Container to encapsulate various operations for quadratic equation of the forms with real coefficients: More...

Inheritance diagram for quadraticEqn:

Collaboration diagram for quadraticEqn:

Public Types
enum	components { A , B , C }
	Component labeling enumeration. More...

Public Types inherited from VectorSpace< quadraticEqn, scalar, 3 >
typedef VectorSpace< quadraticEqn, scalar, Ncmpts >	vsType
	VectorSpace type. More...

typedef scalar	cmptType
	Component type. More...

typedef scalar	magType
	Magnitude type. More...

typedef scalar *	iterator
	Random access iterator for traversing VectorSpace. More...

typedef const scalar *	const_iterator
	Random access iterator for traversing VectorSpace. More...

Public Member Functions
	quadraticEqn ()
	Construct null. More...

	quadraticEqn (const Foam::zero)
	Construct initialized to zero. More...

	quadraticEqn (const scalar a, const scalar b, const scalar c)
	Construct from components. More...

scalar	a () const

scalar	b () const

scalar	c () const

scalar &	a ()

scalar &	b ()

scalar &	c ()

scalar	value (const scalar x) const
	Evaluate the quadratic equation at x. More...

scalar	derivative (const scalar x) const
	Evaluate the derivative of the quadratic equation at x. More...

scalar	error (const scalar x) const
	Estimate the error of evaluation of the quadratic equation at x. More...

Roots< 2 >	roots () const
	Return the roots of the quadratic equation with no particular order. More...

Public Member Functions inherited from VectorSpace< quadraticEqn, scalar, 3 >
	VectorSpace ()=default
	Default construct. More...

	VectorSpace (const Foam::zero)
	Construct initialized to zero. More...

	VectorSpace (const VectorSpace< quadraticEqn, scalar, Ncmpts > &vs)
	Copy construct. More...

	VectorSpace (const VectorSpace< Form2, Cmpt2, Ncmpts > &)
	Copy construct of a VectorSpace with the same size. More...

	VectorSpace (Istream &is)
	Construct from Istream. More...

const scalar &	component (const direction) const

scalar &	component (const direction)

void	component (scalar &, const direction) const

void	replace (const direction, const scalar &)

const scalar *	cdata () const noexcept
	Return const pointer to the first data element. More...

scalar *	data () noexcept
	Return pointer to the first data element. More...

const ConstBlock< SubVector, BStart >	block () const

const Foam::VectorSpace< quadraticEqn, scalar, Ncmpts >::template ConstBlock< SubVector, BStart >	block () const

const scalar &	operator[] (const direction) const

scalar &	operator[] (const direction)

void	operator= (const VectorSpace< quadraticEqn, scalar, Ncmpts > &)

void	operator= (const Foam::zero)

void	operator+= (const VectorSpace< quadraticEqn, scalar, Ncmpts > &)

void	operator-= (const VectorSpace< quadraticEqn, scalar, Ncmpts > &)

void	operator*= (const scalar)

void	operator/= (const scalar)

iterator	begin () noexcept
	Return an iterator to begin of VectorSpace. More...

const_iterator	begin () const noexcept
	Return const_iterator to begin of VectorSpace. More...

iterator	end () noexcept
	Return an iterator to end of VectorSpace. More...

const_iterator	end () const noexcept
	Return const_iterator to end of VectorSpace. More...

const_iterator	cbegin () const noexcept
	Return const_iterator to begin of VectorSpace. More...

const_iterator	cend () const noexcept
	Return const_iterator to end of VectorSpace. More...

Additional Inherited Members
Static Public Member Functions inherited from VectorSpace< quadraticEqn, scalar, 3 >
static constexpr direction	size () noexcept
	The number of elements in the VectorSpace = Ncmpts. More...

static quadraticEqn	uniform (const scalar &s)
	Return a VectorSpace with all elements = s. More...

Public Attributes inherited from VectorSpace< quadraticEqn, scalar, 3 >
scalar	v_ [Ncmpts]
	The components of this vector space. More...

Static Public Attributes inherited from VectorSpace< quadraticEqn, scalar, 3 >
static constexpr direction	dim
	Dimensionality of space. More...

static constexpr direction	nComponents
	Number of components in this vector space. More...

static constexpr direction	mRows

static constexpr direction	nCols

static const char *const	typeName

static const char *const	componentNames []

static const quadraticEqn	zero

static const quadraticEqn	one

static const quadraticEqn	max

static const quadraticEqn	min

static const quadraticEqn	rootMax

static const quadraticEqn	rootMin

Detailed Description

Container to encapsulate various operations for quadratic equation of the forms with real coefficients:

\[ a*x^2 + b*x + c = 0 x^2 + B*x + C = 0 \]

The expressions for the roots of quadraticEqn are as follows:

\[ x1 = - (b + sign(b) sqrt(b^2 - 4ac)/(2*a)) x2 = c/(a*x1) \]

where (b^2 - 4ac) is evaluated by fused multiply-adds to avoid detrimental cancellation.

