OCC.math module¶

class
SwigPyIterator
(*args, **kwargs)¶ Bases:
object

advance
()¶

copy
()¶

decr
()¶

distance
()¶

equal
()¶

incr
()¶

next
()¶

previous
()¶

thisown
¶ The membership flag

value
()¶


class
math
¶ Bases:
object

static
KronrodPointsAndWeights
(*args)¶  Returns a vector of Kronrod points and a vector of their weights for GaussKronrod computation method. Index should be odd and greater then or equal to 3, as the number of Kronrod points is equal to 2*N + 1, where N is a number of Gauss points. Points and Weights should have the size equal to Index. Each even element of Points represents a Gauss point value of Nth Gauss quadrature. The values from Index equal to 3 to 123 are stored in a table (see the file math_Kronrod.cxx). If Index is greater, then points and weights will be computed. Returns Standard_True if Index is odd, it is equal to the size of Points and Weights and the computation of Points and Weights is performed successfully. Otherwise this method returns Standard_False.
Parameters:  Index (int) –
 Points (math_Vector &) –
 Weights (math_Vector &) –
Return type:

static
KronrodPointsMax
(*args)¶  Returns the maximal number of points for that the values are stored in the table. If the number is greater then KronrodPointsMax, the points will be computed.
Return type: int

static
OrderedGaussPointsAndWeights
(*args)¶  Returns a vector of Gauss points and a vector of their weights. The difference with the method GaussPoints is the following:  the points are returned in increasing order.  if Index is greater then GaussPointsMax, the points are computed. Returns Standard_True if Index is positive, Points’ and Weights’ length is equal to Index, Points and Weights are successfully computed.
Parameters:  Index (int) –
 Points (math_Vector &) –
 Weights (math_Vector &) –
Return type:

thisown
¶ The membership flag

static

class
math_Array1OfValueAndWeight
(*args)¶ Bases:
object
Parameters: Return type: Return type: 
Assign
()¶ Parameters: Other (math_Array1OfValueAndWeight &) – Return type: math_Array1OfValueAndWeight

ChangeValue
()¶ Parameters: Index (int) – Return type: math_ValueAndWeight

Set
()¶ Parameters: Other (math_Array1OfValueAndWeight &) – Return type: math_Array1OfValueAndWeight

Value
()¶ Parameters: Index (int) – Return type: math_ValueAndWeight

thisown
¶ The membership flag


class
math_BFGS
(*args)¶ Bases:
object
 Given the starting point StartingPoint, the BroydenFletcherGoldfarbShanno variant of DavidsonFletcherPowell minimization is done on the function F. The tolerance required on F is given by Tolerance. The solution F = Fi is found when : 2.0 * abs(Fi  Fi1) <= Tolerance * (abs(Fi) + abs(Fi1) + ZEPS). The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  Initializes the computation of the minimum of F. Warning A call to the Perform method must be made after this initialization to effectively compute the minimum of the function F.
Parameters: Return type: 
Delete
()¶ Return type: void

DumpToString
()¶ math_BFGS_DumpToString(math_BFGS self) > std::string

Gradient
()¶  Returns the gradient vector at the minimum. Exception NotDone is raised if the minimum was not found.
Return type: math_Vector  Returns the value of the gradient vector at the minimum in Grad. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Grad is not equal to the range of the StartingPoint.
Parameters: Grad (math_Vector &) – Return type: None

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  This method is called at the end of each iteration to check if the solution is found. It can be redefined in a subclass to implement a specific test to stop the iterations.
Parameters: F (math_MultipleVarFunctionWithGradient &) – Return type: bool

Location
()¶  returns the location vector of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: math_Vector  outputs the location vector of the minimum in Loc. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint.
Parameters: Loc (math_Vector &) – Return type: None

Minimum
()¶  returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

NbIterations
()¶  Returns the number of iterations really done in the calculation of the minimum. The exception NotDone is raised if the minimum was not found.
Return type: int

Perform
()¶  Is used internally by the constructors.
Parameters:  F (math_MultipleVarFunctionWithGradient &) –
 StartingPoint (math_Vector &) –
Return type:

thisown
¶ The membership flag

class
math_BissecNewton
(*args)¶ Bases:
object
 A combination of NewtonRaphson and bissection methods is done to find the root of the function F between the bounds Bound1 and Bound2. on the function F. The tolerance required on the root is given by TolX. The solution is found when : abs(Xi  Xi1) <= TolX and F(Xi) * F(Xi1) <= 0 The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type: 
Derivative
()¶  returns the value of the derivative at the root. Exception NotDone is raised if the minimum was not found.
Return type: float

DumpToString
()¶ math_BissecNewton_DumpToString(math_BissecNewton self) > std::string

IsSolutionReached
()¶  This method is called at the end of each iteration to check if the solution has been found. It can be redefined in a subclass to implement a specific test to stop the iterations.
Parameters: F (math_FunctionWithDerivative &) – Return type: bool

Root
()¶  returns the value of the root. Exception NotDone is raised if the minimum was not found.
Return type: float

Value
()¶  returns the value of the function at the root. Exception NotDone is raised if the minimum was not found.
Return type: float

thisown
¶ The membership flag

class
math_BracketMinimum
(*args)¶ Bases:
object
 Given two initial values this class computes a bracketing triplet of abscissae Ax, Bx, Cx (such that Bx is between Ax and Cx, F(Bx) is less than both F(Bx) and F(Cx)) the Brent minimization is done on the function F.
Parameters: Return type:  Given two initial values this class computes a bracketing triplet of abscissae Ax, Bx, Cx (such that Bx is between Ax and Cx, F(Bx) is less than both F(Bx) and F(Cx)) the Brent minimization is done on the function F. This constructor has to be used if F(A) is known.
Parameters: Return type:  Given two initial values this class computes a bracketing triplet of abscissae Ax, Bx, Cx (such that Bx is between Ax and Cx, F(Bx) is less than both F(Bx) and F(Cx)) the Brent minimization is done on the function F. This constructor has to be used if F(A) and F(B) are known.
Parameters: Return type: 
DumpToString
()¶ math_BracketMinimum_DumpToString(math_BracketMinimum self) > std::string

FunctionValues
()¶  returns the bracketed triplet function values. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Parameters:  FA (float &) –
 FB (float &) –
 FC (float &) –
Return type:

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

Values
()¶  Returns the bracketed triplet of abscissae. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Parameters:  A (float &) –
 B (float &) –
 C (float &) –
Return type:

thisown
¶ The membership flag

class
math_BracketedRoot
(*args)¶ Bases:
object
 The Brent method is used to find the root of the function F between the bounds Bound1 and Bound2 on the function F. If F(Bound1)*F(Bound2) >0 the Brent method fails. The tolerance required for the root is given by Tolerance. The solution is found when : abs(Xi  Xi1) <= Tolerance; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type: 
DumpToString
()¶ math_BracketedRoot_DumpToString(math_BracketedRoot self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbIterations
()¶  returns the number of iterations really done during the computation of the Root. Exception NotDone is raised if the minimum was not found.
Return type: int

Root
()¶  returns the value of the root. Exception NotDone is raised if the minimum was not found.
Return type: float

Value
()¶  returns the value of the function at the root. Exception NotDone is raised if the minimum was not found.
Return type: float

thisown
¶ The membership flag

class
math_BrentMinimum
(*args)¶ Bases:
object
 This constructor should be used in a subclass to initialize correctly all the fields of this class.
Parameters: Return type:  This constructor should be used in a subclass to initialize correctly all the fields of this class. It has to be used if F(Bx) is known.
Parameters: Return type:  Given a bracketing triplet of abscissae Ax, Bx, Cx (such as Bx is between Ax and Cx, F(Bx) is less than both F(Bx) and F(Cx)) the Brent minimization is done on the function F. The tolerance required on F is given by Tolerance. The solution is found when : abs(Xi  Xi1) <= TolX * abs(Xi) + ZEPS; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type: 
DumpToString
()¶ math_BrentMinimum_DumpToString(math_BrentMinimum self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  This method is called at the end of each iteration to check if the solution is found. It can be redefined in a subclass to implement a specific test to stop the iterations.
Parameters: F (math_Function &) – Return type: bool

Location
()¶  returns the location value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

Minimum
()¶  returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

NbIterations
()¶  returns the number of iterations really done during the computation of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: int

