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Automatic Differentiation: Introduction

AD: Current Capabilities. Fortran 77: ADIFOR 2.0/3.0Robust, mature tool with excellent language coverageExcellent compiler analysisEfficient forward mode (small number of independents)Adequate reverse mode (small number of dependents)C/C : ADIC 2.0Semi-mature tool with full C language coverag

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Automatic Differentiation: Introduction

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    1. Automatic Differentiation: Introduction Automatic differentiation (AD) is a technology for transforming a subprogram that computes some function into a subprogram that computes the derivatives of that function Derivatives used in optimization, nonlinear solvers, sensitivity analysis, uncertainty quantification Forward mode of AD is efficient for problems with few independent variables or Jacobian-vector products Reverse mode of AD is efficient for problems with few dependent variables or JTv products Efficiency of generated code depends on sophistication of underlying compiler analysis and combinatorial algorithms

    2. AD: Current Capabilities Fortran 77: ADIFOR 2.0/3.0 Robust, mature tool with excellent language coverage Excellent compiler analysis Efficient forward mode (small number of independents) Adequate reverse mode (small number of dependents) C/C++: ADIC 2.0 Semi-mature tool with full C language coverage Sophisticated differentiation algorithms Efficient forward mode Fortran 90: OpenAD/F New tool with partial language coverage Sophisticated differentiation algorithms Accurate and novel compiler analysis Innovative templating mechanism Efficient forward and reverse modes

    3. AD: Application Highlight

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