Bollywood is shorthand for Bombay Hollywood, seat of the largest Indian film industry. But it manufactures only about 200 of the thousand or so Indian feature films; a half-dozen regions boast production sites larger than most of the world’s national cinemas. Madras, capital of the Tamil state, is one such place, and its leader — arguably India’s top pop-film auteur — is Mani Ratnam. His movies, often dramatizing social unrest and political terrorism, churn with narrative tension and camera energy that would be the envy of Hollywood directors, if they were ever to see them. Nayakan, an early, defining work in his career, tells the Godfatherish tale of Velu, a boy who embraces a life of crime after his father is killed by the police. Velu (Kamal Hasan) has trouble juggling his family life with his life-and-death mob “family”; Ratnam has no such difficulty blending melodrama and music, violence and comedy, realism and delirium, into a two-and-a-half-hour demonstration that, when a gangster’s miseries are mounting, the most natural solution is to go singin’ in the rain.