AdvancedMathematics CATMathPolynomXY

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

public class CATMathPolynomXY

Class defining the real polynom of two variables.

Constructor and Destructor Index


o CATMathPolynomXY(CATMathPolynomXY&)
Copy constructor.
o CATMathPolynomXY(CATLONG32,CATLONG32,double*,double,double)
Constructs a CATMathPolynomXY from an array.
o CATMathPolynomXY(CATLONG32,CATLONG32,double**,double,double)
Constructs a CATMathPolynomXY from a double entry array.
o ~CATMathPolynomXY()

Method Index


o Eval(double&,double&)
Evaluates this CATMathPolynomXY.
o Eval(double,double,CATMathOption,double*,double*,double*,double*,double*,double*)
Simultaneously evaluates this CATMathPolynomXY or/and its partial derivatives.
o Eval(CATMathIntervalND&,CATLONG32*,CATMathOption,double*,double*,double*,double*,double*,double*)
Simultaneously evaluates this CATMathPolynomXY or/and its partial derivatives on a regular grid of points.
o EvalAllThirdDerivs(double,double,double&,double&,double&,double&)
Evaluates simultaneously all third partial derivatives of this CATMathPolynomXY .
o EvalFirstDerivX(double&,double&)
Evaluates the first partial derivative with respect to the first variable of this CATMathPolynomXY .
o EvalFirstDerivY(double&,double&)
Evaluates the first partial derivative with respect to the second variable of this CATMathPolynomXY .
o EvalSecondDerivX2(double&,double&)
Evaluates the second partial derivative of this CATMathPolynomXY .
o EvalSecondDerivXY(double&,double&)
Evaluates the second partial derivative of this CATMathPolynomXY .
o EvalSecondDerivY2(double&,double&)
Evaluates the second partial derivative of this CATMathPolynomXY .
o EvalThirdDerivX2Y(double&,double&)
Evaluates the third partial derivative of this CATMathPolynomXY .
o EvalThirdDerivX3(double&,double&)
Evaluates the third partial derivative of this CATMathPolynomXY .
o EvalThirdDerivXY2(double&,double&)
Evaluates the third partial derivative of this CATMathPolynomXY .
o EvalThirdDerivY3(double&,double&)
Evaluates the third partial derivative of this CATMathPolynomXY .
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 CATMathPolynomXY .
o GetCoefficients()
Returns the coefficients of this CATMathPolynomXY.
o GetDegreeX()
Up to V5R20, returns the degree in the first variable.
o GetDegreeX()
From V5R21, returns the degree in the first variable.
o GetDegreeY()
Up to V5R20, returns the degree in the second variable.
o GetDegreeY()
From V5R21, returns the degree in the second variable.
o IsA()
Returns the class name of this CATMathPolynomXY.
o IsAKindOf(CATMathClassId)
Tests whether this CATMathPolynomXY derives from a class (given by its name).
o IsATypeOf(CATMathFunctionXYTypeId)
Tests if this CATMathPolynomXY derives from a class (given by a numerical value).
o IsOption(CATMathOption)
Tests whether an evaluator is available for this CATMathPolynomXY.
o SetCoefficients(CATLONG32,CATLONG32,double*)
Modifies the coefficients of this CATMathPolynomXY.
o SetCoefficients(CATLONG32,CATLONG32,double**)
Modifies the coefficients of this CATMathPolynomXY.

