Pytest Coverage: kp_norm (#246)

* move kp_norm

* pylint bug

* add tests

* use black

* pylint kp_norm

* Revert "pylint bug"

This reverts commit 495c6a0.

* vincent's feedback: pylint schmidt rank

* vincent' feedback: kp_norm pytest parametrize

docs/matrices.rst

@@ -65,6 +65,7 @@ Properties of Matrices and Vectors
     toqito.matrix_props.is_square
     toqito.matrix_props.is_symmetric
     toqito.matrix_props.is_unitary
+    toqito.matrix_props.kp_norm
     toqito.matrix_props.majorizes
     toqito.matrix_props.sk_operator_norm
     toqito.matrix_props.trace_norm

tests/test_matrix_props/test_kp_norm.py

@@ -0,0 +1,33 @@
+"""Tests for the S(k)-norm of a matrix."""
+# Tests in this file, follow the discussion of the characteristics of kp_norm at https://qetlab.com/kpNorm
+
+import re
+
+import numpy as np
+import pytest
+
+from toqito.matrix_props import kp_norm
+from toqito.random import random_unitary
+from toqito.states import bell
+
+
+@pytest.mark.parametrize(
+    "vector, k, p, norm_to_compare",
+    [
+        # When (k=1, p= Inf)the kp_norm(vector) is the same as the trace norm (the 1-norm).
+        (bell(0), 1, np.inf, 1),
+        # When p=2 and k is greater than or equal to one of the input matrix dimensions, the value calculated is the frobenius norm.
+        (random_unitary(5), 5, 2, np.linalg.norm(random_unitary(5), "fro")),
+    ],
+)
+def test_kp_norm(vector, k, p, norm_to_compare):
+    calculated_kp_norm = kp_norm(vector, k, p)
+    assert calculated_kp_norm == pytest.approx(norm_to_compare)
+
+
+def test_no_default_kp_values():
+    """kp_norm does not have any default values for k or p."""
+    with pytest.raises(
+        TypeError, match=re.escape("kp_norm() missing 2 required positional arguments: 'k' and 'p'")
+    ):
+        kp_norm(bell(0))  # pylint: disable=no-value-for-parameter

tests/test_state_props/test_schmidt_rank.py

@@ -3,7 +3,7 @@
 import pytest
 
 from toqito.state_props import schmidt_rank
-from toqito.states import basis, bell
+from toqito.states import bell
 
 
 e_0, e_1 = np.array([[1], [0]]), np.array([[0], [1]])
@@ -41,7 +41,6 @@ def test_schmidt_rank_bell_state(rho, dim, expected_result):
 
 def test_schmidt_rank_entangled_state():
     """Computing Schmidt rank of entangled state should be > 1."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
     phi = (
         (1 + np.sqrt(6)) / (2 * np.sqrt(6)) * np.kron(e_0, e_0)
         + (1 - np.sqrt(6)) / (2 * np.sqrt(6)) * np.kron(e_0, e_1)
@@ -55,6 +54,5 @@ def test_schmidt_rank_singlet_state():
     Computing the Schmidt rank of the entangled singlet state should yield
     a value greater than 1.
     """
-    e_0, e_1 = basis(2, 0), basis(2, 1)
     rho = 1 / np.sqrt(2) * (np.kron(e_0, e_1) - np.kron(e_1, e_0))
     np.testing.assert_equal(schmidt_rank(rho) > 1, True)

toqito/helper/__init__.py

@@ -4,5 +4,4 @@
 from toqito.helper.update_odometer import update_odometer
 from toqito.helper.cvx_kron import cvx_kron
 from toqito.helper.npa_hierarchy import npa_constraints
-from toqito.helper.kp_norm import kp_norm
 from toqito.helper.channel_dim import channel_dim

toqito/matrix_props/__init__.py

@@ -1,5 +1,6 @@
 """Properties of matrices and vectors."""
 from toqito.matrix_props.is_square import is_square
+from toqito.matrix_props.kp_norm import kp_norm
 from toqito.matrix_props.is_hermitian import is_hermitian
 from toqito.matrix_props.is_positive_semidefinite import is_positive_semidefinite
 from toqito.matrix_props.is_density import is_density
@@ -20,3 +21,4 @@
 from toqito.matrix_props.is_block_positive import is_block_positive
 from toqito.matrix_props.trace_norm import trace_norm
 from toqito.matrix_props.is_diagonally_dominant import is_diagonally_dominant
+

toqito/helper/kp_norm.py → toqito/matrix_props/kp_norm.py

@@ -4,7 +4,7 @@
 
 def kp_norm(mat: np.ndarray, k: int, p: int) -> float:
     """
-    Compute the p-norm of the vector of the k-largest singular values of a matrix.
+    Compute the p-norm of the vector or the k-largest singular values of a matrix.
 
     :param mat: 2D numpy ndarray
     :param k: The number of singular values to take.

toqito/matrix_props/sk_norm.py

@@ -8,8 +8,7 @@
 import scipy
 
 from toqito.channels import partial_trace, partial_transpose, realignment
-from toqito.helper import kp_norm
-from toqito.matrix_props import is_hermitian
+from toqito.matrix_props import is_hermitian, kp_norm
 from toqito.perms import swap, symmetric_projection
 from toqito.state_ops.schmidt_decomposition import schmidt_decomposition
 from toqito.state_props.schmidt_rank import schmidt_rank