[fitswcs] I've got this FITS WCS matrix

[Mark Calabretta]

On Tue 2004/08/17 16:55:54 +0100, "Malcolm J. Currie" wrote
in a message to: fitswcs at aoc.nrao.edu

>CD1_1   = 6.02715759044019E-06 / partial of first axis coord w.r.t. x
>CD1_2   = 1.27956486107373E-08 / partial of first axis coord w.r.t. y
>CD2_1   = -1.6056794631393E-08 / partial of second axis coord w.r.t. x
>CD2_2   = -5.96793770760736E-06 / partial of second axis coord w.r.t. y
   :
>the source after dithering.  Using Equation 191 from WCS Paper II, I
>find that rho_a is 179.84 degrees and rho_b is 0.12 degrees to two
>decimal places.  What should one do in such cases?

Malcolm,

The conclusion for this CDi_j matrix is that it cannot be decomposed
into CDELTi and CROTAi cards in the AIPS convention.  This is apparent
just by looking at the signs of the CDi_j matrix elements.

Suppose that a CDi_j matrix is the product of a diagonal (scaling)
matrix times a rotation matrix.

Either the signs of the elements on the top row of the rotation matrix
should differ xor those on the bottom row should differ (not both).
Multiplying on the left by a diagonal scaling matrix will either change
both signs on a row, or leave both alone.  Hence the signs should differ
either on the top xor the bottom row.

The same conclusion can be drawn for the product of a rotation matrix
times a scale matrix.

Cheers, Mark