def test_issue_7840():
# daveknippers' example
C393 = sympify( # noqa
'Piecewise((C391 - 1.65, C390 < 0.5), (Piecewise((C391 - 1.65, \
C391 > 2.35), (C392, True)), True))'
)
C391 = sympify( # noqa
'Piecewise((2.05*C390**(-1.03), C390 < 0.5), (2.5*C390**(-0.625), True))'
)
C393 = C393.subs('C391',C391) # noqa
# simple substitution
sub = {}
sub['C390'] = 0.703451854
sub['C392'] = 1.01417794
ss_answer = C393.subs(sub)
# cse
substitutions, new_eqn = cse(C393)
for pair in substitutions:
sub[pair[0].name] = pair[1].subs(sub)
cse_answer = new_eqn[0].subs(sub)
# both methods should be the same
assert ss_answer == cse_answer
# GitRay's example
expr = sympify(
"Piecewise((Symbol('ON'), Equality(Symbol('mode'), Symbol('ON'))), \
(Piecewise((Piecewise((Symbol('OFF'), StrictLessThan(Symbol('x'), \
Symbol('threshold'))), (Symbol('ON'), S.true)), Equality(Symbol('mode'), \
Symbol('AUTO'))), (Symbol('OFF'), S.true)), S.true))"
)
substitutions, new_eqn = cse(expr)
# this Piecewise should be exactly the same
assert new_eqn[0] == expr
# there should not be any replacements
assert len(substitutions) < 1
def test_issue_7840():
# daveknippers' example
C393 = sympify( # noqa
'Piecewise((C391 - 1.65, C390 < 0.5), (Piecewise((C391 - 1.65, \
C391 > 2.35), (C392, True)), True))'
)
C391 = sympify( # noqa
'Piecewise((2.05*C390**(-1.03), C390 < 0.5), (2.5*C390**(-0.625), True))'
)
C393 = C393.subs('C391',C391) # noqa
# simple substitution
sub = {}
sub['C390'] = 0.703451854
sub['C392'] = 1.01417794
ss_answer = C393.subs(sub)
# cse
substitutions, new_eqn = cse(C393)
for pair in substitutions:
sub[pair[0].name] = pair[1].subs(sub)
cse_answer = new_eqn[0].subs(sub)
# both methods should be the same
assert ss_answer == cse_answer
# GitRay's example
expr = sympify(
"Piecewise((Symbol('ON'), Equality(Symbol('mode'), Symbol('ON'))), \
(Piecewise((Piecewise((Symbol('OFF'), StrictLessThan(Symbol('x'), \
Symbol('threshold'))), (Symbol('ON'), S.true)), Equality(Symbol('mode'), \
Symbol('AUTO'))), (Symbol('OFF'), S.true)), S.true))"
)
substitutions, new_eqn = cse(expr)
# this Piecewise should be exactly the same
assert new_eqn[0] == expr
# there should not be any replacements
assert len(substitutions) < 1
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_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_recursive_matching():
assert cse([x+y, 2+x+y, x+y+z, 3+x+y+z]) == \
([(x0, x + y), (x1, x0 + z)], [x0, x0 + 2, x1, x1 + 3])
assert cse(reversed([x+y, 2+x+y, x+y+z, 3+x+y+z])) == \
([(x0, x + y), (x1, x0 + z)], [x1 + 3, x1, x0 + 2, x0])
# sympy 1.0 gives ([(x0, x*y*z)], [5*x0, w*(x*y), 3*x0])
assert cse([x*y*z*5, x*y*w, x*y*z*3]) == \
([(x0, x*y), (x1, x0*z)], [5*x1, w*x0, 3*x1])
# sympy 1.0 gives ([(x4, x*y*z)], [5*x4, w*x3*x4, 3*x*x0*x1*x2*y])
assert cse([x*y*z*5, x*y*z*w*x3, x*y*3*x0*x1*x2]) == \
([(x4, x*y), (x5, x4*z)], [5*x5, w*x3*x5, 3*x0*x1*x2*x4])
assert cse([2*x*x, x*x*y, x*x*y*w, x*x*y*w*x0, x*x*y*w*x2]) == \
([(x1, x**2), (x3, x1*y), (x4, w*x3)], [2*x1, x3, x4, x0*x4, x2*x4])
