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/libsharp.pxd

@@ -59,6 +59,9 @@ cdef extern from "sharp.h":
         sharp_alm_info *alm_info, int ntrans, int flags, double *time,
         unsigned long long *opcnt) nogil
 
+    void sharp_normalized_associated_legendre_table(int m, int lmax, int ntheta,
+        double *theta, int ncols, double *out) nogil
+
 
 cdef extern from "sharp_geomhelpers.h":
     void sharp_make_subset_healpix_geom_info(
@@ -76,4 +79,3 @@ cdef extern from "sharp_almhelpers.h":
     void sharp_make_mmajor_real_packed_alm_info (int lmax, int stride,
         int nm, const int *ms, sharp_alm_info **alm_info)
 
-

python/libsharp/libsharp.pyx

@@ -1,8 +1,9 @@
 import numpy as np
+cimport cython
 
 __all__ = ['legendre_transform', 'legendre_roots', 'sht', 'synthesis', 'adjoint_synthesis',
            'analysis', 'adjoint_analysis', 'healpix_grid', 'triangular_order', 'rectangular_order',
-           'packed_real_order']
+           'packed_real_order', 'normalized_associated_legendre_table']
 
 
 def legendre_transform(x, bl, out=None):
@@ -254,3 +255,17 @@ cdef class packed_real_order(alm_info):
                                                ms=NULL if ms is None else &ms[0],
                                                alm_info=&self.ainfo)
 
+#
+# 
+#
+
+@cython.boundscheck(False)
+def normalized_associated_legendre_table(int lmax, int m, theta):
+    cdef double[::1] theta_ = np.ascontiguousarray(theta, dtype=np.double)
+    out = np.zeros((theta_.shape[0], lmax - m + 1), np.double)
+    cdef double[:, ::1] out_ = out
+    if lmax < m:
+        raise ValueError("lmax < m")
+    with nogil:
+        sharp_normalized_associated_legendre_table(m, lmax, theta_.shape[0], &theta_[0], lmax - m + 1, &out_[0,0])
+    return out

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, :])