def test_issue_7840():
# daveknippers' example
C393 = sympify( \
'Piecewise((C391 - 1.65, C390 < 0.5), (Piecewise((C391 - 1.65, \
C391 > 2.35), (C392, True)), True))'
)
C391 = sympify( \
'Piecewise((2.05*C390**(-1.03), C390 < 0.5), (2.5*C390**(-0.625), True))'
)
C393 = C393.subs('C391', C391)
# 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'), true)), Equality(Symbol('mode'), \
Symbol('AUTO'))), (Symbol('OFF'), true)), 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_11230():
# a specific test that always failed
a, b, f, k, l, i = symbols('a b f k l i')
p = [a * b * f * k * l, a * i * k**2 * l, f * i * k**2 * l]
R, C = cse(p)
assert not any(i.is_Mul for a in C for i in a.args)
# random tests for the issue
from sympy.core.random import choice
from sympy.core.function import expand_mul
s = symbols('a:m')
# 35 Mul tests, none of which should ever fail
ex = [Mul(*[choice(s) for i in range(5)]) for i in range(7)]
for p in subsets(ex, 3):
p = list(p)
R, C = cse(p)
assert not any(i.is_Mul for a in C for i in a.args)
for ri in reversed(R):
for i in range(len(C)):
C[i] = C[i].subs(*ri)
assert p == C
# 35 Add tests, none of which should ever fail
ex = [Add(*[choice(s[:7]) for i in range(5)]) for i in range(7)]
for p in subsets(ex, 3):
p = list(p)
R, C = cse(p)
assert not any(i.is_Add for a in C for i in a.args)
for ri in reversed(R):
for i in range(len(C)):
C[i] = C[i].subs(*ri)
# use expand_mul to handle cases like this:
# p = [a + 2*b + 2*e, 2*b + c + 2*e, b + 2*c + 2*g]
# x0 = 2*(b + e) is identified giving a rebuilt p that
# is now `[a + 2*(b + e), c + 2*(b + e), b + 2*c + 2*g]`
assert p == [expand_mul(i) for i in C]
def genEval(self):
text = " bool evaluate(\n"
args=[]
for name,v in self.variables:
if v.is_Matrix:
args.append(" const Eigen::MatrixXd & %s" % name)
else:
args.append(" double %s" % name)
args.append(" bool evalF=true,bool evalJ=true")
text += ",\n".join(args) + ") {\n"
text += " if (evalF) {\n"
(interm, expr) = cse(self.function,numbered_symbols("__x"));
for dummy,exp in interm:
text += " double %s = %s;\n" % (str(dummy),ccode(exp))
for i in range(self.function.rows):
text += " F(%d) = %s;\n" % (i,ccode(expr[0][i]))
text += " }\n"
text += " if (evalJ) {\n"
(interm, expr) = cse(self.J,numbered_symbols("__x"));
for dummy,exp in interm:
text += " double %s = %s;\n" % (str(dummy),ccode(exp))
for i in range(self.J.rows):
for j in range(self.J.cols):
text += " J(%d,%d) = %s;\n" % (i,j,ccode(expr[0][i,j]))
text += " }\n"
text += " return true;\n"
text += " }\n"
return text
def test_cse_ignore():
exprs = [exp(y)*(3*y + 3*sqrt(x+1)), exp(y)*(5*y + 5*sqrt(x+1))]
subst1, red1 = cse(exprs)
assert any(y in sub.free_symbols for _, sub in subst1), "cse failed to identify any term with y"
subst2, red2 = cse(exprs, ignore=(y,)) # y is not allowed in substitutions
assert not any(y in sub.free_symbols for _, sub in subst2), "Sub-expressions containing y must be ignored"
assert any(sub - sqrt(x + 1) == 0 for _, sub in subst2), "cse failed to identify sqrt(x + 1) as sub-expression"
def test_cse_MatrixSymbol():
# MatrixSymbols have non-Basic args, so make sure that works
A = MatrixSymbol("A", 3, 3)
assert cse(A) == ([], [A])
n = symbols('n', integer=True)
B = MatrixSymbol("B", n, n)
assert cse(B) == ([], [B])
def test_bypass_non_commutatives():
A, B, C = symbols('A B C', commutative=False)
l = [A * B * C, A * C]
assert cse(l) == ([], l)
l = [A * B * C, A * B]
assert cse(l) == ([], l)
l = [B * C, A * B * C]
assert cse(l) == ([], l)
