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‎README.rst‎

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@@ -8,8 +8,8 @@ Fast Template Periodogram
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:target: https://codecov.io/gh/PrincetonUniversity/FastTemplatePeriodogram
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:Authors:
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John Hoffman (mailto:[email protected])
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Jake Vanderplas (mailto:[email protected])
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|John Hoffman ([email protected])
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|Jake Vanderplas ([email protected])
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:Version:
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0.9.5.dev
@@ -81,7 +81,7 @@ uses non-linear least-squares fitting to compute the optimal parameters
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process scales as ``N_obs*N_f``, where ``N`` is the number of observations and
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``N_f`` is the number of frequencies at which to calculate the periodogram.
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This is more or less the procedure used in [Sesar2017]_ to perform
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This is more or less the procedure used in [Sesar_etal_2017]_ to perform
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template fits to Pan-STARRS photometry, however they used a more sophisticated
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multiband model that locked the phases, amplitudes and
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offsets of all bands together. They found that template fitting was significantly more accurate for estimating periods of RR Lyrae stars, but the computational resources
@@ -96,7 +96,8 @@ better way to perform these fits. Details will be presented in a paper
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(Hoffman *et al.* 2017, *in prep*), but the important part is you can reduce
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the non-linearity of the problem to the following:
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- Finding the zeros of an order ``6H-1`` complex polynomial at each trial frequency
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- Finding the zeros of an order ``6H-1`` complex polynomial at each trial frequency.
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- This is done via the ``numpy.polynomial`` library, which performs singular-value decomposition on the polynomial "companion matrix", and scales as ``O(H^3)``.
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- Computing the coefficients of these polynomials for all trial frequencies simultaneously by leveraging the non-equispaced fast Fourier transform, a process that scales as ``O(HN_f log(HN_f))``.
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@@ -122,7 +123,7 @@ This provides two advantages:
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How is this different than the multi-harmonic periodogram?
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----------------------------------------------------------
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The multi-harmonic periodogram ([Bretthorst1988]_,[SchwarzenbergCzerny1996]_) is another
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The multi-harmonic periodogram ([Bretthorst1988]_, [SchwarzenbergCzerny1996]_) is another
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extension of Lomb-Scargle that fits a truncated Fourier series to the data
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at each trial frequency. This algorithm can also be made to scale as
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``HN_f logHN_f`` [Palmer2009]_.
@@ -133,7 +134,7 @@ In a multi-harmonic periodogram, the relative amplitudes and phases of the Fouri
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The multiharmonic periodogram is more flexible than the template periodogram, but less
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sensitive to a given signal. If you're hoping to find a non-sinusoidal signal with an
136-
unknown shape, it might make more sense to use a multi-harmonic periodogram.]
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unknown shape, it might make more sense to use a multi-harmonic periodogram.
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For more discussion of the multiharmonic periodogram and related extensions, see [VanderPlas_etal_2015]_ and [VanderPlas2017]_.
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@@ -148,7 +149,7 @@ References
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----------
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.. [ZechmeisterKurster2009] `Paper <http://adsabs.harvard.edu/abs/2009A%26A...496..577Z>`_
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.. [ZechmeisterKurster2009] `The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms <http://adsabs.harvard.edu/abs/2009A%26A...496..577Z>`_
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.. [Lomb1976] `Least-squares frequency analysis of unequally spaced data <http://adsabs.harvard.edu/abs/1976Ap%26SS..39..447L>`_
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@@ -160,12 +161,12 @@ References
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.. [VanderPlas2017] `Understanding the Lomb-Scargle Periodogram <https://arxiv.org/abs/1703.09824>`_
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.. [Sesar2017] https://arxiv.org/abs/1611.08596
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.. [Sesar_etal_2017] `Machine-Learned Identification of RR Lyrae Stars from Sparse, Multi-band Data: the PS1 Sample <https://arxiv.org/abs/1611.08596>`_
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.. [Bretthorst1988] https://link.springer.com/book/10.1007%2F978-1-4684-9399-3
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.. [Bretthorst1988] `Bayesian Spectrum Analysis and Parameter Estimation <https://link.springer.com/book/10.1007%2F978-1-4684-9399-3>`_
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.. [SchwarzenbergCzerny1996] http://iopscience.iop.org/article/10.1086/309985/meta
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.. [SchwarzenbergCzerny1996] `Fast and Statistically Optimal Period Search in Uneven Sampled Observations <http://iopscience.iop.org/article/10.1086/309985/meta>`_
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.. [Palmer2009] http://iopscience.iop.org/article/10.1088/0004-637X/695/1/496/meta
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.. [Palmer2009] `A FAST CHI-SQUARED TECHNIQUE FOR PERIOD SEARCH OF IRREGULARLY SAMPLED DATA <http://iopscience.iop.org/article/10.1088/0004-637X/695/1/496/meta>`_
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.. [VanderPlas_etal_2015] http://adsabs.harvard.edu/abs/2015ApJ...812...18V
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.. [VanderPlas_etal_2015] `Periodograms for Multiband Astronomical Time Series <http://adsabs.harvard.edu/abs/2015ApJ...812...18V>`_

‎README.rst.in‎

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Original file line numberDiff line numberDiff line change
@@ -8,8 +8,8 @@ Fast Template Periodogram
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:target: https://codecov.io/gh/PrincetonUniversity/FastTemplatePeriodogram
99

