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AD Mode Interface

XAD provides a set of interface structures that conveniently allow access to the data types needed for different AD modes. These are traits classes with member typedef declarations that allow easy access to mode-specific types.

For example, they can be used as:

using mode = xad::adj<double>;
using adouble = mode::active_type;

// use active type in functions, etc.
adouble my_function(adouble x) {...}

mode::tape_type tape;    // setup tape

Mode Interface Classes

First Order

adj<T, N = 1>

Mode interface class for first order adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwd<T, N = 1>

Mode interface class for first order forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adjd<T, N = 1>

Mode interface class for first order direct forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwdd<T, N = 1>

Mode interface class for first order direct adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

Second Order

fwd_adj<T, N = 1>

Mode interface class for second order forward over adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwd_fwd<T, N = 1>

Mode interface class for second order forward over forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adj_fwd<T, N = 1>

Mode interface class for second order adjoint over forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adj_adj<T, N = 1>

Mode interface class for second order adjoint over adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwd_fwdd<T, N = 1>

Mode interface class for second order forward over direct forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adj_fwdd<T, N = 1>

Mode interface class for second order adjoint over direct forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwd_adjd<T, N = 1>

Mode interface class for second order forward over direct adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adj_adjd<T, N = 1>

Mode interface class for second order adjoint over direct adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwdd_adj<T, N = 1>

Mode interface class for second order direct forward over adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwdd_fwd<T, N = 1>

Mode interface class for second order direct forward over forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwdd_fwdd<T, N = 1>

Mode interface class for second order direct forward over direct forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adjd_fwd<T, N = 1>

Mode interface class for second order direct adjoint over forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adjd_adj<T, N = 1>

Mode interface class for second order direct adjoint over adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adjd_adjd<T, N = 1>

Mode interface class for second order direct adjoint over direct adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

adjd_fwdd<T, N = 1>

Mode interface class for second order direct adjoint over direct forward mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

fwdd_adjd<T, N = 1>

Mode interface class for second order direct forward over direct adjoint mode, where T is the underlying scalar type (e.g. double), and N adds the option of having a vector of derivatives of size N.

Type Members

All mode classes above have type members as described below.

template <typename T, size_t N = 1>
struct mode {
  typedef implementation_defined active_type;   // active data type
  typedef T                      passive_type;  // fully unwrapped passive type
  typedef implementation_defined tape_type;     // tape (void for forward mode)
  typedef passive_type           value_type;    // alias for passive_type

  // for second-order only
  typedef implementation_defined inner_type;    // first-order active type
};