Merge pull request #199 from jhlegarreta/AddPositiveDefiniteCheckUtil

ENH: Add positive definite matrix check util method

docs/developers.rst

@@ -32,6 +32,7 @@ Information on specific functions, classes, and methods.
    api/eddymotion.data
    api/eddymotion.data.dmri
    api/eddymotion.estimator
+   api/eddymotion.math
    api/eddymotion.model
    api/eddymotion.utils
    api/eddymotion.viz

src/eddymotion/math/tests/test_utils.py

@@ -0,0 +1,33 @@
+# emacs: -*- mode: python; py-indent-offset: 4; indent-tabs-mode: nil -*-
+# vi: set ft=python sts=4 ts=4 sw=4 et:
+#
+# Copyright 2024 The NiPreps Developers <[email protected]>
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# We support and encourage derived works from this project, please read
+# about our expectations at
+#
+#     https://www.nipreps.org/community/licensing/
+#
+import numpy as np
+
+from eddymotion.math.utils import is_positive_definite
+
+
+def test_is_positive_definite():
+    matrix = np.array([[4, 1, 2], [1, 3, 1], [2, 1, 5]])
+    assert is_positive_definite(matrix)
+
+    matrix = np.array([[4, 1, 2], [1, -3, 1], [2, 1, 5]])
+    assert not is_positive_definite(matrix)

src/eddymotion/math/utils.py

@@ -0,0 +1,45 @@
+# emacs: -*- mode: python; py-indent-offset: 4; indent-tabs-mode: nil -*-
+# vi: set ft=python sts=4 ts=4 sw=4 et:
+#
+# Copyright 2024 The NiPreps Developers <[email protected]>
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY kIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# We support and encourage derived works from this project, please read
+# about our expectations at
+#
+#     https://www.nipreps.org/community/licensing/
+#
+import numpy as np
+
+
+def is_positive_definite(matrix):
+    """Check whether the given matrix is positive definite. Any positive
+    definite matrix can be decomposed as the product of a lower triangular
+    matrix and its conjugate transpose by performing the Cholesky decomposition.
+    Parameters
+    ----------
+    matrix : np.ndarray
+        The matrix to check.
+    Returns
+    -------
+    True is the matrix is positive definite; False otherwise
+    """
+
+    try:
+        # Attempt Cholesky decomposition
+        np.linalg.cholesky(matrix)
+        return True
+    except np.linalg.LinAlgError:
+        # Matrix is not positive definite
+        return False