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 transformation coefficients (see note)

RETURNED:

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.