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多重積分モンテカルロ
RANDOMIZE
PUBLIC NUMERIC LEVEL
INPUT PROMPT "多重積分 LEVEL=":LEVEL
DIM A(LEVEL),B(LEVEL),N(LEVEL),AA(LEVEL)
FOR I=1 TO LEVEL
!'INPUT PROMPT "下限 =":A(I)
!'INPUT PROMPT "上限 =":B(I)
!'INPUT PROMPT "分割数=":N(I)
READ A(I),B(I),N(I)
NEXT I
PRINT MONTE(LEVEL,A,B,10000)
!'PRINT MONTE2(LEVEL,A,B,10000,2000)
!'PRINT MONTESIMPSON(LEVEL,A,B,10000)
!'PRINT MONTERECURSIVE(LEVEL,AA,A,B,N)
DATA 0,1,50
DATA 0,1,50
DATA 0,1,50
DATA 0,1,50
END
EXTERNAL FUNCTION MONTE(LEV,A(),B(),N)
RANDOMIZE
DIM AA(LEV)
LET H=1
FOR I=1 TO LEV
LET H=H*(B(I)-A(I))
NEXT I
FOR K=1 TO N
FOR I=1 TO LEV
LET AA(I)=A(I)+(B(I)-A(I))*RND
NEXT I
LET S=S+FUNC(AA)
NEXT K
LET MONTE=H*S/N
END FUNCTION
EXTERNAL FUNCTION MONTE2(LEV,A(),B(),N,NN)
RANDOMIZE
DIM AA(LEV)
LET HMAX=-MAXNUM
LET HMIN=MAXNUM
LET HH=1
FOR I=1 TO LEV
LET HH=HH*(B(I)-A(I))
NEXT I
FOR K=1 TO NN
FOR J=1 TO LEV
LET AA(J)=A(J)+(B(J)-A(J))*RND
NEXT J
LET H=FUNC(AA)
LET HMIN=MIN(HMIN,MIN(H,0))
LET HMAX=MAX(H,HMAX)
NEXT K
LET H=HMAX-HMIN
FOR K=1 TO N
FOR J=1 TO LEV
LET AA(J)=A(J)+(B(J)-A(J))*RND
NEXT J
LET Z=H*RND+HMIN
IF FUNC(AA) > 0 THEN
IF Z > 0 AND Z < FUNC(AA) THEN LET M1=M1+1
ELSE
IF Z < 0 AND Z > FUNC(AA) THEN LET M2=M2+1
END IF
NEXT K
LET MONTE2=HH*(M1-M2)/N*H
END FUNCTION
EXTERNAL FUNCTION MONTERECURSIVE(LEV,AA(),A(),B(),N()) !'再帰式モンテカルロ
IF LEV=0 THEN
LET MONTERECURSIVE=FUNC(AA)
ELSE
LET H=B(LEV)-A(LEV)
FOR K=1 TO N(LEV)
LET AA(LEV)=A(LEV)+H*RND
LET S=S+MONTERECURSIVE(LEV-1,AA,A,B,N)
NEXT K
LET MONTERECURSIVE=H*S/N(LEV)
END IF
END FUNCTION
EXTERNAL FUNCTION MONTESIMPSON(LEV,A(),B(),N) !'モンテカルロ＋シンプソン則
RANDOMIZE
DIM AA(LEV),T(LEV),HH(LEV)
LET H=1
FOR I=1 TO LEV
LET H=H*(B(I)-A(I))
LET HH(I)=(B(I)-A(I))/N/2
NEXT I
FOR K=1 TO N
FOR I=1 TO LEV
LET T(I)=(B(I)-A(I))*RND+A(I)
LET AA(I)=A(I)+T(I)
NEXT I
LET S=S+1/3*H*FUNC(AA)
FOR I=1 TO LEVEL
LET AA(I)=A(I)+HH(I)+T(I)
NEXT I
LET S=S+4/3*H*FUNC(AA)
FOR I=1 TO LEVEL
LET AA(I)=A(I)+2*HH(I)+T(I)
NEXT I
LET S=S+1/3*H*FUNC(AA)
NEXT K
LET MONTESIMPSON=S/N/2
END FUNCTION
EXTERNAL FUNCTION FUNC(X())
LET S=1
FOR I=1 TO LEVEL
LET S=S-X(I)*X(I)
NEXT I
IF S > 0 THEN
LET FUNC=SQR(S)
ELSE
LET FUNC=0
END IF
END FUNCTION
-----------------------------------------------
無限区間 多重積分モンテカルロ
PUBLIC NUMERIC LEVEL
INPUT PROMPT "多重積分 LEVEL=":LEVEL
DIM X(LEVEL)
PRINT MONTEDE(LEVEL,X,10000);PI^(LEVEL/2)
END
EXTERNAL FUNCTION MONTEDE(LEV,X(),N) !'モンテカルロ + DE法
RANDOMIZE
LET M=4 !'(要) 調整
LET H=2*M/N
FOR J=1 TO N
LET V=1
FOR I=1 TO LEV
LET K=RND*M*2-M
LET X(I)=Q(K)
LET V=V*QQ(K)
NEXT I
LET S=S+H^LEV*FUNC(X)*V
NEXT J
LET MONTEDE=S*N^(LEV-1)
END FUNCTION
EXTERNAL FUNCTION FUNC(X())
FOR I=1 TO LEVEL
LET S=S-X(I)*X(I)
NEXT I
LET FUNC=EXP(S)
END FUNCTION
EXTERNAL FUNCTION Q(X)
LET Q=SINH(PI/2*SINH(X))
END FUNCTION
EXTERNAL FUNCTION QQ(X)
LET QQ=PI/2*COSH(X)*COSH(PI/2*SINH(X))
END FUNCTION
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