Added named_arrays.PolynomialFunctionArray

named_arrays/_functions/functions.py

@@ -706,3 +706,66 @@ def __setitem__(
         if value_inputs is not None:
             self.inputs[item_inputs] = value_inputs
         self.outputs[item_outputs] = value_outputs
+
+
+@dataclasses.dataclass(eq=False, repr=False)
+class AbstractPolynomialFunctionArray(
+    AbstractFunctionArray,
+):
+    @property
+    @abc.abstractmethod
+    def coefficients(self) -> na.AbstractVectorArray | na.AbstractMatrixArray:
+        """
+        A vector or matrix representing the coefficients of the polynomial.
+
+        If this function is scalar-valued, :attr:`coefficients` should be a vector,
+        and if this function is vector-valued, :attr`coefficients` should be a matrix.
+        """
+
+    @property
+    @abc.abstractmethod
+    def degree(self) -> int:
+        """degree of the polynomial"""
+
+    @property
+    @abc.abstractmethod
+    def components_polynomial(self):
+        """the components of the input that this polynomial depends on"""
+
+    @property
+    @abc.abstractmethod
+    def axis_polynomial(self):
+        """the logical axes along which this polynomial is distributed"""
+
+    @abc.abstractmethod
+    def design_matrix(
+        self,
+        inputs: float | u.Quantity | na.AbstractScalar | na.AbstractVectorArray,
+    ) -> na.AbstractVectorArray:
+        """
+        The `design matrix <https://en.wikipedia.org/wiki/Design_matrix>`_
+        corresponding to the given inputs.
+
+        Note that while this is `called` a matrix, this function returns a vector
+        since the rows are independent observations, and this is concept is
+        already captured by the logical axes in the array.
+
+        Parameters
+        ----------
+        inputs
+            the set of independent variables to convert into the design matrix
+        """
+
+    def __call__(self, inputs: na.ScalarArray | na.AbstractVectorArray):
+
+        inputs_self = self.inputs
+        if not isinstance(inputs_self, na.AbstractVectorArray):
+            pass
+
+        components_inputs = inputs.components
+        for c in components_inputs:
+            if components_inputs[c] is None:
+                pass
+
+        index = self.inputs.index(inputs)
+