add type annotations for adaptive/learner/integrator_coeffs.py

Author: basnijholt

adaptive/learner/integrator_coeffs.py

@@ -2,12 +2,14 @@
 
 from collections import defaultdict
 from fractions import Fraction
+from typing import List, Tuple
 
 import numpy as np
 import scipy.linalg
+from numpy import ndarray
 
 
-def legendre(n):
+def legendre(n: int) -> List[List[Fraction]]:
     """Return the first n Legendre polynomials.
 
     The polynomials have *standard* normalization, i.e.
@@ -28,7 +30,7 @@ def legendre(n):
     return result
 
 
-def newton(n):
+def newton(n: int) -> ndarray:
     """Compute the monomial coefficients of the Newton polynomial over the
     nodes of the n-point Clenshaw-Curtis quadrature rule.
     """
@@ -85,7 +87,7 @@ def newton(n):
     return cf
 
 
-def scalar_product(a, b):
+def scalar_product(a: List[Fraction], b: List[Fraction]) -> Fraction:
     """Compute the polynomial scalar product int_-1^1 dx a(x) b(x).
 
     The args must be sequences of polynomial coefficients.  This
@@ -106,7 +108,7 @@ def scalar_product(a, b):
     return 2 * sum(c[i] / (i + 1) for i in range(0, lc, 2))
 
 
-def calc_bdef(ns):
+def calc_bdef(ns: Tuple[int, int, int, int]) -> List[ndarray]:
     """Calculate the decompositions of Newton polynomials (over the nodes
     of the n-point Clenshaw-Curtis quadrature rule) in terms of
     Legandre polynomials.
@@ -132,7 +134,7 @@ def calc_bdef(ns):
     return result
 
 
-def calc_V(x, n):
+def calc_V(x: ndarray, n: int) -> ndarray:
     V = [np.ones(x.shape), x.copy()]
     for i in range(2, n):
         V.append((2 * i - 1) / i * x * V[-1] - (i - 1) / i * V[-2])