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SUBROUTINE slDCMF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)
*+
* - - - - - -
* D C M F
* - - - - - -
*
* Decompose an [X,Y] linear fit into its constituent parameters:
* zero points, scales, nonperpendicularity and orientation.
*
* 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)
*
* Called: slDA1P
*
* The model relates two sets of [X,Y] coordinates as follows.
* Naming the elements of COEFFS:
*
* COEFFS(1) = A
* COEFFS(2) = B
* COEFFS(3) = C
* COEFFS(4) = D
* COEFFS(5) = E
* COEFFS(6) = F
*
* the model transforms coordinates [X1,Y1] into coordinates
* [X2,Y2] as follows:
*
* X2 = A + B*X1 + C*Y1
* Y2 = D + E*X1 + F*Y1
*
* The transformation can be decomposed into four steps:
*
* 1) Zero points:
*
* x' = XZ + X1
* y' = YZ + Y1
*
* 2) Scales:
*
* x'' = XS*x'
* y'' = YS*y'
*
* 3) Nonperpendicularity:
*
* x''' = cos(PERP/2)*x'' + sin(PERP/2)*y''
* y''' = sin(PERP/2)*x'' + cos(PERP/2)*y''
*
* 4) Orientation:
*
* X2 = cos(ORIENT)*x''' + sin(ORIENT)*y'''
* Y2 =-sin(ORIENT)*y''' + cos(ORIENT)*y'''
*
* See also slFTXY, slPXY, slINVF, slXYXY
*
* P.T.Wallace Starlink 19 December 2001
*
* Copyright (C) 2001 Rutherford Appleton Laboratory
*
* License:
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program (see SLA_CONDITIONS); if not, write to the
* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301 USA
*
* Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
*-
IMPLICIT NONE
DOUBLE PRECISION COEFFS(6),XZ,YZ,XS,YS,PERP,ORIENT
DOUBLE PRECISION A,B,C,D,E,F,RB2E2,RC2F2,XSC,YSC,P1,P2,P,WS,WC,
: OR,HP,SHP,CHP,SOR,COR,DET,X0,Y0,slDA1P
* Copy the six coefficients.
A = COEFFS(1)
B = COEFFS(2)
C = COEFFS(3)
D = COEFFS(4)
E = COEFFS(5)
F = COEFFS(6)
* Scales.
RB2E2 = SQRT(B*B+E*E)
RC2F2 = SQRT(C*C+F*F)
IF (B*F-C*E.GE.0D0) THEN
XSC = RB2E2
ELSE
B = -B
E = -E
XSC = -RB2E2
END IF
YSC = RC2F2
* Non-perpendicularity.
IF (C.NE.0D0.OR.F.NE.0D0) THEN
P1 = ATAN2(C,F)
ELSE
P1 = 0D0
END IF
IF (E.NE.0D0.OR.B.NE.0D0) THEN
P2 = ATAN2(E,B)
ELSE
P2 = 0D0
END IF
P = slDA1P(P1+P2)
* Orientation.
WS = C*RB2E2-E*RC2F2
WC = B*RC2F2+F*RB2E2
IF (WS.NE.0D0.OR.WC.NE.0D0) THEN
OR = ATAN2(WS,WC)
ELSE
OR = 0D0
END IF
* Zero points.
HP = P/2D0
SHP = SIN(HP)
CHP = COS(HP)
SOR = SIN(OR)
COR = COS(OR)
DET = XSC*YSC*(CHP+SHP)*(CHP-SHP)
IF (ABS(DET).GT.0D0) THEN
X0 = YSC*(A*(CHP*COR-SHP*SOR)-D*(CHP*SOR+SHP*COR))/DET
Y0 = XSC*(A*(CHP*SOR-SHP*COR)+D*(CHP*COR+SHP*SOR))/DET
ELSE
X0 = 0D0
Y0 = 0D0
END IF
* Results.
XZ = X0
YZ = Y0
XS = XSC
YS = YSC
PERP = P
ORIENT = OR
END
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