# FoundationClasses
TKMath
PLib

# PLib_JacobiPolynomial Class Reference

This class provides method to work with Jacobi Polynomials
relativly to an order of constraint
q = myWorkDegree-2*(myNivConstr+1)
Jk(t) for k=0,q compose the Jacobi Polynomial base relativly to the weigth W(t)
iorder is the integer value for the constraints:
iorder = 0 <=> ConstraintOrder = GeomAbs_C0
iorder = 1 <=> ConstraintOrder = GeomAbs_C1
iorder = 2 <=> ConstraintOrder = GeomAbs_C2
P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2)
the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:
c0(1) c0(2) .... c0(Dimension)
c1(1) c1(2) .... c1(Dimension)
cDegree(1) cDegree(2) .... cDegree(Dimension)
The coefficients
c0(1) c0(2) .... c0(Dimension)
c2*ordre+1(1) ... c2*ordre+1(dimension)
represents the part of the polynomial in the
canonical base: R(t)
R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1
The following coefficients represents the part of the
polynomial in the Jacobi base ie Q(t)
Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2
.

`#include <PLib_JacobiPolynomial.hxx>`

Inheritance diagram for PLib_JacobiPolynomial:

[legend]

## Public Member Functions

Standard_EXPORT | PLib_JacobiPolynomial (const Standard_Integer WorkDegree, const GeomAbs_Shape ConstraintOrder)
| Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2 .
Standard_EXPORT void | Points (const Standard_Integer NbGaussPoints, TColStd_Array1OfReal &TabPoints) const

returns the Jacobi Points for Gauss integration ie
the positive values of the Legendre roots by increasing values
NbGaussPoints is the number of points choosen for the integral
computation.
TabPoints (0,NbGaussPoints/2)
TabPoints (0) is loaded only for the odd values of NbGaussPoints
The possible values for NbGaussPoints are : 8, 10,
15, 20, 25, 30, 35, 40, 50, 61
NbGaussPoints must be greater than Degree

Standard_EXPORT void | Weights (const Standard_Integer NbGaussPoints, TColStd_Array2OfReal &TabWeights) const

returns the Jacobi weigths for Gauss integration only for
the positive values of the Legendre roots in the order they
are given by the method Points
NbGaussPoints is the number of points choosen for the integral
computation.
TabWeights (0,NbGaussPoints/2,0,Degree)
TabWeights (0,.) are only loaded for the odd values of NbGaussPoints
The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30,
35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree

Standard_EXPORT void | MaxValue (TColStd_Array1OfReal &TabMax) const
| this method loads for k=0,q the maximum value of abs ( W(t)*Jk(t) )for t bellonging to [-1,1] This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1)) MaxValue ( me ; TabMaxPointer : in out Real );
Standard_EXPORT Standard_Real | MaxError (const Standard_Integer Dimension, Standard_Real &JacCoeff, const Standard_Integer NewDegree) const
| This method computes the maximum error on the polynomial W(t) Q(t) obtained by missing the coefficients of JacCoeff from NewDegree +1 to Degree .
Standard_EXPORT void | ReduceDegree (const Standard_Integer Dimension, const Standard_Integer MaxDegree, const Standard_Real Tol, Standard_Real &JacCoeff, Standard_Integer &NewDegree, Standard_Real &MaxError) const
| Compute NewDegree <= MaxDegree so that MaxError is lower than Tol. MaxError can be greater than Tol if it is not possible to find a NewDegree <= MaxDegree. In this case NewDegree = MaxDegree .
Standard_EXPORT Standard_Real | AverageError (const Standard_Integer Dimension, Standard_Real &JacCoeff, const Standard_Integer NewDegree) const
Standard_EXPORT void | ToCoefficients (const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal &JacCoeff, TColStd_Array1OfReal &Coefficients) const
| Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base. .
Standard_EXPORT void | D0 (const Standard_Real U, TColStd_Array1OfReal &BasisValue)
| Compute the values of the basis functions in u .
Standard_EXPORT void | D1 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1)
| Compute the values and the derivatives values of the basis functions in u .
Standard_EXPORT void | D2 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1, TColStd_Array1OfReal &BasisD2)
| Compute the values and the derivatives values of the basis functions in u .
Standard_EXPORT void | D3 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1, TColStd_Array1OfReal &BasisD2, TColStd_Array1OfReal &BasisD3)
| Compute the values and the derivatives values of the basis functions in u .
Standard_Integer | WorkDegree () const
| returns WorkDegree
Standard_Integer | NivConstr () const
| returns NivConstr
Standard_EXPORT const | Handle (Standard_Type)&DynamicType() const

## Private Member Functions

Standard_EXPORT void | D0123 (const Standard_Integer NDerive, const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1, TColStd_Array1OfReal &BasisD2, TColStd_Array1OfReal &BasisD3)
| Compute the values and the derivatives values of the basis functions in u .

