template<typename DerivativeType>
class Eigen::AutoDiffScalar< DerivativeType >

A scalar type replacement with automatic differentiation capability.

Parameters

DerivativeType

the vector type used to store/represent the derivatives. The base scalar type as well as the number of derivatives to compute are determined from this type. Typical choices include, e.g., Vector4f for 4 derivatives, or VectorXf if the number of derivatives is not known at compile time, and/or, the number of derivatives is large. Note that DerivativeType can also be a reference (e.g., VectorXf&) to wrap a existing vector into an AutoDiffScalar. Finally, DerivativeType can also be any Eigen compatible expression.

This class represents a scalar value while tracking its respective derivatives using Eigen's expression template mechanism.

It supports the following list of global math function:

• std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
• internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
• internal::conj, internal::real, internal::imag, numext::abs2.

AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However, in that case, the expression template mechanism only occurs at the top Matrix level, while derivatives are computed right away.