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SUBROUTINE sla_INVF (FWDS,BKWDS,J)
*+
* - - - - -
* I N V F
* - - - - -
*
* Invert a linear model of the type produced by the
* sla_FITXY routine.
*
* Given:
* FWDS d(6) model coefficients
*
* Returned:
* BKWDS d(6) inverse model
* J i status: 0 = OK, -1 = no inverse
*
* The models relate two sets of [X,Y] coordinates as follows.
* Naming the elements of FWDS:
*
* FWDS(1) = A
* FWDS(2) = B
* FWDS(3) = C
* FWDS(4) = D
* FWDS(5) = E
* FWDS(6) = F
*
* where two sets of coordinates [X1,Y1] and [X2,Y1] are related
* thus:
*
* X2 = A + B*X1 + C*Y1
* Y2 = D + E*X1 + F*Y1
*
* the present routine generates a new set of coefficients:
*
* BKWDS(1) = P
* BKWDS(2) = Q
* BKWDS(3) = R
* BKWDS(4) = S
* BKWDS(5) = T
* BKWDS(6) = U
*
* such that:
*
* X1 = P + Q*X2 + R*Y2
* Y1 = S + T*X2 + U*Y2
*
* Two successive calls to sla_INVF will thus deliver a set
* of coefficients equal to the starting values.
*
* To comply with the ANSI Fortran standard, FWDS and BKWDS must
* not be the same array, even though the routine is coded to
* work on the VAX and most other computers even if this rule
* is violated.
*
* See also sla_FITXY, sla_PXY, sla_XY2XY, sla_DCMPF
*
* P.T.Wallace Starlink 11 April 1990
*
* Copyright (C) 1995 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
DOUBLE PRECISION FWDS(6),BKWDS(6)
INTEGER J
DOUBLE PRECISION A,B,C,D,E,F,DET
A=FWDS(1)
B=FWDS(2)
C=FWDS(3)
D=FWDS(4)
E=FWDS(5)
F=FWDS(6)
DET=B*F-C*E
IF (DET.NE.0D0) THEN
BKWDS(1)=(C*D-A*F)/DET
BKWDS(2)=F/DET
BKWDS(3)=-C/DET
BKWDS(4)=(A*E-B*D)/DET
BKWDS(5)=-E/DET
BKWDS(6)=B/DET
J=0
ELSE
J=-1
END IF
END
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