On Symbolic Jacobian Accumulation
نویسنده
چکیده
Abstract: Derivatives are essential ingredients of a wide range of numerical algorithms. We focus on the accumulation of Jacobian matrices by Gaussian elimination on a sparse implementation of the extended Jacobian. A symbolic algorithm is proposed to determine the fill-in. Its runtime undercuts that of the original accumulation algorithm by a factor of ten. On the given computer architecture we are able to handle problems with roughly four times the original size.
منابع مشابه
Toward Low Static Memory Jacobian Accumulation
Derivatives are essential ingredients of a wide range of numerical algorithms. We focus on the accumulation of Jacobian matrices by Gaussian elimination on a sparse implementation of the extended Jacobian. A symbolic algorithm is proposed to determine the fill-in. The first version of the new algorithm results in a speedup of five compared to the elimination algorithm that does not exploit spar...
متن کاملExploitation of structural sparsity in algorithmic differentiation
The background of this thesis is algorithmic differentiation (AD) [GW08] of in practice very computationally expensive vector functions F : R ⊇ D → R given as computer programs. Traditionally, most AD software1 provide forward and reverse modes of AD for calculating the Jacobian matrix ∇F (x) accurately at a given point x on some kind of internal representation of F kept on memory or hard disk....
متن کاملRecursive and Symbolic Calculation of the Stiffness and Mass Matrices of Parallel Robots
This paper presents a symbolic and recursive calculation of the stiffness and mass matrices of parallel robots. In order to reduce the computational time required for simulating the elastodynamic behavior of robots, it is necessary to minimize the number of operators in the symbolic model expression. Some algorithms have been proposed for the rigid case or for parallel robots with lumped spring...
متن کاملOptimized Jacobian Accumulation Techniques
Jacobian matrices can be accumulated using either the forward or reverse mode of Automatic Di erentiation. Alternatively, derivative code can be generated to compute the Jacobian directly at the current argument. The minimisation of the corresponding number of arithmetic operations leads to a computationally hard combinatorial optimisation problem. A method for its approximate solution by dynam...
متن کاملKinematic-, Static- and Workspace Analysis of a 6-p-u-s Parallel Manipulator
Corresponding author, Phone: (716)-645-1430, Fax: (716)-645-2883. ABSTRACT This paper examines the symbolic kinematic modeling of a general 6-P-U-S (prismatic-universal-spherical) parallel kinematic manipulator (PKM). The base location of actuators has been previously shown to lead to: (i) reduction of the (motor) weight carried by the legs; (ii) elimination of the actuation transmission requir...
متن کامل