Perform
()¶  Brent minimization is performed on function F from a given bracketing triplet of abscissas Ax, Bx, Cx (such that Bx is between Ax and Cx, F(Bx) is less than both F(Bx) and F(Cx)) Warning The initialization constructors must have been called before the call to the Perform method.
Parameters: Return type:

thisown
¶ The membership flag

class
math_BullardGenerator
(*args)¶ Bases:
object
 Creates new Xorshift 64bit RNG.
Parameters: theSeed (unsigned int) – default value is 1 Return type: None 
NextInt
()¶  Generates new 64bit integer value.
Return type: unsigned int

thisown
¶ The membership flag

class
math_CompareOfValueAndWeight
(*args)¶ Bases:
object
Return type: None 
IsEqual
()¶  returns True when <Right> and <Left> are equal.
Parameters:  Left (math_ValueAndWeight &) –
 Right (math_ValueAndWeight &) –
Return type:

IsGreater
()¶  Returns True if <Left.Value()> is greater than <Right.Value()>.
Parameters:  Left (math_ValueAndWeight &) –
 Right (math_ValueAndWeight &) –
Return type:

IsLower
()¶  Returns True if <Left.Value()> is lower than <Right.Value()>.
Parameters:  Left (math_ValueAndWeight &) –
 Right (math_ValueAndWeight &) –
Return type:

thisown
¶ The membership flag


class
math_ComputeGaussPointsAndWeights
(*args)¶ Bases:
object
Parameters: Number (int) – Return type: None 
Points
()¶ Return type: math_Vector

Weights
()¶ Return type: math_Vector

thisown
¶ The membership flag


class
math_ComputeKronrodPointsAndWeights
(*args)¶ Bases:
object
Parameters: Number (int) – Return type: None 
Points
()¶ Return type: math_Vector

Weights
()¶ Return type: math_Vector

thisown
¶ The membership flag


class
math_Crout
(*args)¶ Bases:
object
 Given an input matrix A, this algorithm inverts A by the Crout algorithm. The user can give only the inferior triangle for the implementation. A can be decomposed like this: A = L * D * T(L) where L is triangular inferior and D is diagonal. If one element of A is less than MinPivot, A is considered as singular. Exception NotSquare is raised if A is not a square matrix.
Parameters:  A (math_Matrix &) –
 MinPivot (float) – default value is 1.0e20
Return type: 
Determinant
()¶  Returns the value of the determinant of the previously LU decomposed matrix A. Zero is returned if the matrix A is considered as singular. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Return type: float

DumpToString
()¶ math_Crout_DumpToString(math_Crout self) > std::string

Inverse
()¶  returns the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.
Return type: math_Matrix

Invert
()¶  returns in Inv the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.
Parameters: Inv (math_Matrix &) – Return type: None

Solve
()¶  Given an input vector <B>, this routine returns the solution of the set of linear equations A . X = B. Exception NotDone is raised if the decomposition was not done successfully. Exception DimensionError is raised if the range of B is not equal to the rowrange of A.
Parameters:  B (math_Vector &) –
 X (math_Vector &) –
Return type:

thisown
¶ The membership flag

class
math_DirectPolynomialRoots
(*args)¶ Bases:
object
 computes all the real roots of the polynomial Ax4 + Bx3 + Cx2 + Dx + E using a direct method.
Parameters: Return type:  computes all the real roots of the polynomial Ax3 + Bx2 + Cx + D using a direct method.
Parameters: Return type:  computes all the real roots of the polynomial Ax2 + Bx + C using a direct method.
Parameters: Return type:  computes the real root of the polynomial Ax + B.
Parameters: Return type: 
DumpToString
()¶ math_DirectPolynomialRoots_DumpToString(math_DirectPolynomialRoots self) > std::string

InfiniteRoots
()¶  Returns true if there is an infinity of roots, otherwise returns false.
Return type: bool

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbSolutions
()¶  returns the number of solutions. An exception is raised if there are an infinity of roots.
Return type: int

Value
()¶  returns the value of the Nieme root. An exception is raised if there are an infinity of roots. Exception RangeError is raised if Nieme is < 1 or Nieme > NbSolutions.
Parameters: Nieme (int) – Return type: float

thisown
¶ The membership flag

class
math_DoubleTab
(*args)¶ Bases:
object
Parameters: Return type: Return type: Return type: 
thisown
¶ The membership flag


class
math_EigenValuesSearcher
(*args)¶ Bases:
object
Parameters:  Diagonal (TColStd_Array1OfReal &) –
 Subdiagonal (TColStd_Array1OfReal &) –
Return type: 
EigenValue
()¶  Returns the Index_th eigen value of matrix Index must be in [1, Dimension()]
Parameters: Index (int) – Return type: float

EigenVector
()¶  Returns the Index_th eigen vector of matrix Index must be in [1, Dimension()]
Parameters: Index (int) – Return type: math_Vector

thisown
¶ The membership flag

class
math_FRPR
(*args)¶ Bases:
object
 Computes FRPR minimization function F from input vector StartingPoint. The solution F = Fi is found when 2.0 * abs(Fi  Fi1) <= Tolerance * (abs(Fi) + abs(Fi1) + ZEPS). The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  Purpose Initializes the computation of the minimum of F. Warning A call to the Perform method must be made after this initialization to compute the minimum of the function.
Parameters: Return type: 
Delete
()¶ Return type: void

DumpToString
()¶ math_FRPR_DumpToString(math_FRPR self) > std::string

Gradient
()¶  returns the gradient vector at the minimum. Exception NotDone is raised if the minimum was not found.
Return type: math_Vector  outputs the gradient vector at the minimum in Grad. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Grad is not equal to the range of the StartingPoint.
Parameters: Grad (math_Vector &) – Return type: None

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  The solution F = Fi is found when : 2.0 * abs(Fi  Fi1) <= Tolerance * (abs(Fi) + abs(Fi1)) + ZEPS. The maximum number of iterations allowed is given by NbIterations.
Parameters: F (math_MultipleVarFunctionWithGradient &) – Return type: bool

Location
()¶  returns the location vector of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: math_Vector  outputs the location vector of the minimum in Loc. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint.
Parameters: Loc (math_Vector &) – Return type: None

Minimum
()¶  returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

NbIterations
()¶  returns the number of iterations really done during the computation of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: int

Perform
()¶  Use this method after a call to the initialization constructor to compute the minimum of function F. Warning The initialization constructor must have been called before the Perform method is called
Parameters:  F (math_MultipleVarFunctionWithGradient &) –
 StartingPoint (math_Vector &) –
Return type:

thisown
¶ The membership flag

class
math_Function
(*args, **kwargs)¶ Bases:
object

GetStateNumber
()¶  returns the state of the function corresponding to the latest call of any methods associated with the function. This function is called by each of the algorithms described later which defined the function Integer Algorithm::StateNumber(). The algorithm has the responsibility to call this function when it has found a solution (i.e. a root or a minimum) and has to maintain the association between the solution found and this StateNumber. Byu default, this method returns 0 (which means for the algorithm: no state has been saved). It is the responsibility of the programmer to decide if he needs to save the current state of the function and to return an Integer that allows retrieval of the state.
Return type: int

Value
()¶  Computes the value of the function <F> for a given value of variable <X>. returns True if the computation was done successfully, False otherwise.
Parameters:  X (float) –
 F (float &) –
Return type:

thisown
¶ The membership flag


class
math_FunctionAllRoots
(*args)¶ Bases:
object
 The algorithm uses the sample to find intervals on which the function is null. An interval is found if, for at least two consecutive points of the sample, Ui and Ui+1, we get F(Ui)<=EpsNul and F(Ui+1)<=EpsNul. The real bounds of an interval are computed with the FunctionRoots. algorithm. Between two intervals, the roots of the function F are calculated using the FunctionRoots algorithm.
Parameters: Return type: 
DumpToString
()¶ math_FunctionAllRoots_DumpToString(math_FunctionAllRoots self) > std::string

GetInterval
()¶  Returns the interval of parameter of range Index. An exception is raised if IsDone returns False; An exception is raised if Index<=0 or Index >Nbintervals.
Parameters:  Index (int) –
 A (float &) –
 B (float &) –
Return type:

GetIntervalState
()¶  returns the State Number associated to the interval Index. An exception is raised if IsDone returns False; An exception is raised if Index<=0 or Index >Nbintervals.
Parameters:  Index (int) –
 IFirst (int &) –
 ILast (int &) –
Return type:

GetPoint
()¶  Returns the parameter of the point of range Index. An exception is raised if IsDone returns False; An exception is raised if Index<=0 or Index >NbPoints.
Parameters: Index (int) – Return type: float

