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-- File: NewtonFunctionRoot.cdl
-- Created: Tue 14 11:21:21 1991
-- Author: Laurent PAINNOT
-- <lpa@topsn3>
---Copyright: Matra Datavision 1991, 1992
class NewtonFunctionRoot from math
---Purpose:
-- This class implements the calculation of a root of a function of
-- a single variable starting from an initial near guess using the
-- Newton algorithm. Knowledge of the derivative is required.
uses Vector from math, Matrix from math,
FunctionWithDerivative from math,
OStream from Standard
raises NotDone from StdFail
is
Create(F: in out FunctionWithDerivative;
Guess, EpsX, EpsF: Real;
NbIterations: Integer = 100)
---Purpose:
-- 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 - Xi-1) <= EpsX and abs(F(Xi))<= EpsF
-- The maximum number of iterations allowed is given by NbIterations.
returns NewtonFunctionRoot;
Create(F: in out FunctionWithDerivative;
Guess, EpsX, EpsF, A, B: Real;
NbIterations: Integer = 100)
---Purpose:
-- 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 - Xi-1) <= EpsX and abs(F(Xi))<= EpsF
-- The maximum number of iterations allowed is given by NbIterations.
returns NewtonFunctionRoot;
Create(A, B, EpsX, EpsF: Real;
NbIterations: Integer = 100)
---Purpose: is used in a sub-class to initialize correctly all the fields
-- of this class.
returns NewtonFunctionRoot;
Perform(me: in out; F: in out FunctionWithDerivative;
Guess: Real)
---Purpose: is used internally by the constructors.
is static;
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>.
-- Exception NotDone is raised if the root was not found.
---C++: inline
returns Real
raises NotDone
is static;
Derivative(me)
---Purpose: returns the value of the derivative at the root.
-- Exception NotDone is raised if the root was not found.
---C++: inline
returns Real
raises NotDone
is static;
Value(me)
---Purpose: returns the value of the function at the root.
-- Exception NotDone is raised if the root was not found.
---C++: inline
returns Real
raises NotDone
is static;
NbIterations(me)
---Purpose: Returns the number of iterations really done on 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 static;
fields
Done: Boolean;
X : Real;
Fx : Real;
DFx : Real;
It : Integer;
EpsilonX: Real;
EpsilonF: Real;
Itermax: Integer;
Binf: Real;
Bsup: Real;
end NewtonFunctionRoot;
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