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[task #15128] TPV and SIP keywords when WCS distortions are necessary

From: Sachin Kumar Singh
Subject: [task #15128] TPV and SIP keywords when WCS distortions are necessary
Date: Wed, 13 May 2020 16:47:43 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:75.0) Gecko/20100101 Firefox/75.0

Follow-up Comment #1, task #15128 (project gnuastro):

I found these <> ELF 64-bit
LSB binary executable files for sip2pv and pv2sip whose link for python
program is given(the python programs are its prototypes). 

Here are some points:

* This <> file
really made it easy for me to understand the SPIE paper better. 

* I went through the python code and for the first part, I've made a raw C
implementation for `pv2sip`(after this `sip2pv` can be easily done). I'll use
`gal_fits_key_read_from_ptr` to read the keywords. In place of `sympy
expressions` I think using a 2x2 matrix according to the indices of the u-v
expression. The resulting matrix will be an upper triangular matrix so we can
default the remaining values to be null(or something). For calculating the
expression for TPV distortion, I'll just multiply the matrix with the
calculated inverse of a 2x2 CD matrix(But doesn't the paper suggests to use
only SIP and PV keys so that there should be no use of TPV keywords, so why do
we need this TPV expression anyway?).

* This
if-else condition in`calcsip` function seems wrong as it gives the same value
of `rval` either way. Please confirm. 

* Should I calculate the reverse coefficients too?

* And finally should I add options to remove `SIP` or `PV` keywords from the
final header before merging it in the fits data. I think having both keywords
produces uniformity so there shouldn't be any removal. 

What are your suggestions:-)


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