GetPointState
()¶  returns the State Number associated to the point Index. An exception is raised if IsDone returns False; An exception is raised if Index<=0 or Index >Nbintervals.
Parameters: Index (int) – Return type: int

NbIntervals
()¶  Returns the number of intervals on which the function is Null. An exception is raised if IsDone returns False.
Return type: int

NbPoints
()¶  returns the number of points where the function is Null. An exception is raised if IsDone returns False.
Return type: int

thisown
¶ The membership flag

class
math_FunctionRoot
(*args)¶ Bases:
object
 The NewtonRaphson method is done to find the root of the function F from the initial guess Guess.The tolerance required on the root is given by Tolerance. Iterations are stopped if the expected solution does not stay in the range A..B. The solution is found when abs(Xi  Xi1) <= Tolerance; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  The NewtonRaphson method is done to find the root of the function F from the initial guess Guess. The tolerance required on the root is given by Tolerance. Iterations are stopped if the expected solution does not stay in the range A..B The solution is found when abs(Xi  Xi1) <= Tolerance; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type: 
Derivative
()¶  returns the value of the derivative at the root. Exception NotDone is raised if the root was not found.
Return type: float

DumpToString
()¶ math_FunctionRoot_DumpToString(math_FunctionRoot self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbIterations
()¶  returns the number of iterations really done on the computation of the Root. Exception NotDone is raised if the root was not found.
Return type: int

Root
()¶  returns the value of the root. Exception NotDone is raised if the root was not found.
Return type: float

Value
()¶  returns the value of the function at the root. Exception NotDone is raised if the root was not found.
Return type: float

thisown
¶ The membership flag

class
math_FunctionRoots
(*args)¶ Bases:
object
 Calculates all the real roots of a function FK within the range A..B. whithout conditions on A and B A solution X is found when abs(Xi  Xi1) <= Epsx and abs(F(Xi)K) <= EpsF. The function is considered as null between A and B if abs(FK) <= EpsNull within this range.
Parameters: Return type: 
DumpToString
()¶ math_FunctionRoots_DumpToString(math_FunctionRoots self) > std::string

IsAllNull
()¶  returns true if the function is considered as null between A and B. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Return type: bool

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbSolutions
()¶  Returns the number of solutions found. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Return type: int

StateNumber
()¶  returns the StateNumber of the Nieme root. Exception RangeError is raised if Nieme is < 1 or Nieme > NbSolutions.
Parameters: Nieme (int) – Return type: int

Value
()¶  Returns the Nth value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Parameters: Nieme (int) – Return type: float

thisown
¶ The membership flag

class
math_FunctionSample
(*args)¶ Bases:
object
Parameters: Return type: 
Bounds
()¶  Returns the bounds of parameters.
Parameters:  A (float &) –
 B (float &) –
Return type: void

GetParameter
()¶  Returns the value of parameter of the point of range Index : A + ((Index1)/(NbPoints1))*B. An exception is raised if Index<=0 or Index>NbPoints.
Parameters: Index (int) – Return type: float

thisown
¶ The membership flag


class
math_FunctionSet
(*args, **kwargs)¶ Bases:
object

Delete
()¶ Return type: void

GetStateNumber
()¶  Returns the state of the function corresponding to the latestcall of any methods associated with the function. This function is called by each of the algorithms described later which define the function Integer Algorithm::StateNumber(). The algorithm has the responsibility to call this function when it has found a solution (i.e. a root or a minimum) and has to maintain the association between the solution found and this StateNumber. Byu default, this method returns 0 (which means for the algorithm: no state has been saved). It is the responsibility of the programmer to decide if he needs to save the current state of the function and to return an Integer that allows retrieval of the state.
Return type: int

Value
()¶  Computes the values <F> of the functions for the variable <X>. returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 F (math_Vector &) –
Return type:

thisown
¶ The membership flag


class
math_FunctionSetRoot
(*args)¶ Bases:
object
 is used in a subclass to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations.
Parameters:  F (math_FunctionSetWithDerivatives &) –
 Tolerance (math_Vector &) –
 NbIterations (int) – default value is 100
Return type:  is used in a subclass to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations. The method SetTolerance must be called after this constructor.
Parameters:  F (math_FunctionSetWithDerivatives &) –
 NbIterations (int) – default value is 100
Return type:  is used to improve the root of the function F from the initial guess StartingPoint. The maximum number of iterations allowed is given by NbIterations. In this case, the solution is found when: abs(Xi  Xi1)(j) <= Tolerance(j) for all unknowns.
Parameters:  F (math_FunctionSetWithDerivatives &) –
 StartingPoint (math_Vector &) –
 Tolerance (math_Vector &) –
 NbIterations (int) – default value is 100
Return type:  is used to improve the root of the function F from the initial guess StartingPoint. The maximum number of iterations allowed is given by NbIterations. In this case, the solution is found when: abs(Xi  Xi1) <= Tolerance for all unknowns.
Parameters: Return type: 
Delete
()¶ Return type: void

Derivative
()¶  Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found.
Return type: math_Matrix  outputs the matrix value of the derivative at the root in Der. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the column range of <Der> is not equal to the range of the startingPoint.
Parameters: Der (math_Matrix &) – Return type: None

DumpToString
()¶ math_FunctionSetRoot_DumpToString(math_FunctionSetRoot self) > std::string

FunctionSetErrors
()¶  returns the vector value of the error done on the functions at the root. Exception NotDone is raised if the root was not found.
Return type: math_Vector  outputs the vector value of the error done on the functions at the root in Err. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Err is not equal to the range of the StartingPoint.
Parameters: Err (math_Vector &) – Return type: None

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  This routine is called at the end of each iteration to check if the solution was found. It can be redefined in a subclass to implement a specific test to stop the iterations. In this case, the solution is found when: abs(Xi  Xi1) <= Tolerance for all unknowns.
Parameters: F (math_FunctionSetWithDerivatives &) – Return type: bool

NbIterations
()¶  Returns the number of iterations really done during the computation of the root. Exception NotDone is raised if the root was not found.
Return type: int

Perform
()¶  Improves the root of function F from the initial guess StartingPoint. infBound and supBound may be given to constrain the solution. Warning This method is called when computation of the solution is not performed by the constructors.
Parameters:  F (math_FunctionSetWithDerivatives &) –
 StartingPoint (math_Vector &) –
 infBound (math_Vector &) –
 supBound (math_Vector &) –
 theStopOnDivergent (bool) – default value is Standard_False
Return type:

Root
()¶  Returns the value of the root of function F. Exception NotDone is raised if the root was not found.
Return type: math_Vector  Outputs the root vector in Root. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Root is not equal to the range of the StartingPoint.
Parameters: Root (math_Vector &) – Return type: None

SetTolerance
()¶  Initializes the tolerance values.
Parameters: Tolerance (math_Vector &) – Return type: None

StateNumber
()¶  returns the stateNumber (as returned by F.GetStateNumber()) associated to the root found.
Return type: int

thisown
¶ The membership flag

class
math_FunctionSetWithDerivatives
(*args, **kwargs)¶ Bases:
OCC.math.math_FunctionSet

Derivatives
()¶  Returns the values <D> of the derivatives for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 D (math_Matrix &) –
Return type:

Values
()¶  returns the values <F> of the functions and the derivatives <D> for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 F (math_Vector &) –
 D (math_Matrix &) –
Return type:

thisown
¶ The membership flag


class
math_FunctionWithDerivative
(*args, **kwargs)¶ Bases:
OCC.math.math_Function

Delete
()¶ Return type: void

Derivative
()¶  Computes the derivative <D> of the function for the variable <X>. Returns True if the calculation were successfully done, False otherwise.
Parameters:  X (float) –
 D (float &) –
Return type:

Values
()¶  Computes the value <F> and the derivative <D> of the function for the variable <X>. Returns True if the calculation were successfully done, False otherwise.
Parameters:  X (float) –
 F (float &) –
 D (float &) –
Return type:

thisown
¶ The membership flag


class
math_Gauss
(*args)¶ Bases:
object
 Given an input n X n matrix A this constructor performs its LU decomposition with partial pivoting (interchange of rows). This LU decomposition is stored internally and may be used to do subsequent calculation. If the largest pivot found is less than MinPivot the matrix A is considered as singular. Exception NotSquare is raised if A is not a square matrix.
Parameters:  A (math_Matrix &) –
 MinPivot (float) – default value is 1.0e20
Return type: 
Determinant
()¶  This routine returns the value of the determinant of the previously LU decomposed matrix A. Exception NotDone may be raised if the decomposition of A was not done successfully, zero is returned if the matrix A was considered as singular.
Return type: float