def test_recursive_matching():
assert cse([x+y, 2+x+y, x+y+z, 3+x+y+z]) == \
([(x0, x + y), (x1, x0 + z)], [x0, x0 + 2, x1, x1 + 3])
assert cse(reversed([x+y, 2+x+y, x+y+z, 3+x+y+z])) == \
([(x0, x + y), (x1, x0 + z)], [x1 + 3, x1, x0 + 2, x0])
# sympy 1.0 gives ([(x0, x*y*z)], [5*x0, w*(x*y), 3*x0])
assert cse([x*y*z*5, x*y*w, x*y*z*3]) == \
([(x0, x*y), (x1, x0*z)], [5*x1, w*x0, 3*x1])
# sympy 1.0 gives ([(x4, x*y*z)], [5*x4, w*x3*x4, 3*x*x0*x1*x2*y])
assert cse([x*y*z*5, x*y*z*w*x3, x*y*3*x0*x1*x2]) == \
([(x4, x*y), (x5, x4*z)], [5*x5, w*x3*x5, 3*x0*x1*x2*x4])
assert cse([2*x*x, x*x*y, x*x*y*w, x*x*y*w*x0, x*x*y*w*x2]) == \
([(x1, x**2), (x3, x1*y), (x4, w*x3)], [2*x1, x3, x4, x0*x4, x2*x4])
def test_dont_cse_subs():
f = Function("f")
g = Function("g")
name_val, (expr,) = cse(f(x+y).diff(x) + g(x+y).diff(x))
assert name_val == []
def test_issue_4499():
# previously, this gave 16 constants
from sympy.abc import a, b
from sympy import Tuple, S
B = Function("B") # noqa
G = Function("G") # noqa
t = Tuple(*(
a,
a + S(1) / 2,
2 * a,
b,
2 * a - b + 1,
(sqrt(z) / 2)**(-2 * a + 1) * B(2 * a - b, sqrt(z)) *
B(b - 1, sqrt(z)) * G(b) * G(2 * a - b + 1), # noqa
sqrt(z) * (sqrt(z) / 2)**(-2 * a + 1) * B(b, sqrt(z)) * B(
2 * a - b, # noqa
sqrt(z)) * G(b) * G(2 * a - b + 1),
sqrt(z) * (sqrt(z) / 2)**(-2 * a + 1) * B(b - 1, sqrt(z)) *
B(2 * a - b + 1, sqrt(z)) * G(b) * G(2 * a - b + 1),
(sqrt(z) / 2)**(-2 * a + 1) * B(b, sqrt(z)) * B(
2 * a - b + 1, # noqa
sqrt(z)) * G(b) * G(2 * a - b + 1),
1,
0,
S(1) / 2,
z / 2,
-b + 1,
-2 * a + b, # noqa
-2 * a)) # noqa
c = cse(t)
assert len(c[0]) == 11
def run_global_cse(self, extra_exprs=[]):
import time
start_time = time.time()
logger.info("common subexpression elimination: start")
assign_names = sorted(self.assignments)
assign_exprs = [self.assignments[name] for name in assign_names]
# Options here:
# - checked_cse: if you mistrust the result of the cse.
# Uses maxima to verify.
# - sym.cse: The sympy thing.
# - sumpy.cse.cse: Based on sympy, designed to go faster.
#from sumpy.symbolic import checked_cse
from sumpy.cse import cse
new_assignments, new_exprs = cse(assign_exprs + extra_exprs,
symbols=self.symbol_generator)
new_assign_exprs = new_exprs[:len(assign_exprs)]
new_extra_exprs = new_exprs[len(assign_exprs):]
for name, new_expr in zip(assign_names, new_assign_exprs):
self.assignments[name] = new_expr
for name, value in new_assignments:
assert isinstance(name, sym.Symbol)
self.add_assignment(name.name, value)
logger.info(
"common subexpression elimination: done after {dur:.2f} s".format(
dur=time.time() - start_time))
return new_extra_exprs
def test_dont_cse_subs():
f = Function("f")
g = Function("g")
name_val, (expr,) = cse(f(x+y).diff(x) + g(x+y).diff(x))
assert name_val == []
def run_global_cse(self, extra_exprs=[]):
import time
start_time = time.time()
logger.info("common subexpression elimination: start")
assign_names = sorted(self.assignments)
assign_exprs = [self.assignments[name] for name in assign_names]
