add docstring to poly class

src/xspline/poly.py

@@ -1,21 +1,70 @@
 from math import factorial
 
 import numpy as np
-from numpy.typing import NDArray
 
-from xspline.typing import PolyParams
+from xspline.typing import PolyParams, NDArray
 from xspline.xfunction import BundleXFunction, XFunction
 
 
 def poly_val(params: PolyParams, x: NDArray) -> NDArray:
+    """Polynomial value function.
+
+    Parameters
+    ----------
+    params
+        Polynomial coefficients.
+    x
+        Data points.
+
+    Returns
+    -------
+    describe
+        Polynomial function values.
+
+    """
     return np.polyval(params, x)
 
 
 def poly_der(params: PolyParams, x: NDArray, order: int) -> NDArray:
+    """Polynomial derivative function.
+
+    Parameters
+    ----------
+    params
+        Polynomial coefficients.
+    x
+        Data points.
+    order
+        Order of differentiation.
+
+    Returns
+    -------
+    describe
+        Polynomial derivative values.
+
+    """
     return np.polyval(np.polyder(params, order), x)
 
 
 def poly_int(params: PolyParams, x: NDArray, order: int) -> NDArray:
+    """Polynomial definite integral function.
+
+    Parameters
+    ----------
+    params
+        Polynomial coefficients.
+    x
+        Data points.
+    order
+        Order of integration. Here we use negative integer.
+
+    Returns
+    -------
+    describe
+        Polynomial definite integral values.
+
+    """
+
     return np.polyval(np.polyint(params, -order), x)
 
 
@@ -46,16 +95,50 @@ def __init__(self, params: PolyParams) -> None:
 
 
 def get_poly_params(fun: XFunction, x: float, degree: int) -> tuple[float, ...]:
+    """Solve polynomial (taylor) coefficients provided the ``XFunction``.
+
+    Parameters
+    ----------
+    fun
+        Provided ``XFunction`` to be approximated.
+    x
+        The point where we want to approximate ``XFunction`` by the polynomial.
+    degree
+        Degree of the approximation polynomial.
+
+    Returns
+    -------
+    describe
+        The approximation polynomial coefficients.
+
+    """
     if degree < 0:
         return (0.0,)
     rhs = np.array([fun(x, order=i) for i in range(degree, -1, -1)])
     mat = np.zeros((degree + 1, degree + 1))
     for i in range(degree + 1):
         for j in range(i + 1):
-            mat[i, j] = factorial(degree - j) / factorial(i - j) * x**(i - j)
+            mat[i, j] = factorial(degree - j) / factorial(i - j) * x ** (i - j)
     return tuple(np.linalg.solve(mat, rhs))
 
 
 def get_poly_fun(fun: XFunction, x: float, degree: int) -> Poly:
+    """Get the approximation polynomial function.
+
+    Parameters
+    ----------
+    fun
+        Provided ``XFunction`` to be approximated.
+    x
+        The point where we want to approximate ``XFunction`` by the polynomial.
+    degree
+        Degree of the approximation polynomial.
+
+    Returns
+    -------
+    describe
+        Instance of the ``Poly`` class to approximate provided ``XFunction``.
+
+    """
     params = get_poly_params(fun, x, degree)
     return Poly(params)