Mastigostyla is a genus in the Iridaceae family with about 20 species native to the Andes in South America from Ecuador to Argentina. It is similar to Cypella, but has narrow suberect claws and inner tepals that are much smaller than the outer. Filaments are united in a slender column. It is in the Tigridieae tribe. Goldblatt & Manning have decided to lump Cardenanthus in with this genus in their new book The Iris Family (2008).
Mastigostyla chuquisacensis Huaylla & Wilkin in known from two locations in Bolivia where it is found growing in in sandy hollows between rocks, in prepuna (high-altitude, semi-desert with summer rain) vegetation amidst grass. Information from Kew with a photo of this species here.
Mastigostyla cyrtophylla is the type species for this genus. It is native to the desert of northern Chile, where it gets very infrequent, erratic rainfall. You can see a photographs of the flower courtesy of Jardín Botánico Nacional, Viña del Mar, Chile.