Classes | Public Member Functions | List of all members
cubicEqn Class Reference

Cubic equation of the form a*x^3 + b*x^2 + c*x + d = 0. More...

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Classes

struct  coefficient
 Coefficient indexing enumeration. More...
 

Public Member Functions

 cubicEqn ()
 Construct null. More...
 
 cubicEqn (const Foam::zero)
 Construct initialised to zero. More...
 
 cubicEqn (const scalar a, const scalar b, const scalar c, const scalar d)
 Construct from components. More...
 
scalar a () const
 
scalar b () const
 
scalar c () const
 
scalar d () const
 
scalar & a ()
 
scalar & b ()
 
scalar & c ()
 
scalar & d ()
 
scalar value (const scalar x) const
 Evaluate at x. More...
 
scalar derivative (const scalar x) const
 Evaluate the derivative at x. More...
 
scalar error (const scalar x) const
 Estimate the error of evaluation at x. More...
 
Roots< 3 > roots () const
 Get the roots. More...
 
- Public Member Functions inherited from VectorSpace< cubicEqn, scalar, 4 >
 VectorSpace ()
 Construct null. More...
 
 VectorSpace (const Foam::zero)
 Construct initialised to zero. More...
 
 VectorSpace (Istream &)
 Construct from Istream. More...
 
 VectorSpace (const VectorSpace< Form2, Cmpt2, Ncmpts > &)
 Construct as copy of a VectorSpace with the same size. More...
 
const scalar & component (const direction) const
 
scalar & component (const direction)
 
void component (scalar &, const direction) const
 
void replace (const direction, const scalar &)
 
const ConstBlock< SubVector, BStart > block () const
 
const VectorSpace< cubicEqn, scalar, Ncmpts >::template ConstBlock< SubVector, BStart > block () const
 
const scalar & operator[] (const direction) const
 
scalar & operator[] (const direction)
 
void operator+= (const VectorSpace< cubicEqn, scalar, Ncmpts > &)
 
void operator-= (const VectorSpace< cubicEqn, scalar, Ncmpts > &)
 
void operator= (const Foam::zero)
 
void operator*= (const scalar)
 
void operator/= (const scalar)
 

Additional Inherited Members

- Public Types inherited from VectorSpace< cubicEqn, scalar, 4 >
typedef VectorSpace< cubicEqn, scalar, Ncmpts > vsType
 VectorSpace type. More...
 
typedef scalar cmptType
 Component type. More...
 
- Static Public Member Functions inherited from VectorSpace< cubicEqn, scalar, 4 >
static direction size ()
 Return the number of elements in the VectorSpace = Ncmpts. More...
 
static cubicEqn uniform (const scalar &s)
 Return a VectorSpace with all elements = s. More...
 
- Public Attributes inherited from VectorSpace< cubicEqn, scalar, 4 >
scalar v_ [Ncmpts]
 The components of this vector space. More...
 
- Static Public Attributes inherited from VectorSpace< cubicEqn, scalar, 4 >
static const direction dim
 Dimensionality of space. More...
 
static const direction nComponents
 Number of components in this vector space. More...
 
static const direction mRows
 
static const direction nCols
 
static const char *const typeName
 
static const char *const componentNames []
 
static const cubicEqn zero
 
static const cubicEqn one
 
static const cubicEqn max
 
static const cubicEqn min
 
static const cubicEqn rootMax
 
static const cubicEqn rootMin
 

Detailed Description

Cubic equation of the form a*x^3 + b*x^2 + c*x + d = 0.

Source files

Definition at line 49 of file cubicEqn.H.

Constructor & Destructor Documentation

◆ cubicEqn() [1/3]

cubicEqn ( )
inline

Construct null.

Definition at line 28 of file cubicEqnI.H.

Referenced by cubicEqn::cubicEqn().

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◆ cubicEqn() [2/3]

cubicEqn ( const Foam::zero  )
inline

Construct initialised to zero.

Definition at line 32 of file cubicEqnI.H.

References cubicEqn::cubicEqn().

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◆ cubicEqn() [3/3]

cubicEqn ( const scalar  a,
const scalar  b,
const scalar  c,
const scalar  d 
)
inline

Construct from components.

Definition at line 39 of file cubicEqnI.H.

