Cubic equation of the form a*x^3 + b*x^2 + c*x + d = 0. More...
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 bool real=false) 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 Type) |
| void | operator/= (const Type) |
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 |
| static const cubicEqn | nan |
Cubic equation of the form a*x^3 + b*x^2 + c*x + d = 0.
Definition at line 49 of file cubicEqn.H.
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Construct null.
Definition at line 28 of file cubicEqnI.H.
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Construct initialised to zero.
Definition at line 32 of file cubicEqnI.H.
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Construct from components.
Definition at line 38 of file cubicEqnI.H.
References b, and Foam::constant::universal::c.
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Definition at line 55 of file cubicEqnI.H.
Referenced by cubicEqn::roots().
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Definition at line 61 of file cubicEqnI.H.
References b.
Referenced by cubicEqn::roots().
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Definition at line 67 of file cubicEqnI.H.
References Foam::constant::universal::c.
Referenced by cubicEqn::roots().
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Definition at line 73 of file cubicEqnI.H.
Referenced by cubicEqn::roots().
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Definition at line 79 of file cubicEqnI.H.
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Definition at line 85 of file cubicEqnI.H.
References b.
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Definition at line 91 of file cubicEqnI.H.
References Foam::constant::universal::c.
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Definition at line 97 of file cubicEqnI.H.
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Evaluate at x.
Definition at line 103 of file cubicEqnI.H.
References b, Foam::constant::universal::c, and x.
Referenced by Foam::tracking::toMovingTri().
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Evaluate the derivative at x.
Definition at line 109 of file cubicEqnI.H.
References b, Foam::constant::universal::c, and x.
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Estimate the error of evaluation at x.
Definition at line 115 of file cubicEqnI.H.
References b, Foam::constant::universal::c, Foam::mag(), Foam::magSqr(), and x.
| Foam::Roots< 3 > roots | ( | const bool | real = false | ) | const |
Get the roots.
Set real true if the roots are known to be real even if round-off error might cause them to be complex
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, Foam::real, linearEqn::roots(), Foam::sign(), Foam::sin(), Foam::sqrt(), Roots< N >::type(), and x.
Referenced by Foam::eigenValues(), and Foam::triIntersect::solveProjection().
1.9.1 
