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Basic module

To use the Basic module, include the following header:

#include <AutoDiff/Basic>

Supported types

The Basic module supports variables and operations with all value and derivative types T for which std::is_arithmetic_v<T> is true. Remember, the derivative type must be the same for all variables in an expression.

Aliases

For your convenience, the Basic module provides the following type aliases:

// Type aliases provided by the Basic module

namespace AutoDiff {

using Real    = Variable<double, double>;
using Integer = Variable<int, double>;
using Boolean = Variable<bool, double>;

using RealF    = Variable<float, float>;
using IntegerF = Variable<int, float>;
using BooleanF = Variable<bool, float>;

} // namespace AutoDiff

Operations

In binary operations, one of the operands can also be a scalar literal.

Real x(2);
x + 3; // right-hand side literal
3 * x; // left-hand side literal

The following operations are currently supported:

  • +, -, *, /: Arithmetic operations.
  • sin, cos, tan, cot: Trigonometric functions.
  • asin, acos, atan, acot: Inverse trigonometric functions.
  • sinh, cosh, tanh: Hyperbolic functions.
  • exp: Exponential function.
  • log: Natural logarithm.
  • pow: Power function.
  • square: Square function.
  • sqrt: Square root.
  • min, max: Minimum, maximum of a scalar expression and zero.