This provide the ADValue<T,maxOrder,dim> class as a primitive
for automatic differentiation. It that encapsulates a scalar type
T (e.g. T=double) and provides arithmetic operations.
Each ADValue is considered as an intermediate result in
the evaluation of a scalar dim-variate function but does
not store the value only, but the jet of all derivatives up
to maxOrder. Currently only maxOrder<=2 is implemented.
Additionally, this provides some convenience utilities
for using this ADValue:
abs, sin, cos,
log, exp, sqrt, pow).f simply use ADFunction<f>.Usage example:
using std::sin;
using std::exp;
using std::pow;
using namespace Dune::Indices;
// Define and initialize functions arguments of a tri-variate
// twice differentiable function.
auto x0 = ADValue<double,2,3>(23., 0);
auto x1 = ADValue<double,2,3>(42., 1);
auto x2 = ADValue<double,2,3>(13., 2);
// Evaluate expression
auto y = pow(2, exp(sin(x[0]*x[1])*sin(x[2]) + 3));
// Extract value of function, 1st and 2nd order partial derivatives
y.partial();
y.partial(i);
y.partial(j);Why propose this despite the fact we have AdolC bindings?
ADValue. When
using AD for the derivatives of the energy with a Newton
method for the minimal surface equation, assembly is takes
about 20 times as long with AdolC compared to ADValue.
The latter is essentially as fast as with manually implemented
derivatives and evenmore allows for multi-threading (not used
in the comparison).ADValue can be characterized as tapeless forward mode Taylor polynomial AD.ADValue but has some conceptual restrictions:
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