c
c  &&&&&&&&&&&&&&
c
c  these subroutines copied from map5d
c ____________________________
c
c
	subroutine m2r(e,rodr,axis)
	real e(3,3),rodr(4),tmp(3),rnorm
	real det,detm,pi,axis(3)
c
c  converts a MISOR matrix to Rodrigues vector
c
      pi=4.*atan(1.)
c  calc. determinant
c
c	det=e(1,1)*e(2,2)*e(3,3)
c     &	+e(2,1)*e(3,2)*e(1,3)
c     &	+e(3,1)*e(1,2)*e(2,3)
c     &	-e(1,1)*e(3,2)*e(2,3)
c     &	-e(1,2)*e(2,1)*e(3,3)
c     &	-e(1,3)*e(2,2)*e(3,1)
c	if(det.lt.-0.95) det=-1.0
c	if(det.gt.0.95) det=1.0
c	detm=det
c
c  we are only interested in proper vs. improper rotations here
c
c	write(*,*) 'rotation matrixes:  ',(e(ii,1),ii=1,3)
c	write(*,*) 'rotation matrixes:  ',(e(ii,2),ii=1,3)
c	write(*,*) 'rotation matrixes:  ',(e(ii,3),ii=1,3)
c	write(*,*) 'index,  determinant= ',i,det
c	rtmp=(((e(1,1)+e(2,2)+e(3,3))/det)-1.)/2.
	rtmp=(((e(1,1)+e(2,2)+e(3,3)))-1.)/2.
	if(rtmp.lt.-1.) rtmp=-1.
	if(rtmp.gt.1.) rtmp=1.
	rodr(4)=acos(rtmp)
c  magnitude of rotation
c	tmp(1)=(e(2,3)-e(3,2))/det
c	tmp(2)=(e(1,3)-e(3,1))/det
c	tmp(3)=(e(1,2)-e(2,1))/det
	axis(1)=(e(2,3)-e(3,2))
	axis(2)=(e(1,3)-e(3,1))
	axis(3)=(e(1,2)-e(2,1))
c	rnorm=sqrt(tmp(1)**2+tmp(2)**2+tmp(3)**2)
	rnorm=sqrt(axis(1)**2+axis(2)**2+axis(3)**2)
	if(rnorm.lt.1e-5) then
c		tmp(1)=sqrt(1.+e(1,1))
c		tmp(2)=sqrt(1.+e(2,2))
c		tmp(3)=sqrt(1.+e(3,3))
		axis(1)=sqrt(1.+e(1,1))
		axis(2)=sqrt(1.+e(2,2))
		axis(3)=sqrt(1.+e(3,3))
c		rnorm=sqrt(tmp(1)**2+tmp(2)**2+tmp(3)**2)
		rnorm=sqrt(axis(1)**2+axis(2)**2+axis(3)**2)
	endif
c	write(*,*) rnorm, tmp(1),tmp(2),tmp(3),tan(rodr(4)/2)
c	rodr(1)=tmp(1)/rnorm*tan(rodr(4)/2.)
c	rodr(2)=tmp(2)/rnorm*tan(rodr(4)/2.)
c	rodr(3)=tmp(3)/rnorm*tan(rodr(4)/2.)
	rodr(1)=axis(1)/rnorm*tan(rodr(4)/2.)
	rodr(2)=axis(2)/rnorm*tan(rodr(4)/2.)
	rodr(3)=axis(3)/rnorm*tan(rodr(4)/2.)
c  components of the Rodrigues vector
c	write(*,190)  rodr(4)*180./pi
c     &	,rodr(1),rodr(2),rodr(3)
190	format(' angle, vector....',4f9.3)
c
100	continue
	return
	end
c
c
c  ____________________________
c