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原始输出的运行日期、硬件和固件提交未记录；下方完整保留该阶段输出。标签数量不是独立测试用例数量。
============ [tiny_matrix_test start] ============
[Test Organization: Application-Oriented Logic]
Foundation → Basic Ops → Properties → Linear Systems → Decompositions → Applications → Quality
[D1: Gaussian Elimination Tests]
[D1.1] 3x3 Matrix (Simple Upper Triangular)
Original Matrix:
Matrix Elements >>>
2 1 -1 |
-3 -1 2 |
-2 1 2 |
<<< Matrix Elements
After Gaussian Elimination (Should be upper triangular):
Matrix Elements >>>
-3 -1 2 |
0 1.66667 0.666667 |
0 0 0.2 |
<<< Matrix Elements
[D1.2] 3x4 Augmented Matrix (Linear System Ax = b)
Original Augmented Matrix [A | b]:
Matrix Elements >>>
1 2 -1 8 |
-3 -1 2 -11 |
-2 1 2 -3 |
<<< Matrix Elements
After Gaussian Elimination (Row Echelon Form):
Matrix Elements >>>
-3 -1 2 -11 |
0 1.66667 0.666667 4.33333 |
0 0 -1 0 |
<<< Matrix Elements
[D1.3] Singular Matrix (No Unique Solution)
Original Singular Matrix:
Matrix Elements >>>
1 2 |
2 4 |
<<< Matrix Elements
After Gaussian Elimination (Should show rows of zeros):
Matrix Elements >>>
2 4 |
0 0 |
<<< Matrix Elements
[D1.4] Zero Matrix
Matrix Elements >>>
0 0 0 |
0 0 0 |
0 0 0 |
<<< Matrix Elements
After Gaussian Elimination (Should be a zero matrix):
Matrix Elements >>>
0 0 0 |
0 0 0 |
0 0 0 |
<<< Matrix Elements
[D1.5] gaussian_eliminate() - Boundary Case - Empty Matrix
[Error] gaussian_eliminate: matrix data pointer is null
Empty matrix gaussian_eliminate: Empty matrix or error state (Expected) [PASS]
[D1.6] gaussian_eliminate() - Boundary Case - 1x1 Matrix
1x1 matrix after gaussian_eliminate:
Matrix Elements >>>
5 |
<<< Matrix Elements
1x1 matrix gaussian_eliminate: [PASS]
[D2: Row Reduce from Gaussian (RREF) Tests]
[D2.1] 3x4 Augmented Matrix
Original Matrix:
Matrix Elements >>>
1 2 -1 -4 |
2 3 -1 -11 |
-2 0 -3 22 |
<<< Matrix Elements
RREF Result:
Matrix Elements >>>
1 0 0 -8 |
0 1 0 1 |
0 0 1 -2 |
<<< Matrix Elements
[D2.2] 2x3 Matrix
Original Matrix:
Matrix Elements >>>
1 2 3 |
4 5 6 |
<<< Matrix Elements
RREF Result:
Matrix Elements >>>
1 0 -1 |
0 1 2 |
<<< Matrix Elements
[D2.3] Already Reduced Matrix
Original Matrix:
Matrix Elements >>>
1 0 2 |
0 1 3 |
<<< Matrix Elements
RREF Result:
Matrix Elements >>>
1 0 2 |
0 1 3 |
<<< Matrix Elements
[D2.4] row_reduce_from_gaussian() - Boundary Case - Empty Matrix
[Error] row_reduce_from_gaussian: matrix data pointer is null
Empty matrix row_reduce_from_gaussian: Empty matrix or error state (Expected) [PASS]
[D3: Gaussian Inverse Tests]
[D3.1] 2x2 Matrix Inverse
Original matrix (mat1):
Matrix Elements >>>
4 7 |
2 6 |
<<< Matrix Elements
Inverse matrix (mat1):
Matrix Elements >>>
0.6 -0.7 |
-0.2 0.4 |
<<< Matrix Elements
[D3.2] Identity Matrix Inverse
Original matrix (Identity):
Matrix Elements >>>
1 0 0 |
0 1 0 |
0 0 1 |
<<< Matrix Elements
Inverse matrix (Identity):
Matrix Elements >>>
1 0 0 |
0 1 0 |
0 0 1 |
<<< Matrix Elements
[D3.3] Singular Matrix (Expected: No Inverse)
Original matrix (singular):
Matrix Elements >>>
1 2 3 |
4 5 6 |
7 8 9 |
<<< Matrix Elements
[Error] inverse_gje: matrix is singular (left block not identity at (0, 2): expected 0, got -1).
