From af7be1722a20ba50630153b57d7c0eb55884ed39 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:36:34 +0200
Subject: [PATCH 01/10] hartmann

---
 src/hyperactive/experiment/toy/__init__.py  |   2 +
 src/hyperactive/experiment/toy/_hartmann.py | 219 ++++++++++++++++++++
 2 files changed, 221 insertions(+)
 create mode 100644 src/hyperactive/experiment/toy/_hartmann.py

diff --git a/src/hyperactive/experiment/toy/__init__.py b/src/hyperactive/experiment/toy/__init__.py
index 33553866..cbc9cad6 100644
--- a/src/hyperactive/experiment/toy/__init__.py
+++ b/src/hyperactive/experiment/toy/__init__.py
@@ -2,11 +2,13 @@
 
 
 from hyperactive.experiment.toy._ackley import Ackley
+from hyperactive.experiment.toy._hartmann import Hartmann
 from hyperactive.experiment.toy._parabola import Parabola
 from hyperactive.experiment.toy._sphere import Sphere
 
 __all__ = [
     "Ackley",
+    "Hartmann",
     "Parabola",
     "Sphere",
 ]
diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
new file mode 100644
index 00000000..e7472c57
--- /dev/null
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -0,0 +1,219 @@
+"""Hartmann function, common benchmark for optimization algorithms."""
+# copyright: hyperactive developers, MIT License (see LICENSE file)
+
+import numpy as np
+
+from hyperactive.base import BaseExperiment
+
+
+class Hartmann(BaseExperiment):
+    r"""Hartmann function, common benchmark for optimization algorithms.
+
+    The Hartmann function is a non-convex function used to test optimization algorithms.
+    It is defined as:
+
+    .. math::
+
+        f(\mathbf{x}) = - \sum_{i=1}^{4} \alpha_i 
+        \exp \left( - \sum_{j=1}^{6} A_{ij} (x_j - P_{ij})^2 \right),
+        \quad \text{where}
+
+    .. math::
+
+        \alpha = (1.0, \; 1.2, \; 3.0, \; 3.2)^T
+
+    .. math::
+
+        A =
+        \begin{pmatrix}
+        10 & 3 & 17 & 3.50 & 1.7 & 8 \\
+        0.05 & 10 & 17 & 0.1 & 8 & 14 \\
+        3 & 3.5 & 1.7 & 10 & 17 & 8 \\
+        17 & 8 & 0.05 & 10 & 0.1 & 14
+        \end{pmatrix}
+
+    .. math::
+
+        P = 10^{-4} \times
+        \begin{pmatrix}
+        1312 & 1696 & 5569 & 124 & 8283 & 5886 \\
+        2329 & 4135 & 8307 & 3736 & 1004 & 9991 \\
+        2348 & 1451 & 3522 & 2883 & 3047 & 6650 \\
+        4047 & 8828 & 8732 & 5743 & 1091 & 381
+        \end{pmatrix}
+
+    In this function, the constants can be set as parameters,
+    and default to the above values if not specified.
+    The customizable constants are:
+
+    * ``alpha``: the vector of coefficients :math:`\alpha`
+    * ``A``: the matrix :math:`A`
+    * ``P``: the matrix :math:`P`
+
+    The components of the function argument :math:`x`
+    are the input variables of the `score` method,
+    and are set as `x0`, `x1`, ..., `x5` respectively.
+
+    Parameters
+    ----------
+    alpha : 1D array-like of length 4, optional, default=[1.0, 1.2, 3.0, 3.2]
+        Coefficients of the Hartmann function.
+    A : 2D array-like of shape (4, 6), optional, default = as defined above
+        Coefficient matrix of the Hartmann function.
+    P : 2D array-like of shape (4, 6), optional, default = as defined above
+        Parameter matrix of the Hartmann function.
+
+    Example
+    -------
+    >>> from hyperactive.experiment.toy import Hartmann
+    >>> hartmann = Hartmann()
+    >>> params = {"x0": 0.1, "x1": 0.2, "x2": 0.3, "x3": 0.4, "x4": 0.5, "x5": 0.6}
+    >>> score, add_info = hartmann.score(params)
+
+    Quick call without metadata return or dictionary:
+    >>> score = hartmann(x0=0.1, x1=0.2, x2=0.3, x3=0.4, x4=0.5, x5=0.6)
+    """  # noqa: E501
+
+    _tags = {
+        "property:randomness": "deterministic",  # random or deterministic
+        # if deterministic, two calls of score will result in the same value
+        # random = two calls may result in different values; same as "stochastic"
+        "property:higher_or_lower_is_better": "lower",
+        # values are "higher", "lower", "mixed"
+        # whether higher or lower scores are better
+    }
+
+    def __init__(self, alpha=None, A=None, P=None):
+        self.alpha = alpha
+        self.A = A
+        self.P = P
+
+        super().__init__()
+
+        if self.alpha is None:
+            self._alpha = np.array([1.0, 1.2, 3.0, 3.2])
+        else:
