All Frameworks  Class Hierarchy  This Framework  Previous  Next  Indexes

AdvancedMathematics Class CATMathFunctionXY

Mathematics.CATCGMVirtual
  |
  +---AdvancedMathematics.CATMathFunctionGeneral
    |
    +---CATMathFunctionXY
 

Usage: you must use this class as is. You should never derive it.


public class CATMathFunctionXY

Class representing a scalar function of two variables.

 F: RxR   -> R
          (x,y)  -> F(x,y)
 


Method Index


o Eval(CATMathInterval&,CATMathInterval&,CATTolerance&)
Evaluates this CATMathFunctionXY for values defined by intervals.
o Eval(CATMathIntervalND&,CATLONG32*,CATMathOption,double*,double*,double*,double*,double*,double*)
Simultaneously evaluates this CATMathFunctionXY or/and its partial derivatives on a regular grid of points.
o Eval(double&,double&)
Evaluates this CATMathFunctionXY.
o Eval(double,double,CATMathOption,double*,double*,double*,double*,double*,double*)
Simultaneously evaluates this CATMathFunctionXY or/and its partial derivatives.
o EvalAllThirdDerivs(double,double,double&,double&,double&,double&)
Evaluates simultaneously all third partial derivatives of this CATMathFunctionXY .
o EvalFirstDerivX(CATMathInterval&,CATMathInterval&)
Evaluates the first partial derivative with respect to the first variable for values defined by intervals.
o EvalFirstDerivX(double&,double&)
Evaluates the first partial derivative with respect to the first variable of this CATMathFunctionXY .
o EvalFirstDerivY(CATMathInterval&,CATMathInterval&)
Evaluates the first partial derivative with respect to the second variable for values defined by intervals.
o EvalFirstDerivY(double&,double&)
Evaluates the first partial derivative with respect to the second variable of this CATMathFunctionXY .
o EvalSecondDerivX2(CATMathInterval&,CATMathInterval&)
Evaluates the second partial derivative of this CATMathFunctionXY.
o EvalSecondDerivX2(double&,double&)
Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivXY(CATMathInterval&,CATMathInterval&)
Evaluates the second partial derivative of this CATMathFunctionXY.
o EvalSecondDerivXY(double&,double&)
Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivY2(CATMathInterval&,CATMathInterval&)
Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivY2(double&,double&)
Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalThirdDerivX2Y(double&,double&)
Evaluates the third partial derivative of this CATMathFunctionXY .
o EvalThirdDerivX3(double&,double&)
Evaluates the third partial derivative of this CATMathFunctionXY .
o EvalThirdDerivXY2(double&,double&)
Evaluates the third partial derivative of this CATMathFunctionXY .
o EvalThirdDerivY3(double&,double&)
Evaluates the third partial derivative of this CATMathFunctionXY .
o EvalUpToThirdDeriv(double,double,double&,double&,double&,double&,double&,double&,double&,double&,double&,double&)
Evaluates simultaneously the value, and all the first, second and third partial derivatives of this CATMathFunctionXY .
o IsAKindOf(CATMathClassId)
Tests if this CATMathFunctionXY derives from a class (given by its name).