Reference:

    Cancellation-avoiding quadratic formula (tag:F):
        Ford, W. (2014).
        Numerical linear algebra with applications: Using MATLAB.
        London: Elsevier/Academic Press.
        DOI:10.1016/C2011-0-07533-6

    Kahan's algo. to compute 'b^2-a*c' using fused multiply-adds (tag:JML):
        Jeannerod, C. P., Louvet, N., & Muller, J. M. (2013).
        Further analysis of Kahan's algorithm for the accurate
        computation of 2× 2 determinants.
        Mathematics of Computation, 82(284), 2245-2264.
        DOI:10.1090/S0025-5718-2013-02679-8

See also: Test-quadraticEqn.C

Source files

Definition at line 88 of file quadraticEqn.H.

Member Enumeration Documentation

◆ components

enum components

Component labeling enumeration.

Enumerator
A
B
C

Definition at line 95 of file quadraticEqn.H.

Constructor & Destructor Documentation

◆ quadraticEqn() [1/3]

quadraticEqn ( )

inline

Construct null.

Definition at line 30 of file quadraticEqnI.H.

◆ quadraticEqn() [2/3]

quadraticEqn ( const Foam::zero )

inline

Construct initialized to zero.

Definition at line 34 of file quadraticEqnI.H.

◆ quadraticEqn() [3/3]

quadraticEqn	(	const scalar	a,
		const scalar	b,
		const scalar	c
	)

inline

Construct from components.

Definition at line 40 of file quadraticEqnI.H.

References A, b, and B.

Member Function Documentation

◆ a() [1/2]

Foam::scalar a ( ) const

inline

Definition at line 55 of file quadraticEqnI.H.

References A.

Referenced by quadraticEqn::roots().

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◆ b() [1/2]

Foam::scalar b ( ) const

inline

Definition at line 61 of file quadraticEqnI.H.

References B.

Referenced by quadraticEqn::roots().

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◆ c() [1/2]

Foam::scalar c ( ) const

inline

Definition at line 67 of file quadraticEqnI.H.

Referenced by quadraticEqn::roots().

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◆ a() [2/2]

Foam::scalar & a ( )

inline

Definition at line 73 of file quadraticEqnI.H.

References A.

◆ b() [2/2]

Foam::scalar & b ( )

inline

Definition at line 79 of file quadraticEqnI.H.

References B.

◆ c() [2/2]

Foam::scalar & c ( )

inline

Definition at line 85 of file quadraticEqnI.H.

◆ value()

Foam::scalar value ( const scalar x ) const

inline

Evaluate the quadratic equation at x.

Definition at line 91 of file quadraticEqnI.H.

References b, quadraticEqn::value(), and x.

Referenced by quadraticEqn::value().

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◆ derivative()

Foam::scalar derivative ( const scalar x ) const

inline

Evaluate the derivative of the quadratic equation at x.

Definition at line 97 of file quadraticEqnI.H.

References b, and x.

◆ error()

Foam::scalar error ( const scalar x ) const

inline

Estimate the error of evaluation of the quadratic equation at x.

Definition at line 103 of file quadraticEqnI.H.

References b, Foam::mag(), and x.

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◆ roots()

Foam::Roots< 2 > roots ( ) const

Return the roots of the quadratic equation with no particular order.

if discriminant > 0: return two distinct real roots if discriminant < 0: return one of the complex conjugate-pair roots otherwise : return two identical real roots

Definition at line 34 of file quadraticEqn.C.

References quadraticEqn::a(), quadraticEqn::b(), quadraticEqn::c(), Foam::roots::complex, Foam::mag(), Foam::roots::nan, quadraticEqn::roots(), Foam::sign(), Foam::sqrt(), and x.

Referenced by quadraticEqn::roots().

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

src/OpenFOAM/primitives/polynomialEqns/quadraticEqn/quadraticEqn.H
src/OpenFOAM/primitives/polynomialEqns/quadraticEqn/quadraticEqn.C
src/OpenFOAM/primitives/polynomialEqns/quadraticEqn/quadraticEqnI.H

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ components

Constructor & Destructor Documentation

◆ quadraticEqn() [1/3]

◆ quadraticEqn() [2/3]

◆ quadraticEqn() [3/3]

Member Function Documentation

◆ a() [1/2]

◆ b() [1/2]

◆ c() [1/2]

◆ a() [2/2]

◆ b() [2/2]

◆ c() [2/2]

◆ value()

◆ derivative()

◆ error()

◆ roots()