DumpToString
()¶ math_Gauss_DumpToString(math_Gauss self) > std::string

Invert
()¶  This routine outputs Inv the inverse of the previously LU decomposed matrix A. Exception DimensionError is raised if the ranges of B are not equal to the ranges of A.
Parameters: Inv (math_Matrix &) – Return type: None

Solve
()¶  Given the input Vector B this routine returns the solution X of the set of linear equations A . X = B. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A.
Parameters:  B (math_Vector &) –
 X (math_Vector &) –
Return type:  Given the input Vector B this routine solves the set of linear equations A . X = B. B is replaced by the vector solution X. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A.
Parameters: B (math_Vector &) – Return type: None

thisown
¶ The membership flag

class
math_GaussLeastSquare
(*args)¶ Bases:
object
 Given an input n X m matrix A with n >= m this constructor performs the LU decomposition with partial pivoting (interchange of rows) of the matrix AA = A.Transposed() * A; This LU decomposition is stored internally and may be used to do subsequent calculation. If the largest pivot found is less than MinPivot the matrix <A> is considered as singular.
Parameters:  A (math_Matrix &) –
 MinPivot (float) – default value is 1.0e20
Return type: 
DumpToString
()¶ math_GaussLeastSquare_DumpToString(math_GaussLeastSquare self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.e
Return type: bool

Solve
()¶  Given the input Vector <B> this routine solves the set of linear equations A . X = B. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B Inv is not equal to the rowrange of A. Exception DimensionError is raised if the range of X Inv is not equal to the colrange of A.
Parameters:  B (math_Vector &) –
 X (math_Vector &) –
Return type:

thisown
¶ The membership flag

class
math_GaussMultipleIntegration
(*args)¶ Bases:
object
 The GaussLegendre integration with Order = points of integration for each unknow, is done on the function F between the bounds Lower and Upper.
Parameters:  F (math_MultipleVarFunction &) –
 Lower (math_Vector &) –
 Upper (math_Vector &) –
 Order (math_IntegerVector &) –
Return type: 
DumpToString
()¶ math_GaussMultipleIntegration_DumpToString(math_GaussMultipleIntegration self) > std::string

thisown
¶ The membership flag

class
math_GaussSetIntegration
(*args)¶ Bases:
object
 The GaussLegendre integration with Order = points of integration for each unknow, is done on the function F between the bounds Lower and Upper.
Parameters:  F (math_FunctionSet &) –
 Lower (math_Vector &) –
 Upper (math_Vector &) –
 Order (math_IntegerVector &) –
Return type: 
DumpToString
()¶ math_GaussSetIntegration_DumpToString(math_GaussSetIntegration self) > std::string

Value
()¶  returns the value of the integral.
Return type: math_Vector

thisown
¶ The membership flag

class
math_GaussSingleIntegration
(*args)¶ Bases:
object
Return type: None  The GaussLegendre integration with N = Order points of integration, is done on the function F between the bounds Lower and Upper.
Parameters: Return type:  The GaussLegendre integration with N = Order points of integration and given tolerance = Tol is done on the function F between the bounds Lower and Upper.
Parameters: Return type: 
DumpToString
()¶ math_GaussSingleIntegration_DumpToString(math_GaussSingleIntegration self) > std::string

thisown
¶ The membership flag

class
math_GlobOptMin
(*args)¶ Bases:
object
Parameters: Return type: 
Points
()¶  Return solution i, 1 <= i <= NbExtrema.
Parameters:  theIndex (int) –
 theSol (math_Vector &) –
Return type:

SetGlobalParams
()¶ Parameters: Return type:

SetLocalParams
()¶ Parameters:  theLocalA (math_Vector &) –
 theLocalB (math_Vector &) –
Return type:

thisown
¶ The membership flag


class
math_Householder
(*args)¶ Bases:
object
 Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can’t be done. Exception DimensionError is raised if the row number of B is different from the A row number.
Parameters:  A (math_Matrix &) –
 B (math_Matrix &) –
 EPS (float) – default value is 1.0e20
Return type:  Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can’t be done. Exception DimensionError is raised if the row number of B is different from the A row number.
Parameters: Return type:  Given an input matrix A with n>= m, given an input vector B this constructor performs the least square resolution of the set of linear equations A.X = B. If a column norm is less than EPS, the resolution can’t be done. Exception DimensionError is raised if the length of B is different from the A row number.
Parameters:  A (math_Matrix &) –
 B (math_Vector &) –
 EPS (float) – default value is 1.0e20
Return type: 
AllValues
()¶  Returns the matrix sol of all the solutions of the system A.X = B. Exception NotDone is raised is the resolution has not be done.
Return type: math_Matrix

DumpToString
()¶ math_Householder_DumpToString(math_Householder self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

Value
()¶  Given the integer Index, this routine returns the corresponding least square solution sol. Exception NotDone is raised if the resolution has not be done. Exception OutOfRange is raised if Index <=0 or Index is more than the number of columns of B.
Parameters:  sol (math_Vector &) –
 Index (int) – default value is 1
Return type:

thisown
¶ The membership flag

class
math_IntegerRandom
(*args)¶ Bases:
object
 creates a Integer random generator between the values Lower and Upper.
Parameters: Return type: 
thisown
¶ The membership flag

class
math_IntegerVector
(*args)¶ Bases:
object
 contructs an IntegerVector in the range [Lower..Upper]
Parameters: Return type:  contructs an IntegerVector in the range [Lower..Upper] with all the elements set to theInitialValue.
Parameters: Return type:  constructs an IntegerVector in the range [Lower..Upper] which share the ‘c array’ theTab.
Parameters: Return type:  constructs a copy for initialization. An exception is raised if the lengths of the IntegerVectors are different.
Parameters: theOther (math_IntegerVector &) – Return type: None 
Add
()¶  adds the IntegerVector ‘theRight’ to an IntegerVector. An exception is raised if the IntegerVectors have not the same length. An exception is raised if the lengths are not equal.
Parameters: theRight (math_IntegerVector &) – Return type: None  sets an IntegerVector to the sum of the IntegerVector ‘theLeft’ and the IntegerVector ‘theRight’. An exception is raised if the lengths are different.
Parameters:  theLeft (math_IntegerVector &) –
 theRight (math_IntegerVector &) –
Return type:

Added
()¶  adds the IntegerVector ‘theRight’ to an IntegerVector. An exception is raised if the IntegerVectors have not the same length. An exception is raised if the lengths are not equal.
Parameters: theRight (math_IntegerVector &) – Return type: math_IntegerVector

DumpToString
()¶ math_IntegerVector_DumpToString(math_IntegerVector self) > std::string

Init
()¶  Initialize an IntegerVector with all the elements set to theInitialValue.
Parameters: theInitialValue (int) – Return type: None

Initialized
()¶  Initialises an IntegerVector by copying ‘theOther’. An exception is raised if the Lengths are different.
Parameters: theOther (math_IntegerVector &) – Return type: math_IntegerVector

Inverse
()¶  returns the inverse IntegerVector of an IntegerVector.
Return type: math_IntegerVector

Length
()¶  returns the length of an IntegerVector
Return type: inline int

Lower
()¶  returns the value of the Lower index of an IntegerVector.
Return type: inline int

Multiplied
()¶  returns the product of an IntegerVector by an integer value.
Parameters: theRight (int) – Return type: math_IntegerVector  returns the inner product of 2 IntegerVectors. An exception is raised if the lengths are not equal.
Parameters: theRight (math_IntegerVector &) – Return type: int

Multiply
()¶  returns the product of an IntegerVector by an integer value.
Parameters: theRight (int) – Return type: None  returns the multiplication of an integer by an IntegerVector.
Parameters:  theLeft (int) –
 theRight (math_IntegerVector &) –
Return type:

Opposite
()¶  returns the opposite of an IntegerVector.
Return type: math_IntegerVector

Set
()¶  sets an IntegerVector from ‘theI1’ to ‘theI2’ to the IntegerVector ‘theV’; An exception is raised if ‘theI1’ is less than ‘LowerIndex’ or ‘theI2’ is greater than ‘UpperIndex’ or ‘theI1’ is greater than ‘theI2’. An exception is raised if ‘theI2theI1+1’ is different from the Length of ‘theV’.
Parameters: Return type: Return type:

Slice
()¶  slices the values of the IntegerVector between ‘theI1’ and ‘theI2’: Example: [2, 1, 2, 3, 4, 5] becomes [2, 4, 3, 2, 1, 5] between 2 and 5. An exception is raised if ‘theI1’ is less than ‘LowerIndex’ or ‘theI2’ is greater than ‘UpperIndex’.
Parameters: Return type:

Subtract
()¶  sets an IntegerVector to the substraction of ‘theRight’ from ‘theLeft’. An exception is raised if the IntegerVectors have not the same length.
Parameters:  theLeft (math_IntegerVector &) –
 theRight (math_IntegerVector &) –
Return type:  returns the subtraction of ‘theRight’ from ‘me’. An exception is raised if the IntegerVectors have not the same length.
Parameters: theRight (math_IntegerVector &) – Return type: None

Subtracted
()¶  returns the subtraction of ‘theRight’ from ‘me’. An exception is raised if the IntegerVectors have not the same length.
Parameters: theRight (math_IntegerVector &) – Return type: math_IntegerVector

TMultiplied
()¶  returns the product of a vector and a real value.
Parameters: theRight (int) – Return type: math_IntegerVector

Upper
()¶  returns the value of the Upper index of an IntegerVector.
Return type: inline int

Value
()¶  accesses (in read or write mode) the value of index theNum of an IntegerVector.
Parameters: theNum (int) – Return type: inline int

thisown
¶ The membership flag

class
math_Jacobi
(*args)¶ Bases:
object
 Given a Real n X n matrix A, this constructor computes all its eigenvalues and eigenvectors using the Jacobi method. The exception NotSquare is raised if the matrix is not square. No verification that the matrix A is really symmetric is done.
Parameters: A (math_Matrix &) – Return type: None 
DumpToString
()¶ math_Jacobi_DumpToString(math_Jacobi self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

Value
()¶  returns the eigenvalue number Num. Eigenvalues are in the range (1..n). Exception NotDone is raised if calculation is not done successfully.
Parameters: Num (int) – Return type: float

Values
()¶  Returns the eigenvalues vector. Exception NotDone is raised if calculation is not done successfully.
Return type: math_Vector

Vector
()¶  Returns the eigenvector V of number Num. Eigenvectors are in the range (1..n). Exception NotDone is raised if calculation is not done successfully.
Parameters:  Num (int) –
 V (math_Vector &) –
Return type:

Vectors
()¶  returns the eigenvectors matrix. Exception NotDone is raised if calculation is not done successfully.
Return type: math_Matrix

thisown
¶ The membership flag

math_KronrodPointsAndWeights
(*args)¶  Returns a vector of Kronrod points and a vector of their weights for GaussKronrod computation method. Index should be odd and greater then or equal to 3, as the number of Kronrod points is equal to 2*N + 1, where N is a number of Gauss points. Points and Weights should have the size equal to Index. Each even element of Points represents a Gauss point value of Nth Gauss quadrature. The values from Index equal to 3 to 123 are stored in a table (see the file math_Kronrod.cxx). If Index is greater, then points and weights will be computed. Returns Standard_True if Index is odd, it is equal to the size of Points and Weights and the computation of Points and Weights is performed successfully. Otherwise this method returns Standard_False.
Parameters:  Index (int) –
 Points (math_Vector &) –
 Weights (math_Vector &) –
Return type:

math_KronrodPointsMax
(*args)¶  Returns the maximal number of points for that the values are stored in the table. If the number is greater then KronrodPointsMax, the points will be computed.
Return type: int

class
math_KronrodSingleIntegration
(*args)¶ Bases:
object
 An empty constructor.
Return type: None  Constructor. Takes the function, the lower and upper bound values, the initial number of Kronrod points
Parameters: Return type:  Constructor. Takes the function, the lower and upper bound values, the initial number of Kronrod points, the tolerance value and the maximal number of iterations as parameters.
Parameters: Return type: 
static
GKRule
(*args)¶ Parameters: Return type:

OrderReached
()¶  Returns the number of Kronrod points for which the result is computed.
Return type: int

Perform
()¶  Computation of the integral. Takes the function, the lower and upper bound values, the initial number of Kronrod points, the relative tolerance value and the maximal number of iterations as parameters. theNbPnts should be odd and greater then or equal to 3.
Parameters: Return type:  Computation of the integral. Takes the function, the lower and upper bound values, the initial number of Kronrod points, the relative tolerance value and the maximal number of iterations as parameters. theNbPnts should be odd and greater then or equal to 3. Note that theTolerance is relative, i.e. the criterion of solution reaching is: Abs(Kronrod  Gauss)/Abs(Kronrod) < theTolerance. theTolerance should be positive.
Parameters: Return type:

thisown
¶ The membership flag

math_KronrodSingleIntegration_GKRule
(*args)¶ Parameters: Return type:

class
math_Matrix
(*args)¶ Bases:
object
 Constructs a noninitialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] For the constructed matrix:  LowerRow and UpperRow are the indexes of the lower and upper bounds of a row, and  LowerCol and UpperCol are the indexes of the lower and upper bounds of a column.
Parameters: Return type:  constructs a noninitialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] whose values are all initialized with the value InitialValue.
Parameters: Return type:  constructs a matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] Sharing data with a ‘C array’ pointed by Tab.
Parameters: Return type:  constructs a matrix for copy in initialization. An exception is raised if the matrixes have not the same dimensions.
Parameters: Other (math_Matrix &) – Return type: None 
Add
()¶  adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different. Warning In order to save time when copying matrices, it is preferable to use operator += or the function Add whenever possible.
Parameters: Right (math_Matrix &) – Return type: None  sets a matrix to the addition of <Left> and <Right>. An exception is raised if the dimensions are different.
Parameters:  Left (math_Matrix &) –
 Right (math_Matrix &) –
Return type:

Added
()¶  adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different.
Parameters: Right (math_Matrix &) – Return type: math_Matrix

Col
()¶  Returns the column of index <Col> of a matrix.
Parameters: Col (int) – Return type: math_Vector

ColNumber
()¶  Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:  A.RowNumber() = A.UpperRow()  A.LowerRow() + 1  A.ColNumber() = A.UpperCol()  A.LowerCol() + 1  the length of a row of A is equal to the number of columns of A,  the length of a column of A is equal to the number of rows of A.returns the row range of a matrix.
Return type: int

Determinant
()¶  Computes the determinant of a matrix. An exception is raised if the matrix is not a square matrix.
Return type: float

Divide
()¶  divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.
Parameters: Right (float) – Return type: None

Divided
()¶  divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.
Parameters: Right (float) – Return type: math_Matrix

DumpToString
()¶ math_Matrix_DumpToString(math_Matrix self) > std::string

Init
()¶  Initialize all the elements of a matrix to InitialValue.
Parameters: InitialValue (float) – Return type: None

Initialized
()¶  Matrixes are copied through assignement. An exception is raised if the dimensions are differents.
Parameters: Other (math_Matrix &) – Return type: math_Matrix

Inverse
()¶  Returns the inverse of a matrix. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.
Return type: math_Matrix

Invert
()¶  Inverts a matrix using Gauss algorithm. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.
Return type: None

Multiplied
()¶  multiplies all the elements of a matrix by the value <Right>.
Parameters: Right (float) – Return type: math_Matrix  Returns the product of 2 matrices. An exception is raised if the dimensions are different.
Parameters: Right (math_Matrix &) – Return type: math_Matrix  Returns the product of a matrix by a vector. An exception is raised if the dimensions are different.
Parameters: Right (math_Vector &) – Return type: math_Vector

Multiply
()¶  Sets this matrix to the product of the matrix Left, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:  the number of columns of matrix Left, or the number of rows of matrix TLeft is not equal to the number of rows of matrix Right, or  the number of rows of matrix Left, or the number of columns of matrix TLeft is not equal to the number of rows of this matrix, or  the number of columns of matrix Right is not equal to the number of columns of this matrix.
Parameters: Right (float) – Return type: None  Computes a matrix as the product of 2 vectors. An exception is raised if the dimensions are different. <self> = <Left> * <Right>.
Parameters:  Left (math_Vector &) –
 Right (math_Vector &) –
Return type:  Computes a matrix as the product of 2 matrixes. An exception is raised if the dimensions are different.
Parameters:  Left (math_Matrix &) –
 Right (math_Matrix &) –
Return type:  Returns the product of 2 matrices. An exception is raised if the dimensions are different.
Parameters: Right (math_Matrix &) – Return type: None