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_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]
subst42, (red42, ) = cse([42]) # issue_15082
assert len(subst42) == 0 and red42 == 42
subst_half, (red_half, ) = cse([0.5])
assert len(subst_half) == 0 and red_half == 0.5
def test_issue_10228():
assert cse([x * y**2 + x * y]) == ([(x0, x * y)], [x0 * y + x0])
assert cse([x + y, 2 * x + y]) == ([(x0, x + y)], [x0, x + x0])
assert cse((w + 2 * x + y + z, w + x + 1)) == ([(x0, w + x)],
[x0 + x + y + z, x0 + 1])
assert cse(((w + x + y + z) * (w - x)) / (w + x)) == ([(x0, w + x)], [
(x0 + y + z) * (w - x) / x0
])
a, b, c, d, f, g, j, m = symbols('a, b, c, d, f, g, j, m')
exprs = (d * g**2 * j * m, 4 * a * f * g * m, a * b * c * f**2)
assert cse(exprs) == ([(x0, g * m), (x1, a * f)],
[d * g * j * x0, 4 * x0 * x1, b * c * f * x1])
def test_cse_single2():
# Simple substitution, test for being able to pass the expression directly
e = Add(Pow(x + y, 2), sqrt(x + y))
substs, reduced = cse(e)
assert substs == [(x0, x + y)]
assert reduced == [sqrt(x0) + x0**2]
substs, reduced = cse(Matrix([[1]]))
assert isinstance(reduced[0], Matrix)
subst42, (red42, ) = cse(42) # issue 15082
assert len(subst42) == 0 and red42 == 42
subst_half, (red_half, ) = cse(0.5) # issue 15082
assert len(subst_half) == 0 and red_half == 0.5
def test_cse_MatrixSymbol():
# MatrixSymbols have non-Basic args, so make sure that works
A = MatrixSymbol("A", 3, 3)
assert cse(A) == ([], [A])
n = symbols('n', integer=True)
B = MatrixSymbol("B", n, n)
assert cse(B) == ([], [B])
assert cse(A[0] * A[0]) == ([], [A[0] * A[0]])
assert cse(A[0, 0] * A[0, 1] + A[0, 0] * A[0, 1] * A[0, 2]) == ([
(x0, A[0, 0] * A[0, 1])
], [x0 * A[0, 2] + x0])
def test_cse_MatrixExpr():
A = MatrixSymbol('A', 3, 3)
y = MatrixSymbol('y', 3, 1)
expr1 = (A.T * A).I * A * y
expr2 = (A.T * A) * A * y
replacements, reduced_exprs = cse([expr1, expr2])
assert len(replacements) > 0
replacements, reduced_exprs = cse([expr1 + expr2, expr1])
assert replacements
replacements, reduced_exprs = cse([A**2, A + A**2])
assert replacements
def test_derivative_subs():
f = Function('f')
g = Function('g')
assert Derivative(f(x), x).subs(f(x), y) != 0
# need xreplace to put the function back, see #13803
assert Derivative(f(x), x).subs(f(x), y).xreplace({y: f(x)}) == \
Derivative(f(x), x)
# issues 5085, 5037
assert cse(Derivative(f(x), x) + f(x))[1][0].has(Derivative)
assert cse(Derivative(f(x, y), x) +
Derivative(f(x, y), y))[1][0].has(Derivative)
eq = Derivative(g(x), g(x))
assert eq.subs(g, f) == Derivative(f(x), f(x))
assert eq.subs(g(x), f(x)) == Derivative(f(x), f(x))
assert eq.subs(g, cos) == Subs(Derivative(y, y), y, cos(x))
def trigsimp(expr, deep=False, recursive=False):
"""
Usage
=====
trigsimp(expr) -> reduces expression by using known trig identities
Notes
=====
deep ........ apply trigsimp inside functions
recursive ... use common subexpression elimination (cse()) and apply
trigsimp recursively (recursively==True is quite expensive
operation if the expression is large)
Examples
========
>>> from sympy import *
>>> x = Symbol('x')
>>> y = Symbol('y')
>>> e = 2*sin(x)**2 + 2*cos(x)**2
>>> trigsimp(e)
2
>>> trigsimp(log(e))
log(2*cos(x)**2 + 2*sin(x)**2)
>>> trigsimp(log(e), deep=True)
log(2)
"""
from sympy.core.basic import S
sin, cos, tan, cot = C.sin, C.cos, C.tan, C.cot
if recursive:
w, g = cse(expr)
g = trigsimp_nonrecursive(g[0])
for sub in reversed(w):
g = g.subs(sub[0], sub[1])
g = trigsimp_nonrecursive(g)
result = g
else:
result = trigsimp_nonrecursive(expr, deep)
# do some final simplifications like sin/cos -> tan:
a,b,c = map(Wild, 'abc')
matchers = (
(a*sin(b)**c/cos(b)**c, a*tan(b)**c),
)
for pattern, simp in matchers:
res = result.match(pattern)
if res is not None:
# if c is missing or zero, do nothing:
if (not c in res) or res[c] == 0:
continue
# if "a" contains the argument of sin/cos "b", skip the
# simplification:
if res[a].has(res[b]):
continue
# simplify and finish:
result = simp.subs(res)
break
return result
def test_issue_8891():
for cls in (MutableDenseMatrix, MutableSparseMatrix, ImmutableDenseMatrix,
ImmutableSparseMatrix):
m = cls(2, 2, [x + y, 0, 0, 0])
res = cse([x + y, m])
ans = ([(x0, x + y)], [x0, cls([[x0, 0], [0, 0]])])
assert res == ans
assert isinstance(res[1][-1], cls)
def test_cse_ignore_issue_15002():
l = [
w*exp(x)*exp(-z),
exp(y)*exp(x)*exp(-z)
]
substs, reduced = cse(l, ignore=(x,))
rl = [e.subs(reversed(substs)) for e in reduced]
assert rl == l
def test_dont_cse_tuples():
from sympy.core.function import Subs
f = Function("f")
g = Function("g")
name_val, (expr, ) = cse(
Subs(f(x, y), (x, y), (0, 1)) + Subs(g(x, y), (x, y), (0, 1)))
assert name_val == []
assert expr == (Subs(f(x, y), (x, y),
(0, 1)) + Subs(g(x, y), (x, y), (0, 1)))
name_val, (expr, ) = cse(
Subs(f(x, y), (x, y), (0, x + y)) + Subs(g(x, y), (x, y), (0, x + y)))
assert name_val == [(x0, x + y)]
assert expr == Subs(f(x, y), (x, y), (0, x0)) + \
Subs(g(x, y), (x, y), (0, x0))
def test_issue_11577():
def check(eq):
r, c = cse(eq)
assert eq.count_ops() >= \
len(r) + sum([i[1].count_ops() for i in r]) + \
count_ops(c)
eq = x**5 * y**2 + x**5 * y + x**5
assert cse(eq) == ([(x0, x**4),
(x1, x * y)], [x**5 + x0 * x1 * y + x0 * x1])
# ([(x0, x**5*y)], [x0*y + x0 + x**5]) or
# ([(x0, x**5)], [x0*y**2 + x0*y + x0])
check(eq)
eq = x**2 / (y + 1)**2 + x / (y + 1)
assert cse(eq) == ([(x0, y + 1)], [x**2 / x0**2 + x / x0])
# ([(x0, x/(y + 1))], [x0**2 + x0])
check(eq)
def trigsimp(expr, deep=False, recursive=False):
"""
== Usage ==
trigsimp(expr) -> reduces expression by using known trig identities
== Notes ==
deep:
- Apply trigsimp inside functions
recursive:
- Use common subexpression elimination (cse()) and apply
trigsimp recursively (recursively==True is quite expensive
operation if the expression is large)
== Examples ==
>>> from sympy import *
>>> x = Symbol('x')
>>> y = Symbol('y')
>>> e = 2*sin(x)**2 + 2*cos(x)**2
>>> trigsimp(e)
2
>>> trigsimp(log(e))
log(2*cos(x)**2 + 2*sin(x)**2)
>>> trigsimp(log(e), deep=True)
log(2)
"""
from sympy.core.basic import S
sin, cos, tan, cot = C.sin, C.cos, C.tan, C.cot
if recursive:
w, g = cse(expr)
g = trigsimp_nonrecursive(g[0])
for sub in reversed(w):
g = g.subs(sub[0], sub[1])
g = trigsimp_nonrecursive(g)
result = g
else:
result = trigsimp_nonrecursive(expr, deep)
# do some final simplifications like sin/cos -> tan:
a, b, c = map(Wild, 'abc')
matchers = ((a * sin(b)**c / cos(b)**c, a * tan(b)**c), )
for pattern, simp in matchers:
res = result.match(pattern)
if res is not None:
# if c is missing or zero, do nothing:
if (not c in res) or res[c] == 0:
continue
# if "a" contains the argument of sin/cos "b", skip the
# simplification:
if res[a].has(res[b]):
continue
# simplify and finish:
result = simp.subs(res)
break
return result
def cse(self,
symbols=None,
optimizations=None,
postprocess=None,
order='canonical'):
"""
Return a new code block with common subexpressions eliminated
See the docstring of :func:`sympy.simplify.cse_main.cse` for more
information.
