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.

Makefile

@@ -74,5 +74,7 @@ endif
 
 python: $(all_lib) hdrcopy $(CYTHON_MODULES)
 
+# the following test files are automatic; the sht wrapper test
+# must be run manually and requires MPI at the moment..
 pytest: python
-	cd python && nosetests --nocapture libsharp/tests/test_sht.py
+	cd python && nosetests --nocapture libsharp/tests/test_legendre_table.py libsharp/tests/test_legendre.py

libsharp/planck.make

@@ -8,7 +8,7 @@ FULL_INCLUDE+= -I$(SD)
 HDR_$(PKG):=$(SD)/*.h
 LIB_$(PKG):=$(LIBDIR)/libsharp.a
 BIN:=sharp_testsuite
-LIBOBJ:=sharp_ylmgen_c.o sharp.o sharp_announce.o sharp_geomhelpers.o sharp_almhelpers.o sharp_core.o sharp_legendre.o sharp_legendre_roots.o
+LIBOBJ:=sharp_ylmgen_c.o sharp.o sharp_announce.o sharp_geomhelpers.o sharp_almhelpers.o sharp_core.o sharp_legendre.o sharp_legendre_roots.o sharp_legendre_table.o
 ALLOBJ:=$(LIBOBJ) sharp_testsuite.o
 LIBOBJ:=$(LIBOBJ:%=$(OD)/%)
 ALLOBJ:=$(ALLOBJ:%=$(OD)/%)

libsharp/sharp.h

@@ -41,5 +41,6 @@
 #include "sharp_lowlevel.h"
 #include "sharp_legendre.h"
 #include "sharp_legendre_roots.h"
+#include "sharp_legendre_table.h"
 
 #endif

libsharp/sharp_legendre_table.h

@@ -0,0 +1,87 @@
+/*
+ *  This file is part of libsharp.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * met:
+ * 
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 
+ * 3. Neither the name of the copyright holder nor the names of its
+ * contributors may be used to endorse or promote products derived from
+ * this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+ * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*! \file sharp_legendre_table.h
+ *  Interface for computing tables of the normalized associated Legendre transform
+ *
+ *  Copyright (C) 2017 Dag Sverre Seljebotn
+ *  \author Dag Sverre Seljebotn
+ *
+ *  Note: This code was mainly copied from libpsht; only a small high-level wrapper added
+ */
+
+#ifndef SHARP_LEGENDRE_TABLE_H
+#define SHARP_LEGENDRE_TABLE_H
+
+#include <stddef.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef NO_LEGENDRE_TABLE
+
+
+/*! Returns a table of the normalized associated Legendre polynomials. m is a single
+    fixed argument and a table for multiple l and cos(theta) is provided.
+    (Internally, sin(theta) is also used for part of the computation, making theta
+    the most convenient argument.)
+
+    \param m The m-value to compute a table for
+    \param lmax A table will be provided for l = m .. lmax
+    \param ntheta How many theta values to evaluate for
+    \param theta Contiguous 1D array of theta values
+    \param ncols Number of columns in the out-array; should have ncols >= (lmax - m)
+    \param out Contiguous 2D array that will receive the output. Each output entry
+               is assigned to out[itheta * ncols + (l - m)].
+ */
+void sharp_normalized_associated_legendre_table(
+  ptrdiff_t m,
+  ptrdiff_t lmax,
+  ptrdiff_t ntheta,
+  /* contiguous 1D array of theta values to compute for,
+     contains ntheta values */
+  double *theta,
+  /* number of columns in out; see below. Should be >= (lmax - m). */
+  ptrdiff_t ncols,
+  /* contiguous 2D array, in "theta-major ordering". Has `ntheta`
+     rows and `ncols` columns. Indexed as out[itheta * ncols + (l - m)].
+     If `ncols > lmax - m` then those entries are not accessed.
+  */
+  double *out
+);
+
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

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, :])