+            self._alpha = np.asarray(self.alpha)
+
+        if self.A is None:
+            self._A = np.array([
+                [10, 3, 17, 3.50, 1.7, 8],
+                [0.05, 10, 17, 0.1, 8, 14],
+                [3, 3.5, 1.7, 10, 17, 8],
+                [17, 8, 0.05, 10, 0.1, 14]
+            ])
+        else:
+            self._A = np.asarray(self.A)
+
+        if self.P is None:
+            self._P = 1e-4 * np.array([
+                [1312, 1696, 5569, 124, 8283, 5886],
+                [2329, 4135, 8307, 3736, 1004, 9991],
+                [2348, 1451, 3522, 2883, 3047, 6650],
+                [4047, 8828, 8732, 5743, 1091, 381]
+            ])
+        else:
+            self._P = np.asarray(self.P)
+        
+    def _paramnames(self):
+        return [f"x{i}" for i in range(6)]
+
+    def _evaluate(self, params):
+        """Evaluate the parameters.
+
+        Parameters
+        ----------
+        params : dict with string keys
+            Parameters to evaluate.
+
+        Returns
+        -------
+        float
+            The value of the parameters as per evaluation.
+        dict
+            Additional metadata about the search.
+        """
+        x = np.array([params[f"x{i}"] for i in range(6)])
+
+        alpha = self._alpha
+        A = self._A
+        P = self._P
+
+        res = -np.sum(alpha * np.exp(-np.sum(A * (np.array(x) - P) ** 2, axis=1)))
+        return res, {}
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the skbase object.
+
+        ``get_test_params`` is a unified interface point to store
+        parameter settings for testing purposes. This function is also
+        used in ``create_test_instance`` and ``create_test_instances_and_names``
+        to construct test instances.
+
+        ``get_test_params`` should return a single ``dict``, or a ``list`` of ``dict``.
+
+        Each ``dict`` is a parameter configuration for testing,
+        and can be used to construct an "interesting" test instance.
+        A call to ``cls(**params)`` should
+        be valid for all dictionaries ``params`` in the return of ``get_test_params``.
+
+        The ``get_test_params`` need not return fixed lists of dictionaries,
+        it can also return dynamic or stochastic parameter settings.
+
+        Parameters
+        ----------
+        parameter_set : str, default="default"
+            Name of the set of test parameters to return, for use in tests. If no
+            special parameters are defined for a value, will return `"default"` set.
+
+        Returns
+        -------
+        params : dict or list of dict, default = {}
+            Parameters to create testing instances of the class
+            Each dict are parameters to construct an "interesting" test instance, i.e.,
+            `MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance.
+            `create_test_instance` uses the first (or only) dictionary in `params`
+        """
+        # default parameters
+        params0 = {}
+        # parameters different from the default
+        params1 = {
+            "alpha": np.array([4.0, 3.2, 2.0, 1.2]),
+            "A": np.array([
+                [42, 3, 17, 3.50, 1.7, 8],
+                [0.05, 10, 17, 0.1, 8, 14],
+                [3, 3.5, 1.7, 33, 17, 8],
+                [17, 8, 0.05, 10, 0.1, 14]
+            ]),
+            "P": np.array([
+                [1312, 196, 5569, 124, 8283, 5886],
+                [2329, 4135, 8307, 3736, 100, 9991],
+                [2348, 1451, 322, 2883, 3047, 6650],
+                [4047, 8828, 8732, 743, 1091, 381]
+            ])
+        }
+        return [params0, params1]
+
+    @classmethod
+    def _get_score_params(self):
+        """Return settings for testing score/evaluate functions. Used in tests only.
+
+        Returns a list, the i-th element should be valid arguments for
+        self.evaluate and self.score, of an instance constructed with
+        self.get_test_params()[i].
+
+        Returns
+        -------
+        list of dict
+            The parameters to be used for scoring.
+        """
+        params = {
+            "x0": 0.1,
+            "x1": 0.2,
+            "x2": 0.3,
+            "x3": 0.4,
+            "x4": 0.5,
+            "x5": 0.6
+        }
+        return [params, params]

