TOMLAB /MAD: An efficient overloaded implementation of forward mode automatic differentiation in MATLAB. The Mad package described here facilitates the evaluation of first derivatives of multidimensional functions that are defined by computer codes written in MATLAB. The underlying algorithm is the well-known forward mode of automatic differentiation implemented via operator overloading on variables of the class fmad. The main distinguishing feature of this MATLAB implementation is the separation of the linear combination of derivative vectors into a separate derivative vector class derivvec. This allows for the straightforward performance optimization of the overall package. Additionally, by internally using a matrix (two-dimensional) representation of arbitrary dimension directional derivatives, we may utilize MATLAB’s sparse matrix class to propagate sparse directional derivatives for MATLAB code which uses arbitrary dimension arrays. On several examples, the package is shown to be more efficient than Verma’s ADMAT package.

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  1. Baydin, Atılım Güneş; Pearlmutter, Barak A.; Radul, Alexey Andreyevich; Siskind, Jeffrey Mark: Automatic differentiation in machine learning: a survey (2018)
  2. Rump, Siegfried M.: Mathematically rigorous global optimization in floating-point arithmetic (2018)
  3. Elsheikh, Atiyah: An equation-based algorithmic differentiation technique for differential algebraic equations (2015)
  4. Hascoet, Laurent; Pascual, Valérie: The Tapenade automatic differentiation tool, principles, model, and specification (2013)
  5. Milić, Vladimir; Kasać, Josip; Majetić, Dubravko: A back propagation through time-like min-max optimal control algorithm for nonlinear systems (2013)
  6. Patterson, Michael A.; Weinstein, Matthew; Rao, Anil V.: An efficient overloaded method for computing derivatives of mathematical functions in MATLAB (2013)
  7. Andersson, Joel; Åkesson, Johan; Diehl, Moritz: CasADi: a symbolic package for automatic differentiation and optimal control (2012)
  8. Van Willigenburg, L. Gerard; De Koning, Willem L.: Temporal and differential stabilizability and detectability of piecewise constant rank systems (2012)
  9. Xu, Yunjun; Basset, Gareth: Sequential virtual motion camouflage method for nonlinear constrained optimal trajectory control (2012)
  10. De Witte, Virginie; Govaerts, Willy: Numerical computation of normal form coefficients of bifurcations of ODEs in \textscMatlab (2011)
  11. Lampoh, Komlanvi; Charpentier, Isabelle; Daya, El Mostafa: A generic approach for the solution of nonlinear residual equations. III: Sensitivity computations (2011)
  12. Padulo, Mattia; Guenov, Marin D.: Worst-case robust design optimization under distributional assumptions (2011)
  13. Toivanen, Jukka I.; Mäkinen, Raino A. E.: Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization (2011)
  14. Basset, G.; Xu, Y.; Yakimenko, O. A.: Computing short-time aircraft maneuvers using direct methods (2010)
  15. Neidinger, Richard D.: Introduction to automatic differentiation and MATLAB object-oriented programming (2010)
  16. Pryce, J. D.; Ghaziani, R. Khoshsiar; De Witte, V.; Govaerts, W.: Computation of normal form coefficients of cycle bifurcations of maps by algorithmic differentiation (2010)
  17. Bücker, H. Martin; Vehreschild, Andre: Coping with a variable number of arguments when transforming MATLAB programs (2008)
  18. Giles, Mike B.: Collected matrix derivative results for forward and reverse mode algorithmic differentiation (2008)
  19. Hascoët, Laurent; Dauvergne, Benjamin: Adjoints of large simulation codes through automatic differentiation (2008)
  20. Koutsawa, Yao; Charpentier, Isabelle; Daya, El Mostafa; Cherkaoui, Mohammed: A generic approach for the solution of nonlinear residual equations. I: The Diamant toolbox (2008)

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