Useful math equations in CCGL. More...

#include <cmath>
#include "basic.h"
#include "utils_array.h"

Namespaces
namespace	ccgl
	Common Cross-platform Geographic Library (CCGL)

namespace	ccgl::utils_math
	Basic mathematics related functions.

Macros
#define	M_E 2.7182818284590452354 /* e */

#define	M_LOG2E 1.4426950408889634074 /* log 2e */

#define	M_LOG10E 0.43429448190325182765 /* log 10e */

#define	M_LN2 0.69314718055994530942 /* log e2 */

#define	M_LN10 2.30258509299404568402 /* log e10 */

#define	M_PI 3.14159265358979323846 /* pi */

#define	M_PI_2 1.57079632679489661923 /* pi/2 */

#define	M_PI_4 0.78539816339744830962 /* pi/4 */

#define	M_1_PI 0.31830988618379067154 /* 1/pi */

#define	M_2_PI 0.63661977236758134308 /* 2/pi */

#define	M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */

#define	M_SQRT2 1.41421356237309504880 /* sqrt(2) */

#define	M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */

#define	M_2POW23 8388608.0f /* pow(2, 23) */

#define	HUGE ((float)3.40282347e+38) /maximum value of float/

#define	MAXFLOAT ((float)3.40282347e+38) /maximum value of float/

#define	MINFLOAT ((float)1.175494351e-38) /minimum value of float/

#define	M_SQRT3 1.732051f /* sqrt(3) */

#define	M_TC 0.63212055882855767840f /* 1 - 1/e */

#define	M_PI2 6.283185f /* pi2 /

#define	M_GOLDEN 1.618034f /* golden ratio */

#define	M_1_PI2 0.15915494309189534561f /* 1/(pi2) /

#define	M_DIV3 0.3333333333333333333f /* 1/3 */

#define	M_DIV4 0.25f /* 1/4 */

#define	M_DIV5 0.2f /* 1/5 */

#define	M_DIV6 0.1666666666666666666f /* 1/6 */

#define	M_DIV7 0.142857143f /* 1/7 */

#define	M_DIV8 0.125f /* 1/8 */

#define	M_DIV9 0.1111111111111111111f /* 1/9 */

#define	M_DIV10 0.1f /* 1/10 */

#define	M_DIV11 0.090909091f /* 1/11 */

#define	M_DIV12 0.0833333333333333333f /* 1/12 */

#define	M_DIV13 0.076923077f /* 1/13 */

#define	M_DIV14 0.071428571f /* 1/14 */

#define	M_DIV15 0.0666666666666666666f /* 1/15 */

#define	M_DIV16 0.0625f /* 1/16 */

#define	M_DIV_LN10 0.43429448190325182765f /* 1 / ln(10) */

#define	PH_C ((float)299792458) /speed of light (m/s)/

#define	PH_M0 ((float)1.2566370614359172950) /mag permeability (mH/m)/

#define	PH_H ((float)6.62606957e-34) /planck constant (J/Hz)/

#define	PH_HBAR ((float)1.05457172e-34) /diract constant (J.s/rad)*/

#define	PH_K ((float)1.3806488e-23) /boltzmann constant (J/K)/

#define	PH_ME ((float)9.10938291e-31) /mass of electron (kg)/

#define	PH_MP ((float)1.672614e-27) /mass of proton (kg)/

#define	PH_MN ((float)1.674920e-27) /mass of neutron (kg)/

#define	PH_EC ((float)1.6021917e-19) /charge of electron (C)/

#define	PH_F ((float)9.648670e4) /faraday constant (C/mol)/

#define	PH_G ((float)6.6732e-11) /gravitational constant (Nm^2/kg^2)*/

#define	PH_AVO ((float)6.022169e23) /avogadro constant/

#define	Max(a, b) ((a) >= (b) ? (a) : (b))
	Return maximum value.

#define	Min(a, b) ((a) >= (b) ? (b) : (a))
	Return minimum value.

#define	Abs(x) ((x) >= 0 ? (x) : -(x))
	Return absolute value.

Functions
template<typename T1 , typename T2 >
bool	ccgl::utils_math::FloatEqual (T1 v1, T2 v2)
	Whether v1 is equal to v2. More...

float	ccgl::utils_math::Expo (float xx, float upper=20.f, float lower=-20.f)
	Check the argument against upper and lower boundary values prior to doing Exponential function.

float	ccgl::utils_math::Power (float a, float n)
	deal with positive and negative float numbers

template<typename T >
T	ccgl::utils_math::MaxInArray (const T *a, int n)
	Get maximum value in a numeric array with size n. More...

template<typename T >
T	ccgl::utils_math::MinInArray (const T *a, int n)
	Get minimum value in a numeric array with size n. More...

template<typename T >
T	ccgl::utils_math::Sum (int row, const T *data)
	Sum of a numeric array Get sum value of a double array with size row. More...

template<typename T >
T	ccgl::utils_math::Sum (int row, int &idx, const T data)
	Sum of a numeric array Get sum value of a double array with size row and real index idx. More...

template<typename T >
void	ccgl::utils_math::BasicStatistics (const T values, int num, double *derivedvalues, T exclude=static_cast< T >(NODATA_VALUE))
	calculate basic statistics at one time_funcs More...

template<typename T >
void	ccgl::utils_math::BasicStatistics (const T const values, int num, int lyrs, double ***derivedvalues, T exclude=static_cast< T >(NODATA_VALUE))
	calculate basic statistics at one time_funcs for 2D raster data More...

float	ccgl::utils_math::ApprSqrt (float z)
	approximate sqrt More...

double	ccgl::utils_math::ApprSqrt (const double z)

template<typename T >
T	ccgl::utils_math::CalSqrt (T val)

template<typename T >
T	ccgl::utils_math::CalExp (T val)

float	ccgl::utils_math::ApprLn (float z)
	Approximates the natural logarithm, (where the base is 'e'=2.71828)

double	ccgl::utils_math::ApprLn (const double z)

template<typename T >
T	ccgl::utils_math::CalLn (T val)

float	ccgl::utils_math::pow_lookup (const float exp, const float log_base)
	lookup for pow(a, b) function More...

float	ccgl::utils_math::ApprPow (float a, float b)
	Approximates pow(a, b) based on the work of Harrison Ainsworth. More...

template<typename T1 , typename T2 >
double	ccgl::utils_math::CalPow (T1 a, T2 b)

Detailed Description

Useful math equations in CCGL.

Remarks

1. 2018-05-02 - lj - Make part of CCGL.
2. 2021-07-15 - lj - Integrate pal.math for fast pow, exp, and ln

Author: Liangjun Zhu, zlj(a)lreis.ac.cn

Version: 1.1

Namespaces

Macros

Functions

Detailed Description