Examples
========
>>> from sympy import symbols, sin
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> c = CodeBlock(
... Assignment(x, 1),
... Assignment(y, sin(x) + 1),
... Assignment(z, sin(x) - 1),
... )
...
>>> c.cse()
CodeBlock(Assignment(x, 1), Assignment(x0, sin(x)), Assignment(y, x0 +
1), Assignment(z, x0 - 1))
"""
# TODO: Check that the symbols are new
from sympy.simplify.cse_main import cse
if not all(isinstance(i, Assignment) for i in self.args):
# Will support more things later
raise NotImplementedError(
"CodeBlock.cse only supports Assignments")
if any(isinstance(i, AugmentedAssignment) for i in self.args):
raise NotImplementedError(
"CodeBlock.cse doesn't yet work with AugmentedAssignments")
for i, lhs in enumerate(self.left_hand_sides):
if lhs in self.left_hand_sides[:i]:
raise NotImplementedError(
"Duplicate assignments to the same "
"variable are not yet supported (%s)" % lhs)
replacements, reduced_exprs = cse(self.right_hand_sides,
symbols=symbols,
optimizations=optimizations,
postprocess=postprocess,
order=order)
assert len(reduced_exprs) == 1
new_block = tuple(
Assignment(var, expr)
for var, expr in zip(self.left_hand_sides, reduced_exprs[0]))
new_assignments = tuple(Assignment(*i) for i in replacements)
return self.topological_sort(new_assignments + new_block)
def test_cse_Indexed():
len_y = 5
y = IndexedBase('y', shape=(len_y, ))
x = IndexedBase('x', shape=(len_y, ))
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_issue_6559():
assert (-12 * x + y).subs(-x, 1) == 12 + y
# though this involves cse it generated a failure in Mul._eval_subs
x0, x1 = symbols('x0 x1')
e = -log(-12 * sqrt(2) + 17) / 24 - log(-2 * sqrt(2) +
3) / 12 + sqrt(2) / 3
# XXX modify cse so x1 is eliminated and x0 = -sqrt(2)?
assert cse(e) == ([
(x0, sqrt(2))
], [x0 / 3 - log(-12 * x0 + 17) / 24 - log(-2 * x0 + 3) / 12])
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])
assert cse(((w + x + y + z)*(w - y - z))/(w + x)**3) == \
([(x0, w + x), (x1, y + z)], [(w - x1)*(x0 + x1)/x0**3])
def test_cse_list():
_cse = lambda x: cse(x, list=False)
assert _cse(x) == ([], x)
assert _cse('x') == ([], 'x')
it = [x]
for c in (list, tuple, set):
assert _cse(c(it)) == ([], c(it))
#Tuple works different from tuple:
assert _cse(Tuple(*it)) == ([], Tuple(*it))
d = {x: 1}
assert _cse(d) == ([], d)
def test_cse__performance():
nexprs, nterms = 3, 20
x = symbols('x:%d' % nterms)
exprs = [
reduce(add, [x[j] * (-1)**(i + j) for j in range(nterms)])
for i in range(nexprs)
]
assert (exprs[0] + exprs[1]).simplify() == 0
subst, red = cse(exprs)
assert len(subst) > 0, "exprs[0] == -exprs[2], i.e. a CSE"
for i, e in enumerate(red):
assert (e.subs(reversed(subst)) - exprs[i]).simplify() == 0
def Main():
#Read("spec.in")
#Read("spec_warp_simpler.in")
#Read("spec_warpPerspective.in")
Read("spec_rotate.in")
if False:
[(c_name, c_code), (h_name, c_header)] = codegen([("xdst", eqList[0]),
("ydst", eqList[1])],
"C",
"test",
header=False,
empty=False)
print("c_code = %s" % c_code)
print("eqList = %s" % str(eqList))
resEqSysMat = eqs2matrix(eqs=eqList,
unknownSymbols=(xdst, ydst),
augment=True)
print("resEqSysMat = %s" % str(resEqSysMat))
from sympy import Matrix, solve_linear_system
res = solve_linear_system(resEqSysMat, xdst, ydst)
print("The result is (xdst, ydst) = %s" % str(res))
print("res[xdst] = %s" % str(res[xdst]))
print("res[ydst] = %s" % str(res[ydst]))
