unit2.pas

《Delphi常用数值算法集》的配书源码

unit Unit2;

interface
uses
  Windows, Messages, SysUtils, Classes, Graphics, UNIT1,Controls, Forms, Dialogs;
Function BESSJ0(X:real):real;
Procedure ZBRAK(X1, X2:real; N:integer;
                        var XB1, XB2:array of real;var NB:integer);
Function RTFLSP(X1, X2, XACC:real):real;

implementation
Function BESSJ0(X:real):real;
var
   AAA,BBB,CCC,Y,AX,Z,DDD,EEE,XX:real;
const
  P1=1;                    P2=-0.001098628627;
  P3=0.2734510407e-4;      P4=-0.2073370639e-5;
  P5=2.093887211E-07;
  Q1=-0.1562499995e-1;     Q2=0.1430488765e-3;
  Q3=-0.6911147651e-5;     Q4=7.621095161E-07;
  Q5=-9.34945152E-08;
  R1=57568490574;          R2=-13362590354;
  R3=651619640.7;          R4=-11214424.18;
  R5=77392.33017;          R6=-184.9052456;
  S1=57568490411;          S2=1029532985;
  S3=9494680.718;          S4=59272.64853;
  S5=267.8532712;          S6=1;
begin
  If Abs(X) < 8 Then
    begin
      Y:=X * X;
      BBB:=Y* (R4+ Y* (R5+ Y* R6));
      AAA:=R1+ Y* (R2+ Y* (R3+ BBB));
      CCC:=Y* (S3+ Y* (S4+ Y* (S5+ Y* S6)));
      BESSJ0:= AAA / (S1+ Y* (S2+ CCC));
    end
  Else
    begin
      AX:=Abs(X);
      Z:=8/ AX;
      Y:=Z* Z;
      XX:= AX- 0.785398164;
      CCC:=Y* (P3+ Y* (P4+ Y* P5));
      AAA:=P1+ Y* (P2+ CCC);
      DDD:=Y* (Q3+ Y* (Q4+ Y* Q5));
      EEE:=Z* Sin(XX) * (Q1+ Y* (Q2+ DDD));
      BESSJ0:= Sqrt(0.636619772 / AX) * (Cos(XX) * AAA- EEE);
    End;
End;

Procedure ZBRAK(X1, X2:real; N:integer;
                        var XB1, XB2:array of real;var NB:integer);
var
    NBB,I:integer;   X,DX,FP,FC:real;
begin
    NBB:=NB;
    NB:=0;
    X:=X1;
    DX:=(X2 - X1) / N;
    FP:=FUN(X);
    For I:=1 To N do
    begin
        X:=X + DX;
        FC:=FUN(X);
        If FC * FP < 0  Then
        begin
            NB:=NB + 1;
            XB1[NB]:=X - DX;
            XB2[NB]:=X;
        end;
        FP:=FC;
        If NBB = NB Then Exit;
    end; 
end;

Function RTFLSP(X1, X2, XACC:real):real;
Label 99;
var
    XL,XH,SWAP,FL,FH,RTF,DX,F,DEL:real;  J,MAXIT:integer;
begin
    MAXIT:=30;
    FL:=FUN(X1);
    FH:=FUN(X2);
    If FL * FH > 0 Then
        ShowMessage('Root must be bracketed for false position');
    If FL < 0 Then
    begin
        XL:=X1;
        XH:=X2;
    end
    Else
    begin
        XL:=X2;
        XH:=X1;
        SWAP:=FL;
        FL:=FH;
        FH:=SWAP;
    end;
    DX:=XH - XL;
    For J:=1 To MAXIT do
    begin
        RTF:=XL + DX * FL / (FL - FH);
        F:=FUN(RTF);
        If F < 0 Then
        begin
            DEL:=XL - RTF;
            XL:=RTF;
            FL:=F;
        end
        Else
        begin
            DEL:=XH - RTF;
            XH:=RTF;
            FH:=F;
        end;
        DX:=XH - XL;
        If (Abs(DEL) < XACC) Or (F = 0) Then goto 99;
    end; 
    ShowMessage('RTFLSP exceed maximum iterations');
99: RTFLSP:=RTF;
end;

end.