constants.h File Reference

Mathematical constants and default algorithm parameters. More...

#include <limits>
#include <cstdint>

Go to the source code of this file.

Namespaces
namespace	theoretica
	Main namespace of the library which contains all functions and objects.
namespace	th
	Alias for the theoretica namespace.

Macros
#define	THEORETICA_ALGEBRA_ELEMENT_TOL   (10*MACH_EPSILON)
	THEORETICA_DISABLE_X86 Define this macro to disable Assembly x86 optimizations.
#define	THEORETICA_ALGEBRA_EIGEN_TOL   1E-08
	Tolerance for eigensolvers.
#define	THEORETICA_ALGEBRA_EIGEN_ITER   100
	Maximum number of iterations for eigensolvers.
#define	THEORETICA_CORE_TAYLOR_ORDER   12
	Order of Taylor series approximations.
#define	THEORETICA_CALCULUS_INTEGRAL_STEPS   100
	Default number of steps for integral approximation.
#define	THEORETICA_OPTIMIZATION_TOL   1E-08
	Approximation tolerance for root finding.
#define	THEORETICA_OPTIMIZATION_BISECTION_ITER   100
	Maximum number of iterations for bisection.
#define	THEORETICA_OPTIMIZATION_GOLDENSECTION_ITER   100
	Maximum number of iterations for golden section search.
#define	THEORETICA_OPTIMIZATION_HALLEY_ITER   100
	Maximum number of iterations for Halley's method.
#define	THEORETICA_OPTIMIZATION_NEWTON_ITER   100
	Maximum number of iterations for Newton-Raphson root finding.
#define	THEORETICA_OPTIMIZATION_STEFFENSEN_ITER   100
	Maximum number of iterations for Steffensen root finding.
#define	THEORETICA_OPTIMIZATION_CHEBYSHEV_ITER   100
	Maximum number of iterations for Chebyshev root finding.
#define	THEORETICA_OPTIMIZATION_OSTROWSKI_ITER   100
	Maximum number of iterations for Ostrowski root finding.
#define	THEORETICA_OPTIMIZATION_JARRAT_ITER   100
	Maximum number of iterations for Jarrat root finding.
#define	THEORETICA_STATISTICS_TRYANDCATCH_ITER   100
	Maximum number of failed iterations for the Try-and-Catch algorithm.
#define	THEORETICA_CALCULUS_DERIV_STEP   1E-3
	Default variation for derivative approximation.
#define	THEORETICA_OPTIMIZATION_MINGRAD_GAMMA   -0.005
	Default step size for gradient descent minimization.
#define	THEORETICA_OPTIMIZATION_MINGRAD_TOLERANCE   1E-3
	Default tolerance for gradient descent minimization.
#define	THEORETICA_OPTIMIZATION_MINGRAD_ITER   50000
	Maximum number of iterations for gradient descent minimization.
#define	THEORETICA_STATISTICS_RAND_PREC   (uint64_t(1) << 31)
	Default precision for random number generation using rand_uniform()
#define	THEORETICA_STATISTICS_METROPOLIS_DEPTH   16
	Default depth of the Metropolis algorithm.
#define	TH_CONSTEXPR
	Enable constexpr in function declarations if C++14 is supported.
#define	TH_CONSTIF
	Enable constexpr in if statements if C++17 is supported.

Typedefs
using	theoretica::real = double
	A real number, defined as a floating point type.

