pimathbase.h File Reference

Basic mathematical constants and helper algorithms. More...

#include "piinit.h"
#include "pipair.h"
#include "pivector.h"
#include <math.h>

Functions
int	sign (const float &x)
	Returns the sign of a floating-point value.
int	sign (const double &x)
	Returns the sign of a floating-point value.
int	sign (const ldouble &x)
	Returns the sign of a floating-point value.
int	pow2 (const int p)
	Returns 2 raised to integer power p.
float	pow10 (const float &e)
	Returns 10 raised to the specified power.
double	pow10 (const double &e)
	Returns 10 raised to the specified power.
ldouble	pow10 (const ldouble &e)
	Returns 10 raised to the specified power.
double	sinc (const double &v)
	Returns normalized sinc, sin(pi*x)/(pi*x).
constexpr float	toRad (float deg)
	Converts degrees to radians.
constexpr double	toRad (double deg)
	Converts degrees to radians.
constexpr ldouble	toRad (ldouble deg)
	Converts degrees to radians.
constexpr float	toDeg (float rad)
	Converts radians to degrees.
constexpr double	toDeg (double rad)
	Converts radians to degrees.
constexpr ldouble	toDeg (ldouble rad)
	Converts radians to degrees.
template<typename T >
constexpr T	sqr (const T &v)
	Returns square of a value.
template<typename T >
constexpr T	toDb (T val)
	Converts a power ratio to decibels.
template<typename T >
constexpr T	fromDb (T val)
	Converts decibels to a linear power ratio.
double	randomd ()
	Returns a pseudo-random value in the range [-1; 1].
double	randomn (double dv=0., double sv=1.)
	Returns a normally distributed pseudo-random value with mean dv and deviation sv.
template<typename T >
PIVector< T >	piAbs (const PIVector< T > &v)
	Returns vector with absolute values of each element.
template<typename T >
void	normalizeAngleDeg360 (T &a)
	Normalizes an angle to the [0; 360] degree range in place.
template<typename T >
double	normalizedAngleDeg360 (T a)
	Returns an angle normalized to the [0; 360] degree range.
template<typename T >
void	normalizeAngleDeg180 (T &a)
	Normalizes an angle to the [-180; 180] degree range in place.
template<typename T >
double	normalizedAngleDeg180 (T a)
	Returns an angle normalized to the [-180; 180] degree range.
template<typename T >
bool	OLS_Linear (const PIVector< PIPair< T, T > > &input, T *out_a, T *out_b)
	Fits a linear model y = a*x + b with ordinary least squares. More...
template<typename T >
bool	WLS_Linear (const PIVector< PIPair< T, T > > &input, const PIVector< T > &weights, T *out_a, T *out_b)
	Fits a weighted linear model y = a*x + b. More...

Variables
const double	deg2rad = 1.74532925199432957692e-2
	Multiplicative factor for converting degrees to radians.
const double	rad2deg = 57.2957795130823208768
	Multiplicative factor for converting radians to degrees.

Mathematical constants
Natural logarithm of 2
#define	M_LN2   0.69314718055994530942
#define	M_LN10   2.30258509299404568402
	Natural logarithm of 10.
#define	M_SQRT2   1.41421356237309514547
	Square root of 2.
#define	M_SQRT3   1.73205080756887719318
	Square root of 3.
#define	M_1_SQRT2   0.70710678118654746172
	1 divided by square root of 2
#define	M_1_SQRT3   0.57735026918962584208
	1 divided by square root of 3
#define	M_PI   3.141592653589793238462643383280
	Pi constant.
#define	M_2PI   6.283185307179586476925286766559
	2 times Pi
#define	M_PI_3   1.04719755119659774615
	Pi divided by 3.
#define	M_2PI_3   2.0943951023931954923
	2 times Pi divided by 3
#define	M_180_PI   57.2957795130823208768
	180 divided by Pi (degrees to radians conversion factor)
#define	M_PI_180   1.74532925199432957692e-2
	Pi divided by 180 (radians to degrees conversion factor)
#define	M_SQRT_PI   1.772453850905516027298167483341
	Square root of Pi.
#define	M_E   2.7182818284590452353602874713527
	Euler's number.
#define	M_LIGHT_SPEED   2.99792458e+8
	Speed of light in vacuum.
#define	M_RELATIVE_CONST   -4.442807633e-10;
	Relative gas constant.
#define	M_GRAVITY_CONST   398600.4418e9;
	Gravitational constant.

Bessel functions
Bessel function of the first kind of order 0 Bessel function of the first kind J0(x), solution to Bessel's differential equation See also piJ1(), piJn()
double	piJ0 (const double &v)
double	piJ1 (const double &v)
	Bessel function of the first kind of order 1 Bessel function of the first kind J1(x), solution to Bessel's differential equation. More...
double	piJn (int n, const double &v)
	Bessel function of the first kind of order n Bessel function of the first kind Jn(n, x), solution to Bessel's differential equation. More...
double	piY0 (const double &v)
	Bessel function of the second kind of order 0 Bessel function of the second kind Y0(x), also known as Neumann function. More...
double	piY1 (const double &v)
	Bessel function of the second kind of order 1 Bessel function of the second kind Y1(x), also known as Neumann function. More...
double	piYn (int n, const double &v)
	Bessel function of the second kind of order n Bessel function of the second kind Yn(n, x), also known as Neumann function. More...

Detailed Description

Basic mathematical constants and helper algorithms.

Function Documentation

piJ1()

double piJ1

(

const double &

v

)

Bessel function of the first kind of order 1 Bessel function of the first kind J1(x), solution to Bessel's differential equation.

See also

piJ0(), piJn()

piJn()

double piJn	(	int	n,
		const double &	v
	)

Bessel function of the first kind of order n Bessel function of the first kind Jn(n, x), solution to Bessel's differential equation.

See also

piJ0(), piJ1()

piY0()

double piY0

(

const double &

v

)

Bessel function of the second kind of order 0 Bessel function of the second kind Y0(x), also known as Neumann function.

See also

piY1(), piYn()

piY1()

double piY1

(

const double &

v

)

Bessel function of the second kind of order 1 Bessel function of the second kind Y1(x), also known as Neumann function.

See also

piY0(), piYn()

piYn()

double piYn	(	int	n,
		const double &	v
	)

Bessel function of the second kind of order n Bessel function of the second kind Yn(n, x), also known as Neumann function.

See also

piY0(), piY1()

OLS_Linear()

template<typename T >

bool OLS_Linear	(	const PIVector< PIPair< T, T > > &	input,
		T *	out_a,
		T *	out_b
	)

Fits a linear model y = a*x + b with ordinary least squares.

Returns false when fewer than two sample pairs are provided.

WLS_Linear()

template<typename T >

bool WLS_Linear	(	const PIVector< PIPair< T, T > > &	input,
		const PIVector< T > &	weights,
		T *	out_a,
		T *	out_b
	)

Fits a weighted linear model y = a*x + b.

Returns false when the sample is too small or the weights vector has a different size.