def test_minimize_linear():
# see also sympy/sympy#20391
assert minimize([
-2 * x - 3 * y - 2 * z, 2 * x + y + z <= 4, x + 2 * y + z <= 7, z <= 5,
x >= 0, y >= 0, z >= 0
], x, y, z) == (-11, {
x: 0,
y: 3,
z: 1
})
assert minimize([
-2 * x - 3 * y - 2 * z, 2 * x + y + z <= 4, x + 2 * y + z <= 7, z <= 5,
x >= 0, y >= 0, z >= 0
], x, y, z) == (-11, {
x: 0,
y: 3,
z: 1
})
assert minimize([
-2 * x - 3 * y - 2 * z, 2 * x + y + z <= 4, x + 2 * y + z < 7, z <= 5,
x >= 0, y >= 0, z >= 0
], x, y, z) is None
assert minimize([
-2 * x - 3 * y - 4 * z, 3 * x + 2 * y + z <= 10,
2 * x + 5 * y + 3 * z <= 15, x >= 0, y >= 0, z >= 0
], x, y, z) == (-20, {
x: 0,
y: 0,
z: 5
})
assert maximize([
12 * x + 40 * y, x + y <= 15, x + 3 * y <= 36, x <= 10, x >= 0, y >= 0
], x, y) == (480, {
x: 0,
y: 12
})
assert minimize([
-2 * x - 3 * y - 4 * z,
Eq(3 * x + 2 * y + z, 10),
Eq(2 * x + 5 * y + 3 * z, 15), x >= 0, y >= 0, z >= 0
], x, y, z) == (Rational(-130, 7), {
x: Rational(15, 7),
y: 0,
z: Rational(25, 7)
})
assert maximize([2 * x + y, y - x <= 1, x - 2 * y <= 2, x >= 0, y >= 0], x,
y) == (oo, {
x: nan,
y: nan
})
assert minimize([
2 * x + 3 * y - z, 1 <= x + y + z, x + y + z <= 2, 1 <= x - y + z,
x - y + z <= 2,
Eq(x - y - z, 3)
], x, y, z) == (3, {
x: 2,
y: Rational(-1, 2),
z: Rational(-1, 2)
})
assert minimize([
-2 * t + 4 * w + 7 * x + y + 5 * z,
Eq(-t + w + 2 * x + y + 2 * z, 7),
Eq(-t + 2 * w + 3 * x + y + z, 6),
Eq(-t + w + x + 2 * y + z, 4), w >= 0, x >= 0, y >= 0, z >= 0
], t, w, x, y, z) == (19, {
t: -1,
w: 0,
x: 1,
y: 0,
z: 2
})
assert minimize([
-x - y, x + 2 * y <= 8, 3 * x + 2 * y <= 12, x + 3 * y >= 6, x >= 0,
y >= 0
], x, y) == (-5, {
x: 2,
y: 3
})
pytest.raises(
InfeasibleProblem, lambda: minimize([
-x - y, x + 2 * y <= 8, 3 * x + 2 * y <= 12, x + 3 * y >= 13, x >=
0, y >= 0
], x, y))
pytest.raises(
InfeasibleProblem, lambda: minimize([
-x - y, x + 2 * y <= 8, 3 * x + 2 * y <= 12, x + 3 * y >= 13, x >=
0, y >= 0
], x, y))
assert minimize([-x - y, 2 * x + y >= 4,
Eq(x + 2 * y, 6), x >= 0, y >= 0], x, y) == (-6, {
x: 6,
y: 0
})
assert minimize([
6 * x + 3 * y, x + y >= 1, 2 * x - y >= 1, 3 * y <= 2, x >= 0, y >= 0
], x, y) == (5, {
x: Rational(2, 3),
y: Rational(1, 3)
})
def test_minimize_poly():
assert minimize([x - 2 * y, x**2 + y**2 <= 1], x, y)[0] == -sqrt(5)
def test_minimize_analytic():
assert minimize(exp(x**2 + y**2), x, y) == (1, {x: 0, y: 0})
def test_minimize():
assert minimize(1) == (1, {})
assert minimize((x - 2)**2) == (0, {x: 2})
assert minimize((x - 2)**2, x) == (0, {x: 2})
assert minimize(1 / x, x) == (-oo, {x: 0})
assert minimize(2 * x**2 - 4 * x + 5, x) == (3, {x: 1})
assert minimize([2 * x**2 - 4 * x + 5, x > 0], x) == (3, {x: 1})
assert minimize([2 * x**2 - 4 * x + 5, x > 1], x) is None
assert minimize([2 * x**2 - 4 * x + 5, x >= 2], x) == (5, {x: 2})
assert minimize([2 * x**2 - 4 * x + 5, x**2 <= 0], x) == (5, {x: 0})
assert minimize([x**2 - 1,
(x - 1) * (x - 2) * (x - 3) * (4 - x) >= 0]) == (0, {
x: 1
})
assert minimize([x**2, (x + 2) * (x - 1) * (1 - x) >= 0]) == (1, {x: 1})
assert minimize(sign(x), x) == (-1, {x: 0})