  We introduce an original method of multidimensional ridge penalization in
functional local linear regressions. The nonparametric regression of functional
data is extended from its multivariate counterpart, and is known to be
sensitive to the choice of $J$, where $J$ is the dimension of the projection
subspace of the data. Under multivariate setting, a roughness penalty is
helpful for variance reduction. However, among the limited works covering
roughness penalty under the functional setting, most only use a single scalar
for tuning. Our new approach proposes a class of data-adaptive ridge penalties,
meaning that the model automatically adjusts the structure of the penalty
according to the data sets. This structure has $J$ free parameters and enables
a quadratic programming search for optimal tuning parameters that minimize the
estimated mean squared error (MSE) of prediction, and is capable of applying
different roughness penalty levels to each of the $J$ basis.
  The strength of the method in prediction accuracy and variance reduction with
finite data is demonstrated through multiple simulation scenarios and two
real-data examples. Its asymptotic performance is proved and compared to the
unpenalized functional local linear regressions.