From 0508d347506b85136fd8453a5d2e2afa0c246ccc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:45:23 +0200
Subject: [PATCH 02/10] Update _hartmann.py

---
 src/hyperactive/experiment/toy/_hartmann.py | 45 +++++++++++++--------
 1 file changed, 29 insertions(+), 16 deletions(-)

diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index e7472c57..870f4231 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -43,25 +43,30 @@ class Hartmann(BaseExperiment):
         \end{pmatrix}
 
     In this function, the constants can be set as parameters,
-    and default to the above values if not specified.
+    and default to the above values and dimensions if not specified.
     The customizable constants are:
 
-    * ``alpha``: the vector of coefficients :math:`\alpha`
-    * ``A``: the matrix :math:`A`
-    * ``P``: the matrix :math:`P`
+    * ``alpha``: an :math:`m`-vector of coefficients :math:`\alpha`
+    * ``A``: a :math:`(m \times n)` shape matrix :math:`A`
+    * ``P``: a :math:`(m \times n)` position matrix :math:`P`
 
     The components of the function argument :math:`x`
     are the input variables of the `score` method,
-    and are set as `x0`, `x1`, ..., `x5` respectively.
+    and are set as `x0`, `x1`, ..., `x[n-1]` respectively.
 
     Parameters
     ----------
-    alpha : 1D array-like of length 4, optional, default=[1.0, 1.2, 3.0, 3.2]
+    alpha : 1D array-like of length m, optional, default=[1.0, 1.2, 3.0, 3.2]
         Coefficients of the Hartmann function.
-    A : 2D array-like of shape (4, 6), optional, default = as defined above
-        Coefficient matrix of the Hartmann function.
-    P : 2D array-like of shape (4, 6), optional, default = as defined above
-        Parameter matrix of the Hartmann function.
+    A : 2D array-like of shape (m, n), optional, default = as defined above
+        Shape matrix of the Hartmann function.
+    P : 2D array-like of shape (m, n), optional, default = as defined above
+        Position matrix of the Hartmann function.
+
+    References
+    ----------
+    [1] Hartmann, J.L. (1972). "Some Experiments in Global Optimization".
+        Naval Postgraduate School, Monterey, CA.
 
     Example
     -------
@@ -93,7 +98,7 @@ def __init__(self, alpha=None, A=None, P=None):
         if self.alpha is None:
             self._alpha = np.array([1.0, 1.2, 3.0, 3.2])
         else:
-            self._alpha = np.asarray(self.alpha)
+            self._alpha = np.asarray(alpha)
 
         if self.A is None:
             self._A = np.array([
@@ -103,7 +108,7 @@ def __init__(self, alpha=None, A=None, P=None):
                 [17, 8, 0.05, 10, 0.1, 14]
             ])
         else:
-            self._A = np.asarray(self.A)
+            self._A = np.asarray(A)
 
         if self.P is None:
             self._P = 1e-4 * np.array([
@@ -113,10 +118,11 @@ def __init__(self, alpha=None, A=None, P=None):
                 [4047, 8828, 8732, 5743, 1091, 381]
             ])
         else:
-            self._P = np.asarray(self.P)
+            self._P = np.asarray(P)
         
