def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise(
(a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify(
) == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)),
Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y
+ a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify(
) == Piecewise(
(2*x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
args = (2, And(Eq(x, 2), Ge(y ,0))), (x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
args = (1, Eq(x, 0)), (sin(x)/x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
assert Piecewise((2 + y, And(Eq(x, 2), Eq(y, 0))), (x, True)
).simplify() == x
# check that x or f(x) are recognized as being Symbol-like for lhs
args = Tuple((1, Eq(x, 0)), (sin(x) + 1 + x, True))
ans = x + sin(x) + 1
f = Function('f')
assert Piecewise(*args).simplify() == ans
assert Piecewise(*args.subs(x, f(x))).simplify() == ans.subs(x, f(x))
def test_piecewise_interval():
p1 = Piecewise((x, Interval(0, 1).contains(x)), (0, True))
assert p1.subs(x, -0.5) == 0
assert p1.subs(x, 0.5) == 0.5
assert p1.diff(x) == Piecewise((1, Interval(0, 1).contains(x)), (0, True))
assert integrate(
p1, x) == Piecewise((x**2/2, Interval(0, 1).contains(x)), (0, True))
def test_issue_4313():
u = Piecewise((0, x <= 0), (1, x >= a), (x/a, True))
e = (u - u.subs(x, y))**2/(x - y)**2
M = Max(0, a)
assert integrate(e, x).expand() == Piecewise(
(Piecewise(
(0, x <= 0),
(-y**2/(a**2*x - a**2*y) + x/a**2 - 2*y*log(-y)/a**2 +
2*y*log(x - y)/a**2 - y/a**2, x <= M),
(-y**2/(-a**2*y + a**2*M) + 1/(-y + M) -
1/(x - y) - 2*y*log(-y)/a**2 + 2*y*log(-y +
M)/a**2 - y/a**2 + M/a**2, True)),
((a <= y) & (y <= 0)) | ((y <= 0) & (y > -oo))),
(Piecewise(
(-1/(x - y), x <= 0),
(-a**2/(a**2*x - a**2*y) + 2*a*y/(a**2*x - a**2*y) -
y**2/(a**2*x - a**2*y) + 2*log(-y)/a - 2*log(x - y)/a +
2/a + x/a**2 - 2*y*log(-y)/a**2 + 2*y*log(x - y)/a**2 -
y/a**2, x <= M),
(-a**2/(-a**2*y + a**2*M) + 2*a*y/(-a**2*y +
a**2*M) - y**2/(-a**2*y + a**2*M) +
2*log(-y)/a - 2*log(-y + M)/a + 2/a -
2*y*log(-y)/a**2 + 2*y*log(-y + M)/a**2 -
y/a**2 + M/a**2, True)),
a <= y),
(Piecewise(
(-y**2/(a**2*x - a**2*y), x <= 0),
(x/a**2 + y/a**2, x <= M),
(a**2/(-a**2*y + a**2*M) -
a**2/(a**2*x - a**2*y) - 2*a*y/(-a**2*y + a**2*M) +
2*a*y/(a**2*x - a**2*y) + y**2/(-a**2*y + a**2*M) -
y**2/(a**2*x - a**2*y) + y/a**2 + M/a**2, True)),
True))
def test_Function_subs():
from sympy.abc import x, y
f, g, h, i = symbols("f g h i", cls=Function)
p = Piecewise((g(f(x, y)), x < -1), (g(x), x <= 1))
assert p.subs(g, h) == Piecewise((h(f(x, y)), x < -1), (h(x), x <= 1))
assert (f(y) + g(x)).subs({f: h, g: i}) == i(x) + h(y)
def test_piecewise_solve():
abs2 = Piecewise((-x, x <= 0), (x, x > 0))
f = abs2.subs(x, x - 2)
assert solve(f, x) == [2]
assert solve(f - 1,x) == [1, 3]
f = Piecewise(((x - 2)**2, x >= 0), (1, True))
assert solve(f, x) == [2]
g = Piecewise(((x - 5)**5, x >= 4), (f, True))
assert solve(g, x) == [2, 5]
g = Piecewise(((x - 5)**5, x >= 4), (f, x < 4))
assert solve(g, x) == [2, 5]
g = Piecewise(((x - 5)**5, x >= 2), (f, x < 2))
assert solve(g, x) == [5]
g = Piecewise(((x - 5)**5, x >= 2), (f, True))
assert solve(g, x) == [5]
g = Piecewise(((x - 5)**5, x >= 2), (f, True), (10, False))
assert solve(g, x) == [5]
assert solve(Piecewise((x, x < 0), (x, -1))) == [0]
def test_issue_12587():
# sort holes into intervals
p = Piecewise((1, x > 4), (2, Not((x <= 3) & (x > -1))), (3, True))
assert p.integrate((x, -5, 5)) == 23
p = Piecewise((1, x > 1), (2, x < y), (3, True))
lim = x, -3, 3
ans = p.integrate(lim)
for i in range(-1, 3):
assert ans.subs(y, i) == p.subs(y, i).integrate(lim)
def test_conjugate_transpose():
A, B = symbols("A B", commutative=False)
p = Piecewise((A*B**2, x > 0), (A**2*B, True))
assert p.adjoint() == \
Piecewise((adjoint(A*B**2), x > 0), (adjoint(A**2*B), True))
assert p.conjugate() == \
Piecewise((conjugate(A*B**2), x > 0), (conjugate(A**2*B), True))
assert p.transpose() == \
Piecewise((transpose(A*B**2), x > 0), (transpose(A**2*B), True))
def test_issue_6900():
t0, t1, T, t = symbols('t0, t1 T t')
f = Piecewise((0, t < t0), (x, And(t0 <= t, t < t1)), (0, t >= t1))
assert f.integrate(t) == Piecewise(
(0, t <= t0),
(t*x - t0*x, t <= Max(t0, t1)),
(-t0*x + x*Max(t0, t1), True))
assert f.integrate((t, t0, T)) == Piecewise(
(-t0*x + x*Min(T, Max(t0, t1)), T > t0),
(0, True))
def test_piecewise_integrate2():
from itertools import permutations
lim = Tuple(x, c, d)
p = Piecewise((1, x < a), (2, x > b), (3, True))
q = p.integrate(lim)
assert q == Piecewise(
(-c + 2*d - 2*Min(d, Max(a, c)) + Min(d, Max(a, b, c)), c < d),
(-2*c + d + 2*Min(c, Max(a, d)) - Min(c, Max(a, b, d)), True))
for v in permutations((1, 2, 3, 4)):
r = dict(zip((a, b, c, d), v))
assert p.subs(r).integrate(lim.subs(r)) == q.subs(r)
def test_unevaluated_integrals():
f = Function('f')
p = Piecewise((1, Eq(f(x) - 1, 0)), (2, x - 10 < 0), (0, True))
assert p.integrate(x) == Integral(p, x)
assert p.integrate((x, 0, 5)) == Integral(p, (x, 0, 5))
# test it by replacing f(x) with x%2 which will not
# affect the answer: the integrand is essentially 2 over
# the domain of integration
assert Integral(p, (x, 0, 5)).subs(f(x), x%2).n() == 10
# this is a test of using _solve_inequality when
# solve_univariate_inequality fails
assert p.integrate(y) == Piecewise(
(y, Eq(f(x), 1) | ((x < 10) & Eq(f(x), 1))),
(2*y, (x >= -oo) & (x < 10)), (0, True))
def test_piecewise_as_leading_term():
p1 = Piecewise((1/x, x>1), (0, True))
p2 = Piecewise((x, x>1), (0, True))
p3 = Piecewise((1/x, x>1), (x, True))
p4 = Piecewise((x, x>1), (1/x, True))
assert p1.as_leading_term(x) == 0
assert p2.as_leading_term(x) == 0
assert p3.as_leading_term(x) == x
assert p4.as_leading_term(x) == 1/x
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise(
(a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify(
) == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)),
Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y
+ a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify(
) == Piecewise(
(2*x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
def test_piecewise_fold_piecewise_in_cond():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True))
p3 = piecewise_fold(p2)
assert p2.subs(x, -pi / 2) == 0.0
assert p2.subs(x, 1) == 0.0
assert p2.subs(x, -pi / 4) == 1.0
p4 = Piecewise((0, Eq(p1, 0)), (1, True))
assert piecewise_fold(p4) == Piecewise((0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))), (1, True))