## Private Attributes

Standard_Integer | myWorkDegree
Standard_Integer | myNivConstr
Standard_Integer | myDegree
Handle_TColStd_HArray1OfReal | myTNorm
Handle_TColStd_HArray1OfReal | myCofA
Handle_TColStd_HArray1OfReal | myCofB
Handle_TColStd_HArray1OfReal | myDenom

## Constructor & Destructor Documentation

Standard_EXPORT PLib_JacobiPolynomial::PLib_JacobiPolynomial | ( | const Standard_Integer | WorkDegree,
|  | const GeomAbs_Shape | ConstraintOrder
| ) |

## Member Function Documentation

Standard_EXPORT Standard_Real PLib_JacobiPolynomial::AverageError | ( | const Standard_Integer | Dimension,
|  | Standard_Real & | JacCoeff,
|  | const Standard_Integer | NewDegree
| ) | const

Standard_EXPORT void PLib_JacobiPolynomial::D0 | ( | const Standard_Real | U,
|  | TColStd_Array1OfReal & | BasisValue
| ) | `[virtual]`

| Implements PLib_Base.

Standard_EXPORT void PLib_JacobiPolynomial::D0123 | ( | const Standard_Integer | NDerive,
|  | const Standard_Real | U,
|  | TColStd_Array1OfReal & | BasisValue,
|  | TColStd_Array1OfReal & | BasisD1,
|  | TColStd_Array1OfReal & | BasisD2,
|  | TColStd_Array1OfReal & | BasisD3
| ) | `[private]`

Standard_EXPORT void PLib_JacobiPolynomial::D1 | ( | const Standard_Real | U,
|  | TColStd_Array1OfReal & | BasisValue,
|  | TColStd_Array1OfReal & | BasisD1
| ) | `[virtual]`

| Implements PLib_Base.

Standard_EXPORT void PLib_JacobiPolynomial::D2 | ( | const Standard_Real | U,
|  | TColStd_Array1OfReal & | BasisValue,
|  | TColStd_Array1OfReal & | BasisD1,
|  | TColStd_Array1OfReal & | BasisD2
| ) | `[virtual]`

| Implements PLib_Base.

Standard_EXPORT void PLib_JacobiPolynomial::D3 | ( | const Standard_Real | U,
|  | TColStd_Array1OfReal & | BasisValue,
|  | TColStd_Array1OfReal & | BasisD1,
|  | TColStd_Array1OfReal & | BasisD2,
|  | TColStd_Array1OfReal & | BasisD3
| ) | `[virtual]`

| Implements PLib_Base.

Standard_EXPORT const PLib_JacobiPolynomial::Handle | ( | Standard_Type |  | ) | const

| Reimplemented from PLib_Base.

Standard_EXPORT Standard_Real PLib_JacobiPolynomial::MaxError | ( | const Standard_Integer | Dimension,
|  | Standard_Real & | JacCoeff,
|  | const Standard_Integer | NewDegree
| ) | const

Standard_EXPORT void PLib_JacobiPolynomial::MaxValue | ( | TColStd_Array1OfReal & | TabMax | ) | const

Standard_Integer PLib_JacobiPolynomial::NivConstr | ( |  | ) | const`[inline]`

Standard_EXPORT void PLib_JacobiPolynomial::Points | ( | const Standard_Integer | NbGaussPoints,
|  | TColStd_Array1OfReal & | TabPoints
| ) | const

Standard_EXPORT void PLib_JacobiPolynomial::ReduceDegree | ( | const Standard_Integer | Dimension,
|  | const Standard_Integer | MaxDegree,
|  | const Standard_Real | Tol,
|  | Standard_Real & | JacCoeff,
|  | Standard_Integer & | NewDegree,
|  | Standard_Real & | MaxError
| ) | const`[virtual]`

| Implements PLib_Base.

Standard_EXPORT void PLib_JacobiPolynomial::ToCoefficients | ( | const Standard_Integer | Dimension,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | JacCoeff,
|  | TColStd_Array1OfReal & | Coefficients
| ) | const`[virtual]`

| Implements PLib_Base.

Standard_EXPORT void PLib_JacobiPolynomial::Weights | ( | const Standard_Integer | NbGaussPoints,
|  | TColStd_Array2OfReal & | TabWeights
| ) | const

Standard_Integer PLib_JacobiPolynomial::WorkDegree | ( |  | ) | const`[inline, virtual]`

| Implements PLib_Base.

## Field Documentation

Handle_TColStd_HArray1OfReal PLib_JacobiPolynomial::myCofA `[private]`

Handle_TColStd_HArray1OfReal PLib_JacobiPolynomial::myCofB `[private]`

Standard_Integer PLib_JacobiPolynomial::myDegree `[private]`

Handle_TColStd_HArray1OfReal PLib_JacobiPolynomial::myDenom `[private]`

Standard_Integer PLib_JacobiPolynomial::myNivConstr `[private]`

Handle_TColStd_HArray1OfReal PLib_JacobiPolynomial::myTNorm `[private]`

Standard_Integer PLib_JacobiPolynomial::myWorkDegree `[private]`

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

- PLib_JacobiPolynomial.hxx
- PLib_JacobiPolynomial.lxx