iSMART〜The Hyper-Dual Numbers in Fortran
４ヶ月に亘る冬籠りでPython，Juliaの自動微分の実装を終え、Fortran Simulator “iSMART”をJulia言語に変換中にある。スタンフォード大の博士論文を渉猟している折、Hyper-dual numbersなる超実数を用いて厳密に一階偏導関数、加えて二階偏導関数も導出できる論文に出会う。急遽変換を中断し、FortranによるHyper-dual numbersの実装を試みることにする。あの冬籠りは一体何だったんだろうか？After four months of dedication during the winter, I finished the implementation in Python and Julia for the automatic differentiation. I am currently working on converting the in-house Fortran program “iSMART” to Julia. While browsing papers at Stanford University, I came across a Ph.D. thesis on hyper-dual numbers, which is an extension of real numbers that can derive the first-order partial derivatives as well as the second-order partial derivatives in a strict manner. Suddenly I stopped…