#include?“stdafx.h“
#include?“CIntegration.h“
#include?“math.h“
#include?“iostream“
using?namespace?std;

CIntegration::CIntegration（）
{
}


CIntegration::~CIntegration（）
{
}

CIntegration::CIntegration（int?ax?int?ay?int?len）//原點坐標?
{
	p_X?=?new?double[len];
	p_Y?=?new?int[len];
	for?（int?i?=?0;?i	{
		p_X[i]?=?i?/?80.0;
	}
}
CIntegration::CIntegration（double?ma?double?mb）
{
	a?=?ma;?????????????????//a、b分別為積分區間左右端點
	b?=?mb;
	n?=?1;??????????????????//區間二分個數
	h?=?b?-?a;????????????????//步長
	x?=?new?double[n?+?1];?????//存放區間二分點
	x[0]?=?a;
	x[1]?=?b;

	count?=?0;
	tsize?=?0;
}
double?CIntegration::f（double?xx）//被積函數
{
	double?mtemp?=?sin（xx）;
	return?mtemp;
}
double?CIntegration::Sum（void）
{
	double?sum?=?0;
	for?（int?i?=?0;?i	{
		sum?+=?f（（x[i]?+?x[i?+?1]）?/?2）;
	}
	return?sum;
}
void?CIntegration::Divide（void）//該函數實現區間二分和步長更新
{
	count?=?0;
	tempx?=?new?double[100];
	double?*px?=?new?double[2?*?n?+?1];
	//double?*tempx=new?double[n+1];
	for?（int?i?=?0;?i	{
		px[2?*?i]?=?x[i];
		px[2?*?i?+?1]?=?（x[i]?+?x[i?+?1]）?/?2;
		tempx[count++]?=?（x[i]?+?x[i?+?1]）?/?2;
	}
	px[2?*?n]?=?x[n];
	delete[]x;
	x?=?px;
	n?=?n?*?2;
	h?=?h?/?2;
}
double?CIntegration::T1ToT2（double?T1）
{
	double?T2?=?0;
	T2?=?1?/?2.0*T1?+?h?/?2.0?*?Sum（）;??//單次二分過程
	return?T2;
}
double?CIntegration::Trapezium_Recurrence（double?e）//精度
{
	double?T1?T2;
	T1?=?h?/?2.0?*（f（a）?+?f（b））;
	T2?=?T1ToT2（T1）;
	Divide（）;
	while?（fabs（T2?-?T1）?>=?e）??//絕對差值
	{
		T1?=?T2;
		T2?=?T1ToT2（T1）;
		Divide（）;
	}
	return?T2;
}
void?CIntegration::init（void）
{
	n?=?1;
	h?=?b?-?a;
	double?*xx?=?new?double[n?+?1];
	x?=?xx;
	x[0]?=?a;
	x[1]?=?b;
}
double?CIntegration::Trapezium_Recurrence（int?N）//迭代一定次數的梯形法遞推函數
{
	double?T1?T2;
	if?（N?==?1）
	{
		T1?=?h?/?2.0?*（f（a）?+?f（b））;
		return?T1;
	}
	if?（N?==?2）
	{
		T1?=?h?/?2.0?*（f（a）?+?f（b））;
		T2?=?T1ToT2（T1）;
		return?T2;
	}
	init（）;
	T1?=?h?/?2.0?*（f（a）?+?f（b））;
	T2?=?T1ToT2（T1）;
	Divide（）;
	for?（int?i?=?3;?i?<=?N;?i++）
	{
		T1?=?T2;
		T2?=?T1ToT2（T1）;
		Divide（）;
	}
	return?T2;
}
double?CIntegration::R1（double*?T?int?N）//注意?N>=3?下標?要保證T里面有N+1個元素
{
	double?*S?=?new?double[N?+?1];
	double?*C?=?new?double[N?+?1];
	for?（int?i?=?0;?i?<=?N?-?1;?i++）
	{
		S[i]?=?（4?*?T[i?+?1]?-?T[i]）?/?3.0;
	}
	for?（int?i?=?0;?i?<=?N?-?2;?i++）
	{
		C[i]?=?（16?*?S[i?+?1]?-?S[i]）?/?15.0;
	}
	double?R?=?（64?*?C[N?-?2]?-?C[N?-?3]）?/?63.0;
	delete[]S;
	delete[]C;
	return?R;
}
double?CIntegration::Romberg（double?e）//調用函數R1可實現迭代的龍貝格函數
{
	tsize?=?0;
	int?num?=?5;
	double?r1?=?0?r2?=?0;
	sT?=?new?double[100];
	for?（int?i?=?1;?i?<=?4;?i++）
	{
		sT[tsize++]?=?Trapezium_Recurrence（i）;
	}
	r2?=?R1（sT?3）;
	if?（tsize?-?1?==?3）
	{
		r1?=?r2;
	}
	while?（fabs（r2?-?r1）?>=?e）
	{
		r1?=?r2;
		sT[tsize++]?=?Trapezium_Recurrence（num）;//?num?次數????
		r2?=?R1（sT?num?-?1）;//num-1?下標????
		num++;
	}
	//delete?[]sT;
	re

