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Public Member Functions
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:
Inheritance graph
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Public Member Functions

 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

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

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

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_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

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_Real AverageError (const Standard_Integer Dimension, Standard_Real &JacCoeff, const Standard_Integer NewDegree) const
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.


void D0 (const Standard_Real U, TColStd_Array1OfReal &BasisValue)
 Compute the values of the basis functions in u


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

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

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


Constructor & Destructor Documentation


Member Function Documentation

Implements PLib_Base.

Implements PLib_Base.

Implements PLib_Base.

Implements PLib_Base.

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.

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

Implements PLib_Base.

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

Implements PLib_Base.


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