[QUANTITY] Justification for Matrix Quantities (Was: Re: [QUANTITY] Requirements and apology)

[Ed Shaya]

David Berry wrote:

>Brian,
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>
>For instance, for a Quantity holding a 1D array of flux values
>representing a simple spectrum, the [WCS] component would contain a Frame
>representing pixel coordinates, another Frame representing some spectral
>coordinate systems such as frequency (this would contain extra info like
>standard of rest, units, etc), and a Mapping joining these two Frames
>together (this Mapping could for instance implement one of the algorithms
>described in FITS-WCS paper III). Note, Frames and Mappings are *not*
>Quantities in any sense, they just represent part of the *description* of
>a Quantity.
>  
>
Dave,

You are discussing a flux quantity that is dependent on frequency (I 
prefer hasArgument
but they are synonomous).  Frequency is also a quantity.  It is 
something that is measured (in this
case, by measurements on a calibration lamp).  Normally one would simply 
have an array of flux and
an array of frequencies and you would say the flux (quantity array) is 
dependent on the frequency (quantity array).  You introduce with WCS a 
slightly more complex frequency object though because there is one 
additional step of indirection.  Here the frequency of light at certain 
pixels of the ccd
are noted (perhaps 1st and last).  WCS provides the algorithm for 
generating all of the other pixel
frequency pairs.  The pixel numbers are now quantities and they have a 
dependence on frequency.  So altogether now, The flux is dependent on 
pixel numbers and the pixel numbers are dependent on
frequency.  The WCS provides for a more complex type of Argument in 
which the two quantities
at the same index value may not be paired, rather the pairing of 
quantity with argument has a pairing
by algorithm.   One could expand the WCS information into a frequency 
array of the same length as
the flux array and turn it into a simple dependency, so that indicates 
it simply provides an
algorithmic shorthand for what is conceptually the same thing.

The fact that we will come up with algorithmic shorthands does not break 
the overarching principle
that quantities are functions of other quantities.  Indeed it fits right 
into this model if one has
q1=f(g(q2)) so that q1=f(q3), q3=g(q2).  Certainly frequency and 
position fit right in along with
dependencies on time, object, cz etc.

Ed

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