Mathematical constants and default algorithm parameters. More...

#include <limits>
#include <cstdint>

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

	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. More...

#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_CALCULUS_INTEGRAL_TOL 1E-08

#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_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. More...

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::CALCULUS_INTEGRAL_TOL = THEORETICA_CALCULUS_INTEGRAL_TOL

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::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)

Namespaces

Macros

Typedefs

Variables

Detailed Description

Macro Definition Documentation

◆ THEORETICA_ALGEBRA_ELEMENT_TOL