17.9 Recursive Functions
Stan supports recursive function definitions, which can be useful for some applications. For instance, consider the matrix power operation, \(A^n\), which is defined for a square matrix \(A\) and positive integer \(n\) by \[ A^n = \begin{cases} \ \mbox{I} & \mbox{if } n = 0, \mbox{ and} \\[3pt] \ A \, A^{n-1} & \mbox{if } n > 0. \end{cases} \]
where \(\mbox{I}\) is the identity matrix. This definition can be directly translated to a recursive function definition.
matrix matrix_pow(matrix a, int n);
matrix matrix_pow(matrix a, int n) {
if (n == 0)
return diag_matrix(rep_vector(1, rows(a)));
else
return a * matrix_pow(a, n - 1);
}The forward declaration of the function signature before it is defined
is necessary so that the embedded use of matrix_pow is
well-defined when it is encountered. It would be more efficient to
not allow the recursion to go all the way to the base case, adding the
following conditional clause.
else if (n == 1)
return a;