jacobi.f90

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SUBROUTINE jacobi(btens,stret,princ)

!!****f* Rocfrac/Rocfrac/Source/jacobi.f90
!!
!!  NAME
!!    jacobi
!!
!!  FUNCTION
!!
!!     Evaluates the stretches and principal directions given the b matrix
!!     using the Jacobi iteration. Adapted from numerical recpies
!!
!!  INPUTS
!!
!!     btens  -->  left Cauchy-Green tensor
!!
!!  OUTPUT
!!     stret  -->  vector containing the stretches
!!     princ  -->  matrix containing the three principal column vectors
!!
!!****

  IMPLICIT DOUBLE PRECISION (a-h,o-z)
  dimension btens(3,3),stret(3),princ(3,3)
!
!
!     Initialise princ to the identity
!     
  DO i=1,3
     DO j=1,3
        princ(i,j)=0.d0
     ENDDO
     princ(i,i)=1.d0
     stret(i)=btens(i,i)
  ENDDO
!
!     Starts sweeping. 
!
      DO is=1,50
         sum=0.d0
         DO ip=1,2
            DO iq=ip+1,3
               sum=sum+abs(btens(ip,iq))
            ENDDO
         ENDDO
!
!     IF the sum of off-diagonal terms is zero evaluates the 
!     stretches and returns
!
         IF(sum.EQ.0.d0) THEN
            DO i=1,3
               stret(i)=sqrt(stret(i))
            ENDDO
            RETURN
         ENDIF
!
!     Performs the sweep in three rotations. One per off diagonal term     
!
         DO ip=1,2
            DO iq=ip+1,3
               od=100.d0*abs(btens(ip,iq))
               IF((od+abs(stret(ip)).NE.abs(stret(ip))).AND. &
                    (od+abs(stret(iq)).NE.abs(stret(iq)))) THEN
                  hd=stret(iq)-stret(ip)
!
!    Evaluates the rotation angle 
!
                  IF(abs(hd)+od.EQ.abs(hd)) THEN
                    t=btens(ip,iq)/hd
                  ELSE
                    theta=0.5d0*hd/btens(ip,iq)
                     t=1.d0/(abs(theta)+sqrt(1.d0+theta**2))
                     IF(theta.LT.0.d0) t=-t
                  ENDIF
!
!     Re-evaluates the diagonal terms
!
                  c=1.d0/sqrt(1.d0+t**2)
                  s=t*c
                  tau=s/(1.d0+c)
                  h=t*btens(ip,iq)
                  stret(ip)=stret(ip)-h
                  stret(iq)=stret(iq)+h
!
!     Re-evaluates the remaining off-diagonal terms         
!
                  ir=6-ip-iq
                  g=btens(min(ir,ip),max(ir,ip))
                  h=btens(min(ir,iq),max(ir,iq))
                  btens(min(ir,ip),max(ir,ip))=g-s*(h+g*tau)
                  btens(min(ir,iq),max(ir,iq))=h+s*(g-h*tau)
!
!     Rotates the eigenvectors
!
                  DO ir=1,3
                     g=princ(ir,ip)
                     h=princ(ir,iq)
                     princ(ir,ip)=g-s*(h+g*tau)
                     princ(ir,iq)=h+s*(g-h*tau)
                  ENDDO
               ENDIF
               btens(ip,iq)=0.d0
            ENDDO
         ENDDO
      ENDDO
!
!     IF convergence is not achieved stops
!
      WRITE(6,100)
      stop
 100  FORMAT(' Jacobi iteration unable to converge')
      END