_0\left(\left|\sum_i O(h^0_i, d_i)\right|\right) - \frac{1}{2}\sum_i\left[ \left<h^0_i, h^0_i\right> - \left<d_i, d_i\right> \right]
\log p(\Theta|d) \propto \log p(\Theta) +
I_0\left(\left|\sum_i O(h^0_i, d_i)\right|\right) -
\frac{1}{2}\sum_i\left[ \left<h^0_i, h^0_i\right> -
\left<d_i, d_i\right> \right]
This class computes the above expression for the log likelihood.
"""
Expand All @@ -1041,7 +1093,9 @@ def loglr(self, **params):
.. math::
\log \mathcal{L}(\Theta) = I_0\left(\left|\sum_i O(h^0_i, d_i)\right|\right) - \frac{1}{2}\left<h^0_i, h^0_i\right>,
\log \mathcal{L}(\Theta) =
I_0 \left(\left|\sum_i O(h^0_i, d_i)\right|\right) -
\frac{1}{2}\left<h^0_i, h^0_i\right>,
at the given point in parameter space :math:`\Theta`.
Expand Down Expand Up @@ -1087,6 +1141,7 @@ def loglr(self, **params):
MarginalizedPhaseGaussianLikelihood,
)}

__all__ = ['BaseLikelihoodEvaluator', 'TestNormal', 'TestEggbox',
'TestVolcano', 'TestRosenbrock', 'GaussianLikelihood',
__all__ = ['BaseLikelihoodEvaluator',
'TestNormal', 'TestEggbox', 'TestVolcano', 'TestRosenbrock',
'GaussianLikelihood', 'MarginalizedPhaseGaussianLikelihood',
'likelihood_evaluators']
5 changes: 3 additions & 2 deletions gwin/results/scatter_histograms.py
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Expand Up @@ -40,7 +40,7 @@
# This matches the check that matplotlib does internally, but this *may* be
# version dependenant. If this is a problem then remove this and control from
# the executables directly.
if 'matplotlib.backends' not in sys.modules:
if 'matplotlib.backends' not in sys.modules: # nopep8
matplotlib.use('agg')

from matplotlib import (offsetbox, pyplot, gridspec)
Expand Down Expand Up @@ -245,7 +245,8 @@ def create_density_plot(xparam, yparam, samples, plot_density=True,
if ymax is None:
ymax = ysamples.max()
npts = 100
X, Y = numpy.mgrid[xmin:xmax:complex(0, npts), ymin:ymax:complex(0, npts)] # pylint:disable=invalid-slice-index
X, Y = numpy.mgrid[ # pylint:disable=invalid-slice-index
xmin:xmax:complex(0, npts), ymin:ymax:complex(0, npts)]
pos = numpy.vstack([X.ravel(), Y.ravel()])
if use_kombine:
Z = numpy.exp(kde(pos.T).reshape(X.shape))
Expand Down
1 change: 1 addition & 0 deletions gwin/workflow.py
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Original file line number Diff line number Diff line change
Expand Up @@ -177,6 +177,7 @@ def make_inference_prior_plot(workflow, config_file, output_dir,

return node.output_files


def make_inference_summary_table(workflow, inference_file, output_dir,
variable_args=None, name="inference_table",
analysis_seg=None, tags=None):
Expand Down

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