zbrent.txt

《Delphi常用数值算法集》的配书源码

Function ZBRENT(X1, X2, TOL:real):real;
var
    ITMAX,ITER:integer;  ZZ,S,AAA,EPS,FA,FB,FC,C,TOL1,XM,P,Q,R,D,E,A,B:real;
begin
    ITMAX:=100;
    EPS:=0.00000003;
    A:=X1;
    B:=X2;
    FA:=FUN(A);
    FB:=FUN(B);
    If FB * FA > 0  Then
        ShowMessage('Root must be bracketed for ZBRENT');
    FC:=FB;
    For ITER:=1 To ITMAX do
    begin
        If FB * FC > 0 Then
        begin
            C:=A;
            FC:=FA;
            D:=B - A;
            E:=D;
        end;
        If Abs(FC) < Abs(FB) Then
        begin
            A:=B;
            B:=C;
            C:=A;
            FA:=FB;
            FB:=FC;
            FC:=FA;
        end;
        TOL1:=2 * EPS * Abs(B) + 0.5 * TOL;
        XM:=0.5 * (C - B);
        If (Abs(XM) <= TOL1) Or (FB = 0) Then
        begin
            ZBRENT:=B;
            Exit;
        end;
        If (Abs(E) >= TOL1) And (Abs(FA) > Abs(FB)) Then
        begin
            S:=FB / FA;
            If A = C Then
            begin
                P:=2 * XM * S;
                Q:=1 - S;
            end
            Else
            begin
                Q:=FA / FC;
                R:=FB / FC;
                P:=S * (2 * XM * Q * (Q - R) - (B - A) * (R - 1 ));
                Q:=(Q - 1 ) * (R - 1 ) * (S - 1 );
            end;
            If P > 0  Then Q:=-Q;
            P:=Abs(P);
            If 3 * XM * Q - Abs(TOL1*Q) < Abs(E*Q) Then
                AAA:=3  * XM * Q - Abs(TOL1 * Q)
            Else
                AAA:=Abs(E * Q);
            If 2 * P < AAA Then
            begin
                E:=D;
                D:=P / Q;
            end
            Else
            begin
                D:=XM;
                E:=D;
            end;
        end
        Else
        begin
            D:=XM;
            E:=D;
        end;
        A:=B;
        FA:=FB;
        If Abs(D) > TOL1 Then
            B:=B + D
        Else
        Begin
            If XM>=0 then
                ZZ:=1
            Else
                ZZ:=-1;
            B:=B + Abs(TOL1) * ZZ;
        end;
        FB:=FUN(B);
    end; 
    ShowMessage('ZBRENT exceeding maximum iterations.');
    ZBRENT:=B;
end;