     def _paramnames(self):
-        return [f"x{i}" for i in range(6)]
+        n = self._A.shape[1]  # number of dimensions
+        return [f"x{i}" for i in range(n)]
 
     def _evaluate(self, params):
         """Evaluate the parameters.
@@ -193,7 +199,13 @@ def get_test_params(cls, parameter_set="default"):
                 [4047, 8828, 8732, 743, 1091, 381]
             ])
         }
-        return [params0, params1]
+        # different parameters with dimensions 2 x 3
+        params2 = {
+            "alpha": np.array([1.0, 2.0]),
+            "A": np.array([[10, 3, 17], [0.05, 10, 17]]),
+            "P": np.array([[1312, 1696, 5569], [2329, 4135, 8307]])
+        }
+        return [params0, params1, params2]
 
     @classmethod
     def _get_score_params(self):
@@ -216,4 +228,5 @@ def _get_score_params(self):
             "x4": 0.5,
             "x5": 0.6
         }
-        return [params, params]
+        params2 = {"x0": 0.1, "x1": 0.2, "x2": 0.3}
+        return [params, params, params2]

From e01cd64434b99fd73e8d7ae19b7aa0d0a9e9a523 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:55:14 +0200
Subject: [PATCH 03/10] braninhoo

---
 src/hyperactive/experiment/toy/__init__.py    |   2 +
 src/hyperactive/experiment/toy/_branin_hoo.py | 171 ++++++++++++++++++
 2 files changed, 173 insertions(+)
 create mode 100644 src/hyperactive/experiment/toy/_branin_hoo.py

diff --git a/src/hyperactive/experiment/toy/__init__.py b/src/hyperactive/experiment/toy/__init__.py
index cbc9cad6..b9c16855 100644
--- a/src/hyperactive/experiment/toy/__init__.py
+++ b/src/hyperactive/experiment/toy/__init__.py
@@ -2,12 +2,14 @@
 
 
 from hyperactive.experiment.toy._ackley import Ackley
+from hyperactive.experiment.toy._branin_hoo import BraninHoo
 from hyperactive.experiment.toy._hartmann import Hartmann
 from hyperactive.experiment.toy._parabola import Parabola
 from hyperactive.experiment.toy._sphere import Sphere
 