Variables
constexpr real	theoretica::MACH_EPSILON = std::numeric_limits<real>::epsilon()
	Machine epsilon for the real type.
constexpr real	theoretica::PHI = 1.6180339887498948482045868
	The Phi (Golden Section) mathematical constant.
constexpr real	theoretica::INVPHI = 0.6180339887498948482045868
	The inverse of the Golden Section mathematical constant.
constexpr real	theoretica::PI = 3.141592653589793238462643
	The Pi mathematical constant.
constexpr real	theoretica::PI2 = 1.57079632679489655799898
	Half of Pi.
constexpr real	theoretica::PI4 = PI / 4.0
	A quarter of Pi.
constexpr real	theoretica::PIDOUBLE = PI * 2
	Pi multiplied by 2.
constexpr real	theoretica::TAU = PI * 2
	The Tau mathematical constant (Pi times 2)
constexpr real	theoretica::INVPI = 1.0 / PI
	The inverse of Pi.
constexpr real	theoretica::SQRTPI = 1.7724538509055159927
	The square root of Pi.
constexpr real	theoretica::E = 2.718281828459045235360287
	The Euler mathematical constant (e)
constexpr real	theoretica::LOG2E = 1.44269504088896338700465094
	The binary logarithm of e.
constexpr real	theoretica::LOG210 = 3.32192809488736218170856773213
	The binary logarithm of 10.
constexpr real	theoretica::LOG10E = 0.434294481903
	The base-10 logarithm of e.
constexpr real	theoretica::LN2 = 0.69314718056
	The natural logarithm of 2.
constexpr real	theoretica::LN10 = 2.30258509299
	The natural logarithm of 10.
constexpr real	theoretica::DEG2RAD = 0.017453292519943295474371680598
	The scalar conversion factor from degrees to radians.
constexpr real	theoretica::RAD2DEG = 57.2957795130823228646477218717
	The scalar conversion factor from radians to degrees.
constexpr real	theoretica::SQRT2 = 1.4142135623730950488
	The square root of 2.
constexpr real	theoretica::INVSQR2 = 0.7071067811865475
	The inverse of the square root of 2.
constexpr real	theoretica::SQRT3 = 1.732050807568877
	The square root of 3.
constexpr real	theoretica::ALGEBRA_ELEMENT_TOL = THEORETICA_ALGEBRA_ELEMENT_TOL
	Tolerance for the elements of matrices.
constexpr real	theoretica::ALGEBRA_EIGEN_TOL = THEORETICA_ALGEBRA_EIGEN_TOL
	Tolerance for eigensolvers.
constexpr real	theoretica::ALGEBRA_EIGEN_ITER = THEORETICA_ALGEBRA_EIGEN_ITER
	Maximum number of iterations for eigensolvers.
constexpr int	theoretica::CORE_TAYLOR_ORDER = THEORETICA_CORE_TAYLOR_ORDER
	Order of Taylor series approximations.
constexpr int	theoretica::CALCULUS_INTEGRAL_STEPS = THEORETICA_CALCULUS_INTEGRAL_STEPS
	Default number of steps for integral approximation.
constexpr real	theoretica::OPTIMIZATION_TOL = THEORETICA_OPTIMIZATION_TOL
	Approximation tolerance for root finding.
constexpr unsigned int	theoretica::OPTIMIZATION_BISECTION_ITER = THEORETICA_OPTIMIZATION_BISECTION_ITER
	Maximum number of iterations for the bisection algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_GOLDENSECTION_ITER = THEORETICA_OPTIMIZATION_GOLDENSECTION_ITER
	Maximum number of iterations for the golden section search algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_HALLEY_ITER = THEORETICA_OPTIMIZATION_HALLEY_ITER
	Maximum number of iterations for Halley's method.
constexpr unsigned int	theoretica::OPTIMIZATION_NEWTON_ITER = THEORETICA_OPTIMIZATION_NEWTON_ITER
	Maximum number of iterations for the Newton-Raphson algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_STEFFENSEN_ITER = THEORETICA_OPTIMIZATION_STEFFENSEN_ITER
	Maximum number of iterations for the Steffensen algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_CHEBYSHEV_ITER = THEORETICA_OPTIMIZATION_CHEBYSHEV_ITER
	Maximum number of iterations for the Chebyshev algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_OSTROWSKI_ITER = THEORETICA_OPTIMIZATION_OSTROWSKI_ITER
	Maximum number of iterations for the Ostrowski algorithm.
constexpr unsigned int	theoretica::OPTIMIZATION_JARRAT_ITER = THEORETICA_OPTIMIZATION_JARRAT_ITER
	Maximum number of iterations for the Jarrat algorithm.
constexpr unsigned int	theoretica::STATISTICS_TRYANDCATCH_ITER = THEORETICA_STATISTICS_TRYANDCATCH_ITER
	Maximum number of failed iterations for the Try-and-Catch algorithm.
constexpr real	theoretica::CALCULUS_DERIV_STEP = THEORETICA_CALCULUS_DERIV_STEP
	Default variation for derivative approximation.
constexpr real	theoretica::OPTIMIZATION_MINGRAD_GAMMA = THEORETICA_OPTIMIZATION_MINGRAD_GAMMA
	Default step size for gradient descent minimization.
constexpr real	theoretica::OPTIMIZATION_MINGRAD_TOLERANCE = THEORETICA_OPTIMIZATION_MINGRAD_TOLERANCE
	Default tolerance for gradient descent minimization.
constexpr unsigned int	theoretica::OPTIMIZATION_MINGRAD_ITER = THEORETICA_OPTIMIZATION_MINGRAD_ITER
	Maximum number of iterations for gradient descent minimization.
constexpr uint64_t	theoretica::STATISTICS_RAND_PREC = THEORETICA_STATISTICS_RAND_PREC
	Default precision for random number generation using rand_uniform()
constexpr unsigned int	theoretica::STATISTICS_METROPOLIS_DEPTH = THEORETICA_STATISTICS_METROPOLIS_DEPTH
	Default depth of the Metropolis algorithm.

Detailed Description

Mathematical constants and default algorithm parameters.

You may change the library's default behavior by redefining the macros starting with THEORETICA_

Macro Definition Documentation

THEORETICA_ALGEBRA_ELEMENT_TOL

#define THEORETICA_ALGEBRA_ELEMENT_TOL   (10*MACH_EPSILON)

THEORETICA_DISABLE_X86 Define this macro to disable Assembly x86 optimizations.

Tolerance for checking the elements of a matrix (such as algebra::is_square)