unit2.pas

数值分析常用算法编程

unit Unit2;

interface
uses
  Windows, Messages, SysUtils, Classes, Graphics, Controls, unit1,Forms, Dialogs;

Function GASDEV:real;
Procedure FIT(X, Y:array of real; NDATA:integer; SIG:array of real;
     var MWT:integer; var A, B, SIGA, SIGB, CHI2, Q:real);

implementation
Function GASDEV:real;
var
   V1,V2,FAC,R:real;
begin
    If ISET^= 0 Then
    begin
      repeat
        V1:=2 * Random - 1;
        V2:=2 * Random - 1;
        R:=Sqr(V1) + Sqr(V2);
      until (R < 1);
      FAC:=Sqrt(-2 * Ln(R) / R);
      GSET^:=V1 * FAC;
      GASDEV:=V2 * FAC;
      ISET^:=1;
    end
    Else
    begin
      GASDEV:=GSET^;
      ISET^:=0;
    end;
end;

Function GAMMLN(xx:real):real;
CONST
  STP=2.50662827465; HALF=0.5; ONE=1.0; FPF=5.5;
var
  x,tmp,ser:double;
  j:integer;
  cof:array[1..6] of double;
BEGIN
  COF[1]:=76.18009173;      COF[2]:=-86.50532033;
  COF[3]:=24.01409822;      COF[4]:=-1.231739516;
  COF[5]:= 0.120858003e-2;  COF[6]:=-0.536382e-5;
  X:=XX-ONE;
  TMP:=X+FPF;
  TMP:=(X+HALF)*Ln(TMP)-TMP;
  SER:=ONE;
  For J:=1 To 6 do
    BEGIN
      X:=X+ONE;
      SER:=SER+COF[J]/X
    END;
  GAMMLN:=TMP+Ln(STP*SER);
end;

procedure GSER(VAR GAMSER:REAL;A:real;X:REAL;VAR GLN:REAL);
label 1;
CONST
  ITMAX=100;    EPS=0.3E-6;
VAR
  N:Integer;
  SUM,DEL,AP:Real;
begin
  GLN:=GAMMLN(A);
  If X <= 0 Then
    If X < 0 Then
      begin
        ShowMessage('警告：X<0，退出程序。');
        goto 1;
      end
  else
    begin
      GAMSER:=0;
      goto 1;
    end;
  AP:=A;
  Sum:=1 / A;
  DEL:=Sum;
  For N:=1 To ITMAX do
    begin
      AP:=AP + 1;
      DEL:=DEL * X / AP;
      Sum:=Sum + DEL;
      If Abs(DEL) < Abs(Sum) * EPS Then GoTo 1;
    end;
  ShowMessage('A too large, ITMAX too small');
1: GAMSER:=Sum * Exp(-X + A * Ln(X) - GLN);
end;

PROCEDURE GCF(VAR GAMMCF:real; A:real; X:real; var GLN:real);
label 1;
const
  ITMAX=100;    EPS=0.0000003;
var
  N:integer; GOLD,G,FAC,B1,B0,ANF,ANA,AN,A1,A0:real;
begin
  GLN:=GAMMLN(A);
  GOLD:=0;
  A0:=1;
  A1:=X;
  B0:=0;
  B1:=1;
  FAC:=1;
  For N:=1 To ITMAX do
  begin
    AN:=N;
    ANA:=AN - A;
    A0:=(A1 + A0 * ANA)* FAC;
    B0:=(B1 + B0 * ANA)* FAC;
    ANF:=AN * FAC;
    A1:=X * A0 + ANF * A1;
    B1:=X * B0 + ANF * B1;
    If A1 <> 0 Then
    begin
      FAC:=1 / A1;
      G:=B1 * FAC;
      If Abs((G - GOLD)/ G)< EPS Then GoTo 1;
      GOLD:=G;
    end
  end;
  ShowMessage('A too large, ITMAX too small');
1: GAMMCF:=Exp(-X + A * Ln(X)- GLN)* G;
end;

Function GAMMQ(A,X:REAL):REAL;
VAR
  GAMSER,GLN:REAL;
BEGIN
    If (X < 0) Or (A <= 0) Then  ShowMessage('PAUSE');
    If X < A + 1 Then
      begin
        GSER(GAMSER, A, X, GLN);
        GAMMQ:=1-GAMSER;
      end
    Else
      begin
        GCF(GAMSER, A, X, GLN);
        GAMMQ:=GAMSER;
      end;
END;

Procedure FIT(X, Y:array of real; NDATA:integer; SIG:array of real;
     var MWT:integer; var A, B, SIGA, SIGB, CHI2, Q:real);
var
    I,J:integer;   SX,SY,ST2,SS,WT,SXOSS,T,SIGDAT:real;
begin
    SX:=0;
    SY:=0;
    ST2:=0;
    B:=0;
    If MWT <> 0 Then
    begin
        SS:=0;
        For I:=1 To NDATA do
        begin
            WT:=1  / (Sqr(SIG[I]));
            SS:=SS + WT;
            SX:=SX + X[I] * WT;
            SY:=SY + Y[I] * WT;
        end;
    end
    Else
    begin
        For I:=1 To NDATA do
        begin
            SX:=SX + X[I];
            SY:=SY + Y[I];
        end;
        SS:=NDATA;
    end;
    SXOSS:=SX / SS;
    If MWT <> 0 Then
    begin
        For I:=1 To NDATA do
        begin
            T:=(X[I] - SXOSS) / SIG[I];
            ST2:=ST2 + T * T;
            B:=B + T * Y[I] / SIG[I];
        end;
    end
    Else
    begin
        For I:=1 To NDATA do
        begin
            T:=X[I] - SXOSS;
            ST2:=ST2 + T * T;
            B:=B + T * Y[I];
        end;
    end;
    B:=B / ST2;
    A:=(SY - SX * B) / SS;
    SIGA:=Sqrt((1  + SX * SX / (SS * ST2)) / SS);
    SIGB:=Sqrt(1 / ST2);
    CHI2:=0;
    If MWT = 0 Then
    begin
        For I:=1 To NDATA do
            CHI2:=CHI2 + Sqr(Y[I] - A - B * X[I]);
        Q:=1;
        SIGDAT:=Sqrt(CHI2 / (NDATA - 2));
        SIGA:=SIGA * SIGDAT;
        SIGB:=SIGB * SIGDAT
    end
    Else
    begin
        For I:=1 To NDATA do
            CHI2:=CHI2 + Sqr((Y[I] - A - B * X[I]) / SIG[I]);
        Q:=GAMMQ(0.5 * (NDATA - 2), 0.5 * CHI2);
    end;
end;
end.