From 41d0a4018e9e6783d725fc9c128f407425feba5c Mon Sep 17 00:00:00 2001
From: mchikyt3 <mchikyt3@gmail.com>
Date: Mon, 22 May 2023 14:38:48 +0100
Subject: [PATCH 01/29] BUG Fix initializing `precisions_cholesky_` from
 `precisions_init`

---
 sklearn/mixture/_gaussian_mixture.py          | 18 +++++--
 .../mixture/tests/test_gaussian_mixture.py    | 50 +++++++++++++++++++
 2 files changed, 65 insertions(+), 3 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index e0b630f37c163..a3699719b4a1e 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -726,15 +726,27 @@ def _initialize(self, X, resp):
                 covariances, self.covariance_type
             )
         elif self.covariance_type == "full":
+            n_features = self.precisions_init.shape[-1]
+            exchange_matrix = np.fliplr(np.eye(n_features))
             self.precisions_cholesky_ = np.array(
                 [
-                    linalg.cholesky(prec_init, lower=True)
+                    exchange_matrix
+                    @ linalg.cholesky(
+                        exchange_matrix @ prec_init @ exchange_matrix, lower=True
+                    )
+                    @ exchange_matrix
                     for prec_init in self.precisions_init
                 ]
             )
         elif self.covariance_type == "tied":
-            self.precisions_cholesky_ = linalg.cholesky(
-                self.precisions_init, lower=True
+            n_features = self.precisions_init.shape[-1]
+            exchange_matrix = np.fliplr(np.eye(n_features))
+            self.precisions_cholesky_ = (
+                exchange_matrix
+                @ linalg.cholesky(
+                    exchange_matrix @ self.precisions_init @ exchange_matrix, lower=True
+                )
+                @ exchange_matrix
             )
         else:
             self.precisions_cholesky_ = np.sqrt(self.precisions_init)
diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index f2d634b3fffe5..cb2e26e99bb9b 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1325,6 +1325,56 @@ def test_gaussian_mixture_precisions_init_diag():
     )
 
 
+def test_gaussian_mixture_precisions_init():
+    def _generate_data(n_samples, n_features, n_components):
+        """Randomly generate samples and responsibilities"""
+        rs = np.random.RandomState(12345)
+        X = rs.random_sample((n_samples, n_features))
+        resp = rs.random_sample((n_samples, n_components))
+        resp /= resp.sum(axis=1)[:, np.newaxis]
+        return X, resp
+
+    def _calculate_precisions(X, resp, covariance_type):
+        """Calculate precision matrix and its Cholesky decomposition"""
+        reg_covar = 1e-6
+        weights, means, covariances = _estimate_gaussian_parameters(
+            X, resp, reg_covar, covariance_type
+        )
+        precisions_cholesky = _compute_precision_cholesky(covariances, covariance_type)
+
+        _, n_components = resp.shape
+        # Instantiate a `GaussianMixture` model in order to use its
+        # `_set_parameters` method to compute `precisions_` from
+        # `precisions_cholesky_`
+        gmm = GaussianMixture(
+            n_components=n_components, covariance_type=covariance_type
+        )
+        params = (weights, means, covariances, precisions_cholesky)
+        # pylint: disable-next=protected-access
+        gmm._set_parameters(params)
+        return gmm.precisions_, gmm.precisions_cholesky_
+
+    X, resp = _generate_data(n_samples=100, n_features=3, n_components=4)
+
+    for covariance_type in ("full", "tied", "diag", "spherical"):
+        # Arrange
+        precisions_init, precisions_cholesky = _calculate_precisions(
+            X, resp, covariance_type
+        )
+        desired_precisions_cholesky = precisions_cholesky
+
+        # Act
+        gmm = GaussianMixture(
+            covariance_type=covariance_type, precisions_init=precisions_init
+        )
+        # pylint: disable-next=protected-access
+        gmm._initialize(X, resp)
+        actual_precisions_cholesky = gmm.precisions_cholesky_
+
+        # Assert
+        assert_allclose(actual_precisions_cholesky, desired_precisions_cholesky)
+
+
 def test_gaussian_mixture_single_component_stable():
     """
     Non-regression test for #23032 ensuring 1-component GM works on only a

From 61e5249380df1a09ee631e08d07e74f13dfcfabe Mon Sep 17 00:00:00 2001
From: mchikyt3 <mchikyt3@gmail.com>
Date: Tue, 23 May 2023 13:26:22 +0100
Subject: [PATCH 02/29] Added change log.

