Various mathematical functions. More...

Enumerations
enum	EFFTDirection { FORWARD_FFT , BACKWARD_FFT }

Functions
complex_t	Bessel_J0_PowSer (const complex_t z)
	Computes complex Bessel function J0(z), using power series and asymptotic expansion. More...

complex_t	Bessel_J1_PowSer (const complex_t z)
	Computes complex Bessel function J0(z), using power series and asymptotic expansion. More...

double	StandardNormal (double x)

double	Gaussian (double x, double average, double std_dev)

double	IntegratedGaussian (double x, double average, double std_dev)

double	cot (double x)
	cotangent function: $cot(x)\equiv1/tan(x)$

double	Si (double x)
	Sine integral function: $Si(x)\equiv\int_0^x du \sin(u)/u$ .

double	sinc (double x)
	sinc function: $sinc(x)\equiv\sin(x)/x$

complex_t	sinc (const complex_t z)
	Complex sinc function: $sinc(x)\equiv\sin(x)/x$ .

complex_t	tanhc (const complex_t z)
	Complex tanhc function: $tanhc(x)\equiv\tanh(x)/x$ .

double	Laue (const double x, size_t N)
	Real Laue function: $Laue(x,N)\equiv\sin(Nx)/sin(x)$ .

double	erf (double arg)
	Error function of real-valued argument.

double	Bessel_J0 (double x)
	Bessel function of the first kind and order 0.

double	Bessel_J1 (double x)
	Bessel function of the first kind and order 1.

double	Bessel_J1c (double x)
	Bessel function Bessel_J1(x)/x.

double	Bessel_I0 (double x)
	Modified Bessel function of the first kind and order 0.

complex_t	Bessel_J0 (const complex_t z)
	Complex Bessel function of the first kind and order 0.

complex_t	Bessel_J1 (const complex_t z)
	Complex Bessel function of the first kind and order 1.

complex_t	Bessel_J1c (const complex_t z)
	Complex Bessel function Bessel_J1(x)/x.

std::vector< complex_t >	FastFourierTransform (const std::vector< complex_t > &data, EFFTDirection tcase)
	simple (and unoptimized) wrapper function for the discrete fast Fourier transformation library (fftw3)

std::vector< complex_t >	FastFourierTransform (const std::vector< double > &data, EFFTDirection tcase)
	simple (and unoptimized) wrapper function for the discrete fast Fourier transformation library (fftw3); transforms real to complex

std::vector< complex_t >	ConvolveFFT (const std::vector< double > &signal, const std::vector< double > &resfunc)
	convolution of two real vectors of equal size

double	GenerateUniformRandom ()

double	GenerateStandardNormalRandom ()

double	GenerateNormalRandom (double average, double std_dev)

double	GeneratePoissonRandom (double average)

Detailed Description

Various mathematical functions.

Function Documentation

◆ Bessel_J0_PowSer()

complex_t MathFunctions::Bessel_J0_PowSer ( const complex_t z )

Computes complex Bessel function J0(z), using power series and asymptotic expansion.

Computes the complex Bessel function J0(z), using power series and asymptotic expansion.

Forked from unoptimized code at http://www.crbond.com/math.htm, who refers to "Computation of Special Functions", Zhang and Jin, John Wiley and Sons, 1996.

Definition at line 163 of file MathFunctions.cpp.

◆ Bessel_J1_PowSer()

complex_t MathFunctions::Bessel_J1_PowSer ( const complex_t z )

Computes complex Bessel function J0(z), using power series and asymptotic expansion.

Computes the complex Bessel function J1(z), using power series and asymptotic expansion.

Forked from same source as for Bessel_J0_PowSer

Definition at line 223 of file MathFunctions.cpp.

Enumerations

Functions

Detailed Description

Function Documentation

◆ Bessel_J0_PowSer()

◆ Bessel_J1_PowSer()