#sympy.simplify.cse_main.cse(res[xdst], res[ydst])
expListWithBoundedVars = cse([res[xdst], res[ydst]])
print("After performing CSE, we have: %s" % str(expListWithBoundedVars))
print("expListWithBoundedVars[0] (the bounded vars) = %s" %
str(expListWithBoundedVars[0]))
print("expListWithBoundedVars[1][0] = %s" %
str(expListWithBoundedVars[1][0]))
eFinal = []
for e in expListWithBoundedVars[0]:
eFinal.append((str(e[0]), e[1]))
#expListWithBoundedVars[0] + \
expListWithBoundedVars = eFinal + \
[("xdst", expListWithBoundedVars[1][0])] + \
[("ydst", expListWithBoundedVars[1][1])]
print("expListWithBoundedVars = %s" % str(expListWithBoundedVars))
[(c_name, c_code), (h_name, c_header)] = codegen(expListWithBoundedVars,
"C",
"final_test",
header=False,
empty=False)
print("c_code = %s" % c_code)
def test_cse_release_variables():
from sympy.simplify.cse_main import cse_release_variables
_0, _1, _2, _3, _4 = symbols('_:5')
eqs = [(x + y - 1)**2, x, x + y, (x + y) / (2 * x + 1) + (x + y - 1)**2,
(2 * x + 1)**(x + y)]
r, e = cse(eqs, postprocess=cse_release_variables)
# this can change in keeping with the intention of the function
assert r, e == ([(x0, x + y), (x1, (x0 - 1)**2), (x2, 2 * x + 1),
(_3, x0 / x2 + x1), (_4, x2**x0), (x2, None), (_0, x1),
(x1, None), (_2, x0), (x0, None),
(_1, x)], (_0, _1, _2, _3, _4))
r.reverse()
assert eqs == [i.subs(r) for i in e]
def genEval(self):
text = " bool evaluate(\n"
args=[]
for name,v,lD in self.variables:
if isinstance(v, Matrix):
args.append(" const Eigen::Matrix<double, %d, 1> & %s" % (v.rows, name))
else:
args.append(" double %s" % name)
args.append(" Eigen::Matrix<double, %d, 1> * F" % self.function.rows)
for name,v,localDim in self.variables:
if isinstance(v, Matrix):
args.append(" Eigen::Matrix<double, %d, %d> * J%s" % (self.J.rows, localDim, name))
else:
args.append(" Eigen::Matrix<double, %d, 1> * J%s" % (self.J.rows, name))
text += ",\n".join(args) + ") {\n"
text += " if (F) {\n"
(interm, expr) = cse(self.function,numbered_symbols("__x"));
for dummy,exp in interm:
text += " double %s = %s;\n" % (str(dummy),ccode(exp))
for i in range(self.function.rows):
text += " (*F)(%d) = %s;\n" % (i,ccode(expr[0][i]))
text += " }\n"
text += " if (%s) {\n" % " && ".join([ "J" + name for name,v,lD in self.variables ])
(interm, expr) = cse(self.J,numbered_symbols("__x"));
for dummy,exp in interm:
text += " double %s = %s;\n" % (str(dummy),ccode(exp))
colBase = 0;
for name,v,localDim in self.variables:
for i in range(self.J.rows):
for j in range(0, localDim):
text += " (*J%s)(%d,%d) = %s;\n" % (name, i,j,ccode(expr[0][i,colBase + j]))
colBase+=localDim
text += " }\n"
text += " return true;\n"
text += " }\n"
return text
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 build_cse_fn(symname, symfunc, symbolslist):
tmpsyms = numbered_symbols("R")
symbols, simple = cse(symfunc, symbols=tmpsyms)
code = "double %s(%s)\n" % (str(symname), ", ".join(
"double const& %s" % x for x in symbolslist))
code += "{\n"
for s in symbols:
code += " double %s = %s;\n" % (ccode(s[0]), ccode(s[1]))
code += " double result = %s;\n" % ccode(simple[0])
code += " return result;\n"
code += "}\n"
return code
def cse(self, symbols=None, optimizations=None, postprocess=None,
order='canonical'):
"""
Return a new code block with common subexpressions eliminated
See the docstring of :func:`sympy.simplify.cse_main.cse` for more
information.