---
 doc/whats_new/v1.3.rst | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index a4cc3fa690474..b3d759852816f 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -51,6 +51,12 @@ random sampling procedures.
   used each time the kernel is called.
   :pr:`26337` by :user:`Yao Xiao <Charlie-XIAO>`.
 
+- |Fix| Initializing :class:`mixture.GaussianMixture` from user-provided
+  `precisions_init` for `covariance_type` of `full` or `tied` was not correct, and has
+  been fixed. Changes have been made in the `_initialize` method of
+  :class:`mixture.GaussianMixture`.
+  :pr:`26416` by :user:`Yang Tao <mchikyt3>`.
+
 Changes impacting all modules
 -----------------------------
 

From 806c7e6c17c5fa7a222b4208c46d2b7829e19a56 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 19:43:33 +0100
Subject: [PATCH 03/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index cb2e26e99bb9b..e6fa5614a92c9 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1358,10 +1358,9 @@ def _calculate_precisions(X, resp, covariance_type):
 
     for covariance_type in ("full", "tied", "diag", "spherical"):
         # Arrange
-        precisions_init, precisions_cholesky = _calculate_precisions(
+        precisions_init, desired_precisions_cholesky = _calculate_precisions(
             X, resp, covariance_type
         )
-        desired_precisions_cholesky = precisions_cholesky
 
         # Act
         gmm = GaussianMixture(

From 3f816ed177f63a2bfc33f4f463531a4344a6a6a9 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 19:43:50 +0100
Subject: [PATCH 04/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index e6fa5614a92c9..30f2aa82bca67 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1350,7 +1350,6 @@ def _calculate_precisions(X, resp, covariance_type):
             n_components=n_components, covariance_type=covariance_type
         )
         params = (weights, means, covariances, precisions_cholesky)
-        # pylint: disable-next=protected-access
         gmm._set_parameters(params)
         return gmm.precisions_, gmm.precisions_cholesky_
 

From 17acaf4cdea13ee71a66dd4f3a0aa5912b0bba4c Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 19:44:14 +0100
Subject: [PATCH 05/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index 30f2aa82bca67..e05777c6d467a 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1344,8 +1344,9 @@ def _calculate_precisions(X, resp, covariance_type):
 
         _, n_components = resp.shape
         # Instantiate a `GaussianMixture` model in order to use its
-        # `_set_parameters` method to compute `precisions_` from
-        # `precisions_cholesky_`
+        # `_set_parameters` method to return the `precisions_` and
+        #  `precisions_cholesky_` from matching the `covariance_type`
+        # provided.
         gmm = GaussianMixture(
             n_components=n_components, covariance_type=covariance_type
         )

From d172fc7726d11e8347ecaf5c5c7f968355a4c13b Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 19:44:44 +0100
Subject: [PATCH 06/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index e05777c6d467a..ee429027c60c3 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1335,7 +1335,9 @@ def _generate_data(n_samples, n_features, n_components):
         return X, resp
 
     def _calculate_precisions(X, resp, covariance_type):
-        """Calculate precision matrix and its Cholesky decomposition"""
+        """Calculate precision matrix of X and its Cholesky decomposition
+        for the given covariance type.
+        """
         reg_covar = 1e-6
         weights, means, covariances = _estimate_gaussian_parameters(
             X, resp, reg_covar, covariance_type

From 4258ee640c7f88c14ac73f4cb01f6ae31e6cad6b Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 19:44:58 +0100
Subject: [PATCH 07/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index ee429027c60c3..ca92ed311d3e7 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1326,6 +1326,7 @@ def test_gaussian_mixture_precisions_init_diag():
 
 
 def test_gaussian_mixture_precisions_init():
+    """Non-regression test for #26415."""
     def _generate_data(n_samples, n_features, n_components):
         """Randomly generate samples and responsibilities"""
         rs = np.random.RandomState(12345)

From d1a770557702ade9c1e80f135eee3ee6f9d12401 Mon Sep 17 00:00:00 2001
From: mchikyt3 <mchikyt3@gmail.com>
Date: Thu, 1 Jun 2023 23:21:33 +0100
Subject: [PATCH 08/29] Used `np.flipup` and `np.fliplr` to permutate precision
 array. Parameterized `COVARIANCE_TYPE`.

---
 sklearn/mixture/_gaussian_mixture.py          | 22 ++++++++-----------
 .../mixture/tests/test_gaussian_mixture.py    |  8 +------
 2 files changed, 10 insertions(+), 20 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index a3699719b4a1e..e67af5e021471 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -726,27 +726,23 @@ def _initialize(self, X, resp):
                 covariances, self.covariance_type
             )
         elif self.covariance_type == "full":
-            n_features = self.precisions_init.shape[-1]
-            exchange_matrix = np.fliplr(np.eye(n_features))
             self.precisions_cholesky_ = np.array(
                 [
-                    exchange_matrix
-                    @ linalg.cholesky(
-                        exchange_matrix @ prec_init @ exchange_matrix, lower=True
+                    np.flipud(
+                        np.fliplr(
+                            linalg.cholesky(np.flipud(np.fliplr(prec_init)), lower=True)
+                        )
                     )
-                    @ exchange_matrix
                     for prec_init in self.precisions_init
                 ]
             )
         elif self.covariance_type == "tied":
-            n_features = self.precisions_init.shape[-1]
-            exchange_matrix = np.fliplr(np.eye(n_features))
-            self.precisions_cholesky_ = (
-                exchange_matrix
-                @ linalg.cholesky(
-                    exchange_matrix @ self.precisions_init @ exchange_matrix, lower=True
+            self.precisions_cholesky_ = np.flipud(
+                np.fliplr(
+                    linalg.cholesky(
+                        np.flipud(np.fliplr(self.precisions_init)), lower=True
+                    )
                 )
-                @ exchange_matrix
             )
         else:
             self.precisions_cholesky_ = np.sqrt(self.precisions_init)
diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index ca92ed311d3e7..03dafa4d6e327 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1359,21 +1359,15 @@ def _calculate_precisions(X, resp, covariance_type):
 
     X, resp = _generate_data(n_samples=100, n_features=3, n_components=4)
 
-    for covariance_type in ("full", "tied", "diag", "spherical"):
-        # Arrange
+    for covariance_type in COVARIANCE_TYPE:
         precisions_init, desired_precisions_cholesky = _calculate_precisions(
             X, resp, covariance_type
         )
-
-        # Act
         gmm = GaussianMixture(
             covariance_type=covariance_type, precisions_init=precisions_init
         )
-        # pylint: disable-next=protected-access
         gmm._initialize(X, resp)
         actual_precisions_cholesky = gmm.precisions_cholesky_
-
-        # Assert
         assert_allclose(actual_precisions_cholesky, desired_precisions_cholesky)
 
 

From 49e5e6c2e5618f3bad54bd3ea7d4275116af4587 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 1 Jun 2023 23:29:29 +0100
Subject: [PATCH 09/29] Update doc/whats_new/v1.3.rst

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 doc/whats_new/v1.3.rst | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index 30061e1e1623e..feb981e580b93 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -51,10 +51,9 @@ random sampling procedures.
   used each time the kernel is called.
   :pr:`26337` by :user:`Yao Xiao <Charlie-XIAO>`.
 
-- |Fix| Initializing :class:`mixture.GaussianMixture` from user-provided
-  `precisions_init` for `covariance_type` of `full` or `tied` was not correct, and has
-  been fixed. Changes have been made in the `_initialize` method of
-  :class:`mixture.GaussianMixture`.
+- |Fix| The initialization :class:`mixture.GaussianMixture` from user-provided
+  `precisions_init` for `covariance_type` of `full` or `tied` was not correct,
+  and has been fixed.
   :pr:`26416` by :user:`Yang Tao <mchikyt3>`.
 
 Changes impacting all modules

From d3b9fd7d69205f0932bad5a4739498a0dd07df8a Mon Sep 17 00:00:00 2001
From: mchikyt3 <mchikyt3@gmail.com>
Date: Thu, 1 Jun 2023 23:40:13 +0100
Subject: [PATCH 10/29] Typo fixed.

---
 doc/whats_new/v1.3.rst                         | 2 +-
 sklearn/mixture/tests/test_gaussian_mixture.py | 1 +
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index feb981e580b93..30c9468136519 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -51,7 +51,7 @@ random sampling procedures.
   used each time the kernel is called.
   :pr:`26337` by :user:`Yao Xiao <Charlie-XIAO>`.
 
-- |Fix| The initialization :class:`mixture.GaussianMixture` from user-provided
+- |Fix| The initialization of :class:`mixture.GaussianMixture` from user-provided
   `precisions_init` for `covariance_type` of `full` or `tied` was not correct,
   and has been fixed.
   :pr:`26416` by :user:`Yang Tao <mchikyt3>`.
diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index 03dafa4d6e327..5cee0c7a92a82 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1327,6 +1327,7 @@ def test_gaussian_mixture_precisions_init_diag():
 
 def test_gaussian_mixture_precisions_init():
     """Non-regression test for #26415."""
+
     def _generate_data(n_samples, n_features, n_components):
         """Randomly generate samples and responsibilities"""
         rs = np.random.RandomState(12345)

From d75c111dea5f057cc63a0e7b01bc247ba7088cc7 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Fri, 2 Jun 2023 10:45:33 +0100
Subject: [PATCH 11/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index 5cee0c7a92a82..e82cfd26ea837 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1325,7 +1325,8 @@ def test_gaussian_mixture_precisions_init_diag():
     )
 
 
-def test_gaussian_mixture_precisions_init():
+@pytest.mark.parametrize("covariance_type", COVARIANCE_TYPE)
+def test_gaussian_mixture_precisions_init(covariance_type):
     """Non-regression test for #26415."""
 
     def _generate_data(n_samples, n_features, n_components):

From 224fe65fc391ae27717bd15b2724cf9bbccab5ec Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Fri, 2 Jun 2023 10:45:46 +0100
Subject: [PATCH 12/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 .../mixture/tests/test_gaussian_mixture.py    | 19 +++++++++----------
 1 file changed, 9 insertions(+), 10 deletions(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index e82cfd26ea837..e26a42e0f49ab 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1361,16 +1361,15 @@ def _calculate_precisions(X, resp, covariance_type):
 
     X, resp = _generate_data(n_samples=100, n_features=3, n_components=4)
 
-    for covariance_type in COVARIANCE_TYPE:
-        precisions_init, desired_precisions_cholesky = _calculate_precisions(
-            X, resp, covariance_type
-        )
-        gmm = GaussianMixture(
-            covariance_type=covariance_type, precisions_init=precisions_init
-        )
-        gmm._initialize(X, resp)
-        actual_precisions_cholesky = gmm.precisions_cholesky_
-        assert_allclose(actual_precisions_cholesky, desired_precisions_cholesky)
+    precisions_init, desired_precisions_cholesky = _calculate_precisions(
+        X, resp, covariance_type
+    )
+    gmm = GaussianMixture(
+        covariance_type=covariance_type, precisions_init=precisions_init
+    )
+    gmm._initialize(X, resp)
+    actual_precisions_cholesky = gmm.precisions_cholesky_
+    assert_allclose(actual_precisions_cholesky, desired_precisions_cholesky)
 
 
 def test_gaussian_mixture_single_component_stable():

From eba683ed7fe403b6463a3327f766a0b112f6ceea Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Fri, 2 Jun 2023 11:01:39 +0100
Subject: [PATCH 13/29] Update doc/whats_new/v1.3.rst

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 doc/whats_new/v1.3.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index 30c9468136519..0347636ca0aac 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -51,7 +51,7 @@ random sampling procedures.
   used each time the kernel is called.
   :pr:`26337` by :user:`Yao Xiao <Charlie-XIAO>`.
 
-- |Fix| The initialization of :class:`mixture.GaussianMixture` from user-provided
+- |FIX| The initialization of :class:`mixture.GaussianMixture` from user-provided
   `precisions_init` for `covariance_type` of `full` or `tied` was not correct,
   and has been fixed.
   :pr:`26416` by :user:`Yang Tao <mchikyt3>`.

From 5bd554a9447cbf133fe59d046d685f49feb411dd Mon Sep 17 00:00:00 2001
From: Tao Yang SLUK <yang.tao2@mt.com>
Date: Fri, 2 Jun 2023 11:03:31 +0100
Subject: [PATCH 14/29] Moved two helper functions to the file scope, and added
 a `seed` parameter to `_generate_data`.

---
 .../mixture/tests/test_gaussian_mixture.py    | 62 +++++++++----------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index e26a42e0f49ab..ec9c5264e072a 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1325,41 +1325,41 @@ def test_gaussian_mixture_precisions_init_diag():
     )
 
 
+def _generate_data(seed, n_samples, n_features, n_components):
+    """Randomly generate samples and responsibilities."""
+    rs = np.random.RandomState(seed)
+    X = rs.random_sample((n_samples, n_features))
+    resp = rs.random_sample((n_samples, n_components))
+    resp /= resp.sum(axis=1)[:, np.newaxis]
+    return X, resp
+
+
+def _calculate_precisions(X, resp, covariance_type):
+    """Calculate precision matrix of X and its Cholesky decomposition
+    for the given covariance type.
+    """
+    reg_covar = 1e-6
+    weights, means, covariances = _estimate_gaussian_parameters(
+        X, resp, reg_covar, covariance_type
+    )
+    precisions_cholesky = _compute_precision_cholesky(covariances, covariance_type)
+
+    _, n_components = resp.shape
+    # Instantiate a `GaussianMixture` model in order to use its
+    # `_set_parameters` method to return the `precisions_` and
+    #  `precisions_cholesky_` from matching the `covariance_type`
+    # provided.
+    gmm = GaussianMixture(n_components=n_components, covariance_type=covariance_type)
+    params = (weights, means, covariances, precisions_cholesky)
+    gmm._set_parameters(params)
+    return gmm.precisions_, gmm.precisions_cholesky_
+
+
 @pytest.mark.parametrize("covariance_type", COVARIANCE_TYPE)
 def test_gaussian_mixture_precisions_init(covariance_type):
     """Non-regression test for #26415."""
 
