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Energy flow analysis is a fundamental tool to determine the network states of the integrated energy systems (IES). For the widely deployed IES with coupled power grids (PG) and heating networks (HN), we still lack a generic tool that can be easily employed to calculate the quasi-dynamic energy flows of it. In this paper, we have developed a generic code package (named as MATHN) for energy flow analysis of the quality-regulated HN. After that, a generic solution framework that leverages MATPOWER and MATHN to realize decomposed energy flow calculation of PG and HN is proposed. Behind the MATHN tool, a model reformulation technique is proposed to eliminate the massive indirect variables of the basic HN model discretized by finite difference, which finally derives a compact matrix formulation (similar to the network equation of power grid: $\boldsymbol {I}=\boldsymbol {Y}\boldsymbol {U}$ ) for generic description of any HN and also slashes the original model scale by around 20 times. Moreover, the solution strategy behind the MATHN tool further converts this matrix formulation into a standard system of non-homogeneous linear equations, with which some existing well-recognized algorithms can be directly applied for efficient and accurate solution. Case studies on three different scales of test systems demonstrate the generality, efficiency and accuracy of our methods. All the codes and input data are packaged into the MATHN tool and are made open-source for non-commercial use.