C语言实现常见的矩阵运算函数

1.矩阵转置函数

void matrix_t(double **a_matrix, const double **b_matrix, int krow, int kline)

//	a_matrix:转置后的矩阵
//	b_matrix:转置前的矩阵
//	krow    :行数
//	kline   :列数

{
	int k, k2;   

	for (k = 0; k < krow; k++)
	{
		for(k2 = 0; k2 < kline; k2++)
		{
			a_matrix[k2][k] = b_matrix[k][k2];
		}
	}
}

2.矩阵加（减）法函数

void matrix_a(double **a_matrix, const double **b_matrix, const double **c_matrix, 
					int krow, int kline, int ktrl)

//	a_matrix=b_matrix+c_matrix
//	 krow   :行数
//	 kline  :列数
//	 ktrl   :大于0: 加法  不大于0:减法

{
	int k, k2;

	for (k = 0; k < krow; k++)
	{
		for(k2 = 0; k2 < kline; k2++)
		{
			a_matrix[k][k2] = b_matrix[k][k2]
				+ ((ktrl > 0) ? c_matrix[k][k2] : -c_matrix[k][k2]); 
		}
	}
}

3.矩阵乘法函数

void matrix_m(double **a_matrix, const double **b_matrix, const double **c_matrix,
				int krow, int kline, int kmiddle, int ktrl)

//	a_matrix=b_matrix*c_matrix
//	krow  :行数
//	kline :列数
//	ktrl  :	大于0:两个正数矩阵相乘 不大于0:正数矩阵乘以负数矩阵

{
	int k, k2, k4;
	double stmp;

	for (k = 0; k < krow; k++)     
	{
		for (k2 = 0; k2 < kline; k2++)   
		{
			stmp = 0.0;
			for (k4 = 0; k4 < kmiddle; k4++)  
			{
				stmp += b_matrix[k][k4] * c_matrix[k4][k2];
			}
			a_matrix[k][k2] = stmp;
		}
	}
	if (ktrl <= 0)   
	{
		for (k = 0; k < krow; k++)
		{
			for (k2 = 0; k2 < kline; k2++)
			{
				a_matrix[k][k2] = -a_matrix[k][k2];
			}
		}
	}
}

4.矩阵求逆函数

int  matrix_inv(double **a_matrix, int ndimen)

//	a_matrix:矩阵
//	ndimen :维数

{
	double tmp, tmp2, b_tmp[20], c_tmp[20];
	int k, k1, k2, k3, j, i, j2, i2, kme[20], kmf[20];
	i2 = j2 = 0;

	for (k = 0; k < ndimen; k++)  
	{
		tmp2 = 0.0;
		for (i = k; i < ndimen; i++)  
		{
			for (j = k; j < ndimen; j++)  
			{
				if (fabs(a_matrix[i][j] ) <= fabs(tmp2)) 
					continue;
				tmp2 = a_matrix[i][j];
				i2 = i;
				j2 = j;
			}  
		}
		if (i2 != k) 
		{
			for (j = 0; j < ndimen; j++)   
			{
				tmp = a_matrix[i2][j];
				a_matrix[i2][j] = a_matrix[k][j];
				a_matrix[k][j] = tmp;
			}
		}
		if (j2 != k) 
		{
			for (i = 0; i < ndimen; i++)  
			{
				tmp = a_matrix[i][j2];
				a_matrix[i][j2] = a_matrix[i][k];
				a_matrix[i][k] = tmp;
			}    
		}
		kme[k] = i2;
		kmf[k] = j2;
		for (j = 0; j < ndimen; j++)  
		{
			if (j == k)   
			{
				b_tmp[j] = 1.0 / tmp2;
				c_tmp[j] = 1.0;
			}
			else 
			{
				b_tmp[j] = -a_matrix[k][j] / tmp2;
				c_tmp[j] = a_matrix[j][k];
			}
			a_matrix[k][j] = 0.0;
			a_matrix[j][k] = 0.0;
		}
		for (i = 0; i < ndimen; i++)  
		{
			for (j = 0; j < ndimen; j++)  
			{
				a_matrix[i][j] = a_matrix[i][j] + c_tmp[i] * b_tmp[j];
			}  
		}
	}
	for (k3 = 0; k3 < ndimen;  k3++)   
	{
		k  = ndimen - k3 - 1;
		k1 = kme[k];
		k2 = kmf[k];
		if (k1 != k)   
		{
			for (i = 0; i < ndimen; i++)  
			{
				tmp = a_matrix[i][k1];
				a_matrix[i][k1] = a_matrix[i][k];
				a_matrix[i][k] = tmp;
			}  
		}
		if (k2 != k)   
		{
			for(j = 0; j < ndimen; j++)  
			{
				tmp = a_matrix[k2][j];
				a_matrix[k2][j] = a_matrix[k][j];
				a_matrix[k][j] = tmp;
			}
		}
	}
	return (0);
}

5.矩阵乔里斯基分解函数

void chol(double **a_matrix, const double **b_matrix, int ndimen)

//	输入参数:
//		b_matrix:  对称正定方阵    ndimen: 矩阵维数
//	返回值:
//		a_matrix: 下三角矩阵

{
	int i, j, r;
	double m = 0;   
	static double **c_matrix;
	static int flag = 0;

	if (flag == 0)
	{
		flag = 1;
		c_matrix = (double **)malloc(ndimen * sizeof(double *));

		for (i = 0; i < ndimen; i++)
			c_matrix[i] = (double *)malloc(ndimen * sizeof(double));
	}

	for (i = 0; i < ndimen; i++)
	{
		for (j = 0; j < ndimen; j++) 
			c_matrix[i][j] = 0;
	}

	c_matrix[0][0] = sqrt(b_matrix[0][0]);

	for (i = 1; i < ndimen; i++)
	{
		if (c_matrix[0][0] != 0) 
			c_matrix[i][0] = b_matrix[i][0] / c_matrix[0][0];
	}

	for (i = 1; i < ndimen; i++)
	{
		for (r = 0; r < i; r++)		m = m + c_matrix[i][r] * c_matrix[i][r];

		c_matrix[i][i] = sqrt(b_matrix[i][i] - m);
		m = 0.0;

		for (j = i + 1; j < ndimen; j++)
		{
			for (r = 0; r < i; r++)		m = m + c_matrix[i][r] * c_matrix[j][r];
			c_matrix[j][i] = (b_matrix[i][j] - m) / c_matrix[i][i];
			m = 0;
		}
	}

	for (i = 0; i < ndimen; i++)
	{
		for (j = 0; j < ndimen; j++)	
			a_matrix[i][j] = c_matrix[i][j];
	}
}