Methods


o Eval
public virtual CATMathInterval Eval( const CATMathInterval& Du,
const CATMathInterval& Dv,
const CATTolerance& iTolObject=CATGetDefaultTolerance())const
Evaluates this CATMathFunctionXY for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
iTolObject
The tolerance.
Returns:
The interval which contains the values calculated from Du and Dv.
o Eval
public virtual void Eval( const CATMathIntervalND& iDomain,
const CATLONG32* iNbPoints,
const CATMathOption iOptions,
double* ioF,
double* ioFx=0,
double* ioFy=0,
double* ioFx2=0,
double* ioFxy=0,
double* ioFy2=0) const
Simultaneously evaluates this CATMathFunctionXY or/and its partial derivatives on a regular grid of points.
Precondition: The output arrays must have been previously allocated if you asked for the corresponding evaluation. oF[Ny*i+j] contains the evaluation of this at (x_i,y_j).
Parameters:
iDomain
The 2D-interval of definition of the grid [xStart,xEnd] x [yStart,yEnd].
iNbPoints
The array of 2 longs, stating the number of points of the grid in each direction x and y. If iNbPoints[0]=1 and iNbPoints[1]=1, there is only one evaluation made at the parameter (xStart,xStart)
iOptions
The type of evalution.
Legal values:
OptionEval
evaluation of the function
OptionEvalFirstDeriv
evaluation of the first derivatives of the function
OptionEvalSecondDeriv
evaluation of the second derivatives of the function
ioF
The array of the evaluations of this CATMathFunctionXY.
ioFx
The array of the first partial derivative of this CATMathFunctionXY at the grid points.
ioFy
The array of the first partial derivative of this CATMathFunctionXY at the grid points.
ioFx2
The array of the second partial derivative of this CATMathFunctionXY at the grid points.
ioFxy
The array of the second partial derivative of this CATMathFunctionXY at the grid points.
ioFy2
The array of the second partial derivative of this CATMathFunctionXY at the grid points.
o Eval
public virtual double Eval( const double& iX,
const double& iY) const=0
Evaluates this CATMathFunctionXY.
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The result of the evaluation.
o Eval
public virtual void Eval( const double u,
const double v,
const CATMathOption iOptions,
double* ioF,
double* ioFx=0,
double* ioFy=0,
double* ioFx2=0,
double* ioFxy=0,
double* ioFy2=0) const
Simultaneously evaluates this CATMathFunctionXY or/and its partial derivatives.
Precondition:The output arrays must have been previously allocated if you asked for the corresponding evaluation.
Parameters:
iOptions
The type of evalution.
Legal values:
OptionEval
evaluation of the function
OptionEvalFirstDeriv
evaluation of the first derivatives of the function
OptionEvalSecondDeriv
evaluation of the second derivatives of the function
ioF
A pointer to the value of this CATMathFunctionXY.
ioFx
A pointer to the first partial derivative of this CATMathFunctionXY.
ioFy
A pointer to the first partial derivative of this CATMathFunctionXY.
ioFx2
A pointer to the second partial derivative of this CATMathFunctionXY.
ioFxy
A pointer to the second partial derivative of this CATMathFunctionXY.
ioFy2
A pointer to the second partial derivative of this CATMathFunctionXY.
o EvalAllThirdDerivs
public virtual void EvalAllThirdDerivs( const double iX,
const double iY,
double& oFx3,
double& oFx2y,
double& oFxy2,
double& oFy3) const
Evaluates simultaneously all third partial derivatives of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
oFx3
The value of the third partial derivative of this CATMathFunctionXY.
oFx2y
The value of the third partial derivative of this CATMathFunctionXY.
oFxy2
The value of the third partial derivative of this CATMathFunctionXY.
oFy3
The value of the third partial derivative of this CATMathFunctionXY.
o EvalFirstDerivX
public virtual CATMathInterval EvalFirstDerivX( const CATMathInterval& Du,
const CATMathInterval& Dv) const
Evaluates the first partial derivative with respect to the first variable for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
Returns:
The interval which contains the first derivatives values calculated from Du and Dv.
o EvalFirstDerivX
public virtual double EvalFirstDerivX( const double& iX,
const double& iY) const
Evaluates the first partial derivative with respect to the first variable of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the first partial derivative with respect to the first variable.
o EvalFirstDerivY
public virtual CATMathInterval EvalFirstDerivY( const CATMathInterval& Du,
const CATMathInterval& Dv) const
