mx::math::func Namespace Reference

Classes
struct	emgModeFunc

Functions
template<typename realT >
realT	airyPattern (realT x)
	The classical Airy pattern.
template<typename realT >
realT	airyPattern (realT x, realT eps)
	The centrally obscured Airy pattern.
template<typename realT >
realT	airyPattern (realT x, realT y, realT A0, realT A, realT x0, realT y0, realT ps, realT eps)
	The general centrally obscured Airy pattern, with arbitrary center and platescale.
template<typename realT >
void	airyPattern2D (realT *arr, size_t nx, size_t ny, const realT A0, const realT A, const realT x0, const realT y0, realT ps)
	Fill in an array with the 2D arbitrarily-centered classical Airy pattern.
template<typename realT >
realT	seeingHalo (realT x, realT fwhm)
	Seeing Halo Profile.
template<typename realT >
realT	airyPatternEnclosed (realT x)
	Calculate the fraction of enclosed power at a given radius for the unobscured Airy Pattern.
template<typename realT >
realT	apeInt (realT x, void *params)
template<typename realT >
realT	airyPatternEnclosed (realT x, realT eps)
	Calculate the fraction of enclosed power at a given radius for the centrally obscured Airy Pattern.
template<typename T1 , typename T2 >
T2	bessel_j (T1 v, T2 x)
	Bessel Functions of the First Kind.
template<>
float	bessel_j< float, float > (float v, float x)
template<>
float	bessel_j< int, float > (int v, float x)
template<>
double	bessel_j< double, double > (double v, double x)
template<>
double	bessel_j< int, double > (int v, double x)
template<>
long double	bessel_j< long double, long double > (long double v, long double x)
template<>
long double	bessel_j< int, long double > (int v, long double x)
template<typename realT >
realT	expModGaussian (realT x, realT mu, realT sigma, realT lambda)
	The Exponentially Modified Gaussian at a point.
template<typename realT >
realT	expModGaussianMean (realT mu, realT lambda)
	The Mean of the Exponentially Modified Gaussian.
template<typename realT >
realT	expModGaussianVariance (realT sigma, realT lambda)
	The Variance of the Exponentially Modified Gaussian.
template<typename realT >
realT	expModGaussianMode (realT mu, realT sigma, realT lambda)
	The Mode of the Exponentially Modified Gaussian.
template<typename T >
T	factorial (T x)
	The factorial function.
template<>
float	factorial< float > (float x)
template<>
double	factorial< double > (double x)
template<>
long double	factorial< long double > (long double x)
template<typename T >
T	tgamma (T x)
	The Gamma Function.
template<>
float	tgamma< float > (float x)
template<>
double	tgamma< double > (double x)
template<>
long double	tgamma< long double > (long double x)
template<typename realT >
realT	gammaDistributionDenom (realT k, realT q)
	The denominator of the Gamma Distribution.
template<typename realT >
realT	gammaDistribution (realT x, realT x0, realT k, realT q, realT denom)
	The general shifted Gamma Distribution at a point using an arbitrary peak scaling parameter.
template<typename realT >
realT	gammaDistribution (realT x, realT x0, realT k, realT q)
	The general shifted Gamma Distribution at a point.
template<typename realT >
realT	gammaDistributionMean (realT x0, realT k, realT theta)
	The mean of the Gamma Distribution.
template<typename realT >
realT	gammaDistributionMode (realT x0, realT k, realT theta)
	The mode of the Gamma Distribution.
template<typename realT >
realT	gammaDistributionVariance (realT k, realT theta)
	The variance of the Gamma Distribution.
template<typename floatT >
constexpr floatT	twosqrt2log2 ()
	Constant to convert between the Gaussian width parameter and FWHM.
template<typename floatT >
floatT	fwhm2sigma (floatT fw)
	Convert from FWHM to the Gaussian width parameter.
template<typename floatT >
floatT	sigma2fwhm (floatT sig)
	Convert from Gaussian width parameter to FWHM.
template<typename realT >
realT	gaussian (const realT x, const realT G0, const realT G, const realT x0, const realT sigma)
	Find value at position (x) of the 1D arbitrarily-centered symmetric Gaussian.
template<typename realT >
realT	gaussian2D (const realT x, const realT y, const realT G0, const realT G, const realT x0, const realT y0, const realT sigma)
	Find value at position (x,y) of the 2D arbitrarily-centered symmetric Gaussian.
template<typename realT >
void	gaussian2D (realT *arr, size_t nx, size_t ny, const realT G0, const realT G, const realT x0, const realT y0, const realT sigma)
	Fill in an array with the 2D arbitrarily-centered symmetric Gaussian.
template<typename realT >
realT	gaussian2D (const realT x, const realT y, const realT G0, const realT G, const realT x0, const realT y0, const realT a, const realT b, const realT c)
	Find value at position (x,y) of the 2D general elliptical Gaussian.
template<typename realT >
void	gaussian2D_gen2rot (realT &sigma_x, realT &sigma_y, realT &theta, const realT a, const realT b, const realT c)
	Convert from (a,b,c) to ( \(\sigma_x\), \(\sigma_y\), \(\theta\)) for the elliptical Gaussian.
template<typename realT >
void	gaussian2D_rot2gen (realT &a, realT &b, realT &c, const realT sigma_x, const realT sigma_y, const realT theta)