 __all__ = [
     "Ackley",
+    "BraninHoo",
     "Hartmann",
     "Parabola",
     "Sphere",
diff --git a/src/hyperactive/experiment/toy/_branin_hoo.py b/src/hyperactive/experiment/toy/_branin_hoo.py
new file mode 100644
index 00000000..d2a515f3
--- /dev/null
+++ b/src/hyperactive/experiment/toy/_branin_hoo.py
@@ -0,0 +1,171 @@
+"""Branin-Hoo function, common benchmark for optimization algorithms."""
+# copyright: hyperactive developers, MIT License (see LICENSE file)
+
+import numpy as np
+
+from hyperactive.base import BaseExperiment
+
+
+class BraninHoo(BaseExperiment):
+    r"""Branin-Hoo function, common benchmark for optimization algorithms.
+
+    The Branin-Hoo function is a non-convex function used to test optimization
+    algorithms. It is considered on the square domain
+    :math:`x \in [-5, 10], y \in [0, 15]`.
+
+    It has three minima with :math:`f(x^*) = 0.397887` at :math:`x* = (-\pi, 12.275)`,
+    :math:`(\pi, 2.275)`, and :math:`(9.42478, 2.475)`.
+
+    The Branin-Hoo function is defined as:
+
+    .. math::
+
+        f(x, y) = a (y - b x^2 + c x - d)^2 + e (1 - f) \cos(x) + e
+
+    In this function, the six constants can be set as parameters,
+    with default values as defined below.
+
+    Parameters
+    ----------
+    a : float, default=1.0
+        Coefficient of the quartic term.
+    b : float, default=5.1 / (4 * np.pi ** 2)
+        Coefficient of the quadratic term.
+    c : float, default=5 / np.pi
+        Coefficient of the linear term.
+    d : float, default=6.0
+        Constant insie the quartic term.
+    e : float, default=10.0
+        Coefficient of the cosine term and the constant term.
+    f : float, default=1 / (8 * np.pi)
+        Coefficient of the cosine term.
+
+    References
+    ----------
+    [1] Hartmann, J.L. (1972). "Some Experiments in Global Optimization".
+        Naval Postgraduate School, Monterey, CA.
+
+    Example
+    -------
+    >>> from hyperactive.experiment.toy import BraninHoo
+    >>> branin_hoo = BraninHoo()
+    >>> params = {"x": 1.0, "y": 2.0}
+    >>> score, add_info = branin_hoo.score(params)
+
+    Quick call without metadata return or dictionary:
+    >>> score = branin_hoo(x=1.0, y=2.0)
+    """  # noqa: E501
+
+    _tags = {
+        "property:randomness": "deterministic",  # random or deterministic
+        # if deterministic, two calls of score will result in the same value
+        # random = two calls may result in different values; same as "stochastic"
+        "property:higher_or_lower_is_better": "lower",
+        # values are "higher", "lower", "mixed"
+        # whether higher or lower scores are better
+    }
+
+    def __init__(
+        self,
+        a=1.0,
+        b=5.1 / (4 * np.pi ** 2),
+        c=5 / np.pi,
+        d=6.0,
+        e=10.0,
+        f=1 / (8 * np.pi),
+    ):
+    
+        self.a = a
+        self.b = b
+        self.c = c
+        self.d = d
+        self.e = e
+        self.f = f
+
+        super().__init__()
+
+    def _paramnames(self):
+        return ["x", "y"]
+
+    def _evaluate(self, params):
+        """Evaluate the parameters.
+
+        Parameters
+        ----------
+        params : dict with string keys
+            Parameters to evaluate.
+
+        Returns
+        -------
+        float
+            The value of the parameters as per evaluation.
+        dict
+            Additional metadata about the search.
+        """
+        x, y = params["x"], params["y"]
+
+        a = self.a
+        b = self.b
+        c = self.c
+        d = self.d
+        e = self.e
+        f = self.f
+
+        res = a * (y - b * x**2 + c * x - d) ** 2 + e * (1 - f) * np.cos(x)
+        return res, {}
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the skbase object.
+
+        ``get_test_params`` is a unified interface point to store
+        parameter settings for testing purposes. This function is also
+        used in ``create_test_instance`` and ``create_test_instances_and_names``
+        to construct test instances.
+
+        ``get_test_params`` should return a single ``dict``, or a ``list`` of ``dict``.
+
+        Each ``dict`` is a parameter configuration for testing,
+        and can be used to construct an "interesting" test instance.
+        A call to ``cls(**params)`` should
+        be valid for all dictionaries ``params`` in the return of ``get_test_params``.
+
+        The ``get_test_params`` need not return fixed lists of dictionaries,
+        it can also return dynamic or stochastic parameter settings.
+
+        Parameters
+        ----------
+        parameter_set : str, default="default"
+            Name of the set of test parameters to return, for use in tests. If no
+            special parameters are defined for a value, will return `"default"` set.
+
+        Returns
+        -------
+        params : dict or list of dict, default = {}
+            Parameters to create testing instances of the class
+            Each dict are parameters to construct an "interesting" test instance, i.e.,
+            `MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance.
+            `create_test_instance` uses the first (or only) dictionary in `params`
+        """
+        # default parameters
+        params0 = {}
+        # parameters different from the default
+        params1 = {"a": 2.0, "b": 6.0, "c": 4.0, "d": 8.0, "e": 12.0, "f": 1 / 4}
+        return [params0, params1]
+
+    @classmethod
+    def _get_score_params(self):
+        """Return settings for testing score/evaluate functions. Used in tests only.
+
+        Returns a list, the i-th element should be valid arguments for
+        self.evaluate and self.score, of an instance constructed with
+        self.get_test_params()[i].
+
+        Returns
+        -------
+        list of dict
+            The parameters to be used for scoring.
+        """
+        params0 = {"x": 0.0, "y": 0.0}
+        params1 = {"x": 1.0, "y": 2.0}
+        return [params0, params1]

