Remove dependency con pycephes, implement function

Alternative until poliastro/pycephes#1 makes
progress.

.travis.yml

@@ -33,7 +33,7 @@ before_install:
   - source activate test-environment
 
   # Install project requirements
-  - conda install numpy=$NUMPY numba>=0.23 astropy>=1.0 matplotlib scipy jplephem pycephes
+  - conda install numpy=$NUMPY numba>=0.23 astropy>=1.0 matplotlib scipy jplephem
   - pip install coverage pytest pytest-cov codecov pytest-benchmark
 
 install:

appveyor.yml

@@ -38,7 +38,7 @@ install:
   - "pip install pytest codecov pytest-benchmark"
 
   # Install dependencies
-  - "conda install -q numpy=%NUMPY% numba>=0.23 astropy>=1.0 matplotlib scipy jplephem pycephes"
+  - "conda install -q numpy=%NUMPY% numba>=0.23 astropy>=1.0 matplotlib scipy jplephem"
   - "pip install ."  # Test installation correctness
 
 build: off

buildscripts/condarecipe/meta.yaml

@@ -22,7 +22,6 @@ requirements:
     - astropy >=1.0
     - jplephem
     - matplotlib
-    - pycephes
 
 test:
   imports:

environment.yml

@@ -9,4 +9,3 @@ dependencies:
   - numba
   - numpy
   - scipy
-  - pycephes

setup.py

@@ -27,7 +27,6 @@
         "matplotlib",
         "jplephem",
         "scipy",
-        "pycephes",
     ],
     tests_require=[
         "pytest"

src/poliastro/hyper.py

@@ -0,0 +1,26 @@
+"""Utility hypergeometric functions.
+
+"""
+import numpy as np
+
+from poliastro.jit import jit
+
+
+@jit('f8(f8)')
+def hyp2f1b(x):
+    """Hypergeometric function 2F1(3, 1, 5/2, x), see [Battin].
+
+    """
+    if x >= 1.0:
+        return np.inf
+    else:
+        res = 1.0
+        term = 1.0
+        ii = 0
+        while True:
+            term = term * (3 + ii) * (1 + ii) / (5 / 2 + ii) * x / (ii + 1)
+            res_old = res
+            res += term
+            if res_old == res:
+                return res
+            ii += 1

src/poliastro/iod/izzo.py

@@ -7,8 +7,7 @@
 
 from poliastro.jit import jit
 from poliastro.util import norm
-
-from pycephes.hyper import hyp2f1
+from poliastro.hyper import hyp2f1b as hyp2f1
 
 
 def lambert(k, r0, r, tof, M=0, numiter=35, rtol=1e-8):

src/poliastro/tests/test_hyper.py

@@ -0,0 +1,15 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_almost_equal
+from scipy import special
+
+from poliastro.hyper import hyp2f1b as hyp2f1
+
+
+@pytest.mark.parametrize("x", np.linspace(0, 1, num=10))
+def test_hyp2f1_battin_scalar(x):
+    expected_res = special.hyp2f1(3, 1, 5/2, x)
+
+    res = hyp2f1(x)
+    assert_almost_equal(res, expected_res)