1010
:Authors:
11-
John Hoffman (mailto:[email protected])
12-
Jake Vanderplas (mailto:[email protected])
11+
|John Hoffman ([email protected])
12+
|Jake Vanderplas ([email protected])
1313

1414
:Version:
1515
${VERSION}
@@ -81,7 +81,7 @@ uses non-linear least-squares fitting to compute the optimal parameters
8181
process scales as ``N_obs*N_f``, where ``N`` is the number of observations and
8282
``N_f`` is the number of frequencies at which to calculate the periodogram.
8383

84-
This is more or less the procedure used in [Sesar2017]_ to perform
84+
This is more or less the procedure used in [Sesar_etal_2017]_ to perform
8585
template fits to Pan-STARRS photometry, however they used a more sophisticated
8686
multiband model that locked the phases, amplitudes and
8787
offsets of all bands together. They found that template fitting was significantly more accurate for estimating periods of RR Lyrae stars, but the computational resources
@@ -96,7 +96,8 @@ better way to perform these fits. Details will be presented in a paper
9696
(Hoffman *et al.* 2017, *in prep*), but the important part is you can reduce
9797
the non-linearity of the problem to the following:
9898

99-
- Finding the zeros of an order ``6H-1`` complex polynomial at each trial frequency
99+
100+
- Finding the zeros of an order ``6H-1`` complex polynomial at each trial frequency.
100101
- This is done via the ``numpy.polynomial`` library, which performs singular-value decomposition on the polynomial "companion matrix", and scales as ``O(H^3)``.
101102
- Computing the coefficients of these polynomials for all trial frequencies simultaneously by leveraging the non-equispaced fast Fourier transform, a process that scales as ``O(HN_f log(HN_f))``.
102103

@@ -122,7 +123,7 @@ This provides two advantages:
122123
How is this different than the multi-harmonic periodogram?
123124
----------------------------------------------------------
124125

125-
The multi-harmonic periodogram ([Bretthorst1988]_,[SchwarzenbergCzerny1996]_) is another
126+
The multi-harmonic periodogram ([Bretthorst1988]_, [SchwarzenbergCzerny1996]_) is another
126127
extension of Lomb-Scargle that fits a truncated Fourier series to the data
127128
at each trial frequency. This algorithm can also be made to scale as
128129
``HN_f logHN_f`` [Palmer2009]_.
@@ -133,7 +134,7 @@ In a multi-harmonic periodogram, the relative amplitudes and phases of the Fouri
133134

134135
The multiharmonic periodogram is more flexible than the template periodogram, but less
135136
sensitive to a given signal. If you're hoping to find a non-sinusoidal signal with an
136-
unknown shape, it might make more sense to use a multi-harmonic periodogram.]
137+
unknown shape, it might make more sense to use a multi-harmonic periodogram.
137138

138139
For more discussion of the multiharmonic periodogram and related extensions, see [VanderPlas_etal_2015]_ and [VanderPlas2017]_.
139140

@@ -148,7 +149,7 @@ References
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----------
149150

150151

151-
.. [ZechmeisterKurster2009] `Paper <http://adsabs.harvard.edu/abs/2009A%26A...496..577Z>`_
152+
.. [ZechmeisterKurster2009] `The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms <http://adsabs.harvard.edu/abs/2009A%26A...496..577Z>`_
152153

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.. [Lomb1976] `Least-squares frequency analysis of unequally spaced data <http://adsabs.harvard.edu/abs/1976Ap%26SS..39..447L>`_
154155

@@ -160,12 +161,12 @@ References
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.. [VanderPlas2017] `Understanding the Lomb-Scargle Periodogram <https://arxiv.org/abs/1703.09824>`_
162163

163-
.. [Sesar2017] https://arxiv.org/abs/1611.08596
164+
.. [Sesar_etal_2017] `Machine-Learned Identification of RR Lyrae Stars from Sparse, Multi-band Data: the PS1 Sample <https://arxiv.org/abs/1611.08596>`_
164165

165-
.. [Bretthorst1988] https://link.springer.com/book/10.1007%2F978-1-4684-9399-3
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.. [Bretthorst1988] `Bayesian Spectrum Analysis and Parameter Estimation <https://link.springer.com/book/10.1007%2F978-1-4684-9399-3>`_
166167

167-
.. [SchwarzenbergCzerny1996] http://iopscience.iop.org/article/10.1086/309985/meta
168+
.. [SchwarzenbergCzerny1996] `Fast and Statistically Optimal Period Search in Uneven Sampled Observations <http://iopscience.iop.org/article/10.1086/309985/meta>`_
168169

169-
.. [Palmer2009] http://iopscience.iop.org/article/10.1088/0004-637X/695/1/496/meta
170+
.. [Palmer2009] `A FAST CHI-SQUARED TECHNIQUE FOR PERIOD SEARCH OF IRREGULARLY SAMPLED DATA <http://iopscience.iop.org/article/10.1088/0004-637X/695/1/496/meta>`_
170171

171-
.. [VanderPlas_etal_2015] http://adsabs.harvard.edu/abs/2015ApJ...812...18V
172+
.. [VanderPlas_etal_2015] `Periodograms for Multiband Astronomical Time Series <http://adsabs.harvard.edu/abs/2015ApJ...812...18V>`_

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