Implement model from xrt_dem_iterative2.pro

[namurphy]

Your mission, if you choose to accept it, is to implement the DEM model from xrt_dem_iterative2.pro from SSWIDL.

Here are excerpts from the documentation for the SSWIDL routine.

XRT_DEM_ITERATIVE2

Estimate a DEM(T) curve, given some observations B_i in channels "i", and given the temperature response functions in every channel R_i(T). These functions satisfy the equation:

B_i = integral{ DEM(T) * R_i(T) * dT }

The inversion is ill-posed and technically fraught with perils. This routine employs a forward-fitting approach: A DEM is guessed and folded through the R_i(T) to generate "model" observations. This process is iterated to reduce the chi-square between the actual and model observations. The DEM function is interpreted from some spline points, which are directly manipulated by the chi-square fitting routine (MPFIT.pro). There are N_i - 1 splines, representing the degrees of freedom for N_i observations. (Note that the number of temperature bins requested for the DEM solution are usually greater than N_i.)

To estimate errors on the DEM solution, this routine provides for Monte-Carlo iteration. On each iteration, the observations are varied normally by their sigma error, and then solved for a DEM. According to Monte Carlo theory, the distribution of DEM solutions is a measure of the error in DEM(T).

[hayesla]

Are you working on this @namurphy ?

If not I'll have a play around with it :)

[PaulJWright]

Similar code to estimate errors is used in multiple methods. I think Mark Cheung's code uses the same method as here, although I haven't double checked (https://iopscience.iop.org/article/10.1088/0004-637X/807/2/143/meta). Also, many codes will use a similar, if not identical method to recover the SDO/AIA DN values from the DEMs.

[namurphy]

@hayesla - I don't have any plans to work on this, so please feel free to go ahead!

[hayesla]

I've fallen deep in an IDL rabbit hole :P will have a proper stab at this over the weekend 👍