gauss.h

#ifndef _GAUSS_H_
#define _GAUSS_H_ 
#define MAXSIZE 10

bool Gauss(double A[][MAXSIZE], double B[][MAXSIZE], int n)
{
	int i, j, k;
	double max, temp;
	double t[MAXSIZE][MAXSIZE]; //临时矩阵
	//将A矩阵存放在临时矩阵t[n][n]中
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < n; j++)
		{
			t[i][j] = A[i][j];
		}
	}
	//初始化B矩阵为单位阵
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < n; j++)
		{
			B[i][j] = (i == j) ? (float)1 : 0;
		}
	}
	for (i = 0; i < n; i++)
	{
		//寻找主元
		max = t[i][i];
		k = i;
		for (j = i + 1; j < n; j++)
		{
			if (fabs(t[j][i]) > fabs(max))
			{
				max = t[j][i];
				k = j;
			}
		}
		//如果主元所在行不是第i行，进行行交换
		if (k != i)
		{
			for (j = 0; j < n; j++)
			{
				temp = t[i][j];
				t[i][j] = t[k][j];
				t[k][j] = temp;
				//B伴随交换
				temp = B[i][j];
				B[i][j] = B[k][j];
				B[k][j] = temp;
			}
		}
		//判断主元是否为0, 若是, 则矩阵A不是满秩矩阵,不存在逆矩阵
		if (t[i][i] == 0)
		{
			printf("There is no inverse matrix!\n");
			return false;
		}
		//消去A的第i列除去i行以外的各行元素
		temp = t[i][i];
		for (j = 0; j < n; j++)
		{
			t[i][j] = t[i][j] / temp;        //主对角线上的元素变为1
			B[i][j] = B[i][j] / temp;        //伴随计算
		}
		for (j = 0; j < n; j++)        //第0行->第n行
		{
			if (j != i)                //不是第i行
			{
				temp = t[j][i];
				for (k = 0; k < n; k++)        //第j行元素 - i行元素*j列i行元素
				{
					t[j][k] = t[j][k] - t[i][k] * temp;
					B[j][k] = B[j][k] - B[i][k] * temp;
				}
			}
		}
	}
	return true;
}




#endif