Creating a set of river plots for the paper

[ericagol]

• Write a routine for computing river plots for the flux, as well as for the various derivatives.
• Create some plots for the paper showing various examples of river plots.

[ericagol]

@langfzac If I want to compute an array (jac_tot?) with the derivatives of the flux with respect to each of the initial orbital elements (including mass-ratios), transit depths (radius-ratios squared), limb-darkening params & stellar density (or radius), what is the procedure for doing this?

I think I can call compute_photodynamics(\theta), but what is the syntax for calling it? Would it be:

flux, jac_tot = compute_photodynamics(\theta)

[langfzac]

Do you mean in general? Or in the inference.jl file?

[langfzac]

In general, the flux derivatives are contained in the Lightcurve after running the necessary code to compute them. Run the example in README with grad=true, and add the number of nbody parameters (7*n) as an argument to the Lightcurve constructor. The rest is the same.

The fields are defined as below:

Photodynamics.jl/src/Lightcurve.jl

Lines 3 to 18 in a7be91d

	struct Lightcurve{T<:Real}
	dt::T # Exposure time
	tobs::Vector{T} # Observed times
	fobs::Vector{T} # Observed flux
	eobs::Vector{T} # Measurement errors
	nobs::Int64 # number of flux measurements
	flux::Vector{T} # Computed model flux
	dfdu::Matrix{T} # Derivative of flux wrt limbdark coefficients
	dfdk::Matrix{T} # Derivatives wrt the radius ratios
	dfdq0::Matrix{T} # Derivatives wrt initial Nbody Cartesian coordinates and masses
	dfdr::Vector{T} # Derivatives wrt stellar radius
	# Transit parameters
	u_n::Vector{T} # Limbdark coefficients
	k::Vector{T} # radius ratios
	rstar::Vector{T} # Stellar radius

[ericagol]

Do you mean in general? Or in the inference.jl file?

I meant in inference.jl, but the general case is fine too.

[ericagol]

In general, the flux derivatives are contained in the Lightcurve after running the necessary code to compute them. Run the example in README with grad=true, and add the number of nbody parameters (7*n) as an argument to the Lightcurve constructor. The rest is the same.

The fields are defined as below:

Photodynamics.jl/src/Lightcurve.jl

Lines 3 to 18 in a7be91d

	struct Lightcurve{T<:Real}
	dt::T # Exposure time
	tobs::Vector{T} # Observed times
	fobs::Vector{T} # Observed flux
	eobs::Vector{T} # Measurement errors
	nobs::Int64 # number of flux measurements
	flux::Vector{T} # Computed model flux
	dfdu::Matrix{T} # Derivative of flux wrt limbdark coefficients
	dfdk::Matrix{T} # Derivatives wrt the radius ratios
	dfdq0::Matrix{T} # Derivatives wrt initial Nbody Cartesian coordinates and masses
	dfdr::Vector{T} # Derivatives wrt stellar radius
	# Transit parameters
	u_n::Vector{T} # Limbdark coefficients
	k::Vector{T} # radius ratios
	rstar::Vector{T} # Stellar radius

It looks like this contains the initial cartesian coordinate derivatives, not the initial orbital element derivatives.

[langfzac]

It looks like this contains the cartesian coordinate derivatives, not the initial orbital elements.

Yes, I haven't included those. Right now, you'd have to do the transformations manually. (There's an example in inference.jl -- see grad_compute_photometry)

[ericagol]

Okay, that gets back to my question about what gets returned by that routine.

[langfzac]

Oh right, it returns the flux and jacobian array. Although, that function in inference.jl is optimized for that particular problem/system. There's no generalized function that computes the flux (and/or jacobian) for an arbitrary parameter vector.

[ericagol]

@langfzac I still haven't been able to figure this out, so I could use some help with this.

[ericagol]

@langfzac Thanks to your help, I now have some riverplots of derivatives working. Here is the plot with respect to the radius of the star. The blue is negative, which I think is indicating that the radius of the star increases, then the duration increases, so in ingress & egress the flux becomes smaller (i.e. the transit widens). It's hard to see, but the flux is also negative in the middle of the transits, but goes to zero mid-transit. This confused me at first, but I think this is due to the fact that the radius-ratio is being held constant, so the depth of transit is the same, but the stretching of the transit due to a longer duration means that the transit needs to get slightly deeper.

[ericagol]

I'm confused about some of the derivatives with respect to the dynamical parameters, which aren't behaving as I would have expected.... but, the model is complicated...