Constructor and Destructor


o CATMathPolynomXY
public CATMathPolynomXY( const iToCopy)
Copy constructor.
o CATMathPolynomXY
public CATMathPolynomXY( const iDegX= 0,
const iDegY= 0,
const iCoeff= 0,
const iShiftX=0.,
const iShiftY=0.)
Constructs a CATMathPolynomXY from an array.
Parameters:
iDegX
The degree in the first variable
iDegY
The degree in the second variable.
iCoeff
The array such that:
pol=Sum_{i=0..iDegX, j=0..iDegY} iCoeff[i*(degY+1)+j] X^i Y^j.
o CATMathPolynomXY
public CATMathPolynomXY( const iDegX,
const iDegY,
iCoeff,
const iShiftX=0.,
const iShiftY=0.)
Constructs a CATMathPolynomXY from a double entry array.
Parameters:
iDegX
The degree in the first variable
iDegY
The degree in the second variable.
iCoeff
The double entry array such that:
pol=Sum_{i=0..iDegX, j=0..iDegY} iCoeff[i][j] X^i Y^j.
iShiftX,
iShiftY Internal use.
o ~CATMathPolynomXY
public virtual ~CATMathPolynomXY()

Methods


o Eval
public virtual Eval( const iX,
const iY)
Evaluates this CATMathPolynomXY.
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The result of the evaluation.
o Eval
public virtual Eval( const iX,
const iY,
const iOptions,
ioF,
ioFx=0,
ioFy=0,
ioFx2=0,
ioFxy=0,
ioFy2=0)
Simultaneously evaluates this CATMathPolynomXY 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 CATMathPolynomXY.
ioFx
A pointer to the first partial derivative of this CATMathPolynomXY.
ioFy
A pointer to the first partial derivative of this CATMathPolynomXY.
ioFx2
A pointer to the second partial derivative of this CATMathPolynomXY.
ioFxy
A pointer to the second partial derivative of this CATMathPolynomXY.
ioFy2
A pointer to the second partial derivative of this CATMathPolynomXY.
o Eval
public virtual Eval( const iDomain,
const NbPoints,
const iOptions,
ioF,
ioFx=0,
ioFy=0,
ioFx2=0,
ioFxy=0,
ioFy2=0)
Simultaneously evaluates this CATMathPolynomXY 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 CATMathPolynomXY.
ioFx
The array of the first partial derivative of this CATMathPolynomXY at the grid points.
ioFy
The array of the first partial derivative of this CATMathPolynomXY at the grid points.
ioFx2
The array of the second partial derivative of this CATMathPolynomXY at the grid points.
ioFxy
The array of the second partial derivative of this CATMathPolynomXY at the grid points.
ioFy2
The array of the second partial derivative of this CATMathPolynomXY at the grid points.
o EvalAllThirdDerivs
public virtual EvalAllThirdDerivs( const iX,
const iY,
oFx3,
oFx2y,
oFxy2,
oFy3)
Evaluates simultaneously all third partial derivatives of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
oFx3
The value of the third partial derivative of this CATMathPolynomXY.
oFx2y
The value of the third partial derivative of this CATMathPolynomXY.
oFxy2
The value of the third partial derivative of this CATMathPolynomXY.
oFy3
The value of the third partial derivative of this CATMathPolynomXY.
o EvalFirstDerivX
public virtual EvalFirstDerivX( const iX,
const iY)
Evaluates the first partial derivative with respect to the first variable of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the first partial derivative with respect to the first variable.
o EvalFirstDerivY
public virtual EvalFirstDerivY( const iX,
const iY)
Evaluates the first partial derivative with respect to the second variable of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the first partial derivative with respect to the second variable.
o EvalSecondDerivX2
public virtual EvalSecondDerivX2( const iX,
const iY)
Evaluates the second partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalSecondDerivXY
public virtual EvalSecondDerivXY( const iX,
const iY)
Evaluates the second partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalSecondDerivY2
public virtual EvalSecondDerivY2( const iX,
const iY)
Evaluates the second partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the second partial derivative.
o EvalThirdDerivX2Y
public virtual EvalThirdDerivX2Y( const iX,
const iY)
Evaluates the third partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivX3
public virtual EvalThirdDerivX3( const iX,
const iY)
