Add chi-squared confidence level attr to EllipsoidalSet

pyomo/contrib/pyros/tests/test_uncertainty_sets.py

@@ -20,6 +20,7 @@
     attempt_import,
     numpy as np,
     numpy_available,
+    scipy as sp,
     scipy_available,
 )
 from pyomo.environ import SolverFactory
@@ -1863,6 +1864,11 @@ def test_normal_construction_and_update(self):
         np.testing.assert_allclose(
             scale, eset.scale, err_msg="EllipsoidalSet scale not as expected"
         )
+        np.testing.assert_allclose(
+            sp.stats.chi2.cdf(scale ** 0.5, df=2),
+            eset.chi_sq_conf_lvl,
+            err_msg="EllipsoidalSet chi-squared confidence level not as expected",
+        )
 
         # check attributes update
         new_center = [-1, -3]
@@ -1886,6 +1892,40 @@ def test_normal_construction_and_update(self):
         np.testing.assert_allclose(
             new_scale, eset.scale, err_msg="EllipsoidalSet scale update not as expected"
         )
+        np.testing.assert_allclose(
+            sp.stats.chi2.cdf(new_scale ** 0.5, df=2),
+            eset.chi_sq_conf_lvl,
+            err_msg="EllipsoidalSet chi-square confidence level update not as expected"
+        )
+
+    def test_normal_construction_and_update_chi_sq_conf_lvl(self):
+        """
+        Test EllipsoidalSet constructor and setter
+        work normally when arguments are appropriate.
+        """
+        init_conf_lvl = 0.95
+        eset = EllipsoidalSet(
+            center=[0, 0, 0],
+            shape_matrix=np.eye(3),
+            scale=None,
+            chi_sq_conf_lvl=init_conf_lvl,
+        )
+
+        self.assertEqual(eset.chi_sq_conf_lvl, init_conf_lvl)
+        np.testing.assert_allclose(
+            sp.stats.chi2.isf(q=1 - init_conf_lvl, df=eset.dim),
+            eset.scale,
+            err_msg="EllipsoidalSet scale not as expected",
+        )
+
+        new_conf_lvl = 0.99
+        eset.chi_sq_conf_lvl = new_conf_lvl
+        self.assertEqual(eset.chi_sq_conf_lvl, new_conf_lvl)
+        np.testing.assert_allclose(
+            sp.stats.chi2.isf(q=1 - new_conf_lvl, df=eset.dim),
+            eset.scale,
+            err_msg="EllipsoidalSet scale not as expected",
+        )
 
     def test_error_on_ellipsoidal_dim_change(self):
         """
@@ -1926,6 +1966,48 @@ def test_error_on_neg_scale(self):
         with self.assertRaisesRegex(ValueError, exc_str):
             eset.scale = neg_scale
 
+    def test_error_invalid_chi_sq_conf_lvl(self):
+        """
+        Test error when attempting to initialize with chi-squared
+        confidence level outside range.
+        """
+        center = [0, 0]
+        shape_matrix = [[1, 0], [0, 2]]
+        invalid_conf_lvl = 1.001
+
+        exc_str = r"Ensure the confidence level is a value in \[0, 1\)."
+
+        # error on construction
+        with self.assertRaisesRegex(ValueError, exc_str):
+            EllipsoidalSet(
+                center=center,
+                shape_matrix=shape_matrix,
+                scale=None,
+                chi_sq_conf_lvl=invalid_conf_lvl,
+            )
+
+        # error on updating valid ellipsoid
+        eset = EllipsoidalSet(center, shape_matrix, scale=None, chi_sq_conf_lvl=0.95)
+        with self.assertRaisesRegex(ValueError, exc_str):
+            eset.chi_sq_conf_lvl = invalid_conf_lvl
+
+        # negative confidence level
+        eset = EllipsoidalSet(center, shape_matrix, scale=None, chi_sq_conf_lvl=0.95)
+        with self.assertRaisesRegex(ValueError, exc_str):
+            eset.chi_sq_conf_lvl = -0.1
+
+    def test_error_scale_chi_sq_conf_lvl_construction(self):
+        """
+        Test exception raised if neither or both of
+        `scale` and `chi_sq_conf_lvl` are None.
+        """
+        exc_str = r"Exactly one of `scale` and `chi_sq_conf_lvl` should be None"
+        with self.assertRaisesRegex(ValueError, exc_str):
+            EllipsoidalSet([0], [[1]], scale=None, chi_sq_conf_lvl=None)
+
+        with self.assertRaisesRegex(ValueError, exc_str):
+            EllipsoidalSet([0], [[1]], scale=1, chi_sq_conf_lvl=0.95)
+
     def test_error_on_shape_matrix_with_wrong_size(self):
         """
         Test error in event EllipsoidalSet shape matrix

pyomo/contrib/pyros/uncertainty_sets.py

@@ -2374,31 +2374,37 @@ class EllipsoidalSet(UncertaintySet):
     center : (N,) array-like
         Center of the ellipsoid.
     shape_matrix : (N, N) array-like
-        A positive definite matrix characterizing the shape
-        and orientation of the ellipsoid.
-    scale : numeric type, optional
+        A symmetric positive definite matrix characterizing
+        the shape and orientation of the ellipsoid.
+    scale : numeric type or None, optional
         Square of the factor by which to scale the semi-axes
         of the ellipsoid (i.e. the eigenvectors of the shape
         matrix). The default is `1`.
+    chi_sq_conf_lvl : numeric type or None, optional
+        (Fractional) chi-squared confidence level of the multivariate
+        normal distribution with mean `center` and covariance
+        matrix `shape_matrix`.
+        Exactly one of `scale` and `chi_sq_conf_lvl` should be
+        None; otherwise, an exception is raised.
 
