feat: Add Clough-Tocher 2D Interpolator and corresponding tests

ezyrb/approximation/__init__.py

@@ -9,6 +9,7 @@
     "KNeighborsRegressor",
     "RadiusNeighborsRegressor",
     "SklearnApproximation",
+    "CloughTocher",
 ]
 
 from .approximation import Approximation
@@ -19,3 +20,4 @@
 from .kneighbors_regressor import KNeighborsRegressor
 from .radius_neighbors_regressor import RadiusNeighborsRegressor
 from .sklearn_approximation import SklearnApproximation
+from .clough_tocher import CloughTocher

ezyrb/approximation/clough_tocher.py

@@ -0,0 +1,52 @@
+"""Wrapper for Clough-Tocher 2D Interpolator."""
+
+import logging
+import numpy as np
+from scipy.interpolate import CloughTocher2DInterpolator as CT
+
+from .approximation import Approximation
+
+logger = logging.getLogger(__name__)
+
+
+class CloughTocher(Approximation):
+    r"""
+    :math:`C^1` smooth, piecewise cubic interpolator for 2D multivariate approximation.
+
+    Note: This interpolator only supports 2-dimensional parameter spaces
+    (i.e., mapping :math:`\mathbb{R}^2 \to \mathbb{R}^m`).
+
+    :param kwargs: arguments passed to the internal instance of
+        scipy.interpolate.CloughTocher2DInterpolator.
+    """
+
+    def __init__(self, **kwargs):
+        logger.debug("Initializing CloughTocher with kwargs: %s", kwargs)
+        super().__init__()
+        self.kwargs = kwargs
+        self.interpolator = None
+
+    def fit(self, points, values):
+        """
+        Construct the interpolator given `points` and `values`.
+        """
+        as_np_array = np.array(points)
+
+        # Mathematical constraint: CT only works in R^2
+        if as_np_array.ndim != 2 or as_np_array.shape[1] != 2:
+            logger.error(
+                "CloughTocher requested for data with shape %s",
+                as_np_array.shape,
+            )
+            raise ValueError(
+                "CloughTocher interpolator only supports exactly 2D parameter spaces."
+            )
+
+        self.interpolator = CT(as_np_array, values, **self.kwargs)
+        logger.info("CloughTocher fitted successfully")
+
+    def predict(self, new_point):
+        """
+        Evaluate interpolator at given `new_points`.
+        """
+        return self.interpolator(new_point).squeeze()

tests/test_clough_tocher.py

@@ -0,0 +1,41 @@
+import numpy as np
+import pytest
+
+from ezyrb import CloughTocher
+
+np.random.seed(17)
+
+def get_xy():
+    npts = 20
+    dinput = 2
+
+    inp = np.random.uniform(-1, 1, size=(npts, dinput))
+    out = np.array([
+        np.sin(inp[:, 0]) + np.sin(inp[:, 1]**2),
+        np.cos(inp[:, 0]) + np.cos(inp[:, 1]**2)
+    ]).T
+
+    return inp, out
+
+class TestCloughTocher:
+    def test_constructor_empty(self):
+        model = CloughTocher()
+
+    def test_fit(self):
+        x, y = get_xy()
+        approx = CloughTocher()
+        approx.fit(x, y)
+
+    def test_predict_01(self):
+        x, y = get_xy()
+        approx = CloughTocher() 
+        approx.fit(x, y)
+        test_y = approx.predict(x)
+        np.testing.assert_array_almost_equal(y, test_y, decimal=6)
+
+    def test_wrong_dimensions(self):
+        x = np.random.uniform(-1, 1, size=(10, 3))
+        y = np.random.uniform(-1, 1, size=(10, 2))
+        approx = CloughTocher()
+        with pytest.raises(ValueError):
+            approx.fit(x, y)

tests/test_parallel/test_clough_tocher.py

@@ -0,0 +1,7 @@
+import pytest
+
+import ezyrb
+from ezyrb.parallel import ReducedOrderModel as ParallelROM
+ezyrb.ReducedOrderModel = ParallelROM
+
+from tests.test_clough_tocher import *