Evaluates the third partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivXY2
public virtual EvalThirdDerivXY2( const iX,
const iY)
Evaluates the third partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalThirdDerivY3
public virtual EvalThirdDerivY3( const iX,
const iY)
Evaluates the third partial derivative of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
Returns:
The value of the third partial derivative.
o EvalUpToThirdDeriv
public virtual EvalUpToThirdDeriv( const iX,
const iY,
oF,
oFx,
oFy,
oFx2,
oFxy,
oFy2,
oFx3,
oFx2y,
oFxy2,
oFy3)
Evaluates simultaneously the value, and all the first, second and third partial derivatives of this CATMathPolynomXY .
Parameters:
iX
The value of the first variable where this CATMathPolynomXY is evaluated.
iY
The value of the second variable where this CATMathPolynomXY is evaluated.
oF
The value of this CATMathPolynomXY.
oFx
The value of the first partial derivative of this CATMathPolynomXY.
oFy
The value of the first partial derivative of this CATMathPolynomXY.
oFx2
The value of the second partial derivative of this CATMathPolynomXY.
oFxy
The value of the second partial derivative of this CATMathPolynomXY.
oFy2
The value of the second partial derivative of this CATMathPolynomXY.
oFx3
The value of the third partial derivative of this CATMathPolynomXY.
oFx2y
The value of the third partial derivative of this CATMathPolynomXY.
oFxy2
The value of the third partial derivative of this CATMathPolynomXY.
oFy3
The value of the third partial derivative of this CATMathPolynomXY.
o GetCoefficients
public GetCoefficients()
Returns the coefficients of this CATMathPolynomXY.
Returns:
The array of the coefficients. As part of this, it must not be deallocated.
o GetDegreeX
public GetDegreeX()
Up to V5R20, returns the degree in the first variable.
Returns:
The degree.
o GetDegreeX
public GetDegreeX()
From V5R21, returns the degree in the first variable.
Returns:
The degree.
o GetDegreeY
public GetDegreeY()
Up to V5R20, returns the degree in the second variable.
Returns:
The degree.
o GetDegreeY
public GetDegreeY()
From V5R21, returns the degree in the second variable.
Returns:
The degree.
o IsA
public IsA()
Returns the class name of this CATMathPolynomXY.
Returns:
A pointer to the name CATMathPolynomX.
o IsAKindOf
public IsAKindOf( const iClassId)
Tests whether this CATMathPolynomXY 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 CATMathPolynomXY is a kind of iClassId, FALSE otherwise.
o IsATypeOf
public IsATypeOf( const iType)
Tests if this CATMathPolynomXY derives from a class (given by a numerical value).
Parameters:
iType
The numerical value representing the class type.
Returns:
The result of the test.
Legal values: TRUE if this CATMathPolynomXY is a type of iType, FALSE otherwise.
o IsOption
public IsOption( const iOption)
Tests whether an evaluator is available for this CATMathPolynomXY.
Parameters:
iOption
The type of evalution.
Legal values:
OptionEval
evaluation of the function
OptionEvalFirstDeriv
evaluation of the first derivative of the function
OptionEvalSecondDeriv
evaluation of the second derivative of the function
OptionEvalThirdDeriv
evaluation of the third derivative of the function
Returns:
The result of the test.
Legal values: TRUE if the evaluation is available for this CATMathPolynomXY, FALSE otherwise.
o SetCoefficients
public SetCoefficients( const iDegX= 0,
const iDegY= 0,
const iCoef= 0)
Modifies the coefficients of this CATMathPolynomXY.
Parameters:
iDegX
The degree in the first variable
iDegY
The degree in the second variable.
iCoef
The array such that:
pol=Sum_{i=0..iDegX, j=0..iDegY} iCoef[i*(degY+1)+j] X^i Y^j.
o SetCoefficients
public SetCoefficients( const iDegX,
const iDegY,
iCoef)
Modifies the coefficients of this CATMathPolynomXY.
Parameters:
iDegX
The degree in the first variable
iDegY
The degree in the second variable.
iCoef
The double entry array such that:
pol=Sum_{i=0..iDegX, j=0..iDegY} iCoeff[i][j] X^i Y^j.
This object is included in the file: CATMathPolynomXY.h
If needed, your Imakefile.mk should include the module: CATAdvancedMathematics

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