SUBROUTINE sla_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)
*+
*     - - - - - -
*      D C M P 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)
*
*  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 sla_FITXY, sla_PXY, sla_INVF, sla_XY2XY
*
*  P.T.Wallace   Starlink   14 August 1994
*
*  Copyright (C) 1995 Rutherford Appleton Laboratory
*-

      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



*  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
         C=-C
         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=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 corrections
      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