Opposite
()¶  Returns the opposite of a matrix. An exception is raised if the dimensions are different.
Return type: math_Matrix

Row
()¶  Returns the row of index Row of a matrix.
Parameters: Row (int) – Return type: math_Vector

RowNumber
()¶  Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:  A.RowNumber() = A.UpperRow()  A.LowerRow() + 1  A.ColNumber() = A.UpperCol()  A.LowerCol() + 1  the length of a row of A is equal to the number of columns of A,  the length of a column of A is equal to the number of rows of A.returns the row range of a matrix.
Return type: int

Set
()¶  Sets the values of this matrix,  from index I1 to index I2 on the row dimension, and  from index J1 to index J2 on the column dimension, to those of matrix M. Exceptions Standard_DimensionError if:  I1 is less than the index of the lower row bound of this matrix, or  I2 is greater than the index of the upper row bound of this matrix, or  J1 is less than the index of the lower column bound of this matrix, or  J2 is greater than the index of the upper column bound of this matrix, or  I2  I1 + 1 is not equal to the number of rows of matrix M, or  J2  J1 + 1 is not equal to the number of columns of matrix M.
Parameters: Return type: Return type:

SetCol
()¶  Sets the column of index Col of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Col> is inferior to the lower column of the matrix or <Col> is superior to the upper column.
Parameters:  Col (int) –
 V (math_Vector &) –
Return type:

SetDiag
()¶  Sets the diagonal of a matrix to the value <Value>. An exception is raised if the matrix is not square.
Parameters: Value (float) – Return type: None

SetRow
()¶  Sets the row of index Row of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Row> is inferior to the lower row of the matrix or <Row> is superior to the upper row.
Parameters:  Row (int) –
 V (math_Vector &) –
Return type:

Subtract
()¶  Subtracts the matrix <Right> from <self>. An exception is raised if the dimensions are different. Warning In order to avoid timeconsuming copying of matrices, it is preferable to use operator = or the function Subtract whenever possible.
Parameters: Right (math_Matrix &) – Return type: None  Sets a matrix to the Subtraction of the matrix <Right> from the matrix <Left>. An exception is raised if the dimensions are different.
Parameters:  Left (math_Matrix &) –
 Right (math_Matrix &) –
Return type:

Subtracted
()¶  Returns the result of the subtraction of <Right> from <self>. An exception is raised if the dimensions are different.
Parameters: Right (math_Matrix &) – Return type: math_Matrix

SwapCol
()¶  Swaps the columns of index <Col1> and <Col2>. An exception is raised if <Col1> or <Col2> is out of range.
Parameters: Return type:

SwapRow
()¶  Swaps the rows of index Row1 and Row2. An exception is raised if <Row1> or <Row2> is out of range.
Parameters: Return type:

TMultiplied
()¶  Sets this matrix to the product of the transposed matrix TLeft, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:  the number of columns of matrix Left, or the number of rows of matrix TLeft is not equal to the number of rows of matrix Right, or  the number of rows of matrix Left, or the number of columns of matrix TLeft is not equal to the number of rows of this matrix, or  the number of columns of matrix Right is not equal to the number of columns of this matrix.
Parameters: Right (float) – Return type: math_Matrix

TMultiply
()¶  Returns the product of the transpose of a matrix with the matrix <Right>. An exception is raised if the dimensions are different.
Parameters: Right (math_Matrix &) – Return type: math_Matrix  Computes a matrix to the product of the transpose of the matrix <TLeft> with the matrix <Right>. An exception is raised if the dimensions are different.
Parameters:  TLeft (math_Matrix &) –
 Right (math_Matrix &) –
Return type:

Transpose
()¶  Transposes a given matrix. An exception is raised if the matrix is not a square matrix.
Return type: None

Transposed
()¶  Teturns the transposed of a matrix. An exception is raised if the matrix is not a square matrix.
Return type: math_Matrix

Value
()¶  Accesses (in read or write mode) the value of index <Row> and <Col> of a matrix. An exception is raised if <Row> and <Col> are not in the correct range.
Parameters: Return type:

thisown
¶ The membership flag

class
math_MultipleVarFunction
(*args, **kwargs)¶ Bases:
object

Delete
()¶ Return type: void

GetStateNumber
()¶  return the state of the function corresponding to the latestt call of any methods associated to the function. This function is called by each of the algorithms described later which define the function Integer Algorithm::StateNumber(). The algorithm has the responsibility to call this function when it has found a solution (i.e. a root or a minimum) and has to maintain the association between the solution found and this StateNumber. Byu default, this method returns 0 (which means for the algorithm: no state has been saved). It is the responsibility of the programmer to decide if he needs to save the current state of the function and to return an Integer that allows retrieval of the state.
Return type: int

Value
()¶  Computes the values of the Functions <F> for the variable <X>. returns True if the computation was done successfully, otherwise false.
Parameters:  X (math_Vector &) –
 F (float &) –
Return type:

thisown
¶ The membership flag


class
math_MultipleVarFunctionWithGradient
(*args, **kwargs)¶ Bases:
OCC.math.math_MultipleVarFunction

Gradient
()¶  Computes the gradient <G> of the functions for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 G (math_Vector &) –
Return type:

Values
()¶  computes the value <F> and the gradient <G> of the functions for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 F (float &) –
 G (math_Vector &) –
Return type:

thisown
¶ The membership flag


class
math_MultipleVarFunctionWithHessian
(*args, **kwargs)¶ Bases:
OCC.math.math_MultipleVarFunctionWithGradient

Values
()¶  computes the value <F> and the gradient <G> of the functions for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 F (float &) –
 G (math_Vector &) –
Return type:  computes the value <F>, the gradient <G> and the hessian <H> of the functions for the variable <X>. Returns True if the computation was done successfully, False otherwise.
Parameters:  X (math_Vector &) –
 F (float &) –
 G (math_Vector &) –
 H (math_Matrix &) –
Return type:

thisown
¶ The membership flag


class
math_NewtonFunctionRoot
(*args)¶ Bases:
object
 The Newton method is done to find the root of the function F from the initial guess Guess. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi  Xi1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  The Newton method is done to find the root of the function F from the initial guess Guess. The solution must be inside the interval [A, B]. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi  Xi1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  is used in a subclass to initialize correctly all the fields of this class.
Parameters: Return type: 
Derivative
()¶  returns the value of the derivative at the root. Exception NotDone is raised if the root was not found.
Return type: float

DumpToString
()¶ math_NewtonFunctionRoot_DumpToString(math_NewtonFunctionRoot self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbIterations
()¶  Returns the number of iterations really done on the computation of the Root. Exception NotDone is raised if the root was not found.
Return type: int

Perform
()¶  is used internally by the constructors.
Parameters:  F (math_FunctionWithDerivative &) –
 Guess (float) –
Return type:

Root
()¶  Returns the value of the root of function <F>. Exception NotDone is raised if the root was not found.
Return type: float

Value
()¶  returns the value of the function at the root. Exception NotDone is raised if the root was not found.
Return type: float

thisown
¶ The membership flag

class
math_NewtonFunctionSetRoot
(*args)¶ Bases:
object
 This constructor should be used in a subclass to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations.
Parameters: Return type:  This constructor should be used in a subclass to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations. The method SetTolerance must be called before performing the algorithm.
Parameters: Return type:  The Newton method is done to improve the root of the function F from the initial guess StartingPoint. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  The Newton method is done to improve the root of the function F from the initial guess StartingPoint. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i; The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type: 
Delete
()¶ Return type: void

Derivative
()¶  Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found.
Return type: math_Matrix  Outputs the matrix value of the derivative at the root in Der. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Der is not equal to the range of the StartingPoint.
Parameters: Der (math_Matrix &) – Return type: None

DumpToString
()¶ math_NewtonFunctionSetRoot_DumpToString(math_NewtonFunctionSetRoot self) > std::string

FunctionSetErrors
()¶  Returns the vector value of the error done on the functions at the root. Exception NotDone is raised if the root was not found.
Return type: math_Vector  Outputs the vector value of the error done on the functions at the root in Err. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Err is not equal to the range of the StartingPoint.
Parameters: Err (math_Vector &) – Return type: None

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  This method is called at the end of each iteration to check if the solution is found. Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the possible solution Vector Sol and can be inspected to decide whether the solution is reached or not.
Parameters: F (math_FunctionSetWithDerivatives &) – Return type: bool

