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)

COEFFS	D(6)	transformation coefficients (see note)

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:

$x_{2} = a + b x_{1} + c y_{1}$
$y_{2} = d + e x_{1} + f y_{1}$

The sla_DCMPF routine decomposes this transformation into four steps:

(a): Zero points:

$x^{'} = x_{1} + X Z$
$y^{'} = y_{1} + Y Z$
(b): Scales:

$x^{″} = x^{'} X S$
$y^{″} = y^{'} Y S$
(c): Nonperpendicularity:

$x^{‴} = + x^{″} cos P E R P / 2 + y^{″} sin P E R P / 2$
$y^{‴} = + x^{″} sin P E R P / 2 + y^{″} cos P E R P / 2$
(d): Orientation:

$x_{2} = + x^{‴} cos O R I E N T + y^{‴} sin O R I E N T$
$y_{2} = - x^{‴} sin O R I E N T + y^{‴} cos O R I E N T$

(2)

See also sla_FITXY, sla_PXY, sla_INVF, sla_XY2XY.