lu_decompound_for_c++.cpp

应用LU分解法计算矩阵的程序 C++制作 未编译

#include <iostream>
#include <iomanip>
using namespace std;

#define N 100
#define OK 1
#define ERROR 0
#define OVERFLOW -1

typedef int Status;

int n;
int i,j,r,k;
float a[N][N],b[N],l[N][N]={0},u[N][N]={0},y[N],x[N];

//通过键盘初始化方程
Status InitEquation() {
	
	//设定系数矩阵A阶数
	cout <<"Please input how many Line/Colmun your Matrix need:";
	cin >>n;
	if (n>100) {
		cout <<endl<<"Sorry,Your Matrix is too large,please input anotherone";
		return ERROR;
	}
	
	//初始化系数矩阵A
	cout <<endl<<"Ok,Now you have a"<<n<<"*"<<n<<"Matrix."<<endl<<"please input the element of the Matrix:";
	for (i=0;i<n;i++) {
		for (j=0;j<n;j++) cin >>a[i][j];
	}

	//初始化常向量b
	cout <<endl<<"Now please input Constent Constant Vector b:";
	for (i=0;i<n;i++) cin >>b[i];
	
	return OK;
}

//LU分解
Status LUDecompound() {

	//1.求U的第一行
	for (j=0;j<n;j++) u[0][j]=a[0][j];

	//2.求L的第一列
	for (i=0;i<n;i++) l[i][0]=a[i][0]/u[0][0];
	
	//求L&U
	for (r=1;r<n;r++) {
		
		//求U的第R行
		for (j=r;j<n;j++) {
			u[r][j]=a[r][j];
			for (k=0;k<r;k++) u[r][j]=u[r][j]-l[r][k]*u[k][j];
		}

		//求L的第R列
		for (i=r+1;i<n;i++) {
			l[i][r]=a[i][r];
			for (k=0;k<r;k++) l[i][r]=l[i][r]-l[i][k]*u[k][r];
			l[i][r]=l[i][r]/u[r][r];
		}
	}
	
	return OK;
}

//回代求解
Status Bback_Substitution_Solve () {
	
	//解Ly=b
	y[0]=b[0];
	for (i=0;i<n;i++) {
		y[i]=b[i];
		for (k=0;k<i;k++) y[i]=y[i]-l[i][k]*y[k];
	}

	//解Ux=y
	x[n-1]=y[n-1]/u[n-1][n-1];
	for (i=n-1;i>=0;i--) {
		x[i]=y[i];
		for (k=i+1;k<n;k++) x[i]=x[i]-u[i][k]*x[k];
		x[i]=x[i]/u[i][i];
	}
	
	return OK;
}

//打印方程;
inline Status printEquation () {
	cout <<endl<<"The Equation is:";
	for (i=0;i<n;i++) {
		cout <<endl;
		for (j=0;j<n;j++) cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<a[i][j]<<"X"<<j;
		cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<b[i];
	}
	return OK;
}

//打印L/U矩阵
inline Status printLU () {
	cout <<endl<<"Lij is";
	for (i=0;i<n;i++) {
		cout <<endl;
		for (j=0;j<n;j++) cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<l[i][j];
	}

	cout <<endl<<"Uij is";
	for (i=0;i<n;i++) {
		cout <<endl;
		for (j=0;j<n;j++) cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<u[i][j];
	}
	return OK;
}

//打印解
inline Status printSolution() {
	cout <<endl<<"Y is:";
	for (i=0;i<n;i++) cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<y[i];
	cout<<endl<<"The answer X is:";
	for (i=0;i<n;i++) cout <<setw(10)<<setiosflags(ios::fixed)<<setprecision(2)<<x[i];
	return OK;
}

Status main(){
	int op;
	cout<<endl<<"1.Initial the Equation.";
	cout<<endl<<"2.Print the Equation.";
	cout<<endl<<"3.Decompound the L/U Matrix.";
	cout<<endl<<"4.Print the L/U Matrix.";
	cout<<endl<<"5.Solve the Equation";
	cout<<endl<<"6.print the Answer.";
	cout<<endl<<"0.Exit";
	cout<<endl<<"Please input what your want to do :";
	cin >>op;
	while (op!=0) {
		switch (op) {
			case 1 : InitEquation(); break;
			case 2 : printEquation(); break;
			case 3 : LUDecompound(); break;
			case 4 : printLU(); break;
			case 5 : Bback_Substitution_Solve(); break;
			case 6 : printSolution(); break;
			default : printf ("\nWrong operation!"); break;
		}
		cout<<endl<<"1.Initial the Equation.";
		cout<<endl<<"2.Print the Equation.";
		cout<<endl<<"3.Decompound the L/U Matrix.";
		cout<<endl<<"4.Print the L/U Matrix.";
		cout<<endl<<"5.Solve the Equation";
		cout<<endl<<"6.print the Answer.";
		cout<<endl<<"0.Exit";
		cout<<endl<<"Please input what your want to do :";
		cin >>op;
	}
	return OK;
}