I would like to find the second largest element and in general the k^{th} largest element in VectorXd. Currently, I am aware that if 'A' is of type 'VectorXd', then

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s = A.maxCoeff(&r)

stores the maximum value in s and the corresponding index in r.

Thanks

You can use std::nth_element on a copy of the vector using vec.data() and vec.data()+vec.size() as begin/end iterators.
http://en.cppreference.com/w/cpp/algorithm/nth_element