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-- File: PLib_HermitJacobi.cdl
-- Created: Wed Oct 22 10:52:48 1997
-- Author: Philippe MANGIN
-- <ssv@velox.nnov.matra-dtv.fr>
---Copyright: Matra Datavision 1997
class HermitJacobi 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) = H(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
-- Hermit's base: H(t)
-- H(t) = c0H00(t) + c1H01(t) + ...c(iordre)H(0 ;iorder)+ c(iordre+1)H10(t)+...
-- 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,
Shape from GeomAbs,
Matrix from math,
JacobiPolynomial from PLib
raises
ConstructionError from Standard
is
Create ( WorkDegree : Integer ;
ConstraintOrder : Shape from GeomAbs)
returns HermitJacobi 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
--
-- Work in HermitJacobi base
MaxError ( me ; Dimension : Integer ;
HermJacCoeff : 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 ;
HermJacCoeff : 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 ;
HermJacCoeff : 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 ;
HermJacCoeff : Array1OfReal from TColStd ;
Coefficients : out Array1OfReal from TColStd );
---Purpose:
-- Convert the polynomial P(t) = H(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
myH : Matrix from math;
myJacobi : JacobiPolynomial from PLib;
myWCoeff : Array1OfReal; -- The cannonical Coefficients of W(t).
end HermitJacobi;
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