From 20b41019e6b052ec2f278971839ed9caa54ba6c0 Mon Sep 17 00:00:00 2001
From: Matt Wala <wala1@illinois.edu>
Date: Thu, 29 Dec 2016 19:31:32 -0600
Subject: [PATCH] M2L: Speed up derivative taking by borrowing the multipole
 expansion's derivative taker.

---
 sumpy/expansion/local.py     | 34 ++++++++++++++++++++++++++++++----
 sumpy/expansion/multipole.py | 13 ++++++++-----
 2 files changed, 38 insertions(+), 9 deletions(-)

diff --git a/sumpy/expansion/local.py b/sumpy/expansion/local.py
index e3219933..c20eaf20 100644
--- a/sumpy/expansion/local.py
+++ b/sumpy/expansion/local.py
@@ -115,10 +115,36 @@ class VolumeTaylorLocalExpansionBase(LocalExpansionBase):
                     type(self).__name__,
                     self.order))
 
-        from sumpy.tools import MiDerivativeTaker
-        expr = src_expansion.evaluate(src_coeff_exprs, dvec)
-        taker = MiDerivativeTaker(expr, dvec)
-        result = [taker.diff(mi) for mi in self.get_coefficient_identifiers()]
+        from sumpy.expansion.multipole import VolumeTaylorMultipoleExpansionBase
+        if isinstance(src_expansion, VolumeTaylorMultipoleExpansionBase):
+            # We know the general form of the multipole expansion is:
+            #
+            #    coeff0 * diff(kernel, mi0) + coeff1 * diff(kernel, mi1) + ...
+            #
+            # To get the local expansion coefficients, we take derivatives of
+            # the multipole expansion.
+            #
+            # This code speeds up derivative taking by caching all kernel
+            # derivatives.
+            taker = src_expansion.get_kernel_derivative_taker(dvec)
+
+            def mi_sum(a, b):
+                return tuple(aval + bval for aval, bval in zip(a, b))
+
+            result = []
+            for deriv in self.get_coefficient_identifiers():
+                local_result = []
+                for coeff, term in zip(
+                        src_coeff_exprs,
+                        src_expansion.get_coefficient_identifiers()):
+                    kernel_deriv = taker.diff(mi_sum(deriv, term))
+                    local_result.append(coeff * kernel_deriv)
+                result.append(sp.Add(*local_result))
+        else:
+            from sumpy.tools import MiDerivativeTaker
+            expr = src_expansion.evaluate(src_coeff_exprs, dvec)
+            taker = MiDerivativeTaker(expr, dvec)
+            result = [taker.diff(mi) for mi in self.get_coefficient_identifiers()]
 
         logger.info("building translation operator: done")
         return result
diff --git a/sumpy/expansion/multipole.py b/sumpy/expansion/multipole.py
index 79412e17..04441795 100644
--- a/sumpy/expansion/multipole.py
+++ b/sumpy/expansion/multipole.py
@@ -89,16 +89,19 @@ class VolumeTaylorMultipoleExpansionBase(MultipoleExpansionBase):
         return self.full_to_stored(result)
 
     def evaluate(self, coeffs, bvec):
-        ppkernel = self.kernel.postprocess_at_target(
-                self.kernel.get_expression(bvec), bvec)
-
-        from sumpy.tools import MiDerivativeTaker
-        taker = MiDerivativeTaker(ppkernel, bvec)
+        taker = self.get_kernel_derivative_taker(bvec)
         result = sum(
                 coeff * taker.diff(mi)
                 for coeff, mi in zip(coeffs, self.get_coefficient_identifiers()))
         return result
 
+    def get_kernel_derivative_taker(self, bvec):
+        ppkernel = self.kernel.postprocess_at_target(
+                self.kernel.get_expression(bvec), bvec)
+
+        from sumpy.tools import MiDerivativeTaker
+        return MiDerivativeTaker(ppkernel, bvec)
+
     def translate_from(self, src_expansion, src_coeff_exprs, dvec):
         if not isinstance(src_expansion, type(self)):
             raise RuntimeError("do not know how to translate %s to "
-- 
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