	Convert from ( \(\sigma_x\), \(\sigma_y\), \(\theta\)) to (a,b,c) for the elliptical Gaussian.
template<typename realT >
realT	gaussian2D_ang (const realT x, const realT y, const realT G0, const realT G, const realT x0, const realT y0, const realT sigma_x, const realT sigma_y, const realT theta)
	Find value at position (x,y) of the 2D rotated elliptical Gaussian.
template<typename realT >
void	gaussian2D (realT *arr, size_t nx, size_t ny, const realT G0, const realT G, const realT x0, const realT y0, const realT a, const realT b, const realT c)
	Fill in an array with the 2D general elliptical Gaussian.
template<typename realT >
void	gaussian2D_ang (realT *arr, size_t nx, size_t ny, const realT G0, const realT G, const realT x0, const realT y0, const realT sigma_x, const realT sigma_y, const realT theta)
	Fill in an array with the 2D general elliptical Gaussian.
template<typename realT >
void	gaussian2D_jacobian (realT *j, const realT x, const realT y, const realT G0, const realT G, const realT x0, const realT y0, const realT a, const realT b, const realT c)
	Calculate the Jacobian at position (x,y) for the 2D general elliptical Gaussian.
template<typename T >
T	jinc (const T &x)
	The Jinc function.
template float	jinc< float > (const float &x)
template double	jinc< double > (const double &x)
template long double	jinc< long double > (const long double &x)
template<typename T1 , typename T2 >
T2	jincN (const T1 &v, const T2 &x)
	The JincN function.
template float	jincN< float, float > (const float &v, const float &x)
template float	jincN< int, float > (const int &v, const float &x)
template double	jincN< double, double > (const double &v, const double &x)
template double	jincN< int, double > (const int &v, const double &x)
template long double	jincN< long double, long double > (const long double &v, const long double &x)
template long double	jincN< int, long double > (const int &v, const long double &x)
template<typename T >
T	legendre_p (int n, T x)
	Legendre Polynomials.
template<>
float	legendre_p< float > (int n, float x)
template<>
double	legendre_p< double > (int n, double x)
template<>
long double	legendre_p< long double > (int n, long double x)
template<typename T >
T	orthoNormalLegendre (int n, T x)
	The orthonormal Legendre polynomials.
template<typename floatT >
floatT	logistic_param (floatT x, floatT thalf)
	Return the logistic function parameter for a specified rise time.
template<typename floatT >
floatT	logistic (floatT t, floatT t0=0, floatT a=1)
	Return the value of the logistic function.
template<typename realT >
realT	moffat (const realT x, const realT I0, const realT Ipk, const realT x0, const realT alpha, const realT beta)
	Find value at position (x) of the 1D arbitrarily-centered symmetric unnormalized Moffat function.
template float	moffat< float > (const float x, const float I0, const float Ipk, const float x0, const float alpha, const float beta)
template double	moffat< double > (const double x, const double I0, const double Ipk, const double x0, const double alpha, const double beta)
template long double	moffat< long double > (const long double x, const long double I0, const long double Ipk, const long double x0, const long double alpha, const long double beta)
template<typename realT >
realT	moffat2D (const realT x, const realT y, const realT I0, const realT Ipk, const realT x0, const realT y0, const realT alpha, const realT beta)
	Find value at position (x,y) of the 2D arbitrarily-centered unnormalized symmetric Moffat function.
template float	moffat2D< float > (const float x, const float y, const float I0, const float Ipk, const float x0, const float y0, const float alpha, const float beta)
template double	moffat2D< double > (const double x, const double y, const double I0, const double Ipk, const double x0, const double y0, const double alpha, const double beta)
template long double	moffat2D< long double > (const long double x, const long double y, const long double I0, const long double Ipk, const long double x0, const long double y0, const long double alpha, const long double beta)
template<typename realT >
realT	moffatFWHM (realT alpha, realT beta)
	Compute the full-width at half-maximum of a Moffat profile.
template float	moffatFWHM (float alpha, float beta)
template double	moffatFWHM (double alpha, double beta)
template long double	moffatFWHM (long double alpha, long double beta)
template<typename T >
T	root_epsilon ()
	Get the sqrt(epsilon) where epsilon is machine precision.
template<>
float	root_epsilon< float > ()
template<>
double	root_epsilon< double > ()
template<typename T >
T	sign (T x)
	The sign function.
template<>
float	sign< float > (float x)
template<>
double	sign< double > (double x)
template<>
long double	sign< long double > (long double x)
template<typename realT >
realT	weibull_lambda (std::vector< realT > &x, realT k, realT x0=0)
	The MLE of the Weibull distribution lambda parameter.
template<typename realT >
realT	weibull (realT x, realT x0, realT k, realT lambda)
	The general shifted Weibull distribution at a point.
template<typename realT >
realT	weibull (realT x, realT k, realT lambda)
	The Weibull distribution at a point.

