/// <summary> /// 把第r1行的k倍加到r2上 /// </summary> /// <param name="mat">原矩阵</param> /// <param name="row1">第row1行</param> /// <param name="kTimes">k倍</param> /// <param name="row2">第row2行</param> /// <returns>增加后的矩阵</returns> public static FMatrix <T> AddKTimesOfRow1ToRow2(FMatrix <T> mat, int row1, T kTimes, int row2) { FMatrix <T> result = null; result = new FMatrix <T>(mat); result.AddKTimesOfRow1ToRow2(row1, kTimes, row2); return(result); }
/// <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> /// 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); }