Merge pull request #250 from robin-oval/feature/binomial_coefficient

binomial coefficient function

Author: tomvanmele

src/compas/geometry/_primitives/curve.py

@@ -2,8 +2,6 @@
 from __future__ import absolute_import
 from __future__ import division
 
-from math import factorial
-
 from compas.geometry.basic import scale_vector
 from compas.geometry.basic import normalize_vector
 from compas.geometry.basic import add_vectors
@@ -12,36 +10,11 @@
 from compas.geometry._primitives import Point
 from compas.geometry._primitives import Vector
 
+from compas.utilities import binomial_coefficient
 
 __all__ = ['Bezier']
 
 
-def binomial(n, k):
-    """Returns the binomial coefficient of the :math:`x^k` term in the
-    polynomial expansion of the binmoial power :math:`(1 + x)^n` [wikipedia2017j]_.
-
-    Notes
-    -----
-    Arranging binomial coefficients into rows for successive values of `n`,
-    and in which `k` ranges from 0 to `n`, gives a triangular array known as
-    Pascal's triangle.
-
-    Parameters
-    ----------
-    n : int
-        The number of terms.
-    k : int
-        The index of the coefficient.
-
-    Returns
-    -------
-    int
-        The coefficient.
-
-    """
-    return factorial(n) / float(factorial(k) * factorial(n - k))
-
-
 def bernstein(n, k, t):
     """k:sup:`th` of `n` + 1 Bernstein basis polynomials of degree `n`. A
     weighted linear combination of these basis polynomials is called a Bernstein
@@ -71,7 +44,7 @@ def bernstein(n, k, t):
         return 0
     if k > n:
         return 0
-    return binomial(n, k) * t ** k * (1 - t) ** (n - k)
+    return binomial_coefficient(n, k) * t ** k * (1 - t) ** (n - k)
 
 
 class BezierException(Exception):

src/compas/utilities/__init__.py

@@ -72,6 +72,7 @@
     :nosignatures:
 
     fibonacci
+    binomial_coefficient
 
 itertools
 =========

src/compas/utilities/functions.py

@@ -2,9 +2,11 @@
 from __future__ import absolute_import
 from __future__ import division
 
+from math import factorial
 
 __all__ = [
-    'fibonacci'
+    'fibonacci',
+    'binomial_coefficient'
 ]
 
 
@@ -19,10 +21,37 @@ def fibonacci(n, memo={}):
         memo[n] = fibonacci(n - 2, memo) + fibonacci(n - 1, memo)
     return memo[n]
 
+def binomial_coefficient(n, k):
+    """Returns the binomial coefficient of the :math:`x^k` term in the
+    polynomial expansion of the binomial power :math:`(1 + x)^n` [wikipedia2017j]_.
+
+    Notes
+    -----
+    Arranging binomial coefficients into rows for successive values of `n`,
+    and in which `k` ranges from 0 to `n`, gives a triangular array known as
+    Pascal's triangle.
+
+    Parameters
+    ----------
+    n : int
+        The number of terms.
+    k : int
+        The index of the coefficient.
+
+    Returns
+    -------
+    int
+        The coefficient.
+
+    """
+    return int(factorial(n) / float(factorial(k) * factorial(n - k)))
+
 # ==============================================================================
 # Main
 # ==============================================================================
 
 if __name__ == "__main__":
 
     print(fibonacci(100))
+
+    print(binomial_coefficient(10, 4))

tests/utilities/test_functions.py

@@ -0,0 +1,17 @@
+import pytest
+
+from compas.utilities import binomial_coefficient
+
+
+@pytest.mark.parametrize(("n", "k", "result"),
+	[
+	pytest.param(3, 1, 3),
+	pytest.param(21, 10, 352716),
+	pytest.param(10, 0, 1),
+	pytest.param(0, 0, 1),
+	pytest.param(1, 2, 0, marks=pytest.mark.xfail(raises=ValueError)),
+	pytest.param(2, -1, 0, marks=pytest.mark.xfail(raises=ValueError)),
+	]
+)
+def test_binomial(n, k, result):
+    assert binomial_coefficient(n, k) == pytest.approx(result)