Examples
========
>>> from sympy import symbols, sin
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> c = CodeBlock(
... Assignment(x, 1),
... Assignment(y, sin(x) + 1),
... Assignment(z, sin(x) - 1),
... )
...
>>> c.cse()
CodeBlock(Assignment(x, 1), Assignment(x0, sin(x)), Assignment(y, x0 + 1), Assignment(z, x0 - 1))
"""
# TODO: Check that the symbols are new
from sympy.simplify.cse_main import cse
if not all(isinstance(i, Assignment) for i in self.args):
# Will support more things later
raise NotImplementedError("CodeBlock.cse only supports Assignments")
if any(isinstance(i, AugmentedAssignment) for i in self.args):
raise NotImplementedError("CodeBlock.cse doesn't yet work with AugmentedAssignments")
for i, lhs in enumerate(self.left_hand_sides):
if lhs in self.left_hand_sides[:i]:
raise NotImplementedError("Duplicate assignments to the same "
"variable are not yet supported (%s)" % lhs)
replacements, reduced_exprs = cse(self.right_hand_sides, symbols=symbols,
optimizations=optimizations, postprocess=postprocess, order=order)
assert len(reduced_exprs) == 1
new_block = tuple(Assignment(var, expr) for var, expr in
zip(self.left_hand_sides, reduced_exprs[0]))
new_assignments = tuple(Assignment(*i) for i in replacements)
return self.topological_sort(new_assignments + new_block)
def Main():
#Read("spec.in")
#Read("spec_warp_simpler.in")
#Read("spec_warpPerspective.in")
Read("spec_rotate.in")
if False:
[(c_name, c_code), (h_name, c_header)] = codegen(
[("xdst", eqList[0]), ("ydst", eqList[1])], "C", "test", header=False, empty=False)
print("c_code = %s" % c_code)
print("eqList = %s" % str(eqList))
resEqSysMat = eqs2matrix(eqs=eqList, unknownSymbols=(xdst, ydst), augment=True)
print("resEqSysMat = %s" % str(resEqSysMat))
from sympy import Matrix, solve_linear_system
res = solve_linear_system(resEqSysMat, xdst, ydst)
print("The result is (xdst, ydst) = %s" % str(res))
print("res[xdst] = %s" % str(res[xdst]))
print("res[ydst] = %s" % str(res[ydst]))
#sympy.simplify.cse_main.cse(res[xdst], res[ydst])
expListWithBoundedVars = cse([res[xdst], res[ydst]])
print("After performing CSE, we have: %s" % str(expListWithBoundedVars))
print("expListWithBoundedVars[0] (the bounded vars) = %s" % str(expListWithBoundedVars[0]))
print("expListWithBoundedVars[1][0] = %s" % str(expListWithBoundedVars[1][0]))
eFinal = []
for e in expListWithBoundedVars[0]:
eFinal.append( (str(e[0]), e[1]) )
#expListWithBoundedVars[0] + \
expListWithBoundedVars = eFinal + \
[("xdst", expListWithBoundedVars[1][0])] + \
[("ydst", expListWithBoundedVars[1][1])]
print("expListWithBoundedVars = %s" % str(expListWithBoundedVars))
[(c_name, c_code), (h_name, c_header)] = codegen(
expListWithBoundedVars, "C", "final_test", header=False, empty=False)
print("c_code = %s" % c_code)
def test_issue_4499():
# previously, this gave 16 constants
from sympy.abc import a, b
B = Function('B')
G = Function('G')
t = Tuple(*
(a, a + S.Half, 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.Half, z/2, -b + 1, -2*a + b,
-2*a))
c = cse(t)
ans = (
[(x0, 2*a), (x1, -b + x0), (x2, x1 + 1), (x3, b - 1), (x4, sqrt(z)),
(x5, B(x3, x4)), (x6, (x4/2)**(1 - x0)*G(b)*G(x2)), (x7, x6*B(x1, x4)),
(x8, B(b, x4)), (x9, x6*B(x2, x4))],
[(a, a + S.Half, x0, b, x2, x5*x7, x4*x7*x8, x4*x5*x9, x8*x9,
1, 0, S.Half, z/2, -x3, -x1, -x0)])
assert ans == c
def trigsimp_old(expr, **opts):
"""
reduces expression by using known trig identities
Notes
=====
deep:
- Apply trigsimp inside all objects with arguments
recursive:
- Use common subexpression elimination (cse()) and apply
trigsimp recursively (this is quite expensive if the
expression is large)
method:
- Determine the method to use. Valid choices are 'matching' (default),
'groebner', 'combined', 'fu' and 'futrig'. If 'matching', simplify the
expression recursively by pattern matching. If 'groebner', apply an
experimental groebner basis algorithm. In this case further options
are forwarded to ``trigsimp_groebner``, please refer to its docstring.