# Options here:
# - checked_cse: if you mistrust the result of the cse.
# Uses maxima to verify.
# - sym.cse: The sympy thing.
# - sumpy.cse.cse: Based on sympy, designed to go faster.
#from sumpy.symbolic import checked_cse
from sumpy.cse import cse
new_assignments, new_exprs = cse(assign_exprs + extra_exprs,
symbols=self.symbol_generator)
new_assign_exprs = new_exprs[:len(assign_exprs)]
new_extra_exprs = new_exprs[len(assign_exprs):]
for name, new_expr in zip(assign_names, new_assign_exprs):
self.assignments[name] = new_expr
for name, value in new_assignments:
assert isinstance(name, sym.Symbol)
self.add_assignment(name.name, value)
logger.info("common subexpression elimination: done after {dur:.2f} s"
.format(dur=time.time() - start_time))
return new_extra_exprs
def test_issue_6169():
from sympy import CRootOf
r = CRootOf(x**6 - 4*x**5 - 2, 1)
assert cse(r) == ([], [r])
# and a check that the right thing is done with the new
# mechanism
assert sub_post(sub_pre((-x - y)*z - x - y)) == -z*(x + y) - x - y
def test_Piecewise(): # noqa
from sympy import Piecewise, Eq
f = Piecewise((-z + x*y, Eq(y, 0)), (-z - x*y, True))
ans = cse(f)
actual_ans = ([(x0, -z), (x1, x*y)],
[Piecewise((x0+x1, Eq(y, 0)), (x0 - x1, True))])
assert ans == actual_ans
def test_Piecewise(): # noqa
from sympy import Piecewise, Eq
f = Piecewise((-z + x*y, Eq(y, 0)), (-z - x*y, True))
ans = cse(f)
actual_ans = ([(x0, -z), (x1, x*y)],
[Piecewise((x0+x1, Eq(y, 0)), (x0 - x1, True))])
assert ans == actual_ans
def test_issue_6169():
from sympy import CRootOf
r = CRootOf(x**6 - 4*x**5 - 2, 1)
assert cse(r) == ([], [r])
# and a check that the right thing is done with the new
# mechanism
assert sub_post(sub_pre((-x - y)*z - x - y)) == -z*(x + y) - x - y
def test_subtraction_opt():
# Make sure subtraction is optimized.
e = (x - y)*(z - y) + exp((x - y)*(z - y))
substs, reduced = cse(
[e], optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)])
assert substs == [(x0, (x - y)*(y - z))]
assert reduced == [-x0 + exp(-x0)]
e = -(x - y)*(z - y) + exp(-(x - y)*(z - y))
substs, reduced = cse(
[e], optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)])
assert substs == [(x0, (x - y)*(y - z))]
assert reduced == [x0 + exp(x0)]
# issue 4077
n = -1 + 1/x
e = n/x/(-n)**2 - 1/n/x
assert cse(e, optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)]) == \
([], [0])
def test_subtraction_opt():
# Make sure subtraction is optimized.
e = (x - y)*(z - y) + exp((x - y)*(z - y))
substs, reduced = cse(
[e], optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)])
assert substs == [(x0, (x - y)*(y - z))]
assert reduced == [-x0 + exp(-x0)]
e = -(x - y)*(z - y) + exp(-(x - y)*(z - y))
substs, reduced = cse(
[e], optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)])
assert substs == [(x0, (x - y)*(y - z))]
assert reduced == [x0 + exp(x0)]
# issue 4077
n = -1 + 1/x
e = n/x/(-n)**2 - 1/n/x
assert cse(e, optimizations=[(cse_opts.sub_pre, cse_opts.sub_post)]) == \
([], [0])
def test_dont_cse_derivative():
from sumpy.symbolic import Derivative
f = Function("f")
deriv = Derivative(f(x+y), x)
name_val, (expr,) = cse(x + y + deriv)
assert name_val == []
assert expr == x + y + deriv
