``` NAME:
inst2std
PURPOSE: (one line)
Apply photometric transformation from instrumental to standard mags.
DESCRIPTION:
The formula for applying transformation to a photometric measurement
follows the basic formalism (including signs) from Hardie.  A time
dependent term has been added.  The formula looks like this:

m0 = m - kX - n(t-t0)X - k"CX + eC + Z

where
m  = instrumental magnitude
k  = extinction coefficient, mag/airmass
X  = airmass
n  = coefficient of the 1st order expansion of extinction as a
function of time
t  = Time of observation (in hours)
t0 = Reference time for n, time dependent correction is zero at
this time, usually is the middle of the observation set.
k" = second order extinction coefficient
C  = Standard system color of the object
e  = color term
Z  = zero point
m0 = Standard magnitude

This routine also supports two extra terms that fill out the second
order expansion.  These terms are:

+ fX^2 + gC^2

CATEGORY:
Photometry
CALLING SEQUENCE:
inst2std,jd,am,inst,instsig,color,colorsig, \$
tran,transig,jdref,std,stdsig
INPUTS:
jd       - Julian date of observation for each entry.
am       - Floating point array of the airmass of observations.
inst     - Instrumental magnitude
instsig  - Uncertainty of the instrumental magnitude
color    - Standard system color for object.
colorsig - Uncertainty on the standard color
tran     - Transformation coefficients (vector)
tran[0] = (k)  principal extinction coefficient
tran[1] = (k") second order extinction coefficient
tran[2] = (e)  color term
tran[3] = (Z)  zero-point
tran[4] = (n)  time-dependent extinction term
if provided:
tran[5] = (f)  airmass squared term
tran[6] = (g)  color squared term
transig  - Uncertainty on the transformation coefficients (vector).
(no uncertainty on reference time)
tran and transig can either be 5-element vectors or 5xN element arrays.
or either be 7-element vectors or 7xN element arrays.
These two arrays must match in rank and size
jdref    - Time reference point for extinction
must match the number of transformation sets provided
OPTIONAL INPUT PARAMETERS:
KEYWORD INPUT PARAMETERS:
REFAM - Optional air mass reference for the transformation.  The default
is an airmass=0.  The rules for this input are the same as
REFCOLOR.  Either scalar or length N from TIDX.
REFCOLOR - Optional color reference for the color term transformation.
This term is normally C * (B-V) or some other standard
color.  As written, the reference color is zero and this
is the default.  By providing this value you are using
C * ( (B-V) - REFCOLOR ) for the term instead.
This can either be a scalar or a vector.  If a vector it
must match the length N in TIDX.  Vector input is not
allowed if you are not using an array of coefficients.
TIDX     - Indexing array, same length as the input observations.  This
keyword is ignored if the input transformation vectors is
a simple 5-element vector.  If the transformation is provided
as a 5xN array then this keyword is REQUIRED.
Each element gives the index into the set of transformation
values.  This allows combining data that have different
photometric transformation coefficients.
KEYWORD OUTPUT PARAMETERS:
OUTPUTS:
std      - Standard magnitude.
stdsig   - Uncertainty of the standard magnitude.
COMMON BLOCKS:
SIDE EFFECTS:
RESTRICTIONS:
PROCEDURE:
MODIFICATION HISTORY:
Written: Marc W. Buie, Lowell Observatory, 1992/03/31.
1997/02/10, MWB, total rewrite
2013/06/02, MWB, allow option for data to be covered by different
transformation coefficients.