-    def _generate_data(n_samples, n_features, n_components):
-        """Randomly generate samples and responsibilities"""
-        rs = np.random.RandomState(12345)
-        X = rs.random_sample((n_samples, n_features))
-        resp = rs.random_sample((n_samples, n_components))
-        resp /= resp.sum(axis=1)[:, np.newaxis]
-        return X, resp
-
-    def _calculate_precisions(X, resp, covariance_type):
-        """Calculate precision matrix of X and its Cholesky decomposition
-        for the given covariance type.
-        """
-        reg_covar = 1e-6
-        weights, means, covariances = _estimate_gaussian_parameters(
-            X, resp, reg_covar, covariance_type
-        )
-        precisions_cholesky = _compute_precision_cholesky(covariances, covariance_type)
-
-        _, n_components = resp.shape
-        # Instantiate a `GaussianMixture` model in order to use its
-        # `_set_parameters` method to return the `precisions_` and
-        #  `precisions_cholesky_` from matching the `covariance_type`
-        # provided.
-        gmm = GaussianMixture(
-            n_components=n_components, covariance_type=covariance_type
-        )
-        params = (weights, means, covariances, precisions_cholesky)
-        gmm._set_parameters(params)
-        return gmm.precisions_, gmm.precisions_cholesky_
-
-    X, resp = _generate_data(n_samples=100, n_features=3, n_components=4)
+    X, resp = _generate_data(seed=12345, n_samples=100, n_features=3, n_components=4)
 
     precisions_init, desired_precisions_cholesky = _calculate_precisions(
         X, resp, covariance_type

From bdf1277b73e456d7c8b6207f1f7c0b22e7240b26 Mon Sep 17 00:00:00 2001
From: Tao Yang SLUK <yang.tao2@mt.com>
Date: Fri, 2 Jun 2023 15:44:24 +0100
Subject: [PATCH 15/29] Refactored the permutation of matrix and computation of
 `precision_cholesky` into two functions.

---
 sklearn/mixture/_gaussian_mixture.py | 77 ++++++++++++++++++++--------
 1 file changed, 57 insertions(+), 20 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index e67af5e021471..6f34cb71d7bf0 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -350,6 +350,60 @@ def _compute_precision_cholesky(covariances, covariance_type):
     return precisions_chol
 
 
+def _flipudlr(array):
+    """Reverse the rows and columns of an array."""
+    return np.flipud(np.fliplr(array))
+
+
+def _compute_precision_cholesky_from_precision(precisions, covariance_type):
+    """Compute the Cholesky decomposition of the precisions using precisions.
+
+    As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
+    an upper-triangular matrix for each Gaussian components, which can expressed as the
+    $UU^T$ factorization of the precision matrix for each Gaussian component, where $U$
+    is an upper-triangular matrix.
+
+    In order to use the Cholesky decomposition to get $UU^T$, the precision matrix
+    $\Lambda$ needs to be permutated such that its rows and columns are reversed, which
+    can be done by a similarity transformation with an exchange matrix $J$, where the 1
+    elements reside on the anti-diagonal and all other elements are 0. In particular,
+    the Cholesky decomposition of the transformed precision matrix is $J\Lambda J=LL^T$,
+    where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$ and $J=J^{-1}=J^T$,
+    the `precisions_cholesky_` for each Gaussian components can be expressed as $JLJ$.
+
+    Refer to #26415 for more information.
+
+    Parameters
+    ----------
+    precisions : array-like
+        The precision matrix of the current components.
+        The shape depends of the covariance_type.
+
+    covariance_type : {'full', 'tied', 'diag', 'spherical'}
+        The type of precision matrices.
+
+    Returns
+    -------
+    precisions_cholesky : array-like
+        The cholesky decomposition of sample precisions of the current
+        components. The shape depends of the covariance_type.
+    """
+    if covariance_type == "full":
+        precisions_cholesky = np.array(
+            [
+                _flipudlr(linalg.cholesky(_flipudlr(precision), lower=True))
+                for precision in precisions
+            ]
+        )
+    elif covariance_type == "tied":
+        precisions_cholesky = _flipudlr(
+            linalg.cholesky(_flipudlr(precisions), lower=True)
+        )
+    else:
+        precisions_cholesky = np.sqrt(precisions)
+    return precisions_cholesky
+
+
 ###############################################################################
 # Gaussian mixture probability estimators
 def _compute_log_det_cholesky(matrix_chol, covariance_type, n_features):
@@ -725,27 +779,10 @@ def _initialize(self, X, resp):
             self.precisions_cholesky_ = _compute_precision_cholesky(
                 covariances, self.covariance_type
             )
-        elif self.covariance_type == "full":
-            self.precisions_cholesky_ = np.array(
-                [
-                    np.flipud(
-                        np.fliplr(
-                            linalg.cholesky(np.flipud(np.fliplr(prec_init)), lower=True)
-                        )
-                    )
-                    for prec_init in self.precisions_init
-                ]
-            )
-        elif self.covariance_type == "tied":
-            self.precisions_cholesky_ = np.flipud(
-                np.fliplr(
-                    linalg.cholesky(
-                        np.flipud(np.fliplr(self.precisions_init)), lower=True
-                    )
-                )
-            )
         else:
-            self.precisions_cholesky_ = np.sqrt(self.precisions_init)
+            self.precisions_cholesky_ = _compute_precision_cholesky_from_precision(
+                self.precisions_init, self.covariance_type
+            )
 
