newton_complex_step_rel_T1 Subroutine

   impure subroutine newton_complex_step_rel_T1(this, F, x0,  x_sol)
      interface
         impure function Fun4(x) result(res)
            import rk
            complex(rk), dimension(:), intent(in)  :: x
            complex(rk), dimension(:), allocatable :: res
         end function Fun4
      end interface

      procedure(Fun4)  :: F

      class(nlsolver),                  intent(inout) :: this
      complex(rk), dimension(:),        intent(in)    :: x0
      complex(rk), dimension(size(x0)), intent(out)   :: x_sol
      integer                                         :: i

      if (this%verbosity == 1) then
         print '(a)', '-----------------------------------------------'
         print '(a)', 'maxit             tol'
         print '(g0, 10x, f12.8, e12.4)', this%maxit, this%TolFun
         print '(a)', '-----------------------------------------------'
         print '(a)', 'start newton'
         print '(a)', '-----------------------------------------------'
         print '(a)', 'it     ||F||'
      end if

      select case (this%nl_method)
       case ('newton-quasi-cs')
         call quasi_cs_newton_method_T1(this, F, x0,  x_sol)
       case ('newton-quasi-cs-modified')
         call modified_quasi_cs_newton_method_T1(this, F, x0,  x_sol)
      end select

      if (this%verbosity == 1) then
         print '(a)', '-----------------------------------------------'
         print '(a)', 'end newton'
         print '(a)', '-----------------------------------------------'
         do i = 1,size(x_sol)
            print '(a, g0)', 'x_sol = ', real(x_sol(i), kind=rk)
         end do
         ! print '(a, g0)', 'x_sol = ', x_sol
      end if

   end subroutine newton_complex_step_rel_T1