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Commelinaceae family

Gibasis geniculata
(Jacquin) Rohweder
, Abh. Auslandsk., Reihe C, Naturwiss. 18: 143.  1956.
Bas.: Tradescantia geniculata Jacquin (1763).

Indigenous quite common herb of rocky deciduous and semi-evergreen seasonal forest.
St. Martin, Antigua, Guadeloupe, Dominica, Martinique, St. Lucia, St. Vincent, the Grenadines, Grenada, Barbados, Greater Antilles (Hispaniola and Puerto Rico), Trinidad, Mesoamerica, South America.
Leaves very variable in colour, green to purple and in shape. However the inflorescence of small white flowers seems quite consistent. So I assume this is a single species, including the large-leafed form seen around the Pitons. 
Also a cultivated ornamental

    

Large-leafed form