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SLA_DCMPF - Interpret Linear Fit   

ACTION:
Decompose an $[\,x,y\,]$ linear fit into its constituent parameters: zero points, scales, nonperpendicularity and orientation.

CALL:
CALL sla_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)

GIVEN:

COEFFS D(6) transformation coefficients (see note)

RETURNED:

XZ D x zero point
YZ D y zero point
XS D x scale
YS D y scale
PERP D nonperpendicularity (radians)
ORIENT D orientation (radians)

NOTES:
1.
The model relates two sets of $[\,x,y\,]$ coordinates as follows. Naming the six elements of COEFFS a,b,c,d,e & f, the model transforms coordinates $[x_{1},y_{1}\,]$ into coordinates $[x_{2},y_{2}\,]$ as follows:
x2 = a + bx1 + cy1
y2 = d + ex1 + fy1
The sla_DCMPF routine decomposes this transformation into four steps:
(a)
Zero points:
$x' = x_{1} + {\rm XZ}$
$y' = y_{1} + {\rm YZ}$
(b)
Scales:
$x'' = x' {\rm XS}$
$y'' = y' {\rm YS}$
(c)
Nonperpendicularity:
$x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$
$y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$
(d)
Orientation:
$x_{2} = + x''' \cos {\rm ORIENT} +
 y''' \sin {\rm ORIENT}$
$y_{2} = - x''' \sin {\rm ORIENT} +
 y''' \cos {\rm ORIENT}$
2.
See also sla_FITXY, sla_PXY, sla_INVF, sla_XY2XY.


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SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk