Erste Nachricht

.gitignore

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+.venv/
+__pycache__/
+.env

compute.py

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+
+import math
+
+
+def _is_rectangular(matrix: list[list[float]]) -> bool:
+    """Check whether a matrix is non-empty and rectangular."""
+    if not matrix:
+        return False
+
+    first_length = len(matrix[0])
+    return first_length > 0 and all(
+        len(row) == first_length for row in matrix
+    )
+
+
+def matmul(
+    a: list[list[float]],
+    b: list[list[float]],
+) -> list[list[float]]:
+    """Multiply two matrices and return their product.
+
+    Raises:
+        ValueError: If a matrix is invalid or dimensions do not match.
+    """
+    if not _is_rectangular(a) or not _is_rectangular(b):
+        raise ValueError("Both matrices must be non-empty and rectangular.")
+
+    if len(a[0]) != len(b):
+        raise ValueError("Number of columns in a must equal rows in b.")
+
+    result = []
+    for row in a:
+        result_row = []
+        for column_index in range(len(b[0])):
+            total = sum(
+                row[k] * b[k][column_index]
+                for k in range(len(b))
+            )
+            result_row.append(total)
+        result.append(result_row)
+
+    return result
+
+
+def transpose(matrix: list[list[float]]) -> list[list[float]]:
+    """Return the transpose of a matrix.
+
+    Raises:
+        ValueError: If the matrix is invalid.
+    """
+    if not _is_rectangular(matrix):
+        raise ValueError("Matrix must be non-empty and rectangular.")
+
+    return [
+        [matrix[row][column] for row in range(len(matrix))]
+        for column in range(len(matrix[0]))
+    ]
+
+
+def rot_2D(theta: float) -> list[list[float]]:
+    """Create a 2D rotation matrix for an angle in radians."""
+    cos_theta = math.cos(theta)
+    sin_theta = math.sin(theta)
+
+    return [
+        [cos_theta, -sin_theta],
+        [sin_theta, cos_theta],
+    ]
+
+
+def rotate(matrix: list[list[float]]) -> list[list[float]]:
+    """Rotate a matrix 90 degrees clockwise.
+
+    Raises:
+        ValueError: If the matrix is invalid.
+    """
+    if not _is_rectangular(matrix):
+        raise ValueError("Matrix must be non-empty and rectangular.")
+
+    return [
+        [
+            matrix[row][column]
+            for row in range(len(matrix) - 1, -1, -1)
+        ]
+        for column in range(len(matrix[0]))
+    ]
+
+
+if __name__ == "__main__":
+    # Test 1: Matrix multiplication
+    a = [[1, 2, 3], [4, 5, 6]]
+    b = [[7, 8], [9, 10], [11, 12]]
+    assert matmul(a, b) == [[58, 64], [139, 154]]
+    print("Matrix multiplication: passed")
+    print(matmul(a, b))
+
+    # Test 2: Matrix multiplication with another example
+    assert matmul([[1, 2]], [[3], [4]]) == [[11]]
+    print("Second multiplication test: passed")
+
+    # Test 3: Transpose
+    matrix = [[1, 2, 3], [4, 5, 6]]
+    assert transpose(matrix) == [[1, 4], [2, 5], [3, 6]]
+    print("Transpose: passed")
+
+    # Test 4: Rotation clockwise
+    assert rotate(matrix) == [[4, 1], [5, 2], [6, 3]]
+    print("Rotation: passed")
+
+    # Test 5: 2D rotation matrix
+    rotation = rot_2D(0.01)
+    assert len(rotation) == 2 and len(rotation[0]) == 2
+    print("2D rotation matrix: passed")
+    print(rotation)
+
+    # Test 6: Invalid multiplication dimensions
+    try:
+        matmul([[1, 2], [3, 4]], [[5, 6, 7]])
+    except ValueError:
+        print("Invalid multiplication dimensions: handled")
+    else:
+        raise AssertionError("Expected ValueError for matmul")
+
+    # Test 7: Invalid matrices
+    for function in (transpose, rotate):
+        try:
+            function([])
+        except ValueError:
+            print(f"{function.__name__}: invalid matrix handled")
+        else:
+            raise AssertionError(
+                f"Expected ValueError for {function.__name__}"
+            )
+
+    # Test 8: Non-rectangular matrix
+    try:
+        transpose([[1, 2], [3]])
+    except ValueError:
+        print("Non-rectangular matrix: handled")
+    else:
+        raise AssertionError("Expected ValueError for transpose")
+
+    print("All tests passed!")