References cubicEqn::coefficient::a, cubicEqn::a(), cubicEqn::coefficient::b, cubicEqn::b(), cubicEqn::coefficient::c, cubicEqn::c(), cubicEqn::coefficient::d, cubicEqn::d(), and VectorSpace< cubicEqn, scalar, 4 >::v_.

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Member Function Documentation

◆ a() [1/2]

Foam::scalar a ( ) const
inline

Definition at line 55 of file cubicEqnI.H.

References cubicEqn::coefficient::a, and VectorSpace< cubicEqn, scalar, 4 >::v_.

Referenced by cubicEqn::cubicEqn(), cubicEqn::derivative(), cubicEqn::error(), cubicEqn::roots(), and cubicEqn::value().

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◆ b() [1/2]

Foam::scalar b ( ) const
inline

Definition at line 61 of file cubicEqnI.H.

References cubicEqn::coefficient::b, and VectorSpace< cubicEqn, scalar, 4 >::v_.

Referenced by cubicEqn::cubicEqn(), cubicEqn::derivative(), cubicEqn::error(), cubicEqn::roots(), and cubicEqn::value().

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◆ c() [1/2]

Foam::scalar c ( ) const
inline

Definition at line 67 of file cubicEqnI.H.

References cubicEqn::coefficient::c, and VectorSpace< cubicEqn, scalar, 4 >::v_.

Referenced by cubicEqn::cubicEqn(), cubicEqn::derivative(), cubicEqn::error(), cubicEqn::roots(), and cubicEqn::value().

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◆ d() [1/2]

Foam::scalar d ( ) const
inline

Definition at line 73 of file cubicEqnI.H.

References cubicEqn::coefficient::d, and VectorSpace< cubicEqn, scalar, 4 >::v_.

Referenced by cubicEqn::cubicEqn(), cubicEqn::error(), cubicEqn::roots(), and cubicEqn::value().

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◆ a() [2/2]

Foam::scalar & a ( )
inline

Definition at line 79 of file cubicEqnI.H.

References cubicEqn::coefficient::a, and VectorSpace< cubicEqn, scalar, 4 >::v_.

◆ b() [2/2]

Foam::scalar & b ( )
inline

Definition at line 85 of file cubicEqnI.H.

References cubicEqn::coefficient::b, and VectorSpace< cubicEqn, scalar, 4 >::v_.

◆ c() [2/2]

Foam::scalar & c ( )
inline

Definition at line 91 of file cubicEqnI.H.

References cubicEqn::coefficient::c, and VectorSpace< cubicEqn, scalar, 4 >::v_.

◆ d() [2/2]

Foam::scalar & d ( )
inline

Definition at line 97 of file cubicEqnI.H.

References cubicEqn::coefficient::d, and VectorSpace< cubicEqn, scalar, 4 >::v_.

◆ value()

Foam::scalar value ( const scalar  x) const
inline

Evaluate at x.

Definition at line 103 of file cubicEqnI.H.

References cubicEqn::a(), cubicEqn::b(), cubicEqn::c(), and cubicEqn::d().

Referenced by particle::trackToMovingTri().

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◆ derivative()

Foam::scalar derivative ( const scalar  x) const
inline

Evaluate the derivative at x.

Definition at line 109 of file cubicEqnI.H.

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

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◆ error()

Foam::scalar error ( const scalar  x) const
inline

Estimate the error of evaluation at x.

Definition at line 115 of file cubicEqnI.H.

References cubicEqn::a(), cubicEqn::b(), cubicEqn::c(), cubicEqn::d(), Foam::mag(), and Foam::magSqr().

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◆ roots()

Foam::Roots< 3 > roots ( ) const

Get the roots.

Definition at line 32 of file cubicEqn.C.

References cubicEqn::a(), Foam::atan2(), cubicEqn::b(), cubicEqn::c(), Foam::cbrt(), Foam::cos(), cubicEqn::d(), Foam::hypot(), Foam::mag(), Foam::nan, p, linearEqn::roots(), quadraticEqn::roots(), Foam::sign(), Foam::sin(), Foam::sqrt(), Roots< N >::type(), and x.

Referenced by Foam::eigenValues(), and Foam::triIntersect::solveProjection().

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