Inverse matrix (singular):
[Error] Cannot print matrix: data pointer is null.
[D3.4] 3x3 Matrix Inverse
Original matrix (mat4):
Matrix Elements >>>
4 7 2 |
3 5 1 |
8 6 9 |
<<< Matrix Elements
Inverse matrix (mat4):
Matrix Elements >>>
-1.85714 2.42857 0.142857 |
0.904762 -0.952381 -0.0952381 |
1.04762 -1.52381 0.047619 |
<<< Matrix Elements
[D3.5] Non-square Matrix Inverse (Expected Error)
Original matrix (non-square):
Matrix Elements >>>
1 2 3 |
4 5 6 |
<<< Matrix Elements
[Error] inverse_gje: requires a square matrix (got 2x3).
Inverse matrix (non-square):
[Error] Cannot print matrix: data pointer is null.
[D4: Dot Product Tests]
[D4.1] Valid Dot Product (Same Length Vectors)
Vector A:
Matrix Elements >>>
1 |
2 |
3 |
<<< Matrix Elements
Vector B:
Matrix Elements >>>
4 |
5 |
6 |
<<< Matrix Elements
Dot product of vectorA and vectorB: 32
[D4.2] Invalid Dot Product (Dimension Mismatch)
Vector A (3x1):
Matrix Elements >>>
1 |
2 |
3 |
<<< Matrix Elements
Vector C (2x1, different size):
Matrix Elements >>>
1 |
2 |
<<< Matrix Elements
[Error] dotprod: matrices must have the same size (A: 3x1, B: 2x1)
Dot product (dimension mismatch): 0
[D4.3] Dot Product of Zero Vectors
Zero Vector A:
Matrix Elements >>>
0 |
0 |
0 |
<<< Matrix Elements
Zero Vector B:
Matrix Elements >>>
0 |
0 |
0 |
<<< Matrix Elements
Dot product of zero vectors: 0
[D5: Solve Linear System Tests]
[D5.1] Solving a Simple 2x2 System Ax = b
Matrix A:
Matrix Elements >>>
2 1 |
1 3 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
5 |
6 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
1.8 |
1.4 |
<<< Matrix Elements
[D5.2] Solving a 3x3 System Ax = b
Matrix A:
Matrix Elements >>>
1 2 1 |
2 0 3 |
3 2 1 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
9 |
8 |
7 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
-1 |
3.33333 |
3.33333 |
<<< Matrix Elements
[D5.3] Solving a System Where One Row is All Zeros (Expect Failure or Infinite Solutions)
Matrix A (has zero row):
Matrix Elements >>>
1 2 3 |
0 0 0 |
4 5 6 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
9 |
0 |
15 |
<<< Matrix Elements
[Error] solve: zero or near-zero pivot at (2, 2), system is singular or rank-deficient.
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D5.4] Solving a System with Zero Determinant (Singular Matrix)
Matrix A (singular, determinant = 0):
Matrix Elements >>>
2 4 1 |
1 2 3 |
3 6 2 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
5 |
6 |
7 |
<<< Matrix Elements
[Error] solve: zero or near-zero pivot at (2, 2), system is singular or rank-deficient.
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D5.5] Solving a System with Linearly Dependent Rows (Expect Failure or Infinite Solutions)
Matrix A (all rows linearly dependent):
Matrix Elements >>>
1 1 1 |
2 2 2 |
3 3 3 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
6 |
12 |
18 |
<<< Matrix Elements
[Error] solve: zero or near-zero pivot at (2, 2), system is singular or rank-deficient.
