unit2.pas

用于开发税务票据管理的软件

unit Unit2;

interface
uses
  Windows, Messages, SysUtils, Classes, Graphics, unit1,Controls, Forms, Dialogs;
Function F1DIM(X:real):real;
Procedure POWELL(var P:array of real;var XI:matrx2;
              N, NP:integer; FTOL:real;var ITER:integer;var FRET:real);
Function BESSJ0(X:real):real;

implementation
Function F1DIM(X:real):real;
var
    XT:array[0..50] of real;
    J:integer;
begin
    For J:=1 To NCOM do
        XT[J]:=PCOM[J] + X * XICOM[J];
    F1DIM:=FUNC2(XT, NCOM);
end;

Procedure MNBRAK(var AX, BX, CX, FA, FB, FC:real);
const
    GOLD = 1.618034;  GLIMIT = 100;  TINY = 1E-20;
var 
    DUM,R,Q,U,ULIM,FU:real;   DONE:boolean;
begin
    FA:=FUNC(AX);
    FB:=FUNC(BX);
    If FB > FA Then
    begin
        DUM:=AX;
        AX:=BX;
        BX:=DUM;
        DUM:=FB;
        FB:=FA;
        FA:=DUM;
    end;
    CX:=BX + GOLD * (BX - AX);
    FC:=FUNC(CX);
    repeat
        If FB < FC Then break;
        DONE:=true;
        R:=(BX - AX) * (FB - FC);
        Q:=(BX - CX) * (FB - FA);
        DUM:=Q - R;
        If Abs(DUM) < TINY Then DUM:=TINY;
        U:=BX - ((BX - CX) * Q - (BX - AX) * R) / (2 * DUM);
        ULIM:=BX + GLIMIT * (CX - BX);
        If (BX - U) * (U - CX) > 0  Then
        begin
            FU:=FUNC(U);
            If FU < FC Then
            begin
                AX:=BX;
                FA:=FB;
                BX:=U;
                FB:=FU;
                Exit;
            end
            Else If FU > FB Then
            begin
                CX:=U;
                FC:=FU;
                Exit;
            end;
            U:=CX + GOLD * (CX - BX);
            FU:=FUNC(U);
        end
        Else If (CX - U) * (U - ULIM) > 0  Then
        begin
            FU:=FUNC(U);
            If FU < FC Then
            begin
                BX:=CX;
                CX:=U;
                U:=CX + GOLD * (CX - BX);
                FB:=FC;
                FC:=FU;
                FU:=FUNC(U);
            end;
        end
        Else If (U - ULIM) * (ULIM - CX) >= 0  Then
        begin
            U:=ULIM;
            FU:=FUNC(U);
        end
        Else
        begin
            U:=CX + GOLD * (CX - BX);
            FU:=FUNC(U);
        end;
        If DONE Then
        begin
            AX:=BX;
            BX:=CX;
            CX:=U;
            FA:=FB;
            FB:=FC;
            FC:=FU;
        end
        Else
            DONE:=false;
    until not DONE
end;