From 61a4d51c9e587f5ec82387e83772b68b660e1e58 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:55:35 +0200
Subject: [PATCH 04/10] Update _hartmann.py

---
 src/hyperactive/experiment/toy/_hartmann.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index 870f4231..49e45932 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -9,8 +9,10 @@
 class Hartmann(BaseExperiment):
     r"""Hartmann function, common benchmark for optimization algorithms.
 
-    The Hartmann function is a non-convex function used to test optimization algorithms.
-    It is defined as:
+    The Hartmann function is a non-convex function used to test optimization algorithms,
+    typically considered on the unit hypercube.
+
+    The Hartmann function is defined as:
 
     .. math::
 

From 9b5381293ea31fb24f15b9564a4dfd05046dfe1d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:57:08 +0200
Subject: [PATCH 05/10] ref

---
 src/hyperactive/experiment/toy/_branin_hoo.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/hyperactive/experiment/toy/_branin_hoo.py b/src/hyperactive/experiment/toy/_branin_hoo.py
index d2a515f3..9e58bd6e 100644
--- a/src/hyperactive/experiment/toy/_branin_hoo.py
+++ b/src/hyperactive/experiment/toy/_branin_hoo.py
@@ -42,8 +42,9 @@ class BraninHoo(BaseExperiment):
 
     References
     ----------
-    [1] Hartmann, J.L. (1972). "Some Experiments in Global Optimization".
-        Naval Postgraduate School, Monterey, CA.
+    [1] Branin, F.H. (1972). "Widely convergent method for finding
+        multiple solutions of simultaneous nonlinear equations." IBM Journal of
+        Research and Development, 16(1), 504-522.
 
     Example
     -------

From 93cc2d569ad5b54c77ff0519c222809b0fc1f6bd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 22:59:40 +0200
Subject: [PATCH 06/10] linting

---
 src/hyperactive/experiment/toy/__init__.py    |  1 -
 src/hyperactive/experiment/toy/_branin_hoo.py |  3 +-
 src/hyperactive/experiment/toy/_hartmann.py   | 69 ++++++++++---------
 3 files changed, 36 insertions(+), 37 deletions(-)

diff --git a/src/hyperactive/experiment/toy/__init__.py b/src/hyperactive/experiment/toy/__init__.py
index b9c16855..323058c4 100644
--- a/src/hyperactive/experiment/toy/__init__.py
+++ b/src/hyperactive/experiment/toy/__init__.py
@@ -1,6 +1,5 @@
 """Toy experiments."""
 
-
 from hyperactive.experiment.toy._ackley import Ackley
 from hyperactive.experiment.toy._branin_hoo import BraninHoo
 from hyperactive.experiment.toy._hartmann import Hartmann
diff --git a/src/hyperactive/experiment/toy/_branin_hoo.py b/src/hyperactive/experiment/toy/_branin_hoo.py
index 9e58bd6e..1cb27795 100644
--- a/src/hyperactive/experiment/toy/_branin_hoo.py
+++ b/src/hyperactive/experiment/toy/_branin_hoo.py
@@ -69,13 +69,12 @@ class BraninHoo(BaseExperiment):
     def __init__(
         self,
         a=1.0,
-        b=5.1 / (4 * np.pi ** 2),
+        b=5.1 / (4 * np.pi**2),
         c=5 / np.pi,
         d=6.0,
         e=10.0,
         f=1 / (8 * np.pi),
     ):
-    
         self.a = a
         self.b = b
         self.c = c
diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index 49e45932..79a5c606 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -16,7 +16,7 @@ class Hartmann(BaseExperiment):
 
     .. math::
 
-        f(\mathbf{x}) = - \sum_{i=1}^{4} \alpha_i 
+        f(\mathbf{x}) = - \sum_{i=1}^{4} \alpha_i
         \exp \left( - \sum_{j=1}^{6} A_{ij} (x_j - P_{ij})^2 \right),
         \quad \text{where}
 
