module cartesian {       # index transform (vector to matrix) and its inverse
contains
  subroutine line2cart( nn, i, ii) { 
    integer, dimension( :), intent( in) :: nn    # cartesian axes (n1,n2,n3,...)
    integer, dimension( :), intent(out) :: ii    # cartesn coords (i1,i2,i3,...)
    integer               , intent( in) :: i     # equivalent 1-D linear index
    integer                             :: axis, n123
    n123 = 1
    do axis = 1, size(  nn) { 
	ii( axis) = mod( ( i-1)/n123, nn( axis)) + 1
	n123 = n123 * nn( axis)
        }
    }
  subroutine cart2line( nn, ii, i) { 
    integer, dimension( :), intent( in) :: nn, ii
    integer                             :: i, axis, n123
    n123 = 1;    i = 1
    do axis = 1, size(  nn) { 
	i = i + ( ii( axis)-1)*n123
	n123 = n123 * nn( axis)
	}
    }
}