r1 = 1 < Piecewise((1, x < 1), (3, True))
assert piecewise_fold(r1) == Not(x < 1)
p5 = Piecewise((1, x < 0), (3, True))
p6 = Piecewise((1, x < 1), (3, True))
p7 = piecewise_fold(Piecewise((1, p5 < p6), (0, True)))
assert Piecewise((1, And(Not(x < 1), x < 0)), (0, True))
def test_piecewise_integrate1ca():
y = symbols('y', real=True)
g = Piecewise(
(1 - x, Interval(0, 1).contains(x)),
(1 + x, Interval(-1, 0).contains(x)),
(0, True)
)
gy1 = g.integrate((x, y, 1))
g1y = g.integrate((x, 1, y))
assert g.integrate((x, -2, 1)) == gy1.subs(y, -2)
assert g.integrate((x, 1, -2)) == g1y.subs(y, -2)
assert g.integrate((x, 0, 1)) == gy1.subs(y, 0)
assert g.integrate((x, 1, 0)) == g1y.subs(y, 0)
# XXX Make test pass without simplify
assert g.integrate((x, 2, 1)) == gy1.subs(y, 2).simplify()
assert g.integrate((x, 1, 2)) == g1y.subs(y, 2).simplify()
assert piecewise_fold(gy1.rewrite(Piecewise)) == \
Piecewise(
(1, y <= -1),
(-y**2/2 - y + S(1)/2, y <= 0),
(y**2/2 - y + S(1)/2, y < 1),
(0, True))
assert piecewise_fold(g1y.rewrite(Piecewise)) == \
Piecewise(
(-1, y <= -1),
(y**2/2 + y - S(1)/2, y <= 0),
(-y**2/2 + y - S(1)/2, y < 1),
(0, True))
# g1y and gy1 should simplify if the condition that y < 1
# is applied, e.g. Min(1, Max(-1, y)) --> Max(-1, y)
# XXX Make test pass without simplify
assert gy1.simplify() == Piecewise(
(
-Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) +
Min(1, Max(0, y))**2 + S(1)/2, y < 1),
(0, True)
)
assert g1y.simplify() == Piecewise(
(
Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) -
Min(1, Max(0, y))**2 - S(1)/2, y < 1),
(0, True))
def test_piecewise_complex():
p1 = Piecewise((2, x < 0), (1, 0 <= x))
p2 = Piecewise((2*I, x < 0), (I, 0 <= x))
p3 = Piecewise((I*x, x > 1), (1 + I, True))
p4 = Piecewise((-I*conjugate(x), x > 1), (1 - I, True))
assert conjugate(p1) == p1
assert conjugate(p2) == piecewise_fold(-p2)
assert conjugate(p3) == p4
assert p1.is_imaginary is False
assert p1.is_real is True
assert p2.is_imaginary is True
assert p2.is_real is False
assert p3.is_imaginary is None
assert p3.is_real is None
assert p1.as_real_imag() == (p1, 0)
assert p2.as_real_imag() == (0, -I*p2)
def test_piecewise_integrate1cb():
y = symbols('y', real=True)
g = Piecewise(
(0, Or(x <= -1, x >= 1)),
(1 - x, x > 0),
(1 + x, True)
)
gy1 = g.integrate((x, y, 1))
g1y = g.integrate((x, 1, y))
assert g.integrate((x, -2, 1)) == gy1.subs(y, -2)
assert g.integrate((x, 1, -2)) == g1y.subs(y, -2)
assert g.integrate((x, 0, 1)) == gy1.subs(y, 0)
assert g.integrate((x, 1, 0)) == g1y.subs(y, 0)
assert g.integrate((x, 2, 1)) == gy1.subs(y, 2)
assert g.integrate((x, 1, 2)) == g1y.subs(y, 2)
assert piecewise_fold(gy1.rewrite(Piecewise)) == \
Piecewise(
(1, y <= -1),
(-y**2/2 - y + S(1)/2, y <= 0),
(y**2/2 - y + S(1)/2, y < 1),
(0, True))
assert piecewise_fold(g1y.rewrite(Piecewise)) == \
Piecewise(
(-1, y <= -1),
(y**2/2 + y - S(1)/2, y <= 0),
(-y**2/2 + y - S(1)/2, y < 1),
(0, True))
# g1y and gy1 should simplify if the condition that y < 1
# is applied, e.g. Min(1, Max(-1, y)) --> Max(-1, y)
assert gy1 == Piecewise(
(
-Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) +
Min(1, Max(0, y))**2 + S(1)/2, y < 1),
(0, True)
)
assert g1y == Piecewise(
(
Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) -
Min(1, Max(0, y))**2 - S(1)/2, y < 1),
(0, True))
def test_issue_10137():
a = Symbol('a', real=True, finite=True)
b = Symbol('b', real=True, finite=True)
x = Symbol('x', real=True, finite=True)
y = Symbol('y', real=True, finite=True)
p0 = Piecewise((0, Or(x < a, x > b)), (1, True))
p1 = Piecewise((0, Or(a > x, b < x)), (1, True))
assert integrate(p0, (x, y, oo)) == integrate(p1, (x, y, oo))
p3 = Piecewise((1, And(0 < x, x < a)), (0, True))
p4 = Piecewise((1, And(a > x, x > 0)), (0, True))
ip3 = integrate(p3, x)
assert ip3 == Piecewise(
(0, x <= 0),
(x, x <= Max(0, a)),
(Max(0, a), True))
ip4 = integrate(p4, x)
assert ip4 == ip3
assert p3.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2
assert p4.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2
def point_cflexure(self):
"""
Returns a Set of point(s) with zero bending moment and
where bending moment curve of the beam object changes
its sign from negative to positive or vice versa.
Examples
========
There is is 10 meter long overhanging beam. There are
two simple supports below the beam. One at the start
and another one at a distance of 6 meters from the start.
Point loads of magnitude 10KN and 20KN are applied at
2 meters and 4 meters from start respectively. A Uniformly
distribute load of magnitude of magnitude 3KN/m is also
applied on top starting from 6 meters away from starting
point till end.
Using the sign convention of upward forces and clockwise moment
being positive.
>>> from sympy.physics.continuum_mechanics.beam import Beam
>>> from sympy import symbols
>>> E, I = symbols('E, I')
>>> b = Beam(10, E, I)
>>> b.apply_load(-4, 0, -1)
>>> b.apply_load(-46, 6, -1)
>>> b.apply_load(10, 2, -1)
>>> b.apply_load(20, 4, -1)
>>> b.apply_load(3, 6, 0)
>>> b.point_cflexure()
[10/3]
"""
from sympy import solve, Piecewise
# To restrict the range within length of the Beam
moment_curve = Piecewise((float("nan"), self.variable<=0),
(self.bending_moment(), self.variable<self.length),
(float("nan"), True))
points = solve(moment_curve.rewrite(Piecewise), self.variable,
domain=S.Reals)
return points
def test_issue_8458():
x, y = symbols('x y')
# Original issue
p1 = Piecewise((0, Eq(x, 0)), (sin(x), True))
assert p1.simplify() == sin(x)
# Slightly larger variant
p2 = Piecewise((x, Eq(x, 0)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p2.simplify() == sin(x)
# Test for problem highlighted during review
p3 = Piecewise((x+1, Eq(x, -1)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p3.simplify() == Piecewise((0, Eq(x, -1)), (sin(x), True))
def test_has_piecewise():
f = (x * y + 3 / y) ** (3 + 2)
g = Function("g")
h = Function("h")
p = Piecewise((g, x < -1), (1, x <= 1), (f, True))
assert p.has(x)
assert p.has(y)
assert not p.has(z)
assert p.has(1)
assert p.has(3)
assert not p.has(4)
assert p.has(f)
assert p.has(g)
assert not p.has(h)
def test_piecewise_fold_piecewise_in_cond():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True))
p3 = piecewise_fold(p2)
assert(p2.subs(x, -pi/2) == 0.0)
assert(p2.subs(x, 1) == 0.0)
assert(p2.subs(x, -pi/4) == 1.0)
p4 = Piecewise((0, Eq(p1, 0)), (1,True))
ans = piecewise_fold(p4)
for i in range(-1, 1):