Function BRENT(AX, BX, CX, TOL:real;var XMIN:real):real;
label 1,2,3;
const
    ITMAX = 100;  CGOLD = 0.381966;  ZEPS = 0.1e-9;
var
    A,B,D,V,X,W,E,FV1,XM,TOL1,TOL2,FX,FW,P,Q,R,ETEMP,DUM,U,ZZ,FU:real;
    ITER,I:integer;
begin
    A:=AX;
    If CX < AX Then A:=CX;
    B:=AX;
    If CX > AX Then B:=CX;
    V:=BX;
    W:=V;
    X:=V;
    E:=0;
    FX:=FUNC(X);
    FV1:=FX;
    FW:=FX;
    For ITER:=1 To ITMAX do
    begin
        XM:=0.5 * (A + B);
        TOL1:=TOL * Abs(X) + ZEPS;
        TOL2:=2 * TOL1;
        If Abs(X - XM) <= TOL2 - 0.5 * (B - A) Then goto 3;
        If Abs(E) > TOL1 Then
        begin
            R:=(X - W) * (FX - FV1);
            Q:=(X - V) * (FX - FW);
            P:=(X - V) * Q - (X - W) * R;
            Q:=2  * (Q - R);
            If Q > 0  Then P:=-P;
            Q:=Abs(Q);
            ETEMP:=E;
            E:=D;
            DUM:=Abs(0.5 * Q * ETEMP);
            If (Abs(P)>=DUM) or (P<=Q*(B - X)) or (P>=Q*(B - X)) Then
                GOTO 1;
            D:=P / Q;
            U:=X + D;
            If (U - A < TOL2) Or (B - U < TOL2) Then
            begin
              if XM-X>=0 then
                ZZ:=1
              else
                ZZ:=-1;
              D:=Abs(TOL1) * ZZ;
            end;
            goto 2;
        end;
1:      If X >= XM Then
          E:=A - X
        Else
          E:=B - X;
        D:=CGOLD * E;
2:      If Abs(D) >= TOL1 Then
            U:=X + D
        Else 
        begin
            if D >= 0 THEN
                ZZ:=1
            else
                ZZ:=-1;
            U:=X + Abs(TOL1) * ZZ;
        end;
        FU:=FUNC(U);
        If FU <= FX Then
        begin
            If U >= X Then
                A:=X
            Else
                B:=X;
            V:=W;
            FV1:=FW;
            W:=X;
            FW:=FX;
            X:=U;
            FX:=FU;
        end
        else
        begin
            If U < X Then
                A:=U
            else
                B:=U;
            If (FU <= FW) Or (W = X) Then
            begin
                V:=W;
                FV1:=FW;
                W:=U;
                FW:=FU;
            end
            Else If (FU <= FV1) Or (V = X) Or (V = W) Then
            begin
                V:=U;
                FV1:=FU;
            end;
        end;
    end; 
    If ITER > ITMAX Then ShowMessage('Brent exceed maximum iterations.');
3:  XMIN:=X;
    BRENT:=FX;
end;

Procedure LINMIN(var P,XI:array of real; N:integer;var FRET:real);
var
    TOL,AX,BX,XX,FA,FB,FX,XMIN:real; J:integer;
begin
    TOL:=0.0001;
    NCOM:=N;
    For J:=1 To N do
    begin
        PCOM[J]:=P[J];
        XICOM[J]:=XI[J];
    end;
    AX:=0 ;
    XX:=1;
    MNBRAK(AX, XX, BX, FA, FX, FB);
    FRET:=BRENT(AX, XX, BX, TOL, XMIN);
    For J:=1 To N do
    begin
        XI[J]:=XMIN * XI[J];
        P[J]:=P[J] + XI[J];
    end;
end;

Procedure POWELL(var P:array of real;var XI:matrx2;
              N, NP:integer; FTOL:real;var ITER:integer;var FRET:real);
const
    ITMAX = 200;
var
    PT, PTT, XIT:array[0..20] of real;
    I,J,IBIG:integer;  FP,DEL,FPTT,DUM,T:real;
begin
    FRET:=FUNC2(P, N);
    For J:=1 To N do
        PT[J]:=P[J];
    ITER:=0;
    while true do
    begin
      repeat
        repeat
          ITER:=ITER + 1;
          FP:=FRET;
          IBIG:=0;
          DEL:=0; 
          For I:=1 To N do
          begin
              For J:=1 To N do
                  XIT[J]:=XI[J, I];
              FPTT:=FRET;
              LINMIN(P, XIT, N, FRET);
              If Abs(FPTT - FRET) > DEL Then
              begin
                  DEL:=Abs(FPTT - FRET);
                  IBIG:=I;
              end;
          end; 
          If 2 * Abs(FP - FRET) <= FTOL * (Abs(FP) + Abs(FRET)) Then
              Exit;
          If ITER = ITMAX Then
          begin
              ShowMessage('POWELL exceeding maximum iterations');
              Exit;
          end;
          For J:=1 To N do
          begin
              PTT[J]:=2  * P[J] - PT[J];
              XIT[J]:=P[J] - PT[J];
              PT[J]:=P[J];
          end; 
          FPTT:=FUNC2(PTT, N);
        until  FPTT >= FP;
        DUM:=FP - 2 * FRET + FPTT;
        T:=2 * DUM * Sqr(FP - FRET - DEL) - DEL * Sqr(FP - FPTT);
      until  T >= 0;
      LINMIN(P, XIT, N, FRET);
      For J:=1 To N do
          XI[J, IBIG]:=XIT[J]
    end;
end;

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;
end.