roots.hpp File Reference

Declares and defines functions for finding roots. More...

Declares and defines functions for finding roots.

Author

Jared R. Males (jared.nosp@m.male.nosp@m.s@gma.nosp@m.il.c.nosp@m.om)

Definition in file roots.hpp.

Go to the source code of this file.

Namespaces
	mx
	The mxlib c++ namespace.

Functions
template<typename realT >
realT	mx::math::cubicDescriminant (const realT &a, const realT &b, const realT &c, const realT &d)
	Calculate the descriminant for the general cubic. More...
template<typename realT >
realT	mx::math::cubicDescriminant (const realT &p, const realT &q)
	Calculate the descriminant for the depressed cubic. More...
template<typename realT >
void	mx::math::cubicDepressed (realT &p, realT &q, const realT &a, const realT &b, const realT &c, const realT &d)
	Convert a general cubic equation to depressed form. More...
template<typename realT >
realT	mx::math::cubicRealRoot (const realT &p, const realT &q)
	Calculate the real root for a depressed cubic with negative descriminant. More...
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. More...

Function Documentation

cubicDepressed()

template<typename realT >

void mx::math::cubicDepressed	(	realT &	p,
		realT &	q,
		const realT &	a,
		const realT &	b,
		const realT &	c,
		const realT &	d
	)

Convert a general cubic equation to depressed form.

The general cubic is

\[ ax^3 + bx^2 + cx + d = 0 \]

which can be converted to compressed form

\[ t^3 + pt + q = 0 \]

Parameters

[out]	p	the 1st order coefficient of the depressed cubic
[out]	q	the 0th order coefficient of the depressed cubic
[in]	a	the 3rd order coefficient of the general cubic
[in]	b	the 2nd order coefficient of the general cubic
[in]	c	the 1st order coefficient of the general cubic
[in]	d	the 0th order coefficient of the general cubic

Definition at line 81 of file roots.hpp.

References mx::astro::constants::c(), and mx::math::cubicDepressed().

Referenced by mx::math::cubicDepressed().

cubicDescriminant() [1/2]

template<typename realT >

realT mx::math::cubicDescriminant	(	const realT &	a,
		const realT &	b,
		const realT &	c,
		const realT &	d
	)

Calculate the descriminant for the general cubic.

Returns

the descriminant

Parameters

[in]	a	the 3rd order coefficient of the general cubic
[in]	b	the 2nd order coefficient of the general cubic
[in]	c	the 1st order coefficient of the general cubic
[in]	d	the 0th order coefficient of the general cubic

Definition at line 44 of file roots.hpp.

References mx::astro::constants::c(), and mx::math::cubicDescriminant().

Referenced by mx::math::cubicDescriminant().

cubicDescriminant() [2/2]

template<typename realT >

realT mx::math::cubicDescriminant	(	const realT &	p,
		const realT &	q
	)

Calculate the descriminant for the depressed cubic.

Returns

the descriminant

Parameters

[in]	p	the 0th order coefficient of the depressed cubic
[in]	q	the 0th order coefficient of the depressed cubic

Definition at line 62 of file roots.hpp.

References mx::math::cubicDescriminant().

cubicRealRoot()

template<typename realT >

realT mx::math::cubicRealRoot	(	const realT &	p,
		const realT &	q
	)

Calculate the real root for a depressed cubic with negative descriminant.

Returns

the real root for a depressed cubic defined by p and q

Exceptions

std::runtime_error

if there are 3 real roots

Parameters

[in]	p	the 1st order coefficient of the depressed cubic
[in]	q	the 0th order coefficient of the depressed cubic

Definition at line 101 of file roots.hpp.

References mx::math::cubicRealRoot().

Referenced by mx::math::cubicRealRoot().