Evaluates the first partial derivative with respect to the second variable for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
Returns:
The interval which contains the first derivative values calculated from Du and Dv.
o EvalFirstDerivY
public virtual double EvalFirstDerivY( const double& iX,
const double& iY) const
Evaluates the first partial derivative with respect to the second variable of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the first partial derivative with respect to the second variable.
o EvalSecondDerivX2
public virtual CATMathInterval EvalSecondDerivX2( const CATMathInterval& Du,
const CATMathInterval& Dv) const
Evaluates the second partial derivative of this CATMathFunctionXY. for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
Returns:
The interval which contains the second derivative values calculated from Du and Dv.
o EvalSecondDerivX2
public virtual double EvalSecondDerivX2( const double& iX,
const double& iY) const
Evaluates the second partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalSecondDerivXY
public virtual CATMathInterval EvalSecondDerivXY( const CATMathInterval& Du,
const CATMathInterval& Dv) const
Evaluates the second partial derivative of this CATMathFunctionXY. for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
Returns:
The interval which contains the second derivative values calculated from Du and Dv.
o EvalSecondDerivXY
public virtual double EvalSecondDerivXY( const double& iX,
const double& iY) const
Evaluates the second partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalSecondDerivY2
public virtual CATMathInterval EvalSecondDerivY2( const CATMathInterval& Du,
const CATMathInterval& Dv) const
Evaluates the second partial derivative of this CATMathFunctionXY . for values defined by intervals.
Parameters:
Du
The interval containing the values along X.
Dv
The interval containing the values along Y.
Returns:
The interval which contains the second derivative values calculated from Du and Dv.
o EvalSecondDerivY2
public virtual double EvalSecondDerivY2( const double& iX,
const double& iY) const
Evaluates the second partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalThirdDerivX2Y
public virtual double EvalThirdDerivX2Y( const double& iX,
const double& iY) const
Evaluates the third partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivX3
public virtual double EvalThirdDerivX3( const double& iX,
const double& iY) const
Evaluates the third partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivXY2
public virtual double EvalThirdDerivXY2( const double& iX,
const double& iY) const
Evaluates the third partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivY3
public virtual double EvalThirdDerivY3( const double& iX,
const double& iY) const
Evaluates the third partial derivative of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalUpToThirdDeriv
public virtual void EvalUpToThirdDeriv( const double iX,
const double iY,
double& oF,
double& oFx,
double& oFy,
double& oFx2,
double& oFxy,
double& oFy2,
double& oFx3,
double& oFx2y,
double& oFxy2,
double& oFy3) const
Evaluates simultaneously the value, and all the first, second and third partial derivatives of this CATMathFunctionXY .
Parameters:
iX
The value of the first variable where this CATMathFunctionXY is evaluated.
iY
The value of the second variable where this CATMathFunctionXY is evaluated.
oF
The value of this CATMathFunctionXY.
oFx
The value of the first partial derivative of this CATMathFunctionXY.
oFy
The value of the first partial derivative of this CATMathFunctionXY.
oFx2
The value of the second partial derivative of this CATMathFunctionXY.
oFxy
The value of the second partial derivative of this CATMathFunctionXY.
oFy2
The value of the second partial derivative of this CATMathFunctionXY.
oFx3
The value of the third partial derivative of this CATMathFunctionXY.
oFx2y
The value of the third partial derivative of this CATMathFunctionXY.
oFxy2
The value of the third partial derivative of this CATMathFunctionXY.
oFy3
The value of the third partial derivative of this CATMathFunctionXY.
o IsAKindOf
public virtual CATBoolean IsAKindOf( const CATMathClassId iClassId) const
Tests if this CATMathFunctionXY derives from a class (given by its name).
Parameters:
iClassId
The name of the class.
Returns:
The result of the test.
Legal values: TRUE if this CATMathFunctionXY is a kind of iClassId, FALSE otherwise.

This object is included in the file: CATMathFunctionXY.h
If needed, your Imakefile.mk should include the module: CATAdvancedMathematics

Copyright © 2003, Dassault Systèmes. All rights reserved.