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Classes | Namespaces | Macros | Functions
LambertW.hh File Reference
#include <cmath>
#include <limits>

Go to the source code of this file.

Classes

struct  utl::Polynomial< Float, Tag, order >
 
struct  utl::Horner< Float, Tag, order >
 
struct  utl::Horner< Float, Tag, 0 >
 
class  utl::BranchPoint
 
class  utl::AsymptoticPolynomialB< order >
 
class  utl::AsymptoticPolynomialA
 
struct  utl::LogRecursionImpl< Float, branch, order >
 
struct  utl::LogRecursionImpl< Float, branch, 0 >
 
class  utl::Branch< Float, branch >
 
struct  utl::Iterator< Float, IterationStep >
 
struct  utl::Iterator< Float, IterationStep >::Depth< n, class >
 
struct  utl::Iterator< Float, IterationStep >::Depth< 1, T >
 
struct  utl::Iterator< Float, IterationStep >::Depth< 0, T >
 
struct  utl::Pade< Float, branch, n >
 
struct  utl::Pade< Float, 0, 1 >
 
struct  utl::Pade< Float, 0, 2 >
 
struct  utl::Pade< Float, -1, 4 >
 
struct  utl::Pade< Float, -1, 5 >
 
struct  utl::Pade< Float, -1, 6 >
 
struct  utl::Pade< Float, -1, 7 >
 

Namespaces

namespace  utl
 

Macros

#define HORNER_COEFF(_Tag_, _i_, _c_)
 
#define HORNER_COEFF2(_Tag_, _i_, _c_y_)
 
#define HORNER0(F, x, c0)
 
#define HORNER1(F, x, c1, c0)
 
#define HORNER2(F, x, c2, c1, c0)
 
#define HORNER3(F, x, c3, c2, c1, c0)
 
#define HORNER4(F, x, c4, c3, c2, c1, c0)
 
#define HORNER5(F, x, c5, c4, c3, c2, c1, c0)
 
#define HORNER6(F, x, c6, c5, c4, c3, c2, c1, c0)
 
#define HORNER7(F, x, c7, c6, c5, c4, c3, c2, c1, c0)
 
#define HORNER8(F, x, c8, c7, c6, c5, c4, c3, c2, c1, c0)
 
#define HORNER9(F, x, c9, c8, c7, c6, c5, c4, c3, c2, c1, c0)
 
#define Y2(d1, c12, d2)
 
#define Y3(d1, c12, d2, c23, d3)
 
#define Y4(d1, c12, d2, c23, d3, c34, d4)
 
#define Y5(d1, c12, d2, c23, d3, c34, d4, c45, d5)
 
#define Y6(d1, c12, d2, c23, d3, c34, d4, c45, d5, c56, d6)
 
#define Y7(d1, c12, d2, c23, d3, c34, d4, c45, d5, c56, d6, c67, d7)
 

Functions

 utl::HORNER_COEFF (BranchPoint, 0, -1)
 
 utl::HORNER_COEFF (BranchPoint, 1, 1)
 
 utl::HORNER_COEFF (BranchPoint, 2, -0.333333333333333333e0)
 
 utl::HORNER_COEFF (BranchPoint, 3, 0.152777777777777777e0)
 
 utl::HORNER_COEFF (BranchPoint, 4, -0.79629629629629630e-1)
 
 utl::HORNER_COEFF (BranchPoint, 5, 0.44502314814814814e-1)
 
 utl::HORNER_COEFF (BranchPoint, 6, -0.25984714873603760e-1)
 
 utl::HORNER_COEFF (BranchPoint, 7, 0.15635632532333920e-1)
 
 utl::HORNER_COEFF (BranchPoint, 8, -0.96168920242994320e-2)
 
 utl::HORNER_COEFF (BranchPoint, 9, 0.60145432529561180e-2)
 
 utl::HORNER_COEFF (BranchPoint, 10, -0.38112980348919993e-2)
 
 utl::HORNER_COEFF (BranchPoint, 11, 0.24408779911439826e-2)
 
 utl::HORNER_COEFF (BranchPoint, 12, -0.15769303446867841e-2)
 
 utl::HORNER_COEFF (BranchPoint, 13, 0.10262633205076071e-2)
 
 utl::HORNER_COEFF (BranchPoint, 14, -0.67206163115613620e-3)
 
 utl::HORNER_COEFF (BranchPoint, 15, 0.44247306181462090e-3)
 
 utl::HORNER_COEFF (BranchPoint, 16, -0.29267722472962746e-3)
 
 utl::HORNER_COEFF (BranchPoint, 17, 0.19438727605453930e-3)
 
 utl::HORNER_COEFF (BranchPoint, 18, -0.12957426685274883e-3)
 