assert ans.subs(x, i) == p4.subs(x, i)
r1 = 1 < Piecewise((1, x < 1), (3, True))
ans = piecewise_fold(r1)
for i in range(2):
assert ans.subs(x, i) == r1.subs(x, i)
p5 = Piecewise((1, x < 0), (3, True))
p6 = Piecewise((1, x < 1), (3, True))
p7 = Piecewise((1, p5 < p6), (0, True))
ans = piecewise_fold(p7)
for i in range(-1, 2):
assert ans.subs(x, i) == p7.subs(x, i)
def test_piecewise_integrate3_inequality_conditions():
from sympy.utilities.iterables import cartes
lim = (x, 0, 5)
# set below includes two pts below range, 2 pts in range,
# 2 pts above range, and the boundaries
N = (-2, -1, 0, 1, 2, 5, 6, 7)
p = Piecewise((1, x > a), (2, x > b), (0, True))
ans = p.integrate(lim)
for i, j in cartes(N, repeat=2):
reps = dict(zip((a, b), (i, j)))
assert ans.subs(reps) == p.subs(reps).integrate(lim)
assert ans.subs(a, 4).subs(b, 1) == 0 + 2*3 + 1
p = Piecewise((1, x > a), (2, x < b), (0, True))
ans = p.integrate(lim)
for i, j in cartes(N, repeat=2):
reps = dict(zip((a, b), (i, j)))
assert ans.subs(reps) == p.subs(reps).integrate(lim)
def test_issue_6900():
from itertools import permutations
t0, t1, T, t = symbols('t0, t1 T t')
f = Piecewise((0, t < t0), (x, And(t0 <= t, t < t1)), (0, t >= t1))
g = f.integrate(t)
assert g == Piecewise(
(0, t <= t0),
(t*x - t0*x, t <= Max(t0, t1)),
(-t0*x + x*Max(t0, t1), True))
for i in permutations(range(2)):
reps = dict(zip((t0,t1), i))
for tt in range(-1,3):
assert (g.xreplace(reps).subs(t,tt) ==
f.xreplace(reps).integrate(t).subs(t,tt))
lim = Tuple(t, t0, T)
g = f.integrate(lim)
ans = Piecewise(
(-t0*x + x*Min(T, Max(t0, t1)), T > t0),
(0, True))
for i in permutations(range(3)):
reps = dict(zip((t0,t1,T), i))
tru = f.xreplace(reps).integrate(lim.xreplace(reps))
assert tru == ans.xreplace(reps)
assert g == ans
def test_piecewise_integrate1b():
g = Piecewise((1, x > 0), (0, Eq(x, 0)), (-1, x < 0))
assert integrate(g, (x, -1, 1)) == 0
g = Piecewise((1, x - y < 0), (0, True))
assert integrate(g, (y, -oo, 0)) == -Min(0, x)
assert g.subs(x, -3).integrate((y, -oo, 0)) == 3
assert integrate(g, (y, 0, -oo)) == Min(0, x)
assert integrate(g, (y, 0, oo)) == -Max(0, x) + oo
assert integrate(g, (y, -oo, 42)) == -Min(42, x) + 42
assert integrate(g, (y, -oo, oo)) == -x + oo
g = Piecewise((0, x < 0), (x, x <= 1), (1, True))
gy1 = g.integrate((x, y, 1))
g1y = g.integrate((x, 1, y))
for yy in (-1, S.Half, 2):
assert g.integrate((x, yy, 1)) == gy1.subs(y, yy)
assert g.integrate((x, 1, yy)) == g1y.subs(y, yy)
assert gy1 == Piecewise(
(-Min(1, Max(0, y))**2/2 + 1/2, y < 1),
(-y + 1, True))
assert g1y == Piecewise(
(Min(1, Max(0, y))**2/2 - 1/2, y < 1),
(y - 1, True))
def test_piecewise():
# Test canonization
assert Piecewise((x, x < 1), (0, True)) == Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, False), (-1, 1>2)) == Piecewise((x, x < 1))
assert Piecewise((x, True)) == x
raises(TypeError,"Piecewise(x)")
raises(TypeError,"Piecewise((x,x**2))")
# Test subs
p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >=0))
p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >=0))
assert p.subs(x,x**2) == p_x2
assert p.subs(x,-5) == -1
assert p.subs(x,-1) == 1
assert p.subs(x,1) == log(1)
# More subs tests
p2 = Piecewise((1, x < pi), (-1, x < 2*pi), (0, x > 2*pi))
assert p2.subs(x,2) == 1
assert p2.subs(x,4) == -1
assert p2.subs(x,10) == 0
# Test evalf
assert p.evalf() == p
assert p.evalf(subs={x:-2}) == -1
assert p.evalf(subs={x:-1}) == 1
assert p.evalf(subs={x:1}) == log(1)
# Test doit
f_int = Piecewise((Integral(x,(x,0,1)), x < 1))
assert f_int.doit() == Piecewise( (1.0/2.0, x < 1) )
# Test differentiation
f = x
fp = x*p
dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, x >= 0))
fp_dx = x*dp + p
assert diff(p,x) == dp
assert diff(f*p,x) == fp_dx
# Test simple arithmetic
assert x*p == fp
assert x*p + p == p + x*p
assert p + f == f + p
assert p + dp == dp + p
assert p - dp == -(dp - p)
# Test _eval_interval
f1 = x*y + 2
f2 = x*y**2 + 3
peval = Piecewise( (f1, x<0), (f2, x>0))
peval_interval = f1.subs(x,0) - f1.subs(x,-1) + f2.subs(x,1) - f2.subs(x,0)
assert peval._eval_interval(x, -1, 1) == peval_interval
# Test integration
p_int = Piecewise((-x,x < -1), (x**3/3.0, x < 0), (-x + x*log(x), x >= 0))
assert integrate(p,x) == p_int
p = Piecewise((x, x < 1),(x**2, -1 <= x),(x,3<x))
assert integrate(p,(x,-2,2)) == 5.0/6.0
assert integrate(p,(x,2,-2)) == -5.0/6.0
p = Piecewise((0, x < 0), (1,x < 1), (0, x < 2), (1, x < 3), (0, True))
assert integrate(p, (x,-oo,oo)) == 2
p = Piecewise((x, x < -10),(x**2, x <= -1),(x, 1 < x))
raises(ValueError, "integrate(p,(x,-2,2))")
# Test commutativity
assert p.is_commutative is True
def test_piecewise():
# In each case, test eval() the lambdarepr() to make sure there are a
# correct number of parentheses. It will give a SyntaxError if there aren't.
h = "lambda x: "
p = Piecewise((x, True), evaluate=False)
l = lambdarepr(p)
eval(h + l)
assert l == "((x) if (True) else None)"
p = Piecewise((x, x < 0))
l = lambdarepr(p)
eval(h + l)
assert l == "((x) if (x < 0) else None)"
p = Piecewise(
(1, x < 1),
(2, x < 2),
(0, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == "((1) if (x < 1) else (((2) if (x < 2) else " \
"(((0) if (True) else None)))))"
p = Piecewise(
(1, x < 1),
(2, x < 2),
)
l = lambdarepr(p)
eval(h + l)
assert l == "((1) if (x < 1) else (((2) if (x < 2) else None)))"
p = Piecewise(
(x, x < 1),
(x**2, Interval(3, 4, True, False).contains(x)),
(0, True),
)
l = lambdarepr(p)
eval(h + l)
assert l == "((x) if (x < 1) else (((x**2) if (((x <= 4) and " \
"(x > 3))) else (((0) if (True) else None)))))"
p = Piecewise(
(x**2, x < 0),
(x, Interval(0, 1, False, True).contains(x)),
(2 - x, x >= 1),
(0, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == "((x**2) if (x < 0) else (((x) if (((x >= 0) and (x < 1))) " \
"else (((-x + 2) if (x >= 1) else (((0) if (True) else None)))))))"
p = Piecewise(
(x**2, x < 0),
(x, Interval(0, 1, False, True).contains(x)),
(2 - x, x >= 1),
)
l = lambdarepr(p)
eval(h + l)
assert l == "((x**2) if (x < 0) else (((x) if (((x >= 0) and " \
"(x < 1))) else (((-x + 2) if (x >= 1) else None)))))"
p = Piecewise(
(1, x >= 1),
(2, x >= 2),
(3, x >= 3),
(4, x >= 4),
(5, x >= 5),
(6, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == ("((1) if (x >= 1) else (((2) if (x >= 2) else (((3) if "
"(x >= 3) else (((4) if (x >= 4) else (((5) if (x >= 5) else (((6) if "
"(True) else None)))))))))))")
p = Piecewise(
(1, x <= 1),
(2, x <= 2),
(3, x <= 3),
(4, x <= 4),
(5, x <= 5),
(6, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == "((1) if (x <= 1) else (((2) if (x <= 2) else (((3) if " \
"(x <= 3) else (((4) if (x <= 4) else (((5) if (x <= 5) else (((6) if " \
"(True) else None)))))))))))"
p = Piecewise(
(1, x > 1),
(2, x > 2),
(3, x > 3),
(4, x > 4),
(5, x > 5),
(6, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == ("((1) if (x > 1) else (((2) if (x > 2) else (((3) if "
"(x > 3) else (((4) if (x > 4) else (((5) if (x > 5) else (((6) if "
"(True) else None)))))))))))")
p = Piecewise(
(1, x < 1),
(2, x < 2),
(3, x < 3),
(4, x < 4),
(5, x < 5),
(6, True)
)
l = lambdarepr(p)
eval(h + l)
assert l == "((1) if (x < 1) else (((2) if (x < 2) else (((3) if " \
"(x < 3) else (((4) if (x < 4) else (((5) if (x < 5) else (((6) if " \
"(True) else None)))))))))))"
def test_doit():
p1 = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
p2 = Piecewise((x, x < 1), (Integral(2 * x), -1 <= x), (x, 3 < x))
assert p2.doit() == p1
assert p2.doit(deep = False) == p2
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((1 + 1/x**2, Eq(x, 0)), ((-1)**(x + 1), True))
def test_piecewise_as_leading_term():
p1 = Piecewise((1/x, x > 1), (0, True))
p2 = Piecewise((x, x > 1), (0, True))
p3 = Piecewise((1/x, x > 1), (x, True))
p4 = Piecewise((x, x > 1), (1/x, True))
p5 = Piecewise((1/x, x > 1), (x, True))
p6 = Piecewise((1/x, x < 1), (x, True))
p7 = Piecewise((x, x < 1), (1/x, True))
p8 = Piecewise((x, x > 1), (1/x, True))
assert p1.as_leading_term(x) == 0
assert p2.as_leading_term(x) == 0
assert p3.as_leading_term(x) == x
assert p4.as_leading_term(x) == 1/x
assert p5.as_leading_term(x) == x
assert p6.as_leading_term(x) == 1/x
assert p7.as_leading_term(x) == x
assert p8.as_leading_term(x) == 1/x
def test_piecewise_as_leading_term():
p1 = Piecewise((1 / x, x > 1), (0, True))
p2 = Piecewise((x, x > 1), (0, True))
p3 = Piecewise((1 / x, x > 1), (x, True))
p4 = Piecewise((x, x > 1), (1 / x, True))
p5 = Piecewise((1 / x, x > 1), (x, True))
p6 = Piecewise((1 / x, x < 1), (x, True))
p7 = Piecewise((x, x < 1), (1 / x, True))
p8 = Piecewise((x, x > 1), (1 / x, True))
assert p1.as_leading_term(x) == 0
assert p2.as_leading_term(x) == 0
assert p3.as_leading_term(x) == x
assert p4.as_leading_term(x) == 1 / x
assert p5.as_leading_term(x) == x
assert p6.as_leading_term(x) == 1 / x
assert p7.as_leading_term(x) == x
assert p8.as_leading_term(x) == 1 / x
def test_piecewise_duplicate():
p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
assert p == Piecewise(*p.args)
def high(self):
return Piecewise((self.n, Lt(self.n, self.m) != False), (self.m, True))
def pmf(self, x):
return Piecewise((self.p, x == self.succ), (1 - self.p, x == self.fail), (0, True))
def test_geometric_sums():
assert summation(pi**n, (n, 0, b)) == (1 - pi**(b + 1)) / (1 - pi)
assert summation(2 * 3**n, (n, 0, b)) == 3**(b + 1) - 1
assert summation(Rational(1, 2)**n, (n, 1, oo)) == 1
assert summation(2**n, (n, 0, b)) == 2**(b + 1) - 1
assert summation(2**n, (n, 1, oo)) == oo
assert summation(2**(-n), (n, 1, oo)) == 1
assert summation(3**(-n), (n, 4, oo)) == Rational(1, 54)
assert summation(2**(-4*n + 3), (n, 1, oo)) == Rational(8, 15)
assert summation(2**(n + 1), (n, 1, b)).expand() == 4*(2**b - 1)
# issue 6664:
assert summation(x**n, (n, 0, oo)) == \
Piecewise((1/(-x + 1), Abs(x) < 1), (Sum(x**n, (n, 0, oo)), True))
assert summation(-2**n, (n, 0, oo)) == -oo
assert summation(I**n, (n, 0, oo)) == Sum(I**n, (n, 0, oo))
# issue 6802:
assert summation((-1)**(2*x + 2), (x, 0, n)) == n + 1
assert summation((-2)**(2*x + 2), (x, 0, n)) == 4*4**(n + 1)/S(3) - S(4)/3
assert summation((-1)**x, (x, 0, n)) == -(-1)**(n + 1)/S(2) + S(1)/2
assert summation(y**x, (x, a, b)) == \
Piecewise((-a + b + 1, Eq(y, 1)), ((y**a - y**(b + 1))/(-y + 1), True))
assert summation((-2)**(y*x + 2), (x, 0, n)) == \
4*Piecewise((n + 1, Eq((-2)**y, 1)),
((-(-2)**(y*(n + 1)) + 1)/(-(-2)**y + 1), True))
# issue 8251:
assert summation((1/(n + 1)**2)*n**2, (n, 0, oo)) == oo
#issue 9908:
assert Sum(1/(n**3 - 1), (n, -oo, -2)).doit() == summation(1/(n**3 - 1), (n, -oo, -2))
#issue 11642:
result = Sum(0.5**n, (n, 1, oo)).doit()
assert result == 1
assert result.is_Float
result = Sum(0.25**n, (n, 1, oo)).doit()
assert result == 1/3.
assert result.is_Float
result = Sum(0.99999**n, (n, 1, oo)).doit()
assert result == 99999
assert result.is_Float
result = Sum(Rational(1, 2)**n, (n, 1, oo)).doit()
assert result == 1
assert not result.is_Float
result = Sum(Rational(3, 5)**n, (n, 1, oo)).doit()
assert result == S(3)/2
assert not result.is_Float
assert Sum(1.0**n, (n, 1, oo)).doit() == oo
assert Sum(2.43**n, (n, 1, oo)).doit() == oo
# Issue 13979:
i, k, q = symbols('i k q', integer=True)
result = summation(
exp(-2*I*pi*k*i/n) * exp(2*I*pi*q*i/n) / n, (i, 0, n - 1)
)
assert result.simplify() == Piecewise(
(1, Eq(exp(2*I*pi*(-k + q)/n), 1)), (0, True)
)
def _cdf(self, x):
return Piecewise((1 - floor(x) * beta(floor(x), self.rho + 1), x >= 1), (0, True))
def test_karr_convention():
# Test the Karr summation convention that we want to hold.
# See his paper "Summation in Finite Terms" for a detailed
# reasoning why we really want exactly this definition.
# The convention is described on page 309 and essentially
# in section 1.4, definition 3:
#
# \sum_{m <= i < n} f(i) 'has the obvious meaning' for m < n
# \sum_{m <= i < n} f(i) = 0 for m = n
# \sum_{m <= i < n} f(i) = - \sum_{n <= i < m} f(i) for m > n
#
# It is important to note that he defines all sums with
# the upper limit being *exclusive*.
# In contrast, sympy and the usual mathematical notation has:
#
# sum_{i = a}^b f(i) = f(a) + f(a+1) + ... + f(b-1) + f(b)
#
# with the upper limit *inclusive*. So translating between
# the two we find that:
#
# \sum_{m <= i < n} f(i) = \sum_{i = m}^{n-1} f(i)
#
# where we intentionally used two different ways to typeset the
# sum and its limits.
i = Symbol("i", integer=True)
k = Symbol("k", integer=True)
j = Symbol("j", integer=True)
# A simple example with a concrete summand and symbolic limits.
# The normal sum: m = k and n = k + j and therefore m < n:
m = k
n = k + j
a = m
b = n - 1
S1 = Sum(i**2, (i, a, b)).doit()
# The reversed sum: m = k + j and n = k and therefore m > n:
m = k + j
n = k
a = m
b = n - 1
S2 = Sum(i**2, (i, a, b)).doit()
assert simplify(S1 + S2) == 0
# Test the empty sum: m = k and n = k and therefore m = n:
m = k
n = k
a = m
b = n - 1
Sz = Sum(i**2, (i, a, b)).doit()
