linequ.cpp

一个对高斯消元法进行方程式求解的算法的实例展示

//Begin of file linequ.cpp                             //文件2，类实现
#include "linequ.h"                                    //包含类的声明头文件

//the function member of Class Matrix                  //基类成员函数的实现
//Public Function member No.1 : Set Matrix value
void Matrix :: setMatrix(double * rmatr)               //设置矩阵
{
	for (int i = 0; i < index * index; i ++) {
		*(MatrixA + i) = rmatr[i];                     //矩阵成员赋初值
	}
}

//Public Funcion member No.2 : Constructor function
Matrix :: Matrix(int dims)                             //矩阵Matrix类的构造函数
{
	index = dims;                                      //保护数据赋值
	MatrixA = new double[index * index];               //动态内存分配
}

//Public Function member No.3 : Destruction function
Matrix :: ~Matrix()                                    //矩阵Matrix类的析构函数
{
	delete[] MatrixA;                                  //内存释放
}

//Public Function member No.4 : Show Matrix function
void Matrix :: printM()                                //显示矩阵元素
{
	cout << "The Matrix is : " << endl;
	for (int i = 0; i < index; i ++) {
		for (int j = 0; j < index; j ++)
			cout << *(MatrixA + i * index + j) << " ";
		cout << endl;
	}
}

//the function member of Class Linequ                  //派生类的成员函数的实现
//Public Function member No.1 : Construction function
Linequ :: Linequ(int dims) : Matrix(dims)              //派生类Linequ的构造函数
{
	sums = new double[dims];                           //动态内存分配
	solu = new double[dims];
}

//Public FUnction member No.2 : Destruction function
Linequ :: ~Linequ()                                    //派生类Linequ的析构函数
{                                                      //调用基类析构函数         ？？？？？
	delete[] sums;                                     //释放内存
	delete[] solu;
}

//Public Function member No.3 : Set Line Equation function
void Linequ :: setLinequ(double * a, double * b)       //设置线性方程组
{
	setMatrix(a);                                      //调用基类函数
	for (int i = 0; i < index; i ++)
		sums[i] = b[i];
}

//Public Function member No.4 : Show Line Equation function
void Linequ :: printL()                                //显示线性方程组
{
	cout << "线性方程组 : " << endl;
	for (int i = 0; i < index; i ++) {
		for (int j = 0; j < index; j ++)
			cout << *(MatrixA + i * index + j) << " ";
		cout << " " << sums[i] << endl;
	}
	cout << endl;
}

//Public Function member No.5 : Show Solution function
void Linequ :: showX()                                 //输出方程的解
{
	cout << "结果 : " << endl;
	for (int i = 0; i < index; i ++) {
		cout << "X[" << i << "] = "<< solu[i] << endl;
	}
}

//Public Functoin member No.6 : Solve Equation function
int Linequ :: Solve()                                  //全选主元高斯消去法求解方程
{
	int * js, l, k, i, j, is, p, q;
	double d, t;
	js = new int[index];
	l = 1;
	for (k = 0; k <= index - 2; k ++) {                //消去过程
		d = 0.0;
		for (i = k; i <= index - 1; i ++)
			for (j = k; j <= index - 1; j ++) {
				t = fabs(MatrixA[i * index + j]);
				if (t > d) {
					d = t;
					js[k] = j;
					is = i;
				}
			}
			if (d + 1.0 == 1.0)
				l = 0;
			else {
				if (js[k] != k)
					for (i = 0; i <= index - 1; i ++) {
						p = i * index + k;
						q = i * index + js[k];
						t = MatrixA[p];
						MatrixA[p] = MatrixA[q];
						MatrixA[q] = t;
					}
					if (is != k) {
						for (j = k; j <= index - 1; j ++) {
							p = k * index + j;
							q = is * index + j;
							t = MatrixA[p];
							MatrixA[p] = MatrixA[q];
							MatrixA[q] = t;
						}
						t = sums[k];
						sums[k] = sums[is];
						sums[is] = t;
					}
			}
			if (l == 0) {
				delete[] js;
				cout << "fail" << endl;
				return(0);
			}
			d = MatrixA[k * index + k];
			for (j = k + 1; j <= index - 1; j ++) {
				p = k * index + j;
				MatrixA[p] = MatrixA[p] / d;
			}
			sums[k] = sums[k] /d;
			for (i = k + 1; i <= index - 1; i ++) {
				for (j = k + 1; j <= index - 1; j ++) {
					p = i * index + j;
					MatrixA[p] = MatrixA[p] - MatrixA[i * index + k] * MatrixA[k * index +j];
				}
				sums[i] = sums[i] - MatrixA[i * index + k] * sums[k];
			}
	}
	d = MatrixA[(index - 1) * index + index - 1];
	if (fabs(d) + 1.0 == 1.0) {
		delete[] js;
		cout << "fail" << endl;
		return(0);
	}
	solu[index - 1] = sums[index - 1] /d;                          //回代过程
	for (i = index - 2; i >= 0; i --) {
		t = 0.0;
		for (j = i + 1; j <= index - 1; j ++)
			t = t + MatrixA[i * index +j] * solu[j];
		solu[i] = sums[i] - t;
	}
	js[index - 1] = index - 1;
	for (k = index - 1; k >= 0; k --)
		if (js[k] != k) {
			t = solu[k];
			solu[k] = solu[js[k]];
			solu[js[k]] = t;
		}
		delete[] js;
		return(1);
}

//End of file linequ.cpp