If 'combined', first run the groebner basis algorithm with small
default parameters, then run the 'matching' algorithm. 'fu' runs the
collection of trigonometric transformations described by Fu, et al.
(see the `fu` docstring) while `futrig` runs a subset of Fu-transforms
that mimic the behavior of `trigsimp`.
compare:
- show input and output from `trigsimp` and `futrig` when different,
but returns the `trigsimp` value.
Examples
========
>>> from sympy import trigsimp, sin, cos, log, cosh, sinh, tan, cot
>>> from sympy.abc import x, y
>>> e = 2*sin(x)**2 + 2*cos(x)**2
>>> trigsimp(e, old=True)
2
>>> trigsimp(log(e), old=True)
log(2*sin(x)**2 + 2*cos(x)**2)
>>> trigsimp(log(e), deep=True, old=True)
log(2)
Using `method="groebner"` (or `"combined"`) can sometimes lead to a lot
more simplification:
>>> e = (-sin(x) + 1)/cos(x) + cos(x)/(-sin(x) + 1)
>>> trigsimp(e, old=True)
(1 - sin(x))/cos(x) + cos(x)/(1 - sin(x))
>>> trigsimp(e, method="groebner", old=True)
2/cos(x)
>>> trigsimp(1/cot(x)**2, compare=True, old=True)
futrig: tan(x)**2
cot(x)**(-2)
"""
old = expr
first = opts.pop('first', True)
if first:
if not expr.has(*_trigs):
return expr
trigsyms = set().union(*[t.free_symbols for t in expr.atoms(*_trigs)])
if len(trigsyms) > 1:
from sympy.simplify.simplify import separatevars
d = separatevars(expr)
if d.is_Mul:
d = separatevars(d, dict=True) or d
if isinstance(d, dict):
expr = 1
for k, v in d.items():
# remove hollow factoring
was = v
v = expand_mul(v)
opts['first'] = False
vnew = trigsimp(v, **opts)
if vnew == v:
vnew = was
expr *= vnew
old = expr
else:
if d.is_Add:
for s in trigsyms:
r, e = expr.as_independent(s)
if r:
opts['first'] = False
expr = r + trigsimp(e, **opts)
if not expr.is_Add:
break
old = expr
recursive = opts.pop('recursive', False)
deep = opts.pop('deep', False)
method = opts.pop('method', 'matching')
def groebnersimp(ex, deep, **opts):
def traverse(e):
if e.is_Atom:
return e
args = [traverse(x) for x in e.args]
if e.is_Function or e.is_Pow:
args = [trigsimp_groebner(x, **opts) for x in args]
return e.func(*args)
if deep:
ex = traverse(ex)
return trigsimp_groebner(ex, **opts)
trigsimpfunc = {
'matching': (lambda x, d: _trigsimp(x, d)),
'groebner': (lambda x, d: groebnersimp(x, d, **opts)),
'combined': (lambda x, d: _trigsimp(groebnersimp(x,
d, polynomial=True, hints=[2, tan]),
d))
}[method]
if recursive:
w, g = cse(expr)
g = trigsimpfunc(g[0], deep)
for sub in reversed(w):
g = g.subs(sub[0], sub[1])
g = trigsimpfunc(g, deep)
result = g
else:
result = trigsimpfunc(expr, deep)
if opts.get('compare', False):
f = futrig(old)
if f != result:
print('\tfutrig:', f)
return result
def trigsimp_old(expr, **opts):
"""
reduces expression by using known trig identities
Notes
=====
deep:
- Apply trigsimp inside all objects with arguments
recursive:
- Use common subexpression elimination (cse()) and apply
trigsimp recursively (this is quite expensive if the
expression is large)
method:
- Determine the method to use. Valid choices are 'matching' (default),
'groebner', 'combined', 'fu' and 'futrig'. If 'matching', simplify the
expression recursively by pattern matching. If 'groebner', apply an
experimental groebner basis algorithm. In this case further options
are forwarded to ``trigsimp_groebner``, please refer to its docstring.