     def _m_step(self, X, log_resp):
         """M step.

From c2ab97904e4e658221dd76121c4497e74efd64a9 Mon Sep 17 00:00:00 2001
From: Tao Yang SLUK <yang.tao2@mt.com>
Date: Fri, 2 Jun 2023 15:54:49 +0100
Subject: [PATCH 16/29] Typo fixed.

---
 sklearn/mixture/_gaussian_mixture.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 6f34cb71d7bf0..aac69d83872f6 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -359,9 +359,9 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
     """Compute the Cholesky decomposition of the precisions using precisions.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
-    an upper-triangular matrix for each Gaussian components, which can expressed as the
-    $UU^T$ factorization of the precision matrix for each Gaussian component, where $U$
-    is an upper-triangular matrix.
+    an upper-triangular matrix for each Gaussian components, which can be expressed as
+    the $UU^T$ factorization of the precision matrix for each Gaussian component, where
+    $U$ is an upper-triangular matrix.
 
     In order to use the Cholesky decomposition to get $UU^T$, the precision matrix
     $\Lambda$ needs to be permutated such that its rows and columns are reversed, which

From 0e2c14f684dae76d6e5553dc65d1bfd5d0415d9d Mon Sep 17 00:00:00 2001
From: Tao Yang SLUK <yang.tao2@mt.com>
Date: Fri, 2 Jun 2023 20:45:02 +0100
Subject: [PATCH 17/29] Typo fixed.

---
 sklearn/mixture/_gaussian_mixture.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index aac69d83872f6..b7342ae74861c 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -356,7 +356,7 @@ def _flipudlr(array):
 
 
 def _compute_precision_cholesky_from_precision(precisions, covariance_type):
-    """Compute the Cholesky decomposition of the precisions using precisions.
+    r"""Compute the Cholesky decomposition of the precisions using precisions.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
     an upper-triangular matrix for each Gaussian components, which can be expressed as
@@ -371,7 +371,7 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
     where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$ and $J=J^{-1}=J^T$,
     the `precisions_cholesky_` for each Gaussian components can be expressed as $JLJ$.
 
-    Refer to #26415 for more information.
+    Refer to #26415 for details.
 
     Parameters
     ----------

From a090dc3a87bd62932d2dcdf63fd21fee54fa6026 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Sat, 3 Jun 2023 10:26:31 +0100
Subject: [PATCH 18/29] Update doc/whats_new/v1.3.rst

Co-authored-by: Julien Jerphanion <git@jjerphan.xyz>
---
 doc/whats_new/v1.3.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index 0f674abb30370..414fd90565dfe 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -51,7 +51,7 @@ random sampling procedures.
   used each time the kernel is called.
   :pr:`26337` by :user:`Yao Xiao <Charlie-XIAO>`.
 
-- |FIX| The initialization of :class:`mixture.GaussianMixture` from user-provided
+- |Fix| The initialization of :class:`mixture.GaussianMixture` from user-provided
   `precisions_init` for `covariance_type` of `full` or `tied` was not correct,
   and has been fixed.
   :pr:`26416` by :user:`Yang Tao <mchikyt3>`.