Function Documentation

apeInt()

template<typename realT >

realT mx::math::func::apeInt	(	realT	x,
		void *	params
	)

Definition at line 188 of file airyPattern.hpp.

References mx::math::six_fifths().

bessel_j< double, double >()

template<>

double mx::math::func::bessel_j< double, double >	(	double	v,
		double	x
	)

bessel_j< float, float >()

template<>

float mx::math::func::bessel_j< float, float >	(	float	v,
		float	x
	)

bessel_j< int, double >()

template<>

double mx::math::func::bessel_j< int, double >	(	int	v,
		double	x
	)

bessel_j< int, float >()

template<>

float mx::math::func::bessel_j< int, float >	(	int	v,
		float	x
	)

bessel_j< int, long double >()

template<>

long double mx::math::func::bessel_j< int, long double >	(	int	v,
		long double	x
	)

bessel_j< long double, long double >()

template<>

long double mx::math::func::bessel_j< long double, long double >	(	long double	v,
		long double	x
	)

factorial< double >()

template<>

double mx::math::func::factorial< double >

(

double

x

)

factorial< float >()

template<>

float mx::math::func::factorial< float >

(

float

x

)

factorial< long double >()

template<>

long double mx::math::func::factorial< long double >

(

long double

x

)

jinc< double >()

template double mx::math::func::jinc< double > ( const double &  x )

extern

jinc< float >()

template float mx::math::func::jinc< float > ( const float &  x )

extern

jinc< long double >()