assert Sz == 0
# Another example this time with an unspecified summand and
# numeric limits. (We can not do both tests in the same example.)
f = Function("f")
# The normal sum with m < n:
m = 2
n = 11
a = m
b = n - 1
S1 = Sum(f(i), (i, a, b)).doit()
# The reversed sum with m > n:
m = 11
n = 2
a = m
b = n - 1
S2 = Sum(f(i), (i, a, b)).doit()
assert simplify(S1 + S2) == 0
# Test the empty sum with m = n:
m = 5
n = 5
a = m
b = n - 1
Sz = Sum(f(i), (i, a, b)).doit()
assert Sz == 0
e = Piecewise((exp(-i), Mod(i, 2) > 0), (0, True))
s = Sum(e, (i, 0, 11))
assert s.n(3) == s.doit().n(3)
def test_S_srepr_is_identity():
p = Piecewise((10, Eq(x, 0)), (12, True))
q = S(srepr(p))
assert p == q
def test_as_expr_set_pairs():
assert Piecewise((x, x > 0), (-x, x <= 0)).as_expr_set_pairs() == \
[(x, Interval(0, oo, True, True)), (-x, Interval(-oo, 0))]
assert Piecewise(((x - 2)**2, x >= 0), (0, True)).as_expr_set_pairs() == \
[((x - 2)**2, Interval(0, oo)), (0, Interval(-oo, 0, True, True))]
def test_piecewise_fold_piecewise_in_cond_2():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (1 / p1, True))
p3 = Piecewise((0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))),
(1 / cos(x), True))
assert (piecewise_fold(p2) == p3)
def test_doit():
p1 = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
p2 = Piecewise((x, x < 1), (Integral(2 * x), -1 <= x), (x, 3 < x))
assert p2.doit() == p1
assert p2.doit(deep=False) == p2
def test_piecewise_solve2():
f = Piecewise(((x - 2)**2, x >= 0), (0, True))
assert solve(f, x) == [2, Interval(0, oo, True, True)]
def test_piecewise_series():
from sympy import sin, cos, O
p1 = Piecewise((sin(x), x < 0), (cos(x), x > 0))
p2 = Piecewise((x + O(x**2), x < 0), (1 + O(x**2), x > 0))
assert p1.nseries(x, n=2) == p2
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1) / x**2, Eq(x * (1 + x) - x**2, 0)),
((-1)**x * (-1), True))
assert p.simplify() == \
Piecewise((1 + 1/x**2, Eq(x, 0)), ((-1)**(x + 1), True))
def test_piecewise_integrate_independent_conditions():
p = Piecewise((0, Eq(y, 0)), (x * y, True))
assert integrate(p, (x, 1, 3)) == \
Piecewise((0, Eq(y, 0)), (4*y, True))
def test_is_convergent():
# divergence tests --
assert Sum(n/(2*n + 1), (n, 1, oo)).is_convergent() is S.false
assert Sum(factorial(n)/5**n, (n, 1, oo)).is_convergent() is S.false
assert Sum(3**(-2*n - 1)*n**n, (n, 1, oo)).is_convergent() is S.false
assert Sum((-1)**n*n, (n, 3, oo)).is_convergent() is S.false
assert Sum((-1)**n, (n, 1, oo)).is_convergent() is S.false
assert Sum(log(1/n), (n, 2, oo)).is_convergent() is S.false
# root test --
assert Sum((-12)**n/n, (n, 1, oo)).is_convergent() is S.false
# integral test --
# p-series test --
assert Sum(1/(n**2 + 1), (n, 1, oo)).is_convergent() is S.true
assert Sum(1/n**(S(6)/5), (n, 1, oo)).is_convergent() is S.true
assert Sum(2/(n*sqrt(n - 1)), (n, 2, oo)).is_convergent() is S.true
assert Sum(1/(sqrt(n)*sqrt(n)), (n, 2, oo)).is_convergent() is S.false
# comparison test --
assert Sum(1/(n + log(n)), (n, 1, oo)).is_convergent() is S.false
assert Sum(1/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true
assert Sum(1/(n*log(n)), (n, 2, oo)).is_convergent() is S.false
assert Sum(2/(n*log(n)*log(log(n))**2), (n, 5, oo)).is_convergent() is S.true
assert Sum(2/(n*log(n)**2), (n, 2, oo)).is_convergent() is S.true
assert Sum((n - 1)/(n**2*log(n)**3), (n, 2, oo)).is_convergent() is S.true
assert Sum(1/(n*log(n)*log(log(n))), (n, 5, oo)).is_convergent() is S.false
assert Sum((n - 1)/(n*log(n)**3), (n, 3, oo)).is_convergent() is S.false
assert Sum(2/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true
assert Sum(1/(n*sqrt(log(n))*log(log(n))), (n, 100, oo)).is_convergent() is S.false
assert Sum(log(log(n))/(n*log(n)**2), (n, 100, oo)).is_convergent() is S.true
assert Sum(log(n)/n**2, (n, 5, oo)).is_convergent() is S.true
# alternating series tests --
assert Sum((-1)**(n - 1)/(n**2 - 1), (n, 3, oo)).is_convergent() is S.true
# with -negativeInfinite Limits
assert Sum(1/(n**2 + 1), (n, -oo, 1)).is_convergent() is S.true
assert Sum(1/(n - 1), (n, -oo, -1)).is_convergent() is S.false
assert Sum(1/(n**2 - 1), (n, -oo, -5)).is_convergent() is S.true
assert Sum(1/(n**2 - 1), (n, -oo, 2)).is_convergent() is S.true
assert Sum(1/(n**2 - 1), (n, -oo, oo)).is_convergent() is S.true
# piecewise functions
f = Piecewise((n**(-2), n <= 1), (n**2, n > 1))
assert Sum(f, (n, 1, oo)).is_convergent() is S.false
assert Sum(f, (n, -oo, oo)).is_convergent() is S.false
#assert Sum(f, (n, -oo, 1)).is_convergent() is S.true
# integral test
assert Sum(log(n)/n**3, (n, 1, oo)).is_convergent() is S.true
assert Sum(-log(n)/n**3, (n, 1, oo)).is_convergent() is S.true
# the following function has maxima located at (x, y) =
# (1.2, 0.43), (3.0, -0.25) and (6.8, 0.050)
eq = (x - 2)*(x**2 - 6*x + 4)*exp(-x)
assert Sum(eq, (x, 1, oo)).is_convergent() is S.true
assert Sum(eq, (x, 1, 2)).is_convergent() is S.true
assert Sum(1/(x**3), (x, 1, oo)).is_convergent() is S.true
assert Sum(1/(x**(S(1)/2)), (x, 1, oo)).is_convergent() is S.false
def test_piecewise_integrate_symbolic_conditions():
a = Symbol('a', real=True, finite=True)
b = Symbol('b', real=True, finite=True)
x = Symbol('x', real=True, finite=True)
y = Symbol('y', real=True, finite=True)
p0 = Piecewise((0, Or(x < a, x > b)), (1, True))
p1 = Piecewise((0, x < a), (0, x > b), (1, True))
p2 = Piecewise((0, x > b), (0, x < a), (1, True))
p3 = Piecewise((0, x < a), (1, x < b), (0, True))
p4 = Piecewise((0, x > b), (1, x > a), (0, True))
p5 = Piecewise((1, And(a < x, x < b)), (0, True))
assert integrate(p0, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p1, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p2, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p3, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p4, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p5, (x, -oo, y)) == Min(b, y) - Min(a, b, y)
assert integrate(p0, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p1, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p2, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p3, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p4, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p5, (x, y, oo)) == Max(a, b, y) - Max(a, y)
assert integrate(p0, x) == Piecewise((0, Or(x < a, x > b)), (x, True))
assert integrate(p1, x) == Piecewise((0, Or(x < a, x > b)), (x, True))
assert integrate(p2, x) == Piecewise((0, Or(x < a, x > b)), (x, True))
p1 = Piecewise((0, x < a), (0.5, x > b), (1, True))
p2 = Piecewise((0.5, x > b), (0, x < a), (1, True))
p3 = Piecewise((0, x < a), (1, x < b), (0.5, True))
p4 = Piecewise((0.5, x > b), (1, x > a), (0, True))
p5 = Piecewise((1, And(a < x, x < b)), (0.5, x > b), (0, True))
assert integrate(p1,
(x, -oo, y)) == 0.5 * y + 0.5 * Min(b, y) - Min(a, b, y)
assert integrate(p2,
(x, -oo, y)) == 0.5 * y + 0.5 * Min(b, y) - Min(a, b, y)
assert integrate(p3,
(x, -oo, y)) == 0.5 * y + 0.5 * Min(b, y) - Min(a, b, y)
assert integrate(p4,
(x, -oo, y)) == 0.5 * y + 0.5 * Min(b, y) - Min(a, b, y)
assert integrate(p5,
(x, -oo, y)) == 0.5 * y + 0.5 * Min(b, y) - Min(a, b, y)
def test_image_piecewise():
f = Piecewise((x, x <= -1), (1 / x**2, x <= 5), (x**3, True))
f1 = Piecewise((0, x <= 1), (1, x <= 2), (2, True))
assert imageset(x, f, Interval(-5, 5)) == Union(Interval(-5, -1),
Interval(S(1) / 25, oo))
assert imageset(x, f1, Interval(1, 2)) == FiniteSet(0, 1)
def test_piecewise_integrate():
x, y = symbols('x y', real=True, finite=True)
