### SLA_DCMPF

Interpret Linear Fit

ACTION:
Decompose an $\left[\phantom{\rule{0.3em}{0ex}}x,y\phantom{\rule{0.3em}{0ex}}\right]$ 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 $\left[\phantom{\rule{0.3em}{0ex}}x,y\phantom{\rule{0.3em}{0ex}}\right]$ coordinates as follows. Naming the six elements of COEFFS $a,b,c,d,e$ & $f$, the model transforms coordinates $\left[{x}_{1},{y}_{1}\phantom{\rule{0.3em}{0ex}}\right]$ into coordinates $\left[{x}_{2},{y}_{2}\phantom{\rule{0.3em}{0ex}}\right]$ as follows:

${x}_{2}=a+b{x}_{1}+c{y}_{1}$
${y}_{2}=d+e{x}_{1}+f{y}_{1}$

The sla_DCMPF routine decomposes this transformation into four steps:
(a)
Zero points:

${x}^{\prime }={x}_{1}+XZ$
${y}^{\prime }={y}_{1}+YZ$

(b)
Scales:

${x}^{″}={x}^{\prime }XS$
${y}^{″}={y}^{\prime }YS$

(c)
Nonperpendicularity:

${x}^{‴}=+{x}^{″}cosPERP/2+{y}^{″}sinPERP/2$
${y}^{‴}=+{x}^{″}sinPERP/2+{y}^{″}cosPERP/2$

(d)
Orientation:

${x}_{2}=+{x}^{‴}cosORIENT+{y}^{‴}sinORIENT$
${y}_{2}=-{x}^{‴}sinORIENT+{y}^{‴}cosORIENT$

(2)