/** \page TopicCustomizing_CustomScalar Using custom scalar types
\anchor user_defined_scalars
By default, Eigen currently supports standard floating-point types (\c float, \c double, \c std::complex<float>, \c std::complex<double>, \c long \c double), as well as all native integer types (e.g., \c int, \c unsigned \c int, \c short, etc.), and \c bool.
On x86-64 systems, \c long \c double permits to locally enforces the use of x87 registers with extended accuracy (in comparison to SSE).
In order to add support for a custom type \c T you need:
-# make sure the common operator (+,-,*,/,etc.) are supported by the type \c T
-# add a specialization of struct Eigen::NumTraits<T> (see \ref NumTraits)
-# define the math functions that makes sense for your type. This includes standard ones like sqrt, pow, sin, tan, conj, real, imag, etc, as well as abs2 which is Eigen specific.
(see the file Eigen/src/Core/MathFunctions.h)
The math function should be defined in the same namespace than \c T, or in the \c std namespace though that second approach is not recommended.
Here is a concrete example adding support for the Adolc's \c adouble type. <a href="https://projects.coin-or.org/ADOL-C">Adolc</a> is an automatic differentiation library. The type \c adouble is basically a real value tracking the values of any number of partial derivatives.
\code
#ifndef ADOLCSUPPORT_H
#define ADOLCSUPPORT_H
#define ADOLC_TAPELESS
#include <adolc/adouble.h>
#include <Eigen/Core>
namespace Eigen {
template<> struct NumTraits<adtl::adouble>
: NumTraits<double> // permits to get the epsilon, dummy_precision, lowest, highest functions
This other example adds support for the \c mpq_class type from <a href="https://gmplib.org/">GMP</a>. It shows in particular how to change the way Eigen picks the best pivot during LU factorization. It selects the coefficient with the highest score, where the score is by default the absolute value of a number, but we can define a different score, for instance to prefer pivots with a more compact representation (this is an example, not a recommendation). Note that the scores should always be non-negative and only zero is allowed to have a score of zero. Also, this can interact badly with thresholds for inexact scalar types.