# XXX Use '<=' here! '>=' is not yet implemented ..
f = Piecewise(((x - 2)**2, 0 <= x), (1, True))
assert integrate(f, (x, -2, 2)) == Rational(14, 3)
g = Piecewise(((x - 5)**5, 4 <= x), (f, True))
assert integrate(g, (x, -2, 2)) == Rational(14, 3)
assert integrate(g, (x, -2, 5)) == Rational(43, 6)
g = Piecewise(((x - 5)**5, 4 <= x), (f, x < 4))
assert integrate(g, (x, -2, 2)) == Rational(14, 3)
assert integrate(g, (x, -2, 5)) == Rational(43, 6)
g = Piecewise(((x - 5)**5, 2 <= x), (f, x < 2))
assert integrate(g, (x, -2, 2)) == Rational(14, 3)
assert integrate(g, (x, -2, 5)) == -Rational(701, 6)
g = Piecewise(((x - 5)**5, 2 <= x), (f, True))
assert integrate(g, (x, -2, 2)) == Rational(14, 3)
assert integrate(g, (x, -2, 5)) == -Rational(701, 6)
g = Piecewise(((x - 5)**5, 2 <= x), (2 * f, True))
assert integrate(g, (x, -2, 2)) == 2 * Rational(14, 3)
assert integrate(g, (x, -2, 5)) == -Rational(673, 6)
g = Piecewise((1, x > 0), (0, Eq(x, 0)), (-1, x < 0))
assert integrate(g, (x, -1, 1)) == 0
g = Piecewise((1, x - y < 0), (0, True))
assert integrate(g, (y, -oo, 0)) == -Min(0, x)
assert integrate(g, (y, 0, oo)) == oo - Max(0, x)
assert integrate(g, (y, -oo, oo)) == oo - x
g = Piecewise((0, x < 0), (x, x <= 1), (1, True))
assert integrate(g, (x, -5, 1)) == Rational(1, 2)
assert integrate(g, (x, -5, y)).subs(y, 1) == Rational(1, 2)
assert integrate(g, (x, y, 1)).subs(y, -5) == Rational(1, 2)
assert integrate(g, (x, 1, -5)) == -Rational(1, 2)
assert integrate(g, (x, 1, y)).subs(y, -5) == -Rational(1, 2)
assert integrate(g, (x, y, -5)).subs(y, 1) == -Rational(1, 2)
assert integrate(g, (x, -5, y)) == Piecewise(
(0, y < 0), (y**2 / 2, y <= 1), (y - 0.5, True))
assert integrate(g, (x, y, 1)) == Piecewise(
(0.5, y < 0), (0.5 - y**2 / 2, y <= 1), (1 - y, True))
g = Piecewise((1 - x, Interval(0, 1).contains(x)),
(1 + x, Interval(-1, 0).contains(x)), (0, True))
assert integrate(g, (x, -5, 1)) == 1
assert integrate(g, (x, -5, y)).subs(y, 1) == 1
assert integrate(g, (x, y, 1)).subs(y, -5) == 1
assert integrate(g, (x, 1, -5)) == -1
assert integrate(g, (x, 1, y)).subs(y, -5) == -1
assert integrate(g, (x, y, -5)).subs(y, 1) == -1
assert integrate(g, (x, -5, y)) == Piecewise(
(-y**2 / 2 + y + 0.5, Interval(0, 1).contains(y)),
(y**2 / 2 + y + 0.5, Interval(-1, 0).contains(y)), (0, y <= -1),
(1, True))
assert integrate(g, (x, y, 1)) == Piecewise(
(y**2 / 2 - y + 0.5, Interval(0, 1).contains(y)),
(-y**2 / 2 - y + 0.5, Interval(-1, 0).contains(y)), (1, y <= -1),
(0, True))
g = Piecewise((0, Or(x <= -1, x >= 1)), (1 - x, x > 0), (1 + x, True))
assert integrate(g, (x, -5, 1)) == 1
assert integrate(g, (x, -5, y)).subs(y, 1) == 1
assert integrate(g, (x, y, 1)).subs(y, -5) == 1
assert integrate(g, (x, 1, -5)) == -1
assert integrate(g, (x, 1, y)).subs(y, -5) == -1
assert integrate(g, (x, y, -5)).subs(y, 1) == -1
assert integrate(g, (x, -5, y)) == Piecewise((0, y <= -1), (1, y >= 1),
(-y**2 / 2 + y + 0.5, y > 0),
(y**2 / 2 + y + 0.5, True))
assert integrate(g, (x, y, 1)) == Piecewise((1, y <= -1), (0, y >= 1),
(y**2 / 2 - y + 0.5, y > 0),
(-y**2 / 2 - y + 0.5, True))
def test_piecewise():
# Test canonization
assert Piecewise((x, x < 1), (0, True)) == Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, True), (1, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, False), (-1, 1 > 2)) == \
Piecewise((x, x < 1))
assert Piecewise((x, x < 1), (0, x < 1), (0, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, x < 2), (0, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (x, x < 2), (0, True)) == \
Piecewise((x, Or(x < 1, x < 2)), (0, True))
assert Piecewise((x, x < 1), (x, x < 2), (x, True)) == x
assert Piecewise((x, True)) == x
raises(TypeError, lambda: Piecewise(x))
raises(TypeError, lambda: Piecewise((x, x**2)))
# Test subs
p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >= 0))
p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >= 0))
assert p.subs(x, x**2) == p_x2
assert p.subs(x, -5) == -1
assert p.subs(x, -1) == 1
assert p.subs(x, 1) == log(1)
# More subs tests
p2 = Piecewise((1, x < pi), (-1, x < 2*pi), (0, x > 2*pi))
p3 = Piecewise((1, Eq(x, 0)), (1/x, True))
p4 = Piecewise((1, Eq(x, 0)), (2, 1/x>2))
assert p2.subs(x, 2) == 1
assert p2.subs(x, 4) == -1
assert p2.subs(x, 10) == 0
assert p3.subs(x, 0.0) == 1
assert p4.subs(x, 0.0) == 1
f, g, h = symbols('f,g,h', cls=Function)
pf = Piecewise((f(x), x < -1), (f(x) + h(x) + 2, x <= 1))
pg = Piecewise((g(x), x < -1), (g(x) + h(x) + 2, x <= 1))
assert pg.subs(g, f) == pf
assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 0) == 1
assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 1) == 0
assert Piecewise((1, Eq(x, y)), (0, True)).subs(x, y) == 1
assert Piecewise((1, Eq(x, z)), (0, True)).subs(x, z) == 1
assert Piecewise((1, Eq(exp(x), cos(z))), (0, True)).subs(x, z) == \
Piecewise((1, Eq(exp(z), cos(z))), (0, True))
assert Piecewise((1, Eq(x, y*(y + 1))), (0, True)).subs(x, y**2 + y) == 1
p5 = Piecewise( (0, Eq(cos(x) + y, 0)), (1, True))
assert p5.subs(y, 0) == Piecewise( (0, Eq(cos(x), 0)), (1, True))
# Test evalf
assert p.evalf() == p
assert p.evalf(subs={x: -2}) == -1
assert p.evalf(subs={x: -1}) == 1
assert p.evalf(subs={x: 1}) == log(1)
# Test doit
f_int = Piecewise((Integral(x, (x, 0, 1)), x < 1))
assert f_int.doit() == Piecewise( (1.0/2.0, x < 1) )
# Test differentiation
f = x
fp = x*p
dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, x >= 0))
fp_dx = x*dp + p
assert diff(p, x) == dp
assert diff(f*p, x) == fp_dx
# Test simple arithmetic
assert x*p == fp
assert x*p + p == p + x*p
assert p + f == f + p
assert p + dp == dp + p
assert p - dp == -(dp - p)
# Test power
dp2 = Piecewise((0, x < -1), (4*x**2, x < 0), (1/x**2, x >= 0))
assert dp**2 == dp2
# Test _eval_interval
f1 = x*y + 2
f2 = x*y**2 + 3
peval = Piecewise( (f1, x < 0), (f2, x > 0))
peval_interval = f1.subs(
x, 0) - f1.subs(x, -1) + f2.subs(x, 1) - f2.subs(x, 0)
assert peval._eval_interval(x, 0, 0) == 0
assert peval._eval_interval(x, -1, 1) == peval_interval
peval2 = Piecewise((f1, x < 0), (f2, True))
assert peval2._eval_interval(x, 0, 0) == 0
assert peval2._eval_interval(x, 1, -1) == -peval_interval
assert peval2._eval_interval(x, -1, -2) == f1.subs(x, -2) - f1.subs(x, -1)
assert peval2._eval_interval(x, -1, 1) == peval_interval
assert peval2._eval_interval(x, None, 0) == peval2.subs(x, 0)
assert peval2._eval_interval(x, -1, None) == -peval2.subs(x, -1)
# Test integration
p_int = Piecewise((-x, x < -1), (x**3/3.0, x < 0), (-x + x*log(x), x >= 0))
assert integrate(p, x) == p_int
p = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
assert integrate(p, (x, -2, 2)) == 5.0/6.0
assert integrate(p, (x, 2, -2)) == -5.0/6.0
p = Piecewise((0, x < 0), (1, x < 1), (0, x < 2), (1, x < 3), (0, True))
assert integrate(p, (x, -oo, oo)) == 2
p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
raises(ValueError, lambda: integrate(p, (x, -2, 2)))
# Test commutativity
assert p.is_commutative is True
def test_piecewise_free_symbols():
a = symbols('a')
f = Piecewise((x, a < 0), (y, True))
assert f.free_symbols == set([x, y, a])
def test_issue_9778():
assert solveset(x**3 + 1, x, S.Reals) == FiniteSet(-1)
assert solveset(x**(S(3)/5) + 1, x, S.Reals) == S.EmptySet
assert solveset(x**3 + y, x, S.Reals) == Intersection(Interval(-oo, oo), \
FiniteSet((-y)**(S(1)/3)*Piecewise((1, Ne(-im(y), 0)), ((-1)**(S(2)/3), -y < 0), (1, True))))