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2017-12-03?20:41??Integration\
?????目錄???????????0??2017-12-03?13:47??Integration\.vs\
?????目錄???????????0??2017-12-03?13:47??Integration\.vs\Integration\
?????目錄???????????0??2017-12-12?14:45??Integration\.vs\Integration\v15\
?????文件???????48128??2017-12-12?14:45??Integration\.vs\Integration\v15\.suo
?????文件????75051008??2017-12-12?14:45??Integration\.vs\Integration\v15\Browse.VC.db
?????目錄???????????0??2017-12-03?15:33??Integration\.vs\Integration\v15\ipch\
?????目錄???????????0??2017-12-12?14:40??Integration\.vs\Integration\v15\ipch\AutoPCH\
?????目錄???????????0??2017-12-12?14:40??Integration\.vs\Integration\v15\ipch\AutoPCH\_SFI_9AC81674-1CAF-47C0-9725-5EE28ABB43B0_-be62ec4\
?????目錄???????????0??2017-12-12?14:40??Integration\.vs\Integration\v15\ipch\AutoPCH\_SFI_9AC81674-1CAF-47C0-9725-5EE28ABB43B0_-be62ec4\AFXMEM-85603dc8\
?????目錄???????????0??2017-12-03?15:32??Integration\.vs\Integration\v15\ipch\INTEGRATION-5d963a3e\
?????文件???105644032??2017-12-12?14:21??Integration\.vs\Integration\v15\ipch\INTEGRATION-5d963a3e\INTEGRATION-3d746330.ipch
?????目錄???????????0??2017-12-12?14:20??Integration\Debug\
?????文件????10181632??2017-12-12?14:21??Integration\Debug\Integration.exe
?????文件????19427632??2017-12-12?14:21??Integration\Debug\Integration.ilk
?????文件????23252992??2017-12-12?14:44??Integration\Debug\Integration.pdb
?????目錄???????????0??2017-12-05?21:12??Integration\Integration\
?????文件????????3118??2017-12-05?21:12??Integration\Integration\CIntegration.cpp
?????文件?????????568??2017-12-03?14:02??Integration\Integration\CIntegration.h
?????目錄???????????0??2017-12-12?14:19??Integration\Integration\Debug\
?????文件???????39443??2017-12-12?14:19??Integration\Integration\Debug\CIntegration.obj
?????文件????????1873??2017-12-03?21:47??Integration\Integration\Debug\Integration.Build.CppClean.log
?????文件?????????239??2017-12-12?14:21??Integration\Integration\Debug\Integration.log
?????文件???????70206??2017-12-03?21:47??Integration\Integration\Debug\Integration.obj
?????文件????55377920??2017-12-03?21:47??Integration\Integration\Debug\Integration.pch
?????文件?????1432688??2017-12-03?21:47??Integration\Integration\Debug\Integration.res
?????目錄???????????0??2017-12-12?14:21??Integration\Integration\Debug\Integration.tlog\
?????文件????????3438??2017-12-12?14:19??Integration\Integration\Debug\Integration.tlog\CL.command.1.tlog
?????文件??????118650??2017-12-12?14:19??Integration\Integration\Debug\Integration.tlog\CL.read.1.tlog
?????文件????????3530??2017-12-12?14:19??Integration\Integration\Debug\Integration.tlog\CL.write.1.tlog
?????文件?????????228??2017-12-12?14:21??Integration\Integration\Debug\Integration.tlog\Integration.lastbuildstate
............此處省略28個文件信息