NbIterations
()¶  Returns the number of iterations really done during the computation of the Root. Exception NotDone is raised if the root was not found.
Return type: int

Perform
()¶  Improves the root of function F from the initial guess StartingPoint. infBound and supBound may be given, to constrain the solution. Warning This method must be called when the solution is not computed by the constructors.
Parameters:  F (math_FunctionSetWithDerivatives &) –
 StartingPoint (math_Vector &) –
 InfBound (math_Vector &) –
 SupBound (math_Vector &) –
Return type:

Root
()¶  Returns the value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
Return type: math_Vector  outputs the root vector in Root. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Root is not equal to the range of the StartingPoint.
Parameters: Root (math_Vector &) – Return type: None

SetTolerance
()¶  Initializes the tolerance values for the unknowns.
Parameters: XTol (math_Vector &) – Return type: None

thisown
¶ The membership flag

class
math_NewtonMinimum
(*args)¶ Bases:
object
 – Given the starting point StartingPoint, The tolerance required on the solution is given by Tolerance. Iteration are stopped if (!WithSingularity) and H(F(Xi)) is not definite positive (if the smaller eigenvalue of H < Convexity) or IsConverged() returns True for 2 successives Iterations. Warning: Obsolete Constructor (because IsConverged can not be redefined with this. )
Parameters: Return type:  The tolerance required on the solution is given by Tolerance. Iteration are stopped if (!WithSingularity) and H(F(Xi)) is not definite positive (if the smaller eigenvalue of H < Convexity) or IsConverged() returns True for 2 successives Iterations. Warning: This constructor do not computation
Parameters: Return type: 
Delete
()¶ Return type: void

DumpToString
()¶ math_NewtonMinimum_DumpToString(math_NewtonMinimum self) > std::string

Gradient
()¶  returns the gradient vector at the minimum. Exception NotDone is raised if an error has occured.the minimum was not found.
Return type: math_Vector  outputs the gradient vector at the minimum in Grad. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Grad is not equal to the range of the StartingPoint.
Parameters: Grad (math_Vector &) – Return type: None

IsConverged
()¶  This method is called at the end of each iteration to check the convergence :  Xi+1  Xi  < Tolerance or  F(Xi+1)  F(Xi) < Tolerance *  F(Xi)  It can be redefined in a subclass to implement a specific test.
Return type: bool

Location
()¶  returns the location vector of the minimum. Exception NotDone is raised if an error has occured.
Return type: math_Vector  outputs the location vector of the minimum in Loc. Exception NotDone is raised if an error has occured. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint.
Parameters: Loc (math_Vector &) – Return type: None

Minimum
()¶  returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

NbIterations
()¶  returns the number of iterations really done in the calculation of the minimum. The exception NotDone is raised if an error has occured.
Return type: int

Perform
()¶  Search the solution.
Parameters:  F (math_MultipleVarFunctionWithHessian &) –
 StartingPoint (math_Vector &) –
Return type:

thisown
¶ The membership flag

math_OrderedGaussPointsAndWeights
(*args)¶  Returns a vector of Gauss points and a vector of their weights. The difference with the method GaussPoints is the following:  the points are returned in increasing order.  if Index is greater then GaussPointsMax, the points are computed. Returns Standard_True if Index is positive, Points’ and Weights’ length is equal to Index, Points and Weights are successfully computed.
Parameters:  Index (int) –
 Points (math_Vector &) –
 Weights (math_Vector &) –
Return type:

class
math_PSO
(*args)¶ Bases:
object
 /** * Constructor. * * @param theFunc defines the objective function. It should exist during all lifetime of class instance. * @param theLowBorder defines lower border of search space. * @param theUppBorder defines upper border of search space. * @param theSteps defines steps of regular grid, used for particle generation. This parameter used to define stop condition (TerminalVelocity). * @param theNbParticles defines number of particles. * @param theNbIter defines maximum number of iterations. */
Parameters: Return type: 
Perform
()¶  Perform computations, particles array is constructed inside of this function.
Parameters:  theSteps (math_Vector &) –
 theValue (float &) –
 theOutPnt (math_Vector &) –
 theNbIter (int) – default value is 100
Return type:  Perform computations with given particles array.
Parameters: Return type:

thisown
¶ The membership flag

class
math_PSOParticlesPool
(*args)¶ Bases:
object
Parameters: Return type: 
GetBestParticle
()¶ Return type: PSO_Particle *

GetWorstParticle
()¶ Return type: PSO_Particle *

thisown
¶ The membership flag


class
math_Powell
(*args)¶ Bases:
object
 Computes Powell minimization on the function F given StartingPoint, and an initial matrix StartingDirection whose columns contain the initial set of directions. The solution F = Fi is found when 2.0 * abs(Fi  Fi1) = <Tolerance * (abs(Fi) + abs(Fi1) + ZEPS). The maximum number of iterations allowed is given by NbIterations.
Parameters: Return type:  is used in a subclass to initialize correctly all the fields of this class.
Parameters: Return type: 
Delete
()¶ Return type: void

DumpToString
()¶ math_Powell_DumpToString(math_Powell self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

IsSolutionReached
()¶  solution F = Fi is found when : 2.0 * abs(Fi  Fi1) <= Tolerance * (abs(Fi) + abs(Fi1)) + ZEPS. The maximum number of iterations allowed is given by NbIterations.
Parameters: F (math_MultipleVarFunction &) – Return type: bool

Location
()¶  returns the location vector of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: math_Vector  outputs the location vector of the minimum in Loc. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint.
Parameters: Loc (math_Vector &) – Return type: None

Minimum
()¶  Returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: float

NbIterations
()¶  Returns the number of iterations really done during the computation of the minimum. Exception NotDone is raised if the minimum was not found.
Return type: int

Perform
()¶  Use this method after a call to the initialization constructor to compute the minimum of function F. Warning The initialization constructor must have been called before the Perform method is called.
Parameters:  F (math_MultipleVarFunction &) –
 StartingPoint (math_Vector &) –
 StartingDirections (math_Matrix &) –
Return type:

thisown
¶ The membership flag

class
math_QuickSortOfValueAndWeight
¶ Bases:
object

static
Sort
(*args)¶ Parameters:  TheArray (math_Array1OfValueAndWeight &) –
 Comp (math_CompareOfValueAndWeight &) –
Return type: void

thisown
¶ The membership flag

static

math_QuickSortOfValueAndWeight_Sort
(*args)¶ Parameters:  TheArray (math_Array1OfValueAndWeight &) –
 Comp (math_CompareOfValueAndWeight &) –
Return type: void

class
math_RealRandom
(*args)¶ Bases:
object
 creates a real random generator between the values Lower and Upper.
Parameters: Return type: 
thisown
¶ The membership flag

class
math_SVD
(*args)¶ Bases:
object
 Given as input an n X m matrix A with n < m, n = m or n > m this constructor performs the Singular Value Decomposition.
Parameters: A (math_Matrix &) – Return type: None 
DumpToString
()¶ math_SVD_DumpToString(math_SVD self) > std::string

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

PseudoInverse
()¶  Computes the inverse Inv of matrix A such as A * Inverse = Identity. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false). Standard_DimensionError if the ranges of Inv are compatible with the ranges of A.
Parameters:  Inv (math_Matrix &) –
 Eps (float) – default value is 1.0e6
Return type:

Solve
()¶  Given the input Vector B this routine solves the set of linear equations A . X = B. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the rowrange of A. Exception DimensionError is raised if the range of X is not equal to the colrange of A.
Parameters:  B (math_Vector &) –
 X (math_Vector &) –
 Eps (float) – default value is 1.0e6
Return type:

thisown
¶ The membership flag

class
math_TrigonometricFunctionRoots
(*args)¶ Bases:
object
 Given coefficients a, b, c, d , e, this constructor performs the resolution of the equation above. The solutions must be contained in [InfBound, SupBound]. InfBound and SupBound can be set by default to 0 and 2*PI.
Parameters: Return type:  Given the two coefficients d and e, it performs the resolution of d*sin(x) + e = 0. The solutions must be contained in [InfBound, SupBound]. InfBound and SupBound can be set by default to 0 and 2*PI.
Parameters: Return type:  Given the three coefficients c, d and e, it performs the resolution of 2*b*cos(x)*sin(x) + d*sin(x) + e = 0. The solutions must be contained in [InfBound, SupBound]. InfBound and SupBound can be set by default to 0 and 2*PI.
Parameters: Return type: 
DumpToString
()¶ math_TrigonometricFunctionRoots_DumpToString(math_TrigonometricFunctionRoots self) > std::string

