We implemented the charge self-consistent combination of Density Functional Theory and Dynamical Mean Field Theory (DMFT) in two full-potential methods, the Augmented Plane Wave and the Linear Muffin-Tin Orbital methods. We categorize the commonly used projection methods in terms of the causality of the resulting DMFT equations and the amount of partial spectral weight retained. The detailed flow of the Dynamical Mean Field algorithm is described, including the computation of response functions

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... such as transport coefficients. We discuss the implementation of the impurity solvers based on hybridization expansion and an analytic continuation method for self-energy. We also derive the formalism for the bold continuous time quantum Monte Carlo method. We test our method on a classic problem in strongly correlated physics, the isostructural transition in Ce metal. We apply our method to the class of heavy fermion materials CeIrIn_5, CeCoIn_5 and CeRhIn_5 and show that the Ce 4f electrons are more localized in CeRhIn_5 than in the other two, a result corroborated by experiment. We show that CeIrIn_5 is the most itinerant and has a very anisotropic hybridization, pointing mostly towards the out-of-plane In atoms. In CeRhIn_5 we stabilized the antiferromagnetic DMFT solution below 3K, in close agreement with the experimental N\'eel temperature.