def test_piecewise():
# Test canonization
assert Piecewise((x, x < 1), (0, True)) == Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, True), (1, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, False), (-1, 1 > 2)) == \
Piecewise((x, x < 1))
assert Piecewise((x, x < 1), (0, x < 1), (0, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (0, x < 2), (0, True)) == \
Piecewise((x, x < 1), (0, True))
assert Piecewise((x, x < 1), (x, x < 2), (0, True)) == \
Piecewise((x, Or(x < 1, x < 2)), (0, True))
assert Piecewise((x, x < 1), (x, x < 2), (x, True)) == x
assert Piecewise((x, True)) == x
raises(TypeError, lambda: Piecewise(x))
raises(TypeError, lambda: Piecewise((x, x**2)))
# Test subs
p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >= 0))
p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >= 0))
assert p.subs(x, x**2) == p_x2
assert p.subs(x, -5) == -1
assert p.subs(x, -1) == 1
assert p.subs(x, 1) == log(1)
# More subs tests
p2 = Piecewise((1, x < pi), (-1, x < 2 * pi), (0, x > 2 * pi))
p3 = Piecewise((1, Eq(x, 0)), (1 / x, True))
p4 = Piecewise((1, Eq(x, 0)), (2, 1 / x > 2))
assert p2.subs(x, 2) == 1
assert p2.subs(x, 4) == -1
assert p2.subs(x, 10) == 0
assert p3.subs(x, 0.0) == 1
assert p4.subs(x, 0.0) == 1
f, g, h = symbols('f,g,h', cls=Function)
pf = Piecewise((f(x), x < -1), (f(x) + h(x) + 2, x <= 1))
pg = Piecewise((g(x), x < -1), (g(x) + h(x) + 2, x <= 1))
assert pg.subs(g, f) == pf
assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 0) == 1
assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 1) == 0
assert Piecewise((1, Eq(x, y)), (0, True)).subs(x, y) == 1
assert Piecewise((1, Eq(x, z)), (0, True)).subs(x, z) == 1
assert Piecewise((1, Eq(exp(x), cos(z))), (0, True)).subs(x, z) == \
Piecewise((1, Eq(exp(z), cos(z))), (0, True))
assert Piecewise((1, Eq(x, y * (y + 1))), (0, True)).subs(x, y**2 + y) == 1
p5 = Piecewise((0, Eq(cos(x) + y, 0)), (1, True))
assert p5.subs(y, 0) == Piecewise((0, Eq(cos(x), 0)), (1, True))
# Test evalf
assert p.evalf() == p
assert p.evalf(subs={x: -2}) == -1
assert p.evalf(subs={x: -1}) == 1
assert p.evalf(subs={x: 1}) == log(1)
# Test doit
f_int = Piecewise((Integral(x, (x, 0, 1)), x < 1))
assert f_int.doit() == Piecewise((1.0 / 2.0, x < 1))
# Test differentiation
f = x
fp = x * p
dp = Piecewise((0, x < -1), (2 * x, x < 0), (1 / x, x >= 0))
fp_dx = x * dp + p
assert diff(p, x) == dp
assert diff(f * p, x) == fp_dx
# Test simple arithmetic
assert x * p == fp
assert x * p + p == p + x * p
assert p + f == f + p
assert p + dp == dp + p
assert p - dp == -(dp - p)
# Test power
dp2 = Piecewise((0, x < -1), (4 * x**2, x < 0), (1 / x**2, x >= 0))
assert dp**2 == dp2
# Test _eval_interval
f1 = x * y + 2
f2 = x * y**2 + 3
peval = Piecewise((f1, x < 0), (f2, x > 0))
peval_interval = f1.subs(x, 0) - f1.subs(x, -1) + f2.subs(x, 1) - f2.subs(
x, 0)
assert peval._eval_interval(x, 0, 0) == 0
assert peval._eval_interval(x, -1, 1) == peval_interval
peval2 = Piecewise((f1, x < 0), (f2, True))
assert peval2._eval_interval(x, 0, 0) == 0
assert peval2._eval_interval(x, 1, -1) == -peval_interval
assert peval2._eval_interval(x, -1, -2) == f1.subs(x, -2) - f1.subs(x, -1)
assert peval2._eval_interval(x, -1, 1) == peval_interval
assert peval2._eval_interval(x, None, 0) == peval2.subs(x, 0)
assert peval2._eval_interval(x, -1, None) == -peval2.subs(x, -1)
# Test integration
p_int = Piecewise((-x, x < -1), (x**3 / 3.0, x < 0),
(-x + x * log(x), x >= 0))
assert integrate(p, x) == p_int
p = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x))
assert integrate(p, (x, -2, 2)) == 5.0 / 6.0
assert integrate(p, (x, 2, -2)) == -5.0 / 6.0
p = Piecewise((0, x < 0), (1, x < 1), (0, x < 2), (1, x < 3), (0, True))
assert integrate(p, (x, -oo, oo)) == 2
p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x))
raises(ValueError, lambda: integrate(p, (x, -2, 2)))
# Test commutativity
assert p.is_commutative is True
def test_latex_Piecewise():
p = Piecewise((x, x < 1), (x**2, True))
assert latex(p) == "\\begin{cases} x & \\text{for}\: x < 1 \\\\x^{2} &" \
" \\text{otherwise} \\end{cases}"
assert latex(p, itex=True) == "\\begin{cases} x & \\text{for}\: x \\lt 1 \\\\x^{2} &" \
" \\text{otherwise} \\end{cases}"
def pmf(self, x):
x = Symbol('x')
return Lambda(x, Piecewise(*(
[(v, Eq(k, x)) for k, v in self.dict.items()] + [(0, True)])))
from sympy import symbols, Function, exp, var, Piecewise
from ComputabilityGraphs.CMTVS import CMTVS
from bgc_md2.helper import bgc_md2_computers
from .source_minus_1 import mvs as mvs_base
Bib = mvs_base.get_BibInfo()
for name in Bib.sym_dict.keys():
var(name)
mrso = Function('mrso')
tsl = Function('tsl')
NPP = Function('NPP')
subs_dict = {
xi:
Piecewise(
(exp(E * (1 / (10 - T0) - 1 / (tsl(t) - T0))) * mrso(t) /
(KM + mrso(t)), tsl(t) > T0),
#(0,tsl(t)<T0)
(0, True) #catch all
)
}
s = {
mvs_base.get_InternalFluxesBySymbol().subs(subs_dict),
mvs_base.get_OutFluxesBySymbol().subs(subs_dict)
}
mvs = mvs_base.update(s)
def pmf(self):
k = Dummy('k')
return Lambda(k, Piecewise((S.Half, Or(Eq(k, -1), Eq(k, 1))), (0, True)))
def test_piecewise_series():
from sympy import sin, cos, O
p1 = Piecewise((sin(x), x<0),(cos(x),x>0))
p2 = Piecewise((x+O(x**2), x<0),(1+O(x**2),x>0))
assert p1.nseries(x,n=2) == p2
def low(self):
return Piecewise((0, Gt(0, self.n + self.m - self.N) != False), (self.n + self.m - self.N, True))
def write_tdb(dbf, fd, groupby='subsystem', if_incompatible='warn'):
"""
Write a TDB file from a pycalphad Database object.
The goal is to produce TDBs that conform to the most restrictive subset of database specifications. Some of these
can be adjusted for automatically, such as the Thermo-Calc line length limit of 78. Others require changing the
database in non-trivial ways, such as the maximum length of function names (8). The default is to warn the user when
attempting to write an incompatible database and the user must choose whether to warn and write the file anyway or
to fix the incompatibility.
Currently the supported compatibility fixes are:
- Line length <= 78 characters (Thermo-Calc)
- Function names <= 8 characters (Thermo-Calc)
The current unsupported fixes include:
- Keyword length <= 2000 characters (Thermo-Calc)
- Element names <= 2 characters (Thermo-Calc)
- Phase names <= 24 characters (Thermo-Calc)
Other TDB compatibility issues required by Thermo-Calc or other software should be reported to the issue tracker.
Parameters
----------
dbf : Database
A pycalphad Database.
fd : file-like
File descriptor.
groupby : ['subsystem', 'phase'], optional
Desired grouping of parameters in the file.
if_incompatible : string, optional ['raise', 'warn', 'fix']
Strategy if the database does not conform to the most restrictive database specification.
The 'warn' option (default) will write out the incompatible database with a warning.
The 'raise' option will raise a DatabaseExportError.
The 'ignore' option will write out the incompatible database silently.
The 'fix' option will rectify the incompatibilities e.g. through name mangling.
"""
# Before writing anything, check that the TDB is valid and take the appropriate action if not
if if_incompatible not in ['warn', 'raise', 'ignore', 'fix']:
raise ValueError('Incorrect options passed to \'if_invalid\'. Valid args are \'raise\', \'warn\', or \'fix\'.')
