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-- File: PLib_JacobiPolynomial.cdl
-- Created: Tue Oct 8 11:03:16 1996
-- Author: Jeannine PANTIATICI
-- <jpi@sgi64>
---Copyright: Matra Datavision 1996
class JacobiPolynomial from PLib
inherits Base from PLib
--- Purpose: 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
uses
Array2OfReal from TColStd,
Array1OfReal from TColStd,
HArray1OfReal from TColStd,
Shape from GeomAbs
raises
ConstructionError from Standard
is
-- Create returns JacobiPolynomial from PLib;
Create ( WorkDegree : Integer ;
ConstraintOrder : Shape from GeomAbs)
returns JacobiPolynomial from PLib
---Purpose:
-- Initialize the polynomial class
-- Degree has to be <= 30
-- ConstraintOrder has to be GeomAbs_C0
-- GeomAbs_C1
-- GeomAbs_C2
raises ConstructionError from Standard;
-- if Degree or ConstraintOrder is non valid
--
-- Jacobi characteristics
--
Points ( me ; NbGaussPoints : Integer ;
TabPoints : out Array1OfReal from TColStd )
---Purpose:
-- 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
raises ConstructionError from Standard;
-- Invalid NbGaussPoints
Weights (me ; NbGaussPoints : Integer ;
TabWeights : out Array2OfReal from TColStd )
--- Purpose:
-- 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
raises ConstructionError from Standard;
-- Invalid NbGaussPoints
MaxValue ( me ; TabMax : out Array1OfReal from TColStd );
---Purpose:
-- 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 );
--
-- Work in Jacobi base
MaxError ( me ; Dimension : Integer ;
JacCoeff : in out Real;
NewDegree : Integer )
returns Real;
---Purpose:
-- 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
ReduceDegree ( me ; Dimension , MaxDegree : Integer ; Tol : Real ;
JacCoeff : in out Real;
NewDegree : out Integer ;
MaxError : out Real);
---Purpose:
-- 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
--
AverageError ( me ; Dimension : Integer ;
JacCoeff : in out Real;
NewDegree : Integer )
-- This method computes the average error on the polynomial W(t)Q(t)
-- obtained by missing the
-- coefficients JacCoeff from NewDegree +1 to Degree
returns Real;
ToCoefficients ( me ; Dimension, Degree : Integer ;
JacCoeff : Array1OfReal from TColStd ;
Coefficients : out Array1OfReal from TColStd );
---Purpose:
-- Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.
--
D0123 (me : mutable; NDerive : Integer; U : Real;
BasisValue : out Array1OfReal from TColStd;
BasisD1 : out Array1OfReal from TColStd;
BasisD2 : out Array1OfReal from TColStd;
BasisD3 : out Array1OfReal from TColStd)
---Purpose: Compute the values and the derivatives values of
-- the basis functions in u
is private;
D0 (me : mutable; U : Real;
BasisValue : out Array1OfReal from TColStd);
---Purpose: Compute the values of the basis functions in u
--
D1 (me : mutable; U : Real;
BasisValue : out Array1OfReal from TColStd;
BasisD1 : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
-- the basis functions in u
D2 (me : mutable; U : Real;
BasisValue : out Array1OfReal from TColStd;
BasisD1 : out Array1OfReal from TColStd;
BasisD2 : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
-- the basis functions in u
D3 (me : mutable; U : Real;
BasisValue : out Array1OfReal from TColStd;
BasisD1 : out Array1OfReal from TColStd;
BasisD2 : out Array1OfReal from TColStd;
BasisD3 : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
-- the basis functions in u
WorkDegree (me)
---Purpose: returns WorkDegree
---C++: inline
returns Integer;
NivConstr (me)
---Purpose: returns NivConstr
---C++: inline
returns Integer;
fields
myWorkDegree : Integer;
myNivConstr : Integer;
myDegree : Integer;
-- the following arrays are used for an optimization of computation in D0-D3
myTNorm : HArray1OfReal from TColStd;
myCofA : HArray1OfReal from TColStd;
myCofB : HArray1OfReal from TColStd;
myDenom : HArray1OfReal from TColStd;
end;
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