InfiniteRoots
()¶  Returns true if there is an infinity of roots, otherwise returns false.
Return type: bool

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbSolutions
()¶  Returns the number of solutions found. An exception is raised if NotDone. An exception is raised if there is an infinity of solutions.
Return type: int

Value
()¶  Returns the solution of range Index. An exception is raised if NotDone. An exception is raised if Index>NbSolutions. An exception is raised if there is an infinity of solutions.
Parameters: Index (int) – Return type: float

thisown
¶ The membership flag

class
math_Uzawa
(*args)¶ Bases:
object
 Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (only = equations) with a minimization of Norme(XX0). The maximun iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. Exception ConstuctionError is raised if the line number of Cont is different from the length of Secont.
Parameters: Return type:  Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (the Nce first equations are equal equations and the Nci last equations are inequalities <) with a minimization of Norme(XX0). The maximun iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. There are no conditions on Nce and Nci. Exception ConstuctionError is raised if the line number of Cont is different from the length of Secont and from Nce + Nci.
Parameters: Return type: 
Duale
()¶  returns the duale variables V of the systeme.
Parameters: V (math_Vector &) – Return type: None

DumpToString
()¶ math_Uzawa_DumpToString(math_Uzawa self) > std::string

Error
()¶  Returns the difference between X solution and the StartingPoint. An exception is raised if NotDone.
Return type: math_Vector

InitialError
()¶  Returns the initial error Cont*StartingPointSecont. An exception is raised if NotDone.
Return type: math_Vector

InverseCont
()¶  returns the inverse matrix of (C * Transposed(C)). This result is needed for the computation of the gradient when approximating a curve.
Return type: math_Matrix

IsDone
()¶  Returns true if the computations are successful, otherwise returns false.
Return type: bool

NbIterations
()¶  returns the number of iterations really done. An exception is raised if NotDone.
Return type: int

Value
()¶  Returns the vector solution of the system above. An exception is raised if NotDone.
Return type: math_Vector

thisown
¶ The membership flag

class
math_ValueAndWeight
(*args)¶ Bases:
object
Return type: Parameters: Return type: 
thisown
¶ The membership flag


class
math_Vector
(*args)¶ Bases:
object
 Contructs a noninitialized vector in the range [theLower..theUpper] ‘theLower’ and ‘theUpper’ are the indexes of the lower and upper bounds of the constructed vector.
Parameters: Return type:  Contructs a vector in the range [theLower..theUpper] whose values are all initialized with the value ‘theInitialValue’
Parameters: Return type:  Constructs a vector in the range [theLower..theUpper] with the ‘c array’ theTab.
Parameters: Return type:  Constructs a copy for initialization. An exception is raised if the lengths of the vectors are different.
Parameters: theOther (math_Vector &) – Return type: None 
Add
()¶  adds the vector ‘theRight’ to a vector. An exception is raised if the vectors have not the same length. Warning In order to avoid timeconsuming copying of vectors, it is preferable to use operator += or the function Add whenever possible.
Parameters: theRight (math_Vector &) – Return type: None  sets a vector to the sum of the vector ‘theLeft’ and the vector ‘theRight’. An exception is raised if the lengths are different.
Parameters:  theLeft (math_Vector &) –
 theRight (math_Vector &) –
Return type:

Added
()¶  adds the vector theRight to a vector. An exception is raised if the vectors have not the same length. An exception is raised if the lengths are not equal.
Parameters: theRight (math_Vector &) – Return type: math_Vector

Divide
()¶  divides a vector by the value ‘theRight’. An exception is raised if ‘theRight’ = 0.
Parameters: theRight (float) – Return type: None

Divided
()¶  divides a vector by the value ‘theRight’. An exception is raised if ‘theRight’ = 0.
Parameters: theRight (float) – Return type: math_Vector

DumpToString
()¶ math_Vector_DumpToString(math_Vector self) > std::string

Init
()¶  Initialize all the elements of a vector with ‘theInitialValue’.
Parameters: theInitialValue (float) – Return type: None

Initialized
()¶  Initialises a vector by copying ‘theOther’. An exception is raised if the Lengths are differents.
Parameters: theOther (math_Vector &) – Return type: math_Vector

Inverse
()¶  Inverts this vector and creates a new vector.
Return type: math_Vector

Length
()¶  Returns the length of a vector
Return type: inline int

Lower
()¶  Returns the value of the theLower index of a vector.
Return type: inline int

Multiplied
()¶  returns the product of a vector and a real value.
Parameters: theRight (float) – Return type: math_Vector  returns the inner product of 2 vectors. An exception is raised if the lengths are not equal.
Parameters: theRight (math_Vector &) – Return type: float  returns the product of a vector by a matrix.
Parameters: theRight (math_Matrix &) – Return type: math_Vector

Multiply
()¶  returns the product of a vector and a real value.
Parameters: theRight (float) – Return type: None  sets a vector to the product of the vector ‘theLeft’ with the matrix ‘theRight’.
Parameters:  theLeft (math_Vector &) –
 theRight (math_Matrix &) –
Return type:  //!sets a vector to the product of the matrix ‘theLeft’ with the vector ‘theRight’.
Parameters:  theLeft (math_Matrix &) –
 theRight (math_Vector &) –
Return type:  returns the multiplication of a real by a vector. ‘me’ = ‘theLeft’ * ‘theRight’
Parameters:  theLeft (float) –
 theRight (math_Vector &) –
Return type:

Normalize
()¶  Normalizes this vector (the norm of the result is equal to 1.0) and assigns the result to this vector Exceptions Standard_NullValue if this vector is null (i.e. if its norm is less than or equal to Standard_Real::RealEpsilon().
Return type: None

Normalized
()¶  Normalizes this vector (the norm of the result is equal to 1.0) and creates a new vector Exceptions Standard_NullValue if this vector is null (i.e. if its norm is less than or equal to Standard_Real::RealEpsilon().
Return type: math_Vector

Opposite
()¶  returns the opposite of a vector.
Return type: math_Vector

Set
()¶  sets a vector from ‘theI1’ to ‘theI2’ to the vector ‘theV’; An exception is raised if ‘theI1’ is less than ‘LowerIndex’ or ‘theI2’ is greater than ‘UpperIndex’ or ‘theI1’ is greater than ‘theI2’. An exception is raised if ‘theI2theI1+1’ is different from the ‘Length’ of ‘theV’.
Parameters: Return type: Return type:

Slice
()¶  //!Creates a new vector by inverting the values of this vector between indexes ‘theI1’ and ‘theI2’. If the values of this vector were (1., 2., 3., 4.,5., 6.), by slicing it between indexes 2 and 5 the values of the resulting vector are (1., 5., 4., 3., 2., 6.)
Parameters: Return type:

Subtract
()¶  sets a vector to the Subtraction of the vector theRight from the vector theLeft. An exception is raised if the vectors have not the same length. Warning In order to avoid timeconsuming copying of vectors, it is preferable to use operator = or the function Subtract whenever possible.
Parameters:  theLeft (math_Vector &) –
 theRight (math_Vector &) –
Return type:  returns the subtraction of ‘theRight’ from ‘me’. An exception is raised if the vectors have not the same length.
Parameters: theRight (math_Vector &) – Return type: None

Subtracted
()¶  returns the subtraction of ‘theRight’ from ‘me’. An exception is raised if the vectors have not the same length.
Parameters: theRight (math_Vector &) – Return type: math_Vector

TMultiplied
()¶  returns the product of a vector and a real value.
Parameters: theRight (float) – Return type: math_Vector

TMultiply
()¶  sets a vector to the product of the transpose of the matrix ‘theTLeft’ by the vector ‘theRight’.
Parameters:  theTLeft (math_Matrix &) –
 theRight (math_Vector &) –
Return type:  sets a vector to the product of the vector ‘theLeft’ by the transpose of the matrix ‘theTRight’.
Parameters:  theLeft (math_Vector &) –
 theTRight (math_Matrix &) –
Return type:

Upper
()¶  Returns the value of the theUpper index of a vector.
Return type: inline int

Value
()¶  accesses (in read or write mode) the value of index ‘theNum’ of a vector.
Parameters: theNum (int) – Return type: inline float

thisown
¶ The membership flag

register_handle
(handle, base_object)¶ Inserts the handle into the base object to prevent memory corruption in certain cases