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-- File: NewtonFunctionSetRoot.cdl
-- Created: Tue May 14 14:33:12 1991
-- Author: Laurent PAINNOT
-- <lpa@topsn3>
---Copyright: Matra Datavision 1991, 1992
class NewtonFunctionSetRoot from math
---Purpose:
-- This class computes the root of a set of N functions of N variables,
-- knowing an initial guess at the solution and using the
-- Newton Raphson algorithm. Knowledge of all the partial
-- derivatives (Jacobian) is required.
uses Vector from math, Matrix from math, IntegerVector from math,
FunctionSetWithDerivatives from math,
OStream from Standard
raises NotDone from StdFail,
DimensionError from Standard
is
Create(F: in out FunctionSetWithDerivatives;
XTol: Vector; FTol: Real;
NbIterations: Integer = 100)
---Purpose:
-- This constructor should be used in a sub-class to initialize
-- correctly all the fields of this class.
-- The range (1, F.NbVariables()) must be especially respected for
-- all vectors and matrix declarations.
returns NewtonFunctionSetRoot;
Create(F: in out FunctionSetWithDerivatives;
FTol: Real; NbIterations: Integer = 100)
---Purpose:
-- This constructor should be used in a sub-class 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.
returns NewtonFunctionSetRoot;
Create(F: in out FunctionSetWithDerivatives;
StartingPoint: Vector;
XTol: Vector; FTol: Real;
NbIterations: Integer = 100)
---Purpose:
-- 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 - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;
-- The maximum number of iterations allowed is given by NbIterations.
returns NewtonFunctionSetRoot;
Create(F: in out FunctionSetWithDerivatives;
StartingPoint: Vector;
InfBound, SupBound: Vector;
XTol: Vector; FTol: Real;
NbIterations: Integer = 100)
---Purpose:
-- 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 - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;
-- The maximum number of iterations allowed is given by NbIterations.
returns NewtonFunctionSetRoot;
Delete(me:out) is virtual;
---C++: alias "Standard_EXPORT virtual ~math_NewtonFunctionSetRoot(){Delete();}"
SetTolerance(me: in out; XTol: Vector)
---Purpose: Initializes the tolerance values for the unknowns.
is static;
Perform(me: in out; F:in out FunctionSetWithDerivatives;
StartingPoint: Vector;
InfBound, SupBound: Vector)
---Purpose: 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.
is static;
IsSolutionReached(me: in out; F: in out FunctionSetWithDerivatives)
---Purpose:
-- 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.
returns Boolean
is virtual;
IsDone(me)
---Purpose: Returns true if the computations are successful, otherwise returns false.
---C++: inline
returns Boolean
is static;
Root(me)
---Purpose: Returns the value of the root of function F.
-- Exceptions
-- StdFail_NotDone if the algorithm fails (and IsDone returns false).
---C++: inline
---C++: return const&
returns Vector
raises NotDone
is static;
Root(me; Root: out Vector)
---Purpose: 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.
---C++: inline
raises NotDone,
DimensionError
is static;
StateNumber(me)
---Purpose: Outputs the state number associated with the solution
-- vector root.
---C++: inline
returns Integer
raises NotDone
is static;
Derivative(me)
---Purpose: Returns the matrix value of the derivative at the root.
-- Exception NotDone is raised if the root was not found.
---C++: inline
---C++: return const&
returns Matrix
raises NotDone
is static;
Derivative(me; Der: out Matrix)
---Purpose: 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.
---C++: inline
raises NotDone,
DimensionError
is static;
FunctionSetErrors(me)
---Purpose: Returns the vector value of the error done on the
-- functions at the root.
-- Exception NotDone is raised if the root was not found.
---C++: inline
---C++: return const&
returns Vector
raises NotDone
is static;
FunctionSetErrors(me; Err: out Vector)
---Purpose: 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.
---C++: inline
raises NotDone,
DimensionError
is static;
NbIterations(me)
---Purpose: Returns the number of iterations really done
-- during the computation of the Root.
-- Exception NotDone is raised if the root was not found.
---C++: inline
returns Integer
raises NotDone
is static;
Dump(me; o: in out OStream)
---Purpose: Prints information on the current state of the object.
-- Is used to redefine the operator <<.
is static;
fields
Done: Boolean;
State: Integer;
TolX: Vector is protected;
TolF: Real is protected;
Iter: Integer;
Indx: IntegerVector is protected;
Scratch: Vector is protected;
Sol: Vector is protected;
DeltaX: Vector is protected;
FValues: Vector is protected;
Jacobian: Matrix is protected;
Itermax: Integer;
end NewtonFunctionSetRoot;
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