 utl::HORNER_COEFF (BranchPoint, 19, 0.86650358052081260e-4)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 2 >, 0, 0)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 2 >, 1, -1)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 2 >, 2, 1./2)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 3 >, 0, 0)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 3 >, 1, 1)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 3 >, 2, -3./2)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 3 >, 3, 1./3)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 4 >, 0, 0)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 4 >, 1, -1)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 4 >, 2, 3)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 4 >, 3, -11./6)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 4 >, 4, 1./4)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 0, 0)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 1, 1)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 2, -5)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 3, 35./6)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 4, -25./12)
 
 utl::HORNER_COEFF (AsymptoticPolynomialB< 5 >, 5, 1./5)
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 0, -y)
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 1, y)
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 2,(Horner< Float, AsymptoticPolynomialB< 2 >, 2 >::Eval(y)))
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 3,(Horner< Float, AsymptoticPolynomialB< 3 >, 3 >::Eval(y)))
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 4,(Horner< Float, AsymptoticPolynomialB< 4 >, 4 >::Eval(y)))
 
 utl::HORNER_COEFF2 (AsymptoticPolynomialA, 5,(Horner< Float, AsymptoticPolynomialB< 5 >, 5 >::Eval(y)))
 
template<typename Float , int order>
Float utl::AsymptoticExpansionImpl (const Float a, const Float b)
 
template<typename Float >
Float utl::HalleyStep (const Float x, const Float w)
 
template<typename Float >
Float utl::FritschStep (const Float x, const Float w)
 
template<typename Float >
Float utl::SchroederStep (const Float x, const Float w)
 
template<int branch>
double utl::LambertW (const double x)
 
template<>
double utl::LambertW< 0 > (const double x)
 
template<>
double utl::LambertW<-1 > (const double x)
 
double utl::LambertW (const int branch, const double x)
 

Macro Definition Documentation

◆ HORNER_COEFF

#define HORNER_COEFF ( _Tag_,
_i_,
_c_ )
Value:
template<typename Float> struct Polynomial<Float, _Tag_, _i_> { static Float Coeff() { return Float(_c_); } }

Definition at line 62 of file LambertW.hh.

62#define HORNER_COEFF(_Tag_, _i_, _c_) \
63 template<typename Float> struct Polynomial<Float, _Tag_, _i_> { static Float Coeff() { return Float(_c_); } }

◆ HORNER_COEFF2

#define HORNER_COEFF2 ( _Tag_,
_i_,
_c_y_ )
Value:
template<typename Float> struct Polynomial<Float, _Tag_, _i_> { static Float Coeff(const Float y) { return Float(_c_y_); } }

Definition at line 64 of file LambertW.hh.

64#define HORNER_COEFF2(_Tag_, _i_, _c_y_) \
65 template<typename Float> struct Polynomial<Float, _Tag_, _i_> { static Float Coeff(const Float y) { return Float(_c_y_); } }

◆ HORNER0

#define HORNER0 ( F,
x,
c0 )
Value:
(F)(c0)

Definition at line 68 of file LambertW.hh.

◆ HORNER1

#define HORNER1 ( F,
x,
c1,
c0 )
Value:
HORNER0(F, x, (F)(c1)*(x) + (F)(c0) )
c1
TCanvas * c1
Global variables to handle mouse events.
Definition JDrawModule3D.cc:35
HORNER0
#define HORNER0(F, x, c0)
Definition LambertW.hh:68

Definition at line 69 of file LambertW.hh.

◆ HORNER2

#define HORNER2 ( F,
x,
c2,
c1,
c0 )
Value:
HORNER1(F, x, (F)(c2)*(x) + (F)(c1), c0)
HORNER1
#define HORNER1(F, x, c1, c0)
Definition LambertW.hh:69

Definition at line 70 of file LambertW.hh.

◆ HORNER3

#define HORNER3 ( F,
x,
c3,
c2,
c1,
c0 )
Value:
HORNER2(F, x, (F)(c3)*(x) + (F)(c2), c1, c0)
HORNER2
#define HORNER2(F, x, c2, c1, c0)
Definition LambertW.hh:70

Definition at line 71 of file LambertW.hh.

◆ HORNER4

#define HORNER4 ( F,
x,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER3(F, x, (F)(c4)*(x) + (F)(c3), c2, c1, c0)
HORNER3
#define HORNER3(F, x, c3, c2, c1, c0)
Definition LambertW.hh:71

Definition at line 72 of file LambertW.hh.

◆ HORNER5

#define HORNER5 ( F,
x,
c5,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER4(F, x, (F)(c5)*(x) + (F)(c4), c3, c2, c1, c0)
HORNER4
#define HORNER4(F, x, c4, c3, c2, c1, c0)
Definition LambertW.hh:72

Definition at line 73 of file LambertW.hh.