If 'combined', first run the groebner basis algorithm with small
default parameters, then run the 'matching' algorithm. 'fu' runs the
collection of trigonometric transformations described by Fu, et al.
(see the `fu` docstring) while `futrig` runs a subset of Fu-transforms
that mimic the behavior of `trigsimp`.
compare:
- show input and output from `trigsimp` and `futrig` when different,
but returns the `trigsimp` value.
Examples
========
>>> from sympy import trigsimp, sin, cos, log, cosh, sinh, tan, cot
>>> from sympy.abc import x, y
>>> e = 2*sin(x)**2 + 2*cos(x)**2
>>> trigsimp(e, old=True)
2
>>> trigsimp(log(e), old=True)
log(2*sin(x)**2 + 2*cos(x)**2)
>>> trigsimp(log(e), deep=True, old=True)
log(2)
Using `method="groebner"` (or `"combined"`) can sometimes lead to a lot
more simplification:
>>> e = (-sin(x) + 1)/cos(x) + cos(x)/(-sin(x) + 1)
>>> trigsimp(e, old=True)
(1 - sin(x))/cos(x) + cos(x)/(1 - sin(x))
>>> trigsimp(e, method="groebner", old=True)
2/cos(x)
>>> trigsimp(1/cot(x)**2, compare=True, old=True)
futrig: tan(x)**2
cot(x)**(-2)
"""
old = expr
first = opts.pop('first', True)
if first:
if not expr.has(*_trigs):
return expr
trigsyms = set().union(*[t.free_symbols for t in expr.atoms(*_trigs)])
if len(trigsyms) > 1:
from sympy.simplify.simplify import separatevars
d = separatevars(expr)
if d.is_Mul:
d = separatevars(d, dict=True) or d
if isinstance(d, dict):
expr = 1
for k, v in d.items():
# remove hollow factoring
was = v
v = expand_mul(v)
opts['first'] = False
vnew = trigsimp(v, **opts)
if vnew == v:
vnew = was
expr *= vnew
old = expr
else:
if d.is_Add:
for s in trigsyms:
r, e = expr.as_independent(s)
if r:
opts['first'] = False
expr = r + trigsimp(e, **opts)
if not expr.is_Add:
break
old = expr
recursive = opts.pop('recursive', False)
deep = opts.pop('deep', False)
method = opts.pop('method', 'matching')
def groebnersimp(ex, deep, **opts):
def traverse(e):
if e.is_Atom:
return e
args = [traverse(x) for x in e.args]
if e.is_Function or e.is_Pow:
args = [trigsimp_groebner(x, **opts) for x in args]
return e.func(*args)
if deep:
ex = traverse(ex)
return trigsimp_groebner(ex, **opts)
trigsimpfunc = {
'matching': (lambda x, d: _trigsimp(x, d)),
'groebner': (lambda x, d: groebnersimp(x, d, **opts)),
'combined': (lambda x, d: _trigsimp(
groebnersimp(x, d, polynomial=True, hints=[2, tan]), d))
}[method]
if recursive:
w, g = cse(expr)
g = trigsimpfunc(g[0], deep)
for sub in reversed(w):
g = g.subs(sub[0], sub[1])
g = trigsimpfunc(g, deep)
result = g
else:
result = trigsimpfunc(expr, deep)
if opts.get('compare', False):
f = futrig(old)
if f != result:
print('\tfutrig:', f)
return result
def cse_print(expr):
cses, simple_expr = cse(expr)
print
print sympy.pretty(simple_expr)
pp(cses)
print
