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AdvancedMathematics 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)

Constructor and Destructor Index

o ~CATMathFunctionXY()

Method Index

o Eval(double&,double&): Evaluates this CATMathFunctionXY.
o Eval(CATMathInterval&,CATMathInterval&,CATTolerance&): Evaluates this CATMathFunctionXY for values defined by intervals.
o Eval(double,double,CATMathOption,double*,double*,double*,double*,double*,double*): Simultaneously evaluates this CATMathFunctionXY or/and its partial derivatives.
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 EvalAllThirdDerivs(double,double,double&,double&,double&,double&): Evaluates simultaneously all third partial derivatives of this CATMathFunctionXY .
o EvalFirstDerivX(double&,double&): Evaluates the first partial derivative with respect to the first variable of this CATMathFunctionXY .
o EvalFirstDerivX(CATMathInterval&,CATMathInterval&): Evaluates the first partial derivative with respect to the first 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 EvalFirstDerivY(CATMathInterval&,CATMathInterval&): Evaluates the first partial derivative with respect to the second variable for values defined by intervals.
o EvalSecondDerivX2(double&,double&): Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivX2(CATMathInterval&,CATMathInterval&): Evaluates the second partial derivative of this CATMathFunctionXY.
o EvalSecondDerivXY(double&,double&): Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivXY(CATMathInterval&,CATMathInterval&): Evaluates the second partial derivative of this CATMathFunctionXY.
o EvalSecondDerivY2(double&,double&): Evaluates the second partial derivative of this CATMathFunctionXY .
o EvalSecondDerivY2(CATMathInterval&,CATMathInterval&): 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).
o IsATypeOf(CATMathFunctionXYTypeId): Tests if this CATMathFunctionXY derives from a class (given by a numerical value).

Constructor and Destructor

o ~CATMathFunctionXY

public virtual ~CATMathFunctionXY(

)

Methods

o Eval

public virtual Eval(	const	`iX`,
	const	`iY`)

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 Eval(	const	`Du`,
	const	`Dv`,
	const	`iTolObject`	`=CATGetDefaultTolerance()`)

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 Eval(	const	`u`,
	const	`v`,
	const	`iOptions`,
		`ioF`,
		`ioFx`	`= 0`,
		`ioFy`	`= 0`,
		`ioFx2`	`= 0`,
		`ioFxy`	`= 0`,
		`ioFy2`	`= 0`)

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 Eval

public virtual Eval(	const	`iDomain`,
	const	`iNbPoints`,
	const	`iOptions`,
		`ioF`,
		`ioFx`	`= 0`,
		`ioFy`	`= 0`,
		`ioFx2`	`= 0`,
		`ioFxy`	`= 0`,
		`ioFy2`	`= 0`)

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 EvalAllThirdDerivs

public virtual EvalAllThirdDerivs(	const	`iX`,
	const	`iY`,
		`oFx3`,
		`oFx2y`,
		`oFxy2`,
		`oFy3`)

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 EvalFirstDerivX(	const	`iX`,
	const	`iY`)

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 EvalFirstDerivX

public virtual EvalFirstDerivX(	const	`Du`,
	const	`Dv`)

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 EvalFirstDerivY

public virtual EvalFirstDerivY(	const	`iX`,
	const	`iY`)

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 EvalFirstDerivY

public virtual EvalFirstDerivY(	const	`Du`,
	const	`Dv`)

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 EvalSecondDerivX2

public virtual EvalSecondDerivX2(	const	`iX`,
	const	`iY`)

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 EvalSecondDerivX2

public virtual EvalSecondDerivX2(	const	`Du`,
	const	`Dv`)

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 EvalSecondDerivXY(	const	`iX`,
	const	`iY`)

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 EvalSecondDerivXY(	const	`Du`,
	const	`Dv`)

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 EvalSecondDerivY2(	const	`iX`,
	const	`iY`)

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 EvalSecondDerivY2(	const	`Du`,
	const	`Dv`)

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 EvalThirdDerivX2Y

public virtual EvalThirdDerivX2Y(	const	`iX`,
	const	`iY`)

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 EvalThirdDerivX3(	const	`iX`,
	const	`iY`)

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 EvalThirdDerivXY2(	const	`iX`,
	const	`iY`)

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 EvalThirdDerivY3(	const	`iX`,
	const	`iY`)

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 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 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 IsAKindOf( const iClassId)

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.

o IsATypeOf

public virtual IsATypeOf( const iType)

Tests if this CATMathFunctionXY 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 CATMathFunction is a type of iType, FALSE otherwise.

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

AdvancedMathematics writeClassCharacteristic(); CATMathFunctionXY

Constructor and Destructor Index

Method Index

Constructor and Destructor

Methods

AdvancedMathematics CATMathFunctionXY