◆ HORNER6

#define HORNER6 ( F,
x,
c6,
c5,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER5(F, x, (F)(c6)*(x) + (F)(c5), c4, c3, c2, c1, c0)
HORNER5
#define HORNER5(F, x, c5, c4, c3, c2, c1, c0)
Definition LambertW.hh:73

Definition at line 74 of file LambertW.hh.

◆ HORNER7

#define HORNER7 ( F,
x,
c7,
c6,
c5,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER6(F, x, (F)(c7)*(x) + (F)(c6), c5, c4, c3, c2, c1, c0)
HORNER6
#define HORNER6(F, x, c6, c5, c4, c3, c2, c1, c0)
Definition LambertW.hh:74

Definition at line 75 of file LambertW.hh.

◆ HORNER8

#define HORNER8 ( F,
x,
c8,
c7,
c6,
c5,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER7(F, x, (F)(c8)*(x) + (F)(c7), c6, c5, c4, c3, c2, c1, c0)
HORNER7
#define HORNER7(F, x, c7, c6, c5, c4, c3, c2, c1, c0)
Definition LambertW.hh:75

Definition at line 76 of file LambertW.hh.

◆ HORNER9

#define HORNER9 ( F,
x,
c9,
c8,
c7,
c6,
c5,
c4,
c3,
c2,
c1,
c0 )
Value:
HORNER8(F, x, (F)(c9)*(x) + (F)(c8), c7, c6, c5, c4, c3, c2, c1, c0)
HORNER8
#define HORNER8(F, x, c8, c7, c6, c5, c4, c3, c2, c1, c0)
Definition LambertW.hh:76

Definition at line 77 of file LambertW.hh.

◆ Y2

#define Y2 ( d1,
c12,
d2 )
Value:
((c12) ? (d1) : (d2))

Definition at line 82 of file LambertW.hh.

82#define Y2(d1, c12, d2) \
83 ((c12) ? (d1) : (d2))

◆ Y3

#define Y3 ( d1,
c12,
d2,
c23,
d3 )
Value:
Y2(Y2(d1, c12, d2), c23, d3)
Y2
#define Y2(d1, c12, d2)
Definition LambertW.hh:82

Definition at line 84 of file LambertW.hh.

84#define Y3(d1, c12, d2, c23, d3) \
85 Y2(Y2(d1, c12, d2), c23, d3)

◆ Y4

#define Y4 ( d1,
c12,
d2,
c23,
d3,
c34,
d4 )
Value:
Y3(d1, c12, d2, c23, Y2(d3, c34, d4))
Y3
#define Y3(d1, c12, d2, c23, d3)
Definition LambertW.hh:84

Definition at line 86 of file LambertW.hh.

86#define Y4(d1, c12, d2, c23, d3, c34, d4) \
87 Y3(d1, c12, d2, c23, Y2(d3, c34, d4))

◆ Y5

#define Y5 ( d1,
c12,
d2,
c23,
d3,
c34,
d4,
c45,
d5 )
Value:
Y4(Y2(d1, c12, d2), c23, d3, c34, d4, c45, d5)
Y4
#define Y4(d1, c12, d2, c23, d3, c34, d4)
Definition LambertW.hh:86

Definition at line 88 of file LambertW.hh.

88#define Y5(d1, c12, d2, c23, d3, c34, d4, c45, d5) \
89 Y4(Y2(d1, c12, d2), c23, d3, c34, d4, c45, d5)

◆ Y6

#define Y6 ( d1,
c12,
d2,
c23,
d3,
c34,
d4,
c45,
d5,
c56,
d6 )
Value:
Y5(d1, c12, d2, c23, d3, c34, d4, c45, Y2(d5, c56, d6))
Y5
#define Y5(d1, c12, d2, c23, d3, c34, d4, c45, d5)
Definition LambertW.hh:88

Definition at line 90 of file LambertW.hh.

90#define Y6(d1, c12, d2, c23, d3, c34, d4, c45, d5, c56, d6) \
91 Y5(d1, c12, d2, c23, d3, c34, d4, c45, Y2(d5, c56, d6))

◆ Y7

#define Y7 ( d1,
c12,
d2,
c23,
d3,
c34,
d4,
c45,
d5,
c56,
d6,
c67,
d7 )
Value:
Y6(d1, c12, d2, c23, Y2(d3, c34, d4), c45, d5, c56, d6, c67, d7)
Y6
#define Y6(d1, c12, d2, c23, d3, c34, d4, c45, d5, c56, d6)
Definition LambertW.hh:90

Definition at line 92 of file LambertW.hh.

92#define Y7(d1, c12, d2, c23, d3, c34, d4, c45, d5, c56, d6, c67, d7) \
93 Y6(d1, c12, d2, c23, Y2(d3, c34, d4), c45, d5, c56, d6, c67, d7)
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