/// <summary>
/// 行最简形
/// </summary>
/// <param name="mat">原矩阵</param>
/// <returns>行最简形式的矩阵</returns>
public static FMatrix <double> RowSimplestFormOf(FMatrix <T> mat)
{
FMatrix <double> result = null;
bool flag1;
int searchi;
if (mat.matrix != null && mat.column > 0 && mat.row > 0) //合理矩阵，方阵，
{
result = new FMatrix <double>(mat.row, mat.column, 0.0);
for (int i = 0; i < mat.row; i++)
{
for (int j = 0; j < mat.column; j++)
{
result[i][j] = Convert.ToDouble(mat[i][j]);
}
}
for (int a = 0; a < result.row; a++) //当前行
{
flag1 = true;
for (searchi = a; searchi < result.row; searchi++)
{
if (!IsZero_DBL(result[searchi][a]))
{
flag1 = false; //找到某一行当前位置不是0
break;
}
else
{
result[searchi][a] = 0.0;
}
}
if (flag1)
{
continue; //某一列全为零,换下一列
}
if (searchi != a)
{
result.ExchangeR1R2(searchi, a); //交换两行，保证不为零
}
for (int i = 0; i < result.row; i++)
{
if (i == a)
{
continue; //绕过当前行
}
result.AddKTimesOfRow1ToRow2(a, -1.0 * result[i][a] / result[a][a], i); //清零当前列
}
result.RowXMultiplyK(a, 1.0 / result[a][a]); //当前行
}
}
return(result);
}
/// <summary>
/// 交换矩阵的r1与r2行
/// </summary>
/// <param name="mat">原矩阵</param>
/// <param name="r1">r1行</param>
/// <param name="r2">r2行</param>
/// <returns>交换后的矩阵</returns>
public static FMatrix <T> ExchangeR1R2(FMatrix <T> mat, int r1, int r2)
{
FMatrix <T> result = null;
if (mat.matrix != null && r1 >= 0 && r1 < mat.row && r2 >= 0 && r2 < mat.row) //可用的矩阵
{
result = new FMatrix <T>(mat);
result.ExchangeR1R2(r1, r2);
}
return(result);
}
/// <summary>
/// 矩阵的逆矩阵（返回矩阵内部类型一定是double）
/// </summary>
/// <param name="mat">原矩阵</param>
/// <returns>double的逆矩阵</returns>
public static FMatrix <double> Inverse(FMatrix <T> mat)
{
FMatrix <double> result = null;
bool flag1; //“第一位”为空（每一行都必须非0，这样才能保证）
int searchi;
if (mat.matrix != null && mat.row == mat.column && mat.row > 0) //合理矩阵，方阵，
{
result = new FMatrix <double>(mat.row, mat.row, 0.0);
FMatrix <double> AE = new FMatrix <double>(mat.row, mat.row + mat.row, 0); //mat放置一个单位矩阵
for (int i = 0; i < mat.row; i++)
{
for (int j = 0; j < mat.column; j++)
{
AE[i][j] = Convert.ToDouble(mat[i][j]);
if (i == j)
{
AE[i][j + mat.row] = 1; //对角线
}
else
{
AE[i][j + mat.row] = 0;
}
}
}
for (int a = 0; a < AE.row; a++) //当前行
{
flag1 = true;
for (searchi = a; searchi < AE.row; searchi++)
{
if (!IsZero_DBL(AE[searchi][a]))
{
flag1 = false; //找到某一行当前位置不是0
break;
}
}
if (flag1)
{
return(null); //某一列全为零,不存在逆矩阵，返回空
}
if (searchi != a)
{
AE.ExchangeR1R2(searchi, a); //交换两行，保证不为零
}
for (int i = 0; i < AE.row; i++)
{
if (i == a)
{
continue; //绕过当前行
}
AE.AddKTimesOfRow1ToRow2(a, -1.0 * AE[i][a] / AE[a][a], i); //清零当前列
}
AE.RowXMultiplyK(a, 1.0 / AE[a][a]); //当前行
}
for (int i = 0; i < AE.row; i++)
{
for (int j = 0; j < AE.row; j++)
{
result[i][j] = AE[i][j + AE.row];
}
}
return(result);
}
return(null);
}