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

#include <quadraticEqn.H>

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.
typedef scalar	cmptType
	Component type.
typedef scalar	magType
	Magnitude type.
typedef direction	size_type
	The type to represent the size of a VectorSpace.
typedef scalar *	iterator
	Random access iterator for traversing VectorSpace.
typedef const scalar *	const_iterator
	Random access iterator for traversing VectorSpace.

Public Member Functions
	quadraticEqn ()=default
	Default construct.
	quadraticEqn (const Foam::zero)
	Construct initialized to zero.
	quadraticEqn (const scalar a, const scalar b, const scalar c)
	Construct from components.
scalar	a () const noexcept
scalar	b () const noexcept
scalar	c () const noexcept
scalar &	a () noexcept
scalar &	b () noexcept
scalar &	c () noexcept
scalar	value (const scalar x) const
	Evaluate the quadratic equation at x.
scalar	derivative (const scalar x) const
	Evaluate the derivative of the quadratic equation at x.
scalar	error (const scalar x) const
	Estimate the error of evaluation of the quadratic equation at x.
Roots< 2 >	roots () const
	Return the roots of the quadratic equation with no particular order.
Public Member Functions inherited from VectorSpace< quadraticEqn, scalar, 3 >
const Foam::VectorSpace< quadraticEqn, scalar, Ncmpts >::template ConstBlock< SubVector, BStart >	block () const
	VectorSpace ()=default
	Default construct.
const scalar &	component (const direction) const
void	replace (const direction, const scalar &)
const scalar *	cdata () const noexcept
	Return const pointer to the first data element.
scalar *	data () noexcept
	Return pointer to the first data element.
void	fill (const scalar &s)
	Assign all components to given value.
const scalar &	operator[] (const direction) const
void	operator= (const VectorSpace< quadraticEqn, scalar, Ncmpts > &)
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 (pointer) to begin of VectorSpace.
const_iterator	cbegin () const noexcept
	Return const_iterator (const pointer) to begin of VectorSpace.
iterator	end () noexcept
	Return an iterator (pointer) to end of VectorSpace.
const_iterator	cend () const noexcept
	Return const_iterator (const pointer) to end of VectorSpace.

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.
static quadraticEqn	uniform (const scalar &s)
	Return a VectorSpace with all elements = s.
Public Attributes inherited from VectorSpace< quadraticEqn, scalar, 3 >
scalar	v_ [Ncmpts]
	The components of this vector space.
Static Public Attributes inherited from VectorSpace< quadraticEqn, scalar, 3 >
static constexpr direction	dim
	Dimensionality of space.
static constexpr direction	nComponents
	Number of components in this vector space.
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 84 of file quadraticEqn.H.

Member Enumeration Documentation

◆ components

enum components

Component labeling enumeration.

Enumerator
A
B
C

Definition at line 93 of file quadraticEqn.H.

Constructor & Destructor Documentation

◆ quadraticEqn() [1/3]

quadraticEqn ( )

default

Default construct.

References a(), b(), and c().

Referenced by quadraticEqn().

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◆ quadraticEqn() [2/3]

quadraticEqn ( const Foam::zero )

inline

Construct initialized to zero.

Definition at line 23 of file quadraticEqnI.H.

References quadraticEqn(), VectorSpace< quadraticEqn, scalar, 3 >::VectorSpace(), and VectorSpace< quadraticEqn, scalar, 3 >::zero.

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◆ quadraticEqn() [3/3]

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

inline

Construct from components.

Definition at line 29 of file quadraticEqnI.H.

References A, a(), B, b(), C, c(), and VectorSpace< quadraticEqn, scalar, 3 >::v_.

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Member Function Documentation

◆ a() [1/2]

scalar a ( ) const

inlinenoexcept

Definition at line 118 of file quadraticEqn.H.

References A, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

Referenced by derivative(), error(), quadraticEqn(), quadraticEqn(), roots(), and value().

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◆ b() [1/2]

scalar b ( ) const

inlinenoexcept

Definition at line 119 of file quadraticEqn.H.

References B, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

Referenced by quadraticEqn(), quadraticEqn(), and roots().

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◆ c() [1/2]

scalar c ( ) const

inlinenoexcept

Definition at line 120 of file quadraticEqn.H.

References C, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

Referenced by error(), quadraticEqn(), quadraticEqn(), roots(), and value().

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◆ a() [2/2]

scalar & a ( )

inlinenoexcept

Definition at line 122 of file quadraticEqn.H.

References A, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

◆ b() [2/2]

scalar & b ( )

inlinenoexcept

Definition at line 123 of file quadraticEqn.H.

References B, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

◆ c() [2/2]

scalar & c ( )

inlinenoexcept

Definition at line 124 of file quadraticEqn.H.

References C, Foam::noexcept, and VectorSpace< quadraticEqn, scalar, 3 >::v_.

◆ value()

Foam::scalar value ( const scalar x ) const

inline

Evaluate the quadratic equation at x.

Definition at line 44 of file quadraticEqnI.H.

References a(), b, c(), and x.

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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 50 of file quadraticEqnI.H.

References a(), b, and x.

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◆ error()

Foam::scalar error ( const scalar x ) const

inline

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

Definition at line 56 of file quadraticEqnI.H.

References a(), b, c(), 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 27 of file quadraticEqn.C.

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

Referenced by 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()