template long double mx::math::func::jinc< long double > ( const long double &  x )

extern

jincN< double, double >()

template double mx::math::func::jincN< double, double > ( const double &  v, const double &  x  )

extern

jincN< float, float >()

template float mx::math::func::jincN< float, float > ( const float &  v, const float &  x  )

extern

jincN< int, double >()

template double mx::math::func::jincN< int, double > ( const int &  v, const double &  x  )

extern

jincN< int, float >()

template float mx::math::func::jincN< int, float > ( const int &  v, const float &  x  )

extern

jincN< int, long double >()

template long double mx::math::func::jincN< int, long double > ( const int &  v, const long double &  x  )

extern

jincN< long double, long double >()

template long double mx::math::func::jincN< long double, long double > ( const long double &  v, const long double &  x  )

extern

legendre_p< double >()

template<>

double mx::math::func::legendre_p< double >	(	int	n,
		double	x
	)

legendre_p< float >()

template<>

float mx::math::func::legendre_p< float >	(	int	n,
		float	x
	)

legendre_p< long double >()

template<>

long double mx::math::func::legendre_p< long double >	(	int	n,
		long double	x
	)

moffat2D< double >()

template double mx::math::func::moffat2D< double > ( const double  x, const double  y, const double  I0, const double  Ipk, const double  x0, const double  y0, const double  alpha, const double  beta  )

extern

Referenced by SCENARIO().

moffat2D< float >()

template float mx::math::func::moffat2D< float > ( const float  x, const float  y, const float  I0, const float  Ipk, const float  x0, const float  y0, const float  alpha, const float  beta  )

extern

moffat2D< long double >()

template long double mx::math::func::moffat2D< long double > ( const long double  x, const long double  y, const long double  I0, const long double  Ipk, const long double  x0, const long double  y0, const long double  alpha, const long double  beta  )

extern

moffat< double >()

template double mx::math::func::moffat< double > ( const double  x, const double  I0, const double  Ipk, const double  x0, const double  alpha, const double  beta  )

extern

Referenced by SCENARIO().

moffat< float >()

template float mx::math::func::moffat< float > ( const float  x, const float  I0, const float  Ipk, const float  x0, const float  alpha, const float  beta  )

extern

moffat< long double >()

template long double mx::math::func::moffat< long double > ( const long double  x, const long double  I0, const long double  Ipk, const long double  x0, const long double  alpha, const long double  beta  )

extern

moffatFWHM() [1/3]

template double mx::math::func::moffatFWHM ( double  alpha, double  beta  )

extern

moffatFWHM() [2/3]

template float mx::math::func::moffatFWHM ( float  alpha, float  beta  )

extern

moffatFWHM() [3/3]

template long double mx::math::func::moffatFWHM ( long double  alpha, long double  beta  )

extern

orthoNormalLegendre()

template<typename T >

T mx::math::func::orthoNormalLegendre	(	int	n,
		T	x
	)

The orthonormal Legendre polynomials.

A version of the Legendre polynomials which are orthonormal on the interval -1 <= x <= 1.

Returns

the value of the n-th orthonormal Legendre polynomial at x.

Definition at line 87 of file legendre.hpp.

References mx::math::six_fifths().

root_epsilon< double >()

template<>

double mx::math::func::root_epsilon< double >

(

)

root_epsilon< float >()

template<>

float mx::math::func::root_epsilon< float >

(

)

sign< double >()

template<>

double mx::math::func::sign< double >

(

double

x

)

sign< float >()

template<>

float mx::math::func::sign< float >

(

float

x

)

sign< long double >()

template<>

long double mx::math::func::sign< long double >

(

long double

x

)

tgamma< double >()

template<>

double mx::math::func::tgamma< double >

(

double

x

)

tgamma< float >()

template<>

float mx::math::func::tgamma< float >

(

float

x

)

tgamma< long double >()

template<>

long double mx::math::func::tgamma< long double >

(

long double

x

)