From 8d9f5fe3287432f7d13ae1796e76acbe895bbbef Mon Sep 17 00:00:00 2001
From: mchikyt3 <mchikyt3@gmail.com>
Date: Tue, 11 Jul 2023 15:47:24 +0100
Subject: [PATCH 19/29] Added change log.

---
 doc/whats_new/v1.4.rst | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/doc/whats_new/v1.4.rst b/doc/whats_new/v1.4.rst
index 4ba357c52d136..61df2297ace1c 100644
--- a/doc/whats_new/v1.4.rst
+++ b/doc/whats_new/v1.4.rst
@@ -19,6 +19,11 @@ parameters, may produce different models from the previous version. This often
 occurs due to changes in the modelling logic (bug fixes or enhancements), or in
 random sampling procedures.
 
+- |Fix| The initialization of :class:`mixture.GaussianMixture` from user-provided
+  `precisions_init` for `covariance_type` of `full` or `tied` was not correct,
+  and has been fixed.
+  :pr:`26416` by :user:`Yang Tao <mchikyt3>`.
+
 Changes impacting all modules
 -----------------------------
 

From a8a2ab74dd4a564d0219835f1a9b7e70d06c0a4b Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:18 +0100
Subject: [PATCH 20/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 75fa8aff58196..738c6669ab198 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -375,7 +375,7 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
     ----------
     precisions : array-like
         The precision matrix of the current components.
-        The shape depends of the covariance_type.
+        The shape depends on the covariance_type.
 
     covariance_type : {'full', 'tied', 'diag', 'spherical'}
         The type of precision matrices.

From ead1671a79ffd20372e45e284378575499b424b8 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:31 +0100
Subject: [PATCH 21/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 738c6669ab198..7f16250fc0cc4 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -354,7 +354,7 @@ def _flipudlr(array):
 
 
 def _compute_precision_cholesky_from_precision(precisions, covariance_type):
-    r"""Compute the Cholesky decomposition of the precisions using precisions.
+    r"""Compute the Cholesky decomposition of the specified precisions using the precisions themselves.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
     an upper-triangular matrix for each Gaussian components, which can be expressed as

From 1e1f8d1e78132964eab72775109b5dc5020f365c Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:38 +0100
Subject: [PATCH 22/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 7f16250fc0cc4..91988935e1945 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -357,7 +357,7 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
     r"""Compute the Cholesky decomposition of the specified precisions using the precisions themselves.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
-    an upper-triangular matrix for each Gaussian components, which can be expressed as
+    an upper-triangular matrix for each Gaussian component, which can be expressed as
     the $UU^T$ factorization of the precision matrix for each Gaussian component, where
     $U$ is an upper-triangular matrix.
 

From 8d38aab62c5b5657ce7d7d824767f98143656579 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:46 +0100
Subject: [PATCH 23/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 91988935e1945..eaaea3a17aa8a 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -363,7 +363,7 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
 
     In order to use the Cholesky decomposition to get $UU^T$, the precision matrix
     $\Lambda$ needs to be permutated such that its rows and columns are reversed, which
-    can be done by a similarity transformation with an exchange matrix $J$, where the 1
+    can be done by applying a similarity transformation with an exchange matrix $J$, where the 1
     elements reside on the anti-diagonal and all other elements are 0. In particular,
     the Cholesky decomposition of the transformed precision matrix is $J\Lambda J=LL^T$,
     where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$ and $J=J^{-1}=J^T$,

From e8cbb9830211568b40ef08605ac7cd851e614241 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:52 +0100
Subject: [PATCH 24/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index eaaea3a17aa8a..b044124ba5a97 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -384,7 +384,7 @@ def _compute_precision_cholesky_from_precision(precisions, covariance_type):
     -------
     precisions_cholesky : array-like
         The cholesky decomposition of sample precisions of the current
-        components. The shape depends of the covariance_type.
+        components. The shape depends on the covariance_type.
     """
     if covariance_type == "full":
         precisions_cholesky = np.array(

From f841414ae8796ff3ae10c6d8200e085b15e87959 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:56:58 +0100
Subject: [PATCH 25/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index b044124ba5a97..aeb850cbec5e6 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -778,7 +778,7 @@ def _initialize(self, X, resp):
                 covariances, self.covariance_type
             )
         else:
-            self.precisions_cholesky_ = _compute_precision_cholesky_from_precision(
+            self.precisions_cholesky_ = _compute_precision_cholesky_from_precisions(
                 self.precisions_init, self.covariance_type
             )
 

