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Computes the maximum likelihood estimator of the generalised additive and index regression with shape constraints. Each additive component function is assumed to obey one of the nine possible shape restrictions: linear, increasing, decreasing, convex, convex increasing, convex decreasing, concave, concave increasing, or concave decreasing. For details, see Chen and Samworth (2016) doi:10.1111/rssb.12137.