MtxIntDiff.Romberg Function

Numerical integration by using recursive Romberg algorithm.

Pascal

function Romberg(Fun: TRealFunction; lb: double; ub: double; const FloatPrecision: TMtxFloatPrecision; Const Constants: TVec; Const ObjConst: Array of TObject; out StopReason: TIntStopReason; Tolerance: double = 1.0e-4; MaxIter: Integer = 100): double;

File

MtxIntDiff

Parameters

Parameters	Description
Fun	Integrating function.
lb	Defines lower bound.
ub	Defines upper bound.
FloatPrecision	Defines the computational precision to be used by the routine.
Constants	Additional constants defining Fun function, usually nil/null.
ObjConst	Additional objects defining Fun function, usually nil/null.
StopReason	Returns algorithm stop reason.
Tolerance	Defines integration tolerance.
MaxIter	Defines maximum number of alorithm iterations.

Returns

the numerical approximate on integral of function Fun between limits lb and ub.

See Also

QuadGauss

Example

Evaluate fuction Sin(x)*Exp(-x^2) on interval [0,PI/2] by using Romberg algorithm.

Uses Math387, MtxIntDiff; // Integrating function function IntFunc(const Parameters: TVec; const Constants: TVec; const ObjConst: Array of TObject): double; var x: double; begin x := Parameters[0]; IntFunc := Sin(x)*Exp(-x*x); end; // Integrate procedure DoIntegrate; var area: double; sr: TIntStopReason; begin area := Romberg(IntFunc,0,0.5*PI,sr); end;

#include "MtxExpr.hpp" #include "Math387.hpp" #include "MtxIntDiff.hpp" // Integrating function double __fastcall IntFun(TVec* const Parameters, TVec* const Constants, System::TObject* const * ObjConst, const int ObjConst_Size) { double x = (*Parameters)[0]; return Math.Sin(x)*Math.Exp(-x*x); } void __fastcall Example(); { TIntStopReason sr; double area = Romberg(IntFun,0.0,5*PI,NULL,NULL,sr); }

MtxIntDiff, Functions, Example, See Also

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