@@ -103,25 +103,29 @@ def __init__(self, alpha=None, A=None, P=None):
             self._alpha = np.asarray(alpha)
 
         if self.A is None:
-            self._A = np.array([
-                [10, 3, 17, 3.50, 1.7, 8],
-                [0.05, 10, 17, 0.1, 8, 14],
-                [3, 3.5, 1.7, 10, 17, 8],
-                [17, 8, 0.05, 10, 0.1, 14]
-            ])
+            self._A = np.array(
+                [
+                    [10, 3, 17, 3.50, 1.7, 8],
+                    [0.05, 10, 17, 0.1, 8, 14],
+                    [3, 3.5, 1.7, 10, 17, 8],
+                    [17, 8, 0.05, 10, 0.1, 14],
+                ]
+            )
         else:
             self._A = np.asarray(A)
 
         if self.P is None:
-            self._P = 1e-4 * np.array([
-                [1312, 1696, 5569, 124, 8283, 5886],
-                [2329, 4135, 8307, 3736, 1004, 9991],
-                [2348, 1451, 3522, 2883, 3047, 6650],
-                [4047, 8828, 8732, 5743, 1091, 381]
-            ])
+            self._P = 1e-4 * np.array(
+                [
+                    [1312, 1696, 5569, 124, 8283, 5886],
+                    [2329, 4135, 8307, 3736, 1004, 9991],
+                    [2348, 1451, 3522, 2883, 3047, 6650],
+                    [4047, 8828, 8732, 5743, 1091, 381],
+                ]
+            )
         else:
             self._P = np.asarray(P)
-        
+
     def _paramnames(self):
         n = self._A.shape[1]  # number of dimensions
         return [f"x{i}" for i in range(n)]
@@ -188,18 +192,22 @@ def get_test_params(cls, parameter_set="default"):
         # parameters different from the default
         params1 = {
             "alpha": np.array([4.0, 3.2, 2.0, 1.2]),
-            "A": np.array([
-                [42, 3, 17, 3.50, 1.7, 8],
-                [0.05, 10, 17, 0.1, 8, 14],
-                [3, 3.5, 1.7, 33, 17, 8],
-                [17, 8, 0.05, 10, 0.1, 14]
-            ]),
-            "P": np.array([
-                [1312, 196, 5569, 124, 8283, 5886],
-                [2329, 4135, 8307, 3736, 100, 9991],
-                [2348, 1451, 322, 2883, 3047, 6650],
-                [4047, 8828, 8732, 743, 1091, 381]
-            ])
+            "A": np.array(
+                [
+                    [42, 3, 17, 3.50, 1.7, 8],
+                    [0.05, 10, 17, 0.1, 8, 14],
+                    [3, 3.5, 1.7, 33, 17, 8],
+                    [17, 8, 0.05, 10, 0.1, 14],
+                ]
+            ),
+            "P": np.array(
+                [
+                    [1312, 196, 5569, 124, 8283, 5886],
+                    [2329, 4135, 8307, 3736, 100, 9991],
+                    [2348, 1451, 322, 2883, 3047, 6650],
+                    [4047, 8828, 8732, 743, 1091, 381],
+                ]
+            )
         }
         # different parameters with dimensions 2 x 3
         params2 = {
@@ -222,13 +230,6 @@ def _get_score_params(self):
         list of dict
             The parameters to be used for scoring.
         """
-        params = {
-            "x0": 0.1,
-            "x1": 0.2,
-            "x2": 0.3,
-            "x3": 0.4,
-            "x4": 0.5,
-            "x5": 0.6
-        }
+        params = {"x0": 0.1, "x1": 0.2, "x2": 0.3, "x3": 0.4, "x4": 0.5, "x5": 0.6}
         params2 = {"x0": 0.1, "x1": 0.2, "x2": 0.3}
         return [params, params, params2]

