#393 Epoch of maximum/minimum estimation for Fourier models

[Doug Welch]

When an ephemeris is being sought, it is desirable to have a time of maximum and/or minimum brightness determined. At present the "epoch" used in a phase plot appears to be based on the mid-time of the set of observations. Certainly, the epoch reported in an ephemeris is usually the maximum or minimum closest to the mid-time of the observation set. If a Fourier model is produced, it should be possible to find the epoch of minimum or maximum from that and report it as the epoch.

[David Benn]

[David Benn]

Hi Doug

Thanks for your Fortran code. I've attached it to this ticket.

The following ticket is related to your request:

"Find minima/maxima of a model"
https://sourceforge.net/p/vstar/bugs-and-features/304/

I'm using the Apache Commons Math library for various things, including model function representation purposes, e.g. in Model dialog entries and for plotting a continuous line (in the works). Generalised time of minimum/maximum is possible via this. So, that was the approach I was planning to take. This would apply to any model, whether Fourier, polynomial fit, Loess fit etc. How does that seem to you?

David

[Doug Welch]

Hi David,

I agree that the request is basically the same. One difference with
eclipsing binaries is that you may only want to fit the region around
the minimum itself rather than the whole lightcurve.

But, yes - anytime you can analyically fit the whole lightcurve, then
you can also analytically find the maxima and minima.

One point I want to emphasize is to report not only the phase of the
extrema but also the JD nearest the mid-time of the whole set of
observations to which they correspond.

Thanks for looking into this!

Cheers,
Doug

On 12/01/2013 03:55 AM, David Benn wrote:

Hi Doug

Thanks for your Fortran code. I've attached it to this ticket.

The following ticket is related to your request:

"Find minima/maxima of a model"
https://sourceforge.net/p/vstar/bugs-and-features/304/

I'm using the Apache Commons Math library for various things, including model function representation purposes, e.g. in Model dialog entries and for plotting a continuous line (in the works). Generalised time of minimum/maximum is possible via this. So, that was the approach I was planning to take. This would apply to any model, whether Fourier, polynomial fit, Loess fit etc. How does that seem to you?

David

---

[bugs-and-features:#393] Epoch of maximum/minimum estimation

Status: open
Created: Thu Nov 28, 2013 07:23 PM UTC by Doug Welch
Last Updated: Sun Dec 01, 2013 08:47 AM UTC
Owner: nobody

When an ephemeris is being sought, it is desirable to have a time of maximum and/or minimum brightness determined. At present the "epoch" used in a phase plot appears to be based on the mid-time of the set of observations. Certainly, the epoch reported in an ephemeris is usually the maximum or minimum closest to the mid-time of the observation set. If a Fourier model is produced, it should be possible to find the epoch of minimum or maximum from that and report it as the epoch.

---

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[Doug Welch]

Hi David,

Here is a .csv data file and a lightcurve showing an "eye-balled" epoch
of maximum brightness which is likely off the true maximum by more than
0.015 days.

Cheers,
Doug

On 12/02/2013 11:40 AM, Doug Welch wrote:

Hi David,

I agree that the request is basically the same. One difference with
eclipsing binaries is that you may only want to fit the region around
the minimum itself rather than the whole lightcurve.

But, yes - anytime you can analyically fit the whole lightcurve, then
you can also analytically find the maxima and minima.

One point I want to emphasize is to report not only the phase of the
extrema but also the JD nearest the mid-time of the whole set of
observations to which they correspond.

Thanks for looking into this!

Cheers,
Doug

On 12/01/2013 03:55 AM, David Benn wrote:

Hi Doug

Thanks for your Fortran code. I've attached it to this ticket.

The following ticket is related to your request:

"Find minima/maxima of a model"
https://sourceforge.net/p/vstar/bugs-and-features/304/

I'm using the Apache Commons Math library for various things, including model function representation purposes, e.g. in Model dialog entries and for plotting a continuous line (in the works). Generalised time of minimum/maximum is possible via this. So, that was the approach I was planning to take. This would apply to any model, whether Fourier, polynomial fit, Loess fit etc. How does that seem to you?

David

---

[bugs-and-features:#393] Epoch of maximum/minimum estimation

Status: open
Created: Thu Nov 28, 2013 07:23 PM UTC by Doug Welch
Last Updated: Sun Dec 01, 2013 08:47 AM UTC
Owner: nobody

When an ephemeris is being sought, it is desirable to have a time of maximum and/or minimum brightness determined. At present the "epoch" used in a phase plot appears to be based on the mid-time of the set of observations. Certainly, the epoch reported in an ephemeris is usually the maximum or minimum closest to the mid-time of the observation set. If a Fourier model is produced, it should be possible to find the epoch of minimum or maximum from that and report it as the epoch.

---

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---

[bugs-and-features:#393] Epoch of maximum/minimum estimation

Status: open
Created: Thu Nov 28, 2013 07:23 PM UTC by Doug Welch
Last Updated: Sun Dec 01, 2013 08:55 AM UTC
Owner: nobody

When an ephemeris is being sought, it is desirable to have a time of maximum and/or minimum brightness determined. At present the "epoch" used in a phase plot appears to be based on the mid-time of the set of observations. Certainly, the epoch reported in an ephemeris is usually the maximum or minimum closest to the mid-time of the observation set. If a Fourier model is produced, it should be possible to find the epoch of minimum or maximum from that and report it as the epoch.

---

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[Doug Welch]

Here are the XXVir files alluded to in an earlier message!

[Doug Welch]

Grant Foster has graciously agreed to allow me to share the epoch-finding scripts that he has written in R. I'm attaching three files:

Rprogs.r - which contains many/most of the time-series routines he developed so far including those that implement CLEANest
smex.r - which does smoothing
epoch.r - which finds the epoch of minimum or maximum, its unceratinty, and an estimate of the extreme magnitude and its uncertainty

In R, the following (adjusted for your own working directory) will read in the file XXVir_sg.csv and output the desired extremum values - as well as displaying some graphs.

source("/1/home/welch/VPHOT/Rprogs.r")
source("/1/home/welch/VPHOT/smex.r")
source("/1/home/welch/VPHOT/epoch.r")

setwd("/1/home/welch/VPHOT/")

options(digits=10)

varphot = read.csv("XXVir_sg.csv",header=F)
t = varphot[,1]-2400000.0
x = varphot[,2]
unc = varphot[,3]
period = 1.348207

w = epoch(t,x,period)

produces:

    epoch       se.epoch   lo.epoch    hi.epoch         mag         se.mag

1 56075.19857 0.007084085997 56075.1836 56075.21193 11.57954736 0.006281620226

[David Benn]

Thanks Doug (and Grant)! This will at the very least be useful for validation and any VStar implementation. Having the source code is always a bonus.

[David Benn]

Increasing the priority of this ticket. I want to get extrema finding working (the current approach doesn't work well; see https://sourceforge.net/p/vstar/bugs-and-features/304/).