Ocean::EquationT< T > Class Template Reference

This class provides several functions to solve equations with different degree using floating point values with the precission specified by type T. More...

#include <Equation.h>

Static Public Member Functions
static bool	solveLinear (const T a, const T b, T &x)
	Solves a linear eqation with the form:
static bool	solveQuadratic (const T a, const T b, const T c, T &x1, T &x2)
	Solves an quadratic equation with the form:
static unsigned int	solveCubic (const T a, const T b, const T c, const T d, T &x1, T &x2, T &x3, const bool refine=true)
	Solves a cubic equation with the from:
static unsigned int	solveQuartic (const T a, const T b, const T c, const T d, const T e, T *x, const bool refine=true)
	Solves a quartic equation with the form:
static unsigned int	optimizeCubic (const T a, const T b, const T c, const T d, T &x, const unsigned int maxIterations=10u, const T updateFactor=T(1.0))
	Optimizes a root of a cubic equation using Newton-Raphson iterations.
static unsigned int	optimizeQuartic (const T a, const T b, const T c, const T d, const T e, T &x, const unsigned int maxIterations=10u, const T updateFactor=T(1.0))
	Optimizes a root of a quartic equation using Newton-Raphson iterations.

Detailed Description

template<typename T>
class Ocean::EquationT< T >

This class provides several functions to solve equations with different degree using floating point values with the precission specified by type T.

Template Parameters

T	Type of passed floating point values

See also

Equation, EquationF, EquationD.

Member Function Documentation

optimizeCubic()

template<typename T >

unsigned int Ocean::EquationT< T >::optimizeCubic ( const T  a, const T  b, const T  c, const T  d, T &  x, const unsigned int  maxIterations = 10u, const T  updateFactor = T(1.0)  )

static

Optimizes a root of a cubic equation using Newton-Raphson iterations.

The function optimizes a known x for the following equation:

ax^3 + bx^2 + cx + d = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
c	C parameter, with range (-infinity, infinity)
d	D parameter, with range (-infinity, infinity)
x	The known root to optimize, with range (-infinity, infinity)
maxIterations	The maximum number of Newton-Raphson iterations, with range [1, infinity)
updateFactor	The update factor for the Newton-Raphson iterations, with range (0, 2]

Returns

The number of applied iterations, with range [0, maxIterations], 0 if the root could not be optimized

optimizeQuartic()

template<typename T >

unsigned int Ocean::EquationT< T >::optimizeQuartic ( const T  a, const T  b, const T  c, const T  d, const T  e, T &  x, const unsigned int  maxIterations = 10u, const T  updateFactor = T(1.0)  )

static

Optimizes a root of a quartic equation using Newton-Raphson iterations.

The function optimizes a known x for the following equation:

ax^4 + bx^3 + cx^2 + dx + e = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
c	C parameter, with range (-infinity, infinity)
d	D parameter, with range (-infinity, infinity)
e	E parameter, with range (-infinity, infinity)
x	The known root to optimize, with range (-infinity, infinity)
maxIterations	The maximum number of Newton-Raphson iterations, with range [1, infinity)
updateFactor	The update factor for the Newton-Raphson iterations, with range (0, 2]

Returns

The number of applied iterations, with range [0, maxIterations], 0 if the root could not be optimized

solveCubic()

template<typename T >

unsigned int Ocean::EquationT< T >::solveCubic ( const T  a, const T  b, const T  c, const T  d, T &  x1, T &  x2, T &  x3, const bool  refine = true  )

static

Solves a cubic equation with the from:

ax^3 + bx^2 + cx + d = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
c	C parameter, with range (-infinity, infinity)
d	D parameter, with range (-infinity, infinity)
x1	First resulting solution, with range (-infinity, infinity)
x2	Second resulting solution, with range (-infinity, infinity)
x3	Third resulting solution, with range (-infinity, infinity)
refine	True, to refine the calculated solutions with an iterative algorithm; False, to use the roots as calculated

Returns

The number of solutions, with range [0, 3]

solveLinear()

template<typename T >

bool Ocean::EquationT< T >::solveLinear ( const T  a, const T  b, T &  x  )

static

Solves a linear eqation with the form:

ax + b = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
x	Resulting solution

Returns

True, if succeeded

solveQuadratic()

template<typename T >

bool Ocean::EquationT< T >::solveQuadratic ( const T  a, const T  b, const T  c, T &  x1, T &  x2  )

static

Solves an quadratic equation with the form:

ax^2 + bx + c = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
c	C parameter, with range (-infinity, infinity)
x1	First resulting solution, with range (-infinity, infinity)
x2	Second resulting solution, with range (-infinity, infinity)

Returns

True, if succeeded

solveQuartic()

template<typename T >

unsigned int Ocean::EquationT< T >::solveQuartic ( const T  a, const T  b, const T  c, const T  d, const T  e, T *  x, const bool  refine = true  )

static

Solves a quartic equation with the form:

ax^4 + bx^3 + cx^2 + dx + e = 0

Parameters

a	A parameter, with range (-infinity, infinity) \ {0}, (must not be 0)
b	B parameter, with range (-infinity, infinity)
c	C parameter, with range (-infinity, infinity)
d	D parameter, with range (-infinity, infinity)
e	E parameter, with range (-infinity, infinity)
x	Array with at least four scalar values receiving the (at most) four solutions
refine	True, to refine the calculated solutions with an iterative algorithm; False, to use the roots as calculated

Returns

The number of solutions, with range [0, 4]

y^4 + alpha * y^2 + beta * y + gamma = 0

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The documentation for this class was generated from the following file:

• Equation.h