From e20ff70ebd3b938c9a5b8c23dc3d9705c8517304 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 23:04:22 +0200
Subject: [PATCH 07/10] linting

---
 src/hyperactive/experiment/toy/_hartmann.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index 79a5c606..f5eba209 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -207,13 +207,13 @@ def get_test_params(cls, parameter_set="default"):
                     [2348, 1451, 322, 2883, 3047, 6650],
                     [4047, 8828, 8732, 743, 1091, 381],
                 ]
-            )
+            ),
         }
         # different parameters with dimensions 2 x 3
         params2 = {
             "alpha": np.array([1.0, 2.0]),
             "A": np.array([[10, 3, 17], [0.05, 10, 17]]),
-            "P": np.array([[1312, 1696, 5569], [2329, 4135, 8307]])
+            "P": np.array([[1312, 1696, 5569], [2329, 4135, 8307]]),
         }
         return [params0, params1, params2]
 

From 08e2367b5a768537e4649313dec9b8ff5cbde8a5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 23:06:24 +0200
Subject: [PATCH 08/10] Update _hartmann.py

---
 src/hyperactive/experiment/toy/_hartmann.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index f5eba209..06b073b6 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -145,7 +145,7 @@ def _evaluate(self, params):
         dict
             Additional metadata about the search.
         """
-        x = np.array([params[f"x{i}"] for i in range(6)])
+        x = np.array([params[xi] for xi in self.paramnames()])
 
         alpha = self._alpha
         A = self._A

From 31b754ea0d92f3d5521b8c9fade946f54b2fd414 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 23:39:43 +0200
Subject: [PATCH 09/10] minima

---
 src/hyperactive/experiment/toy/_branin_hoo.py | 2 +-
 src/hyperactive/experiment/toy/_hartmann.py   | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/src/hyperactive/experiment/toy/_branin_hoo.py b/src/hyperactive/experiment/toy/_branin_hoo.py
index 1cb27795..3ea87fdc 100644
--- a/src/hyperactive/experiment/toy/_branin_hoo.py
+++ b/src/hyperactive/experiment/toy/_branin_hoo.py
@@ -13,7 +13,7 @@ class BraninHoo(BaseExperiment):
     algorithms. It is considered on the square domain
     :math:`x \in [-5, 10], y \in [0, 15]`.
 
-    It has three minima with :math:`f(x^*) = 0.397887` at :math:`x* = (-\pi, 12.275)`,
+    It has three minima with :math:`f(x^*) = 0.397887` at :math:`x^* = (-\pi, 12.275)`,
     :math:`(\pi, 2.275)`, and :math:`(9.42478, 2.475)`.
 
     The Branin-Hoo function is defined as:
diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index 06b073b6..177de679 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -12,6 +12,9 @@ class Hartmann(BaseExperiment):
     The Hartmann function is a non-convex function used to test optimization algorithms,
     typically considered on the unit hypercube.
 
+    It has six local minima and one global minimum :math:`f(x^*) = -3.32237` at
+    :math:`x^* = (0.20169, 0.15001, 0.476874, 0.275332, 0.311652, 0.6573)`.
+
     The Hartmann function is defined as:
 
     .. math::

From 6b0b7eecbc0ade968b8c46ad2814575cc5c951fa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Franz=20Kir=C3=A1ly?= <fkiraly@gcos.ai>
Date: Thu, 14 Aug 2025 23:40:12 +0200
Subject: [PATCH 10/10] Update _hartmann.py

---
 src/hyperactive/experiment/toy/_hartmann.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/hyperactive/experiment/toy/_hartmann.py b/src/hyperactive/experiment/toy/_hartmann.py
index 177de679..cdc80bdb 100644
--- a/src/hyperactive/experiment/toy/_hartmann.py
+++ b/src/hyperactive/experiment/toy/_hartmann.py
@@ -25,7 +25,7 @@ class Hartmann(BaseExperiment):
 
     .. math::
 
-        \alpha = (1.0, \; 1.2, \; 3.0, \; 3.2)^T
+        \alpha = (1.0, \; 1.2, \; 3.0, \; 3.2)
 
     .. math::