A reply to an old post, but maybe useful?

Could it be impatiens samporii? I wouldn't exactly call it a reed, but they have dark purple stalks, green leaves, and delicate flowers. They like moist, bright shade and are a true joy! The flowers look like little orchids and they will reseed themselves -- just sweep those flowers that fall off (and the little white seeds that spring out too) back into your flower bed. They will flower best with enough water -- fun to give to friends. If you have bright shade and can keep them moist, these are a great plant for a beginner, popping up in unexpected places!