ainv.f90

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SUBROUTINE ainv(ajac,ajacin,det,ndim)

  IMPLICIT NONE

!!****f* Rocfrac/Rocfrac/Source/ainv.f90
!!
!!  NAME
!!    ainv
!!
!!  FUNCTION
!!    Computes the det and inverse of a (3x3) matrix
!!
!!  USED BY
!!    shcalc, shcalc_3d10
!!
!!  INPUTS
!!    ndim -- size of input array (must be 3)
!!    ajac -- Input array (ndim x ndim)
!!
!!  OUTPUT
!!    ajacin -- inverse of ajac
!!    det -- determinate of ajac
!!
!!***

  INTEGER :: ndim
  REAL*8, DIMENSION(ndim,ndim) :: ajac, ajacin
  REAL*8 :: det, asmall

  asmall = 1.d-15

  det = ajac(1,1)*( ajac(2,2)*ajac(3,3) - ajac(2,3)* &
       ajac(3,2) ) &
       - ajac(1,2)*( ajac(2,1)*ajac(3,3) - ajac(2,3)* &
       ajac(3,1) ) &
       + ajac(1,3)*( ajac(2,1)*ajac(3,2) - ajac(2,2)* &
       ajac(3,1) )
      
  IF(dabs(det).LT.asmall) THEN
     print*, 'cannot invert matrix in ainv'
     print*,'ABS(det) =', dabs(det)
     stop
  END IF


  det = 1.d0/det

!     construct inverse

  ajacin(1,1) = det*( ajac(2,2)*ajac(3,3) &
       - ajac(2,3)*ajac(3,2) )
  ajacin(1,2) = -det*( ajac(1,2)*ajac(3,3) &
       - ajac(1,3)*ajac(3,2) )
  ajacin(1,3) = det*( ajac(1,2)*ajac(2,3) &
       - ajac(1,3)*ajac(2,2) )
  ajacin(2,1) = -det*( ajac(2,1)*ajac(3,3) &
       - ajac(2,3)*ajac(3,1) )
  ajacin(2,2) = det*( ajac(1,1)*ajac(3,3) &
       - ajac(1,3)*ajac(3,1) )
  ajacin(2,3) = -det*( ajac(1,1)*ajac(2,3) &
       - ajac(1,3)*ajac(2,1) )
  ajacin(3,1) = det*( ajac(2,1)*ajac(3,2) &
       - ajac(2,2)*ajac(3,1) )
  ajacin(3,2) = -det*( ajac(1,1)*ajac(3,2) &
       - ajac(1,2)*ajac(3,1) )
  ajacin(3,3) = det*( ajac(1,1)*ajac(2,2) &
       - ajac(1,2)*ajac(2,1) )
  
  det = 1.d0/det
  
  RETURN
END SUBROUTINE ainv