def test_dont_cse_derivative():
from sumpy.symbolic import Derivative
f = Function("f")
deriv = Derivative(f(x+y), x)
name_val, (expr,) = cse(x + y + deriv)
assert name_val == []
assert expr == x + y + deriv
def test_cse_Indexed(): # noqa
from sympy import IndexedBase, Idx
len_y = 5
y = IndexedBase('y', shape=(len_y,))
x = IndexedBase('x', shape=(len_y,))
Dy = IndexedBase('Dy', shape=(len_y-1,)) # noqa
i = Idx('i', len_y-1)
expr1 = (y[i+1]-y[i])/(x[i+1]-x[i])
expr2 = 1/(x[i+1]-x[i])
replacements, reduced_exprs = cse([expr1, expr2])
assert len(replacements) > 0
def test_cse_Indexed(): # noqa
from sympy import IndexedBase, Idx
len_y = 5
y = IndexedBase('y', shape=(len_y,))
x = IndexedBase('x', shape=(len_y,))
Dy = IndexedBase('Dy', shape=(len_y-1,)) # noqa
i = Idx('i', len_y-1)
expr1 = (y[i+1]-y[i])/(x[i+1]-x[i])
expr2 = 1/(x[i+1]-x[i])
replacements, reduced_exprs = cse([expr1, expr2])
assert len(replacements) > 0
def test_pow_invpow():
assert cse(1/x**2 + x**2) == \
([(x0, x**2)], [x0 + 1/x0])
assert cse(x**2 + (1 + 1/x**2)/x**2) == \
([(x0, x**2), (x1, 1/x0)], [x0 + x1*(x1 + 1)])
assert cse(1/x**2 + (1 + 1/x**2)*x**2) == \
([(x0, x**2), (x1, 1/x0)], [x0*(x1 + 1) + x1])
assert cse(cos(1/x**2) + sin(1/x**2)) == \
([(x0, x**(-2))], [sin(x0) + cos(x0)])
assert cse(cos(x**2) + sin(x**2)) == \
([(x0, x**2)], [sin(x0) + cos(x0)])
assert cse(y/(2 + x**2) + z/x**2/y) == \
([(x0, x**2)], [y/(x0 + 2) + z/(x0*y)])
assert cse(exp(x**2) + x**2*cos(1/x**2)) == \
([(x0, x**2)], [x0*cos(1/x0) + exp(x0)])
assert cse((1 + 1/x**2)/x**2) == \
([(x0, x**(-2))], [x0*(x0 + 1)])
assert cse(x**(2*y) + x**(-2*y)) == \
([(x0, x**(2*y))], [x0 + 1/x0])
def test_pow_invpow():
assert cse(1/x**2 + x**2) == \
([(x0, x**2)], [x0 + 1/x0])
assert cse(x**2 + (1 + 1/x**2)/x**2) == \
([(x0, x**2), (x1, 1/x0)], [x0 + x1*(x1 + 1)])
assert cse(1/x**2 + (1 + 1/x**2)*x**2) == \
([(x0, x**2), (x1, 1/x0)], [x0*(x1 + 1) + x1])
assert cse(cos(1/x**2) + sin(1/x**2)) == \
([(x0, x**(-2))], [sin(x0) + cos(x0)])
assert cse(cos(x**2) + sin(x**2)) == \
([(x0, x**2)], [sin(x0) + cos(x0)])
assert cse(y/(2 + x**2) + z/x**2/y) == \
([(x0, x**2)], [y/(x0 + 2) + z/(x0*y)])
assert cse(exp(x**2) + x**2*cos(1/x**2)) == \
([(x0, x**2)], [x0*cos(1/x0) + exp(x0)])
assert cse((1 + 1/x**2)/x**2) == \
([(x0, x**(-2))], [x0*(x0 + 1)])
assert cse(x**(2*y) + x**(-2*y)) == \
([(x0, x**(2*y))], [x0 + 1/x0])
def test_issue_4499():
# previously, this gave 16 constants
from sympy.abc import a, b
from sympy import Tuple, S
B = Function('B') # noqa
G = Function('G') # noqa
t = Tuple(
*(a, a + S(1)/2, 2*a, b, 2*a - b + 1, (sqrt(z)/2)**(-2*a + 1)*B(2*a
- b, sqrt(z))*B(b - 1, sqrt(z))*G(b)*G(2*a - b + 1),
sqrt(z)*(sqrt(z)/2)**(-2*a + 1)*B(b, sqrt(z))*B(2*a - b,
sqrt(z))*G(b)*G(2*a - b + 1), sqrt(z)*(sqrt(z)/2)**(-2*a + 1)*B(b - 1,
sqrt(z))*B(2*a - b + 1, sqrt(z))*G(b)*G(2*a - b + 1),
(sqrt(z)/2)**(-2*a + 1)*B(b, sqrt(z))*B(2*a - b + 1,
sqrt(z))*G(b)*G(2*a - b + 1), 1, 0, S(1)/2, z/2, -b + 1, -2*a + b,
-2*a)) # noqa
c = cse(t)
assert len(c[0]) == 11
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]
def test_name_conflict():
z1 = x0 + y
z2 = x2 + x3
l_ = [cos(z1) + z1, cos(z2) + z2, x0 + x2]
substs, reduced = cse(l_)
assert [e.subs(dict(substs)) for e in reduced] == l_
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_name_conflict_cust_symbols():
z1 = x0 + y
z2 = x2 + x3
l = [cos(z1) + z1, cos(z2) + z2, x0 + x2]
substs, reduced = cse(l, symbols("x:10"))
assert [e.subs(dict(substs)) for e in reduced] == l
def test_symbols_exhausted_error():
l = cos(x+y)+x+y+cos(w+y)+sin(w+y)
sym = [x, y, z]
with pytest.raises(ValueError):
print(cse(l, symbols=sym))
def test_name_conflict_cust_symbols():
z1 = x0 + y
z2 = x2 + x3
l_ = [cos(z1) + z1, cos(z2) + z2, x0 + x2]
substs, reduced = cse(l_, symbols("x:10"))
assert [e.subs(dict(substs)) for e in reduced] == l_
def test_name_conflict():
z1 = x0 + y
z2 = x2 + x3
l = [cos(z1) + z1, cos(z2) + z2, x0 + x2]
substs, reduced = cse(l)
assert [e.subs(dict(substs)) for e in reduced] == l
def test_issue_4203():
assert cse(sin(x**x)/x**x) == ([(x0, x**x)], [sin(x0)/x0])
def test_symbols_exhausted_error():
l_ = cos(x+y)+x+y+cos(w+y)+sin(w+y)
sym = [x, y, z]
with pytest.raises(ValueError):
print(cse(l_, symbols=sym))
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]
def test_multiple_expressions():
e1 = (x + y)*z
e2 = (x + y)*w
substs, reduced = cse([e1, e2])
assert substs == [(x0, x + y)]
assert reduced == [x0*z, x0*w]
l_ = [w*x*y + z, w*y]
substs, reduced = cse(l_)
rsubsts, _ = cse(reversed(l_))
assert substs == rsubsts
assert reduced == [z + x*x0, x0]
l_ = [w*x*y, w*x*y + z, w*y]
substs, reduced = cse(l_)
rsubsts, _ = cse(reversed(l_))
assert substs == rsubsts
assert reduced == [x1, x1 + z, x0]
f = Function("f")
l_ = [f(x - z, y - z), x - z, y - z]
substs, reduced = cse(l_)
rsubsts, _ = cse(reversed(l_))
assert substs == [(x0, -z), (x1, x + x0), (x2, x0 + y)]
assert rsubsts == [(x0, -z), (x1, x0 + y), (x2, x + x0)]
assert reduced == [f(x1, x2), x1, x2]
l_ = [w*y + w + x + y + z, w*x*y]
assert cse(l_) == ([(x0, w*y)], [w + x + x0 + y + z, x*x0])
assert cse([x + y, x + y + z]) == ([(x0, x + y)], [x0, z + x0])
assert cse([x + y, x + z]) == ([], [x + y, x + z])
assert cse([x*y, z + x*y, x*y*z + 3]) == \
([(x0, x*y)], [x0, z + x0, 3 + x0*z])
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_issue_4203():
assert cse(sin(x**x)/x**x) == ([(x0, x**x)], [sin(x0)/x0])
def test_multiple_expressions():
e1 = (x + y)*z
e2 = (x + y)*w
substs, reduced = cse([e1, e2])
assert substs == [(x0, x + y)]
assert reduced == [x0*z, x0*w]
l = [w*x*y + z, w*y]
substs, reduced = cse(l)
rsubsts, _ = cse(reversed(l))
assert substs == rsubsts
assert reduced == [z + x*x0, x0]
l = [w*x*y, w*x*y + z, w*y]
substs, reduced = cse(l)
rsubsts, _ = cse(reversed(l))
assert substs == rsubsts
assert reduced == [x1, x1 + z, x0]
f = Function("f")
l = [f(x - z, y - z), x - z, y - z]
substs, reduced = cse(l)
rsubsts, _ = cse(reversed(l))
assert substs == [(x0, -z), (x1, x + x0), (x2, x0 + y)]
assert rsubsts == [(x0, -z), (x1, x0 + y), (x2, x + x0)]
assert reduced == [f(x1, x2), x1, x2]
l = [w*y + w + x + y + z, w*x*y]
assert cse(l) == ([(x0, w*y)], [w + x + x0 + y + z, x*x0])
assert cse([x + y, x + y + z]) == ([(x0, x + y)], [x0, z + x0])
assert cse([x + y, x + z]) == ([], [x + y, x + z])
assert cse([x*y, z + x*y, x*y*z + 3]) == \
([(x0, x*y)], [x0, z + x0, 3 + x0*z])