     Examples
     --------
-    3D origin-centered unit hypersphere:
+    A 3D origin-centered unit ball:
 
     >>> from pyomo.contrib.pyros import EllipsoidalSet
     >>> import numpy as np
-    >>> hypersphere = EllipsoidalSet(
+    >>> ball = EllipsoidalSet(
     ...     center=[0, 0, 0],
     ...     shape_matrix=np.eye(3),
     ...     scale=1,
     ... )
-    >>> hypersphere.center
+    >>> ball.center
     array([0, 0, 0])
-    >>> hypersphere.shape_matrix
+    >>> ball.shape_matrix
     array([[1., 0., 0.],
            [0., 1., 0.],
            [0., 0., 1.]])
-    >>> hypersphere.scale
+    >>> ball.scale
     1
 
     A 2D ellipsoid with custom rotation and scaling:
@@ -2416,13 +2422,42 @@ class EllipsoidalSet(UncertaintySet):
     >>> rotated_ellipsoid.scale
     0.5
 
+    A 4D 95% confidence ellipsoid:
+
+    >>> conf_ellipsoid = EllipsoidalSet(
+    ...     center=np.zeros(4),
+    ...     shape_matrix=np.diag(range(1, 5)),
+    ...     scale=None,
+    ...     chi_sq_conf_lvl=0.95,
+    ... )
+    >>> conf_ellipsoid.center
+    array([0, 0, 0, 0])
+    >>> conf_ellipsoid.shape_matrix
+    array([[1, 0, 0, 0]],
+           [0, 2, 0, 0]],
+           [0, 0, 3, 0]],
+           [0, 0, 0. 4]])
+    >>> conf_ellipsoid.scale
+    ...9.4877...
+    >>> conf_ellipsoid.chi_sq_conf_lvl
+    0.95
+
     """
 
-    def __init__(self, center, shape_matrix, scale=1):
+    def __init__(self, center, shape_matrix, scale=1, chi_sq_conf_lvl=None):
         """Initialize self (see class docstring)."""
         self.center = center
         self.shape_matrix = shape_matrix
-        self.scale = scale
+
+        if scale is not None and chi_sq_conf_lvl is None:
+            self.scale = scale
+        elif scale is None and chi_sq_conf_lvl is not None:
+            self.chi_sq_conf_lvl = chi_sq_conf_lvl
+        else:
+            raise ValueError(
+                "Exactly one of `scale` and `chi_sq_conf_lvl` should be "
+                f"None (got {scale=}, {chi_sq_conf_lvl=})"
+            )
 
     @property
     def type(self):
@@ -2456,7 +2491,7 @@ def center(self, val):
             if val_arr.size != self.dim:
                 raise ValueError(
                     "Attempting to set attribute 'center' of "
-                    f"AxisAlignedEllipsoidalSet of dimension {self.dim} "
+                    f"{type(self).__name__} of dimension {self.dim} "
                     f"to value of dimension {val_arr.size}"
                 )
 
@@ -2535,7 +2570,7 @@ def shape_matrix(self, val):
         if hasattr(self, "_center"):
             if not all(size == self.dim for size in shape_mat_arr.shape):
                 raise ValueError(
-                    f"EllipsoidalSet attribute 'shape_matrix' "
+                    f"{type(self).__name__} attribute 'shape_matrix' "
                     f"must be a square matrix of size "
                     f"{self.dim} to match set dimension "
                     f"(provided matrix with shape {shape_mat_arr.shape})"
@@ -2558,12 +2593,41 @@ def scale(self, val):
         validate_arg_type("scale", val, valid_num_types, "a valid numeric type", False)
         if val < 0:
             raise ValueError(
-                "EllipsoidalSet attribute "
+                f"{type(self).__name__} attribute "
                 f"'scale' must be a non-negative real "
                 f"(provided value {val})"
             )
 
         self._scale = val
+        self._chi_sq_conf_lvl = sp.stats.chi2.cdf(x=val ** 0.5, df=self.dim)
+
+    @property
+    def chi_sq_conf_lvl(self):
+        """
+        numeric type : (Fractional) chi-squared confidence level of the
+        multivariate normal distribution with mean ``self.origin``
+        and covariance ``self.shape_matrix`` for ellipsoidal region
+        with square magnification factor ``self.scale``.
+        """
+        return self._chi_sq_conf_lvl
+
+    @chi_sq_conf_lvl.setter
+    def chi_sq_conf_lvl(self, val):
+        validate_arg_type(
+            "chi_sq_conf_lvl",
+            val,
+            valid_num_types,
+            "a valid numeric type",
+            False,
+        )
+        self._chi_sq_conf_lvl = val
+        self._scale = sp.stats.chi2.isf(q=1 - val, df=self.dim)
+        if np.isnan(self._scale) or np.isinf(self._scale):
+            raise ValueError(
+                f"Squared scaling factor calculation for confidence level {val} "
+                f"and set dimension {self.dim} returned {self._scale}. "
+                "Ensure the confidence level is a value in [0, 1)."
+            )
 
     @property
     def dim(self):