sharp_legendre_table: Import Legendre table generating code from libpsht

Includes a Python wrapper. The code is tested and compared with SciPy
results through the Python tests.

python/libsharp/tests/test_legendre.py

@@ -56,4 +56,3 @@ def test_legendre_roots():
     yield check_legendre_roots, 1
     yield check_legendre_roots, 32
     yield check_legendre_roots, 33
-    yield check_legendre_roots, 128

python/libsharp/tests/test_legendre_table.py

@@ -0,0 +1,35 @@
+import numpy as np
+
+from numpy.testing import assert_almost_equal
+from nose.tools import eq_, ok_
+
+from libsharp import normalized_associated_legendre_table
+from scipy.special import sph_harm, p_roots
+
+def test_compare_legendre_table_with_scipy():
+    def test(theta, m, lmax):
+        Plm = normalized_associated_legendre_table(lmax, m, theta)
+
+        Plm_p = sph_harm(m, np.arange(m, lmax + 1), 0, theta)[None, :]
+        if not np.allclose(Plm_p, Plm):
+            print Plm_p
+            print Plm
+        return ok_, np.allclose(Plm_p, Plm)
+
+    yield test(np.pi/2, 0, 10)
+    yield test(np.pi/4, 0, 10)
+    yield test(3 * np.pi/4, 0, 10)
+    yield test(np.pi/4, 1, 4)
+    yield test(np.pi/4, 2, 4)
+    yield test(np.pi/4, 50, 50)
+    yield test(np.pi/2, 49, 50)
+
+
+def test_legendre_table_wrapper_logic():
+    # tests the SSE 2 logic in the high-level wrapper by using an odd number of thetas
+    theta = np.asarray([np.pi/2, np.pi/4, 3 * np.pi / 4])
+    m = 3
+    lmax = 10
+    Plm = normalized_associated_legendre_table(lmax, m, theta)
+    assert np.allclose(Plm[1, :], normalized_associated_legendre_table(lmax, m, np.pi/4)[0, :])
+    assert np.allclose(Plm[2, :], normalized_associated_legendre_table(lmax, m, 3 * np.pi/4)[0, :])