[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

linear_algebra/matrix_trace.py

@@ -14,7 +14,7 @@
 
 def trace(matrix: NDArray[float64]) -> float:
     """
-    Calculate the trace of a square matrix.    
+    Calculate the trace of a square matrix.
     The trace is the sum of the diagonal elements of a square matrix.
     Parameters:
         matrix (NDArray[float64]): A square matrix
@@ -40,96 +40,96 @@ def trace(matrix: NDArray[float64]) -> float:
     """
     if matrix.shape[0] != matrix.shape[1]:
         raise ValueError("Matrix must be square")
-    
+
     return float(np.sum(np.diag(matrix)))
 
 
 def trace_properties_demo(matrix: NDArray[float64]) -> dict:
     """
     Demonstrate various properties of the trace operation.
     Parameters:
-        matrix (NDArray[float64]): A square matrix        
+        matrix (NDArray[float64]): A square matrix
     Returns:
         dict: Dictionary containing trace properties and calculations
     """
     if matrix.shape[0] != matrix.shape[1]:
         raise ValueError("Matrix must be square")
-    
+
     n = matrix.shape[0]
-    
+
     # Calculate trace
     tr = trace(matrix)
-    
+
     # Calculate transpose trace (should be equal to original)
     tr_transpose = trace(matrix.T)
-    
+
     # Calculate trace of scalar multiple
     scalar = 2.0
     tr_scalar = trace(scalar * matrix)
-    
+
     # Create identity matrix for comparison
     identity = np.eye(n, dtype=float64)
     tr_identity = trace(identity)
-    
+
     return {
         "original_trace": tr,
         "transpose_trace": tr_transpose,
         "scalar_multiple_trace": tr_scalar,
         "scalar_factor": scalar,
         "identity_trace": tr_identity,
         "trace_equals_transpose": abs(tr - tr_transpose) < 1e-10,
-        "scalar_property_check": abs(tr_scalar - scalar * tr) < 1e-10
+        "scalar_property_check": abs(tr_scalar - scalar * tr) < 1e-10,
     }
 
 
 def test_trace() -> None:
     """
-    Test function for matrix trace calculation.    
+    Test function for matrix trace calculation.
     >>> test_trace()  # self running tests
     """
     # Test 1: 2x2 matrix
     matrix_2x2 = np.array([[1.0, 2.0], [3.0, 4.0]], dtype=float)
     tr_2x2 = trace(matrix_2x2)
     assert abs(tr_2x2 - 5.0) < 1e-10, "2x2 trace calculation failed"
-    
+
     # Test 2: 3x3 matrix
-    matrix_3x3 = np.array([[2.0, -1.0, 3.0], 
-                          [4.0, 5.0, -2.0], 
-                          [1.0, 0.0, 7.0]], dtype=float)
+    matrix_3x3 = np.array(
+        [[2.0, -1.0, 3.0], [4.0, 5.0, -2.0], [1.0, 0.0, 7.0]], dtype=float
+    )
     tr_3x3 = trace(matrix_3x3)
     assert abs(tr_3x3 - 14.0) < 1e-10, "3x3 trace calculation failed"
-    
+
     # Test 3: Identity matrix
     identity_4x4 = np.eye(4, dtype=float)
     tr_identity = trace(identity_4x4)
-    assert (
-        abs(tr_identity - 4.0) < 1e-10
-    ), "Identity matrix trace should equal dimension"
-    
+    assert abs(tr_identity - 4.0) < 1e-10, (
+        "Identity matrix trace should equal dimension"
+    )
+
     # Test 4: Zero matrix
     zero_matrix = np.zeros((3, 3), dtype=float)
     tr_zero = trace(zero_matrix)
     assert abs(tr_zero) < 1e-10, "Zero matrix should have zero trace"
-    
+
     # Test 5: Trace properties
-    test_matrix = np.array([[1.0, 2.0, 3.0], 
-                           [4.0, 5.0, 6.0], 
-                           [7.0, 8.0, 9.0]], dtype=float)
+    test_matrix = np.array(
+        [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]], dtype=float
+    )
     properties = trace_properties_demo(test_matrix)
     assert properties["trace_equals_transpose"], "Trace should equal transpose trace"
     assert properties["scalar_property_check"], "Scalar multiplication property failed"
-    
+
     # Test 6: Diagonal matrix
     diagonal_matrix = np.diag([1.0, 2.0, 3.0, 4.0])
     tr_diagonal = trace(diagonal_matrix)
     expected = 1.0 + 2.0 + 3.0 + 4.0
-    assert (
-        abs(tr_diagonal - expected) < 1e-10
-    ), "Diagonal matrix trace should equal sum of diagonal elements"
+    assert abs(tr_diagonal - expected) < 1e-10, (
+        "Diagonal matrix trace should equal sum of diagonal elements"
+    )
 
 
 if __name__ == "__main__":
     import doctest
-    
+
     doctest.testmod()
     test_trace()