GitHub - utsa-idl/NewtonRaphsonExamples: Examples of forward-difference, automatic differentiation and complex-step Jacobian calculation in a Newton-Raphson solver.

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Examples of forward-difference, automatic differentiation and complex-step Jacobian calculation in a Newton-Raphson solver.

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Name		Name	Last commit message	Last commit date
Latest commit History 4 Commits
LICENSE		LICENSE
README		README
automatic_differentiation.cpp		automatic_differentiation.cpp
compile_AD_example.sh		compile_AD_example.sh
compile_CS_example.sh		compile_CS_example.sh
compile_FD_example.sh		compile_FD_example.sh
complex_step.cpp		complex_step.cpp
forward_difference.cpp		forward_difference.cpp

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Description of NewtonRaphsonExamples repository:

The cpp files contain implementations of different methods for computing what
are known as 'tangent-stiffness' matrices in computational mechanics or
'Jacobian' matrices in mathematics.

These examples are not general purpose, but give an idea of how to use each
Jacobian calculation method in solving a nonlinear system within the
Newton-Raphson method.

Included in the examples is a method using forward difference, which is one
type of finite difference, a method using automatic differentiation, which is a
computerized implementation of the chain rule of calculus, and complex step,
which is a method for calculating a Jacobian based on complex Taylor series
expansion.

All three examples were written and tested on a system running
Ubuntu Linux 13.04 64bit with GCC 4.7 for compiler.

The examples depend on the Armadillo API, available at sourceforge.net, as well
as the Trilinos API with Teuchos and Sacado packages, available at
trilinos.sandia.gov.