newton_complex_step_rel_T0 Subroutine

   impure subroutine newton_complex_step_rel_T0(this, F, x0,  x_sol)
      interface
         impure function Fun3(x) result(res)
            import rk
            complex(rk), intent(in) :: x
            complex(rk)             :: res
         end function Fun3
      end interface

      procedure(Fun3) :: F

      class(nlsolver), intent(inout) :: this
      complex(rk),     intent(in)    :: x0
      complex(rk),     intent(out)   :: x_sol

      if (this%verbosity == 1) then
         print '(a)', '-----------------------------------------------'
         print '(a)', 'maxit             x0                   tol'
         print '(g0, 10x, f12.8, 10x, e12.4)', this%maxit, real(x0, kind=rk), this%TolFun
         print '(a)', '-----------------------------------------------'
         print '(a)', 'start newton'
         print '(a)', '-----------------------------------------------'
         print '(a)', 'it        xn           F(xn)        dF(xn)/dxn'
      end if

      select case (this%nl_method)
       case ('newton-quasi-cs')
         call quasi_cs_newton_method_T0(this, F, x0,  x_sol)
       case ('newton-quasi-cs-modified')
         call modified_quasi_cs_newton_method_T0(this, F, x0,  x_sol)
      end select

      if (this%verbosity == 1) then
         print '(a)', '-----------------------------------------------'
         print '(a)', 'end newton'
         print '(a)', '-----------------------------------------------'
         print '(a, g0)', 'x_sol = ', x_sol
      end if

   end subroutine newton_complex_step_rel_T0