/// <summary>
/// 矩阵转置
/// </summary>
/// <returns></returns>
public CMatrix Translocation()
{
CMatrix matTmp = new CMatrix(this.Col(), this.Row());
for (int i = 0; i < this.Row(); i++)
{
for (int j = 0; j < this.Col(); j++)
{
matTmp[j, i] = this[i, j];
}
}
return(matTmp);
}
/// <summary>
/// 拷贝构造函数
/// </summary>
/// <param name="m"></param>
public CMatrix(CMatrix m)
{
iRow = m.Row();
iCol = m.Col();
dMatData = new double[iRow][];
for (int i = 0; i < iRow; i++)
{
dMatData[i] = new double[iCol];
for (int j = 0; j < iCol; j++)
{
Array.Copy(m.dMatData[i], dMatData[i], iCol);
}
}
}
/// <summary>
/// 重载+
/// </summary>
public static CMatrix operator +(CMatrix m1, CMatrix m2)
{
if ((m1.Col() != m2.Col()) || (m1.Row() != m2.Row()))
{
throw new Exception
("Cmatrix:operator+:The two matrix have difference size!");
}
CMatrix matTmp = new CMatrix(m1.Row(), m1.Col());
for (int i = 0; i < m1.Row(); i++)
{
for (int j = 0; j < m1.Col(); j++)
{
matTmp[i, j] = m1[i, j] + m2[i, j];
}
}
return(matTmp);
}
/// <summary>
/// 重载*
/// </summary>
public static CMatrix operator *(CMatrix m1, CMatrix m2)
{
if ((m1.Col() != m2.Row()) || (m1.Row() != m2.Col()))
{
throw new Exception
("Cmatrix:operator*:The two matrix have difference size!");
}
CMatrix matTmp = new CMatrix(m1.Row(), m2.Col());
for (int i = 0; i < m1.Row(); i++)
{
for (int j = 0; j < m2.Col(); j++)
{
double sum = 0;
for (int k = 0; k < m2.Row(); k++)
{
sum += m1[i, k] * m2[k, j];
}
matTmp[i, j] = sum;
}
}
return(matTmp);
}
/// <summary>
/// 矩阵求逆
/// </summary>
/// <returns></returns>
public CMatrix Inv()
{
if (iRow != iCol)
{
throw new Exception("CMatrix:Inv:待求逆的矩阵行列不相等！");
}
int i, j, k, vv;
CMatrix InvMat = new CMatrix(iRow, iRow);
InvMat = new CMatrix(this);
int[] MainRow = new int[iRow];
int[] MainCol = new int[iRow]; //用于记录主元素的行和列
double dMainCell; //主元元素的值
double dTemp; //临时变量
for (k = 0; k < iRow; k++)
{
dMainCell = 0;
//全选主元
for (i = k; i < iRow; i++)
{
for (j = k; j < iRow; j++)
{
dTemp = Math.Abs(InvMat[i, j]);
if (dTemp > dMainCell)
{
dMainCell = dTemp;
MainRow[k] = i;
MainCol[k] = j;
}
}
}
if (Math.Abs(dMainCell) < 0.0000000000001)
{
throw new Exception("CMatrix:Inv:矩阵秩亏");//矩阵秩亏，不能求逆
}
if (MainRow[k] != k)
{
for (j = 0; j < iRow; j++) //交换行
{
vv = MainRow[k];
dTemp = InvMat[k, j];
InvMat[k, j] = InvMat[vv, j];
InvMat[vv, j] = dTemp;
}
}
if (MainCol[k] != k) //交换列
{
for (i = 0; i < iRow; i++)
{
vv = MainRow[k];
dTemp = InvMat[i, k];
InvMat[i, k] = InvMat[i, vv];
InvMat[i, vv] = dTemp;
}
}
InvMat[k, k] = 1.0 / InvMat[k, k]; //计算乘数
for (j = 0; j < iRow; j++) //计算主行
{
if (j != k)
{
InvMat[k, j] = InvMat[k, j] * InvMat[k, k];
}
}
for (i = 0; i < iRow; i++) //消元
{
if (i != k)
{
for (j = 0; j < iRow; j++)
{
if (j != k)
{
InvMat[i, j] -= InvMat[i, k] * InvMat[k, j];
}
}
}
}
for (i = 0; i < iRow; i++)
{
if (i != k)
{
InvMat[i, k] = -InvMat[i, k] * InvMat[k, k];
}
}
}
for (k = iRow - 1; k >= 0; k--)
{
if (MainCol[k] != k) //交换行
{
for (j = 0; j < iRow; j++)
{
vv = MainCol[k];
dTemp = InvMat[k, j];
InvMat[k, j] = InvMat[vv, j];
InvMat[vv, j] = dTemp;
}
}
if (MainRow[k] != k) //交换行
{
for (i = 0; i < iRow; i++)
{
vv = MainCol[k];
dTemp = InvMat[i, k];
InvMat[i, k] = InvMat[i, vv];
InvMat[i, vv] = dTemp;
}
}
}
return(InvMat);
}