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D5.6] Solving a Larger 4x4 System Ax = b
Matrix A:
Matrix Elements >>>
4 2 3 1 |
2 5 1 2 |
3 1 6 3 |
1 2 3 4 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
10 |
12 |
14 |
16 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
1.80645 |
0.258065 |
-0.516129 |
3.80645 |
<<< Matrix Elements
[D5.7] solve() - Boundary Case - Empty Matrix
[Error] solve: matrix A data pointer is null.
Empty system solve: Empty matrix or error state (Expected) [PASS]
[D5.8] solve() - Error Handling - Dimension Mismatch
[Error] solve: dimensions do not match (A: 2x2, b: 3x1, expected b: 2x1).
Dimension mismatch solve: Empty matrix or error state (Expected) [PASS]
[D6: Band Solve Tests]
[D6.1] Simple 3x3 Band Matrix
Matrix A:
Matrix Elements >>>
2 1 0 |
1 3 2 |
0 1 4 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
5 |
6 |
7 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
2.5 |
0 |
1.75 |
<<< Matrix Elements
[D6.2] 4x4 Band Matrix
Matrix A:
Matrix Elements >>>
2 1 0 0 |
1 3 2 0 |
0 1 4 2 |
0 0 1 5 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
8 |
9 |
10 |
11 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
3.51429 |
0.971429 |
1.28571 |
1.94286 |
<<< Matrix Elements
[D6.3] Incompatible Dimensions (Expect Error)
Matrix A (3x3):
Matrix Elements >>>
1 2 3 |
4 5 6 |
7 8 9 |
<<< Matrix Elements
Vector b (2x1, incompatible):
Matrix Elements >>>
10 |
11 |
<<< Matrix Elements
[Error] band_solve: dimensions do not match (A: 3x3, b: 2x1, expected b: 3x1).
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D6.4] Singular Matrix (No Unique Solution)
Matrix A (singular, linearly dependent rows):
Matrix Elements >>>
1 2 3 |
2 4 6 |
3 6 9 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
10 |
20 |
30 |
<<< Matrix Elements
[Error] band_solve: zero or near-zero pivot at (1, 1) = 0; matrix is singular or requires pivoting.
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D6.5] band_solve() - Boundary Case - Empty Matrix
[Error] band_solve: matrix A data pointer is null.
Empty system band_solve: Empty matrix or error state (Expected) [PASS]
[D6.6] band_solve() - Error Handling - Invalid Bandwidth
[Error] band_solve: bandwidth k must be >= 1 (got -1).
band_solve with k=-1: Empty matrix or error state (Expected) [PASS]
[D7: Roots Tests]
[D7.1] Solving a Simple 2x2 System Ax = b
Matrix A:
Matrix Elements >>>
2 1 |
1 3 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
5 |
6 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
1.8 |
1.4 |
<<< Matrix Elements
[D7.2] Solving a 3x3 System Ax = b
Matrix A:
Matrix Elements >>>
1 2 1 |
2 0 3 |
3 2 1 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
9 |
8 |
7 |
<<< Matrix Elements
Solution x:
Matrix Elements >>>
-1 |
3.33333 |
3.33333 |
<<< Matrix Elements
[D7.3] Singular Matrix (No Unique Solution)
Matrix A (singular, linearly dependent rows):
Matrix Elements >>>
1 2 |
2 4 |
<<< Matrix Elements
Vector b:
Matrix Elements >>>
5 |
6 |
<<< Matrix Elements
[Error] solve: zero or near-zero pivot at (1, 1), system is singular or rank-deficient.
Solution x:
[Error] Cannot print matrix: data pointer is null.
[D7.4] Incompatible Dimensions (Expect Error)
Matrix A (3x3):
Matrix Elements >>>
1 2 3 |
4 5 6 |
7 8 9 |
<<< Matrix Elements
Vector b (2x1, incompatible):
Matrix Elements >>>
10 |
11 |
<<< Matrix Elements
[Error] solve: dimensions do not match (A: 3x3, b: 2x1, expected b: 3x1).
Dimension mismatch roots: Empty matrix or error state (Expected) [PASS]
[D7.5] roots() - Boundary Case - Empty Matrix
[Error] solve: matrix A data pointer is null.
Empty system roots: Empty matrix or error state (Expected) [PASS]
============ [tiny_matrix_test end] ============