General Mathematics

General mathematical utilities.

Classes
class	mx::math::histogramUniform< realT >
	A histogram with uniform bin spacing. More...

Modules
	Constants and units
	Geometry and Geodesy
	Special Functions
	Templatized BLAS and Lapack
	Integration
	Interpolation
	Data Fitting
	Plotting Data
	Random Numbers
	Vector Utilities
	Fourier Transforms
	Methods for calculating the Fourier Transform.
	NVIDIA Cuda Interface
	Gen. Math Files

Functions
template<typename realT >
void	mx::math::quarticRoots (std::vector< std::complex< realT > > &x, realT a, realT b, realT c, realT d, realT e)
	Find the roots of the general quartic equation.

Function Documentation

quarticRoots()

template<typename realT >

void mx::math::quarticRoots	(	std::vector< std::complex< realT > > &	x,
		realT	a,
		realT	b,
		realT	c,
		realT	d,
		realT	e
	)

Find the roots of the general quartic equation.

Finds the roots of

\[ f(x) = a x^4 + b x^3 + c x^2 + d x + e \]

using the general formula for quartic roots. See https://en.wikipedia.org/wiki/Quartic_function.

Template Parameters

realT

is the floating point type used for calculations.

Parameters

[out]	x	On exit contains the 4 roots, is resized to length 4.
[in]	a	the coefficient of the \(x^4\) term.
[in]	b	the coefficient of the \(x^3\) term.
[in]	c	the coefficient of the \(x^2\) term.
[in]	d	the coefficient of the \(x^1\) term.
[in]	e	the coefficient of the \(x^0\) term.

Definition at line 126 of file roots.hpp.

References mx::math::six_fifths().

Referenced by mx::AO::analysis::aoSystem< _realT, _inputSpectT, iosT >::optimumTauWFS().