# Handle function names > 8 characters
long_function_names = {k for k in dbf.symbols.keys() if len(k) > 8}
if len(long_function_names) > 0:
if if_incompatible == 'raise':
raise DatabaseExportError('The following function names are beyond the 8 character TDB limit: {}. Use the keyword argument \'if_incompatible\' to control this behavior.'.format(long_function_names))
elif if_incompatible == 'fix':
# if we are going to make changes, make the changes to a copy and leave the original object untouched
dbf = deepcopy(dbf) # TODO: if we do multiple fixes, we should only copy once
symbol_name_map = {}
for name in long_function_names:
hashed_name = 'F' + str(hashlib.md5(name.encode('UTF-8')).hexdigest()).upper()[:7] # this is implictly upper(), but it is explicit here
symbol_name_map[name] = hashed_name
_apply_new_symbol_names(dbf, symbol_name_map)
elif if_incompatible == 'warn':
warnings.warn('Ignoring that the following function names are beyond the 8 character TDB limit: {}. Use the keyword argument \'if_incompatible\' to control this behavior.'.format(long_function_names))
# Begin constructing the written database
writetime = datetime.datetime.now()
maxlen = 78
output = ""
# Comment header block
# Import here to prevent circular imports
from pycalphad import __version__
output += ("$" * maxlen) + "\n"
output += "$ Date: {}\n".format(writetime.strftime("%Y-%m-%d %H:%M"))
output += "$ Components: {}\n".format(', '.join(sorted(dbf.elements)))
output += "$ Phases: {}\n".format(', '.join(sorted(dbf.phases.keys())))
output += "$ Generated by {} (pycalphad {})\n".format(getpass.getuser(), __version__)
output += ("$" * maxlen) + "\n\n"
for element in sorted(dbf.elements):
output += "ELEMENT {0} BLANK 0 0 0 !\n".format(element.upper())
if len(dbf.elements) > 0:
output += "\n"
for species in sorted(dbf.species, key=lambda s: s.name):
if species.name not in dbf.elements:
# construct the charge part of the specie
if species.charge != 0:
if species.charge >0:
charge_sign = '+'
else:
charge_sign = ''
charge = '/{}{}'.format(charge_sign, species.charge)
else:
charge = ''
species_constituents = ''.join(['{}{}'.format(el, val) for el, val in sorted(species.constituents.items(), key=lambda t: t[0])])
output += "SPECIES {0} {1}{2} !\n".format(species.name.upper(), species_constituents, charge)
if len(dbf.species) > 0:
output += "\n"
# Write FUNCTION block
for name, expr in sorted(dbf.symbols.items()):
if not isinstance(expr, Piecewise):
# Non-piecewise exprs need to be wrapped to print
# Otherwise TC's TDB parser will complain
expr = Piecewise((expr, And(v.T >= 1, v.T < 10000)))
expr = TCPrinter().doprint(expr).upper()
if ';' not in expr:
expr += '; N'
output += "FUNCTION {0} {1} !\n".format(name.upper(), expr)
output += "\n"
# Boilerplate code
output += "TYPE_DEFINITION % SEQ * !\n"
output += "DEFINE_SYSTEM_DEFAULT ELEMENT 2 !\n"
default_elements = [i.upper() for i in sorted(dbf.elements) if i.upper() == 'VA' or i.upper() == '/-']
if len(default_elements) > 0:
output += 'DEFAULT_COMMAND DEFINE_SYSTEM_ELEMENT {} !\n'.format(' '.join(default_elements))
output += "\n"
typedef_chars = list("^&*()'ABCDEFGHIJKLMNOPQSRTUVWXYZ")[::-1]
# Write necessary TYPE_DEF based on model hints
typedefs = defaultdict(lambda: ["%"])
for name, phase_obj in sorted(dbf.phases.items()):
model_hints = phase_obj.model_hints.copy()
possible_options = set(phase_options.keys()).intersection(model_hints)
# Phase options are handled later
for option in possible_options:
del model_hints[option]
if ('ordered_phase' in model_hints.keys()) and (model_hints['ordered_phase'] == name):
new_char = typedef_chars.pop()
typedefs[name].append(new_char)
typedefs[model_hints['disordered_phase']].append(new_char)
output += 'TYPE_DEFINITION {} GES AMEND_PHASE_DESCRIPTION {} DISORDERED_PART {} !\n'\
.format(new_char, model_hints['ordered_phase'].upper(),
model_hints['disordered_phase'].upper())
del model_hints['ordered_phase']
del model_hints['disordered_phase']
if ('disordered_phase' in model_hints.keys()) and (model_hints['disordered_phase'] == name):
# We handle adding the correct typedef when we write the ordered phase
del model_hints['ordered_phase']
del model_hints['disordered_phase']
if 'ihj_magnetic_afm_factor' in model_hints.keys():
new_char = typedef_chars.pop()
typedefs[name].append(new_char)
output += 'TYPE_DEFINITION {} GES AMEND_PHASE_DESCRIPTION {} MAGNETIC {} {} !\n'\
.format(new_char, name.upper(), model_hints['ihj_magnetic_afm_factor'],
model_hints['ihj_magnetic_structure_factor'])
del model_hints['ihj_magnetic_afm_factor']
del model_hints['ihj_magnetic_structure_factor']
if len(model_hints) > 0:
# Some model hints were not properly consumed
raise ValueError('Not all model hints are supported: {}'.format(model_hints))
# Perform a second loop now that all typedefs / model hints are consistent
for name, phase_obj in sorted(dbf.phases.items()):
# model_hints may also contain "phase options", e.g., ionic liquid
model_hints = phase_obj.model_hints.copy()
name_with_options = str(name.upper())
possible_options = set(phase_options.keys()).intersection(model_hints.keys())
if len(possible_options) > 0:
name_with_options += ':'
for option in possible_options:
name_with_options += phase_options[option]
output += "PHASE {0} {1} {2} {3} !\n".format(name_with_options, ''.join(typedefs[name]),
len(phase_obj.sublattices),
' '.join([str(i) for i in phase_obj.sublattices]))
constituents = ':'.join([','.join([spec.name for spec in sorted(subl)]) for subl in phase_obj.constituents])
output += "CONSTITUENT {0} :{1}: !\n".format(name_with_options, constituents)
output += "\n"
# PARAMETERs by subsystem
param_sorted = defaultdict(lambda: list())
paramtuple = namedtuple('ParamTuple', ['phase_name', 'parameter_type', 'complexity', 'constituent_array',
'parameter_order', 'diffusing_species', 'parameter', 'reference'])
for param in dbf._parameters.all():
if groupby == 'subsystem':
components = set()
for subl in param['constituent_array']:
components |= set(subl)
if param['diffusing_species'] != Species(None):
components |= {param['diffusing_species']}
# Wildcard operator is not a component
components -= {'*'}
desired_active_pure_elements = [list(x.constituents.keys()) for x in components]
components = set([el.upper() for constituents in desired_active_pure_elements for el in constituents])
# Remove vacancy if it's not the only component (pure vacancy endmember)
if len(components) > 1:
components -= {'VA'}
components = tuple(sorted([c.upper() for c in components]))
grouping = components
elif groupby == 'phase':
grouping = param['phase_name'].upper()
else:
raise ValueError('Unknown groupby attribute \'{}\''.format(groupby))
# We use the complexity parameter to help with sorting the parameters logically
param_sorted[grouping].append(paramtuple(param['phase_name'], param['parameter_type'],
sum([len(i) for i in param['constituent_array']]),
param['constituent_array'], param['parameter_order'],
param['diffusing_species'], param['parameter'],
param['reference']))
def write_parameter(param_to_write):
constituents = ':'.join([','.join(sorted([i.name.upper() for i in subl]))
for subl in param_to_write.constituent_array])
# TODO: Handle references
paramx = param_to_write.parameter
if not isinstance(paramx, Piecewise):
# Non-piecewise parameters need to be wrapped to print correctly
# Otherwise TC's TDB parser will fail
paramx = Piecewise((paramx, And(v.T >= 1, v.T < 10000)))
exprx = TCPrinter().doprint(paramx).upper()
if ';' not in exprx:
exprx += '; N'
if param_to_write.diffusing_species != Species(None):
ds = "&" + param_to_write.diffusing_species.name
else:
ds = ""
return "PARAMETER {}({}{},{};{}) {} !\n".format(param_to_write.parameter_type.upper(),
param_to_write.phase_name.upper(),
ds,
constituents,
param_to_write.parameter_order,
exprx)
if groupby == 'subsystem':
for num_species in range(1, 5):
subsystems = list(itertools.combinations(sorted([i.name.upper() for i in dbf.species]), num_species))
for subsystem in subsystems:
parameters = sorted(param_sorted[subsystem])
if len(parameters) > 0:
output += "\n\n"
output += "$" * maxlen + "\n"
output += "$ {}".format('-'.join(sorted(subsystem)).center(maxlen, " ")[2:-1]) + "$\n"
output += "$" * maxlen + "\n"
output += "\n"
for parameter in parameters:
output += write_parameter(parameter)
# Don't generate combinatorics for multi-component subsystems or we'll run out of memory
if len(dbf.species) > 4:
subsystems = [k for k in param_sorted.keys() if len(k) > 4]
for subsystem in subsystems:
parameters = sorted(param_sorted[subsystem])
for parameter in parameters:
output += write_parameter(parameter)
elif groupby == 'phase':
for phase_name in sorted(dbf.phases.keys()):
parameters = sorted(param_sorted[phase_name])
if len(parameters) > 0:
output += "\n\n"
output += "$" * maxlen + "\n"
output += "$ {}".format(phase_name.upper().center(maxlen, " ")[2:-1]) + "$\n"
output += "$" * maxlen + "\n"
output += "\n"
for parameter in parameters:
output += write_parameter(parameter)
else:
raise ValueError('Unknown groupby attribute {}'.format(groupby))
# Reflow text to respect character limit per line
fd.write(reflow_text(output, linewidth=maxlen))
def test_piecewise_fold_piecewise_in_cond():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True))
p3 = piecewise_fold(p2)
assert (p2.subs(x, -pi / 2) == 0.0)
assert (p2.subs(x, 1) == 0.0)
assert (p2.subs(x, -pi / 4) == 1.0)
p4 = Piecewise((0, Eq(p1, 0)), (1, True))
assert (piecewise_fold(p4) == Piecewise(
(0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))), (1, True)))
r1 = 1 < Piecewise((1, x < 1), (3, True))
assert (piecewise_fold(r1) == Not(x < 1))
p5 = Piecewise((1, x < 0), (3, True))
p6 = Piecewise((1, x < 1), (3, True))
p7 = piecewise_fold(Piecewise((1, p5 < p6), (0, True)))
assert (Piecewise((1, And(Not(x < 1), x < 0)), (0, True)))
