def diff(self, mi):
"""
:arg mi: a multi-index (tuple) indicating how many x/y derivatives are
to be taken.
"""
try:
expr = self.cache_by_mi[mi]
except KeyError:
from six import iteritems
from sumpy.symbolic import Add
closest_mi = self.get_closest_cached_mi(mi)
expr = self.cache_by_mi[closest_mi]
# Try to reduce the derivative using recurrences first, and if that
# fails fall back to derivative taking.
for next_deriv, next_mi in (self.get_derivative_taking_sequence(
closest_mi, mi)):
recurrence = (self.wrangler.try_get_recurrence_for_derivative(
next_mi, self.cache_by_mi))
if recurrence is not None:
expr = Add(*tuple(
coeff * self.cache_by_mi[ident]
for ident, coeff in iteritems(recurrence)))
else:
expr = expr.diff(next_deriv)
self.cache_by_mi[next_mi] = expr
return expr
def diff(self, mi):
"""
:arg mi: a multi-index (tuple) indicating how many x/y derivatives are
to be taken.
"""
try:
expr = self.cache_by_mi[mi]
except KeyError:
from six import iteritems
from sumpy.symbolic import Add
closest_mi = self.get_closest_cached_mi(mi)
expr = self.cache_by_mi[closest_mi]
# Try to reduce the derivative using recurrences first, and if that
# fails fall back to derivative taking.
for next_deriv, next_mi in (
self.get_derivative_taking_sequence(closest_mi, mi)):
recurrence = (
self.wrangler.try_get_recurrence_for_derivative(
next_mi, self.cache_by_mi))
if recurrence is not None:
expr = Add(*tuple(
coeff * self.cache_by_mi[ident]
for ident, coeff in iteritems(recurrence)))
else:
expr = expr.diff(next_deriv)
self.cache_by_mi[next_mi] = expr
return expr
def test_cse_not_possible():
# No substitution possible.
e = Add(x, y)
substs, reduced = cse([e])
assert substs == []
assert reduced == [x + y]
# issue 6329
eq = (meijerg((1, 2), (y, 4), (5,), [], x) +
meijerg((1, 3), (y, 4), (5,), [], x))
assert cse(eq) == ([], [eq])
def test_nested_substitution():
# Substitution within a substitution.
e = Add(Pow(w*x + y, 2), sqrt(w*x + y))
substs, reduced = cse([e])
assert substs == [(x0, w*x + y)]
assert reduced == [sqrt(x0) + x0**2]
def test_cse_single():
# Simple substitution.
e = Add(Pow(x + y, 2), sqrt(x + y))
substs, reduced = cse([e])
assert substs == [(x0, x + y)]
assert reduced == [sqrt(x0) + x0**2]