Update of H: Newly added functions and methods in versions 2 and 3

H Phi [aitch-phi] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal block preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the ab initio low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode-simplified input format in H Phi-to use these functions and methods. We explain the basics of the implemented methods and how to use them. Program summary Program Title: H Phi [aitch-phi] CPC Library link to program files: https://doi.org/10.17632/vnfthtyctm.2 Developer's repository link: https://github.com/issp-center-dev/HPhi Licensing provisions: GPLv3 Programming language: C, Fortran Journal reference of previous version: Comput. Phys. Commun. 217 (2017) 180-192 Does the new version supersede the previous version?: Yes. The latest version has compatibility with the old versions. Although most functions are available in newer versions, some redundant/unnecessary functions were abolished in newer versions. Reasons for the new version: Implementation of new functions and methods, development of utilities, and bug fixes. Summary of revisions: We added new functions to obtain excited spectrum, low-energy excited states, and time-dependent physical quantities. We also implemented the full diagonalization method by using MAGMA on GPGPUs and finite-temperature simulations by using the canonical thermal pure quantum state method. In addition, we developed utilities for connection with RESPACK and a submodule for a generator of input files. Nature of problem: Physical properties in quantum lattice models with finite system sizes