From 4841f905f1d2e627db1e38fc231f6e0d08ede30d Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:57:07 +0100
Subject: [PATCH 26/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index aeb850cbec5e6..bd3e121b3d4c9 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -353,7 +353,7 @@ def _flipudlr(array):
     return np.flipud(np.fliplr(array))
 
 
-def _compute_precision_cholesky_from_precision(precisions, covariance_type):
+def _compute_precision_cholesky_from_precisions(precisions, covariance_type):
     r"""Compute the Cholesky decomposition of the specified precisions using the precisions themselves.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is

From 521d4df904e545a21ba8f1290f0472099b21d3c7 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Wed, 19 Jul 2023 19:57:13 +0100
Subject: [PATCH 27/29] Update sklearn/mixture/_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/_gaussian_mixture.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index bd3e121b3d4c9..25ee65b177cc2 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -367,7 +367,7 @@ def _compute_precision_cholesky_from_precisions(precisions, covariance_type):
     elements reside on the anti-diagonal and all other elements are 0. In particular,
     the Cholesky decomposition of the transformed precision matrix is $J\Lambda J=LL^T$,
     where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$ and $J=J^{-1}=J^T$,
-    the `precisions_cholesky_` for each Gaussian components can be expressed as $JLJ$.
+    the `precisions_cholesky_` for each Gaussian component can be expressed as $JLJ$.
 
     Refer to #26415 for details.
 

From e07130de85436346bf7526a273eabcb6b25afefe Mon Sep 17 00:00:00 2001
From: Tao Yang SLUK <yang.tao2@mt.com>
Date: Wed, 19 Jul 2023 20:10:05 +0100
Subject: [PATCH 28/29] Fixed long lines in the docstring.

---
 sklearn/mixture/_gaussian_mixture.py | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 25ee65b177cc2..9fcc791032c48 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -354,7 +354,7 @@ def _flipudlr(array):
 
 
 def _compute_precision_cholesky_from_precisions(precisions, covariance_type):
-    r"""Compute the Cholesky decomposition of the specified precisions using the precisions themselves.
+    r"""Compute the Cholesky decomposition of precisions using precisions themselves.
 
     As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
     an upper-triangular matrix for each Gaussian component, which can be expressed as
@@ -363,11 +363,12 @@ def _compute_precision_cholesky_from_precisions(precisions, covariance_type):
 
     In order to use the Cholesky decomposition to get $UU^T$, the precision matrix
     $\Lambda$ needs to be permutated such that its rows and columns are reversed, which
-    can be done by applying a similarity transformation with an exchange matrix $J$, where the 1
-    elements reside on the anti-diagonal and all other elements are 0. In particular,
-    the Cholesky decomposition of the transformed precision matrix is $J\Lambda J=LL^T$,
-    where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$ and $J=J^{-1}=J^T$,
-    the `precisions_cholesky_` for each Gaussian component can be expressed as $JLJ$.
+    can be done by applying a similarity transformation with an exchange matrix $J$,
+    where the 1 elements reside on the anti-diagonal and all other elements are 0. In
+    particular, the Cholesky decomposition of the transformed precision matrix is
+    $J\Lambda J=LL^T$, where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$
+    and $J=J^{-1}=J^T$, the `precisions_cholesky_` for each Gaussian component can be
+    expressed as $JLJ$.
 
     Refer to #26415 for details.
 

From 36615aef6bffbf62b4b1649e18c591563725ce87 Mon Sep 17 00:00:00 2001
From: Yang Tao <56955779+mchikyt3@users.noreply.github.com>
Date: Thu, 20 Jul 2023 10:26:51 +0100
Subject: [PATCH 29/29] Update sklearn/mixture/tests/test_gaussian_mixture.py

Co-authored-by: Omar Salman <omar.salman@arbisoft.com>
---
 sklearn/mixture/tests/test_gaussian_mixture.py | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index 7b162a4f3844e..2f39033faed6b 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1357,10 +1357,15 @@ def _calculate_precisions(X, resp, covariance_type):
 
 
 @pytest.mark.parametrize("covariance_type", COVARIANCE_TYPE)
-def test_gaussian_mixture_precisions_init(covariance_type):
+def test_gaussian_mixture_precisions_init(covariance_type, global_random_seed):
     """Non-regression test for #26415."""
 
-    X, resp = _generate_data(seed=12345, n_samples=100, n_features=3, n_components=4)
+    X, resp = _generate_data(
+        seed=global_random_seed,
+        n_samples=100,
+        n_features=3,
+        n_components=4,
+    )
 
     precisions_init, desired_precisions_cholesky = _calculate_precisions(
         X, resp, covariance_type