| 63 | } |
| 64 | |
| 65 | public static void main(String[] args) { |
| 66 | // 唯一解 |
| 67 | // 1*x1 + 2*x2 - 1*x3 = 9 |
| 68 | // 2*x1 - 1*x2 + 2*x3 = 7 |
| 69 | // 1*x1 - 2*x2 + 2*x3 = 0 |
| 70 | System.out.println("唯一解"); |
| 71 | mat[1][1] = 1; mat[1][2] = 2; mat[1][3] = -1; mat[1][4] = 9; |
| 72 | mat[2][1] = 2; mat[2][2] = -1; mat[2][3] = 2; mat[2][4] = 7; |
| 73 | mat[3][1] = 1; mat[3][2] = -2; mat[3][3] = 2; mat[3][4] = 0; |
| 74 | gauss(3); |
| 75 | print(3); |
| 76 | |
| 77 | // 矛盾 |
| 78 | // 1*x1 + 1*x2 = 3 |
| 79 | // 2*x1 + 2*x2 = 7 |
| 80 | System.out.println("矛盾"); |
| 81 | mat[1][1] = 1; mat[1][2] = 1; mat[1][3] = 3; |
| 82 | mat[2][1] = 2; mat[2][2] = 2; mat[2][3] = 7; |
| 83 | gauss(2); |
| 84 | print(2); |
| 85 | |
| 86 | // 多解 |
| 87 | // 1*x1 + 1*x2 = 3 |
| 88 | // 2*x1 + 2*x2 = 6 |
| 89 | System.out.println("多解"); |
| 90 | mat[1][1] = 1; mat[1][2] = 1; mat[1][3] = 3; |
| 91 | mat[2][1] = 2; mat[2][2] = 2; mat[2][3] = 6; |
| 92 | gauss(2); |
| 93 | print(2); |
| 94 | |
| 95 | // 表达式冗余，唯一解 |
| 96 | // 1*x1 + 2*x2 - 1*x3 + 0*x4 = 9 |
| 97 | // 2*x1 + 4*x2 - 2*x3 + 0*x4 = 18 |
| 98 | // 2*x1 - 1*x2 + 2*x3 + 0*x4 = 7 |
| 99 | // 1*x1 - 2*x2 + 2*x3 + 0*x4 = 0 |
| 100 | System.out.println("表达式冗余，唯一解"); |
| 101 | mat[1][1] = 1; mat[1][2] = 2; mat[1][3] = -1; mat[1][4] = 0; mat[1][5] = 9; |
| 102 | mat[2][1] = 2; mat[2][2] = 4; mat[2][3] = -2; mat[2][4] = 0; mat[2][5] = 18; |
| 103 | mat[3][1] = 2; mat[3][2] = -1; mat[3][3] = 2; mat[3][4] = 0; mat[3][5] = 7; |
| 104 | mat[4][1] = 1; mat[4][2] = -2; mat[4][3] = 2; mat[4][4] = 0; mat[4][5] = 0; |
| 105 | gauss(4); |
| 106 | print(4); |
| 107 | |
| 108 | // 表达式冗余，矛盾 |
| 109 | // 1*x1 + 2*x2 - 1*x3 = 9 |
| 110 | // 2*x1 + 4*x2 - 2*x3 = 18 |
| 111 | // 2*x1 - 1*x2 + 2*x3 = 7 |
| 112 | // 4*x1 - 2*x2 + 4*x3 = 10 |
| 113 | System.out.println("表达式冗余，矛盾"); |
| 114 | mat[1][1] = 1; mat[1][2] = 2; mat[1][3] = -1; mat[1][4] = 0; mat[1][5] = 9; |
| 115 | mat[2][1] = 2; mat[2][2] = 4; mat[2][3] = -2; mat[2][4] = 0; mat[2][5] = 18; |
| 116 | mat[3][1] = 2; mat[3][2] = -1; mat[3][3] = 2; mat[3][4] = 0; mat[3][5] = 7; |
| 117 | mat[4][1] = 4; mat[4][2] = -2; mat[4][3] = 4; mat[4][4] = 0; mat[4][5] = 10; |
| 118 | gauss(4); |
| 119 | print(4); |
| 120 | |
| 121 | // 表达式冗余，多解 |
| 122 | // 1*x1 + 2*x2 - 1*x3 = 9 |