Chamerion angustifolium; Rosebay Willowherb is regarded as an alien on Iceland. It can be found in rural regions and along roadsides. I have seen this species thriving also in the woods of Hallormstaðir. It is a semi-tall species growing up to 30-70 cm. As such it is taller than the Arctic Riverbeauty (Chamerion latifolium) but the flowers are smaller, however larger than the "Epilobium" species. The tall inflorescence stems are quite characteristic. I encountered this species next to Hallormstaðir also west of Keflavik along the roadside. It only starts to bloom at the end of july (into august).
It is member of the Willowherb family (Onagraceae). The Icelandic name of this species is Sigurskúfur.