def test_trig(self):
z = interval[-10,
10].newton(lambda x: imath.cospi(x / 3) - 0.5,
lambda x: -imath.pi * imath.sinpi(x / 3) / 3)
w = interval(-7, -5, -1, 1, 5, 7)
assert w in z
assert max(helpers.ulpwidth(z)) == 4
def test_cospi(self):
assert imath.cospi(fpu.infinity) == interval[-1, 1]
assert imath.cospi(-fpu.infinity) == interval[-1, 1]
assert imath.cospi(interval[0.5, 1.5]) == interval[-1, 0]
assert imath.cospi(interval[-0.5, 0.5]) == interval[0, 1]
assert imath.cospi(1/interval[3]) == interval[helpers.nudge(0.5,-2), helpers.nudge(0.5, 1)]
assert imath.cospi(-1/interval[3]) == interval[helpers.nudge(0.5,-2), helpers.nudge(0.5, 1)]
assert imath.cospi(2/interval[3]) == interval[helpers.nudge(-0.5,-2), helpers.nudge(-0.5,2)]
assert imath.cospi(interval[6]**-1) == imath.sqrt(3)/2
def test_cospi(self):
assert imath.cospi(fpu.infinity) == interval[-1, 1]
assert imath.cospi(-fpu.infinity) == interval[-1, 1]
assert imath.cospi(interval[0.5, 1.5]) == interval[-1, 0]
assert imath.cospi(interval[-0.5, 0.5]) == interval[0, 1]
assert imath.cospi(1 / interval[3]) == interval[helpers.nudge(0.5, -2),
helpers.nudge(0.5, 1)]
assert imath.cospi(-1 /
interval[3]) == interval[helpers.nudge(0.5, -2),
helpers.nudge(0.5, 1)]
assert imath.cospi(2 /
interval[3]) == interval[helpers.nudge(-0.5, -2),
helpers.nudge(-0.5, 2)]
assert imath.cospi(interval[6]**-1) == imath.sqrt(3) / 2
def initial_state_interval():
v_0 = interval[1.0, 1.01]
pos_x_0 = interval[0.3, 0.31]
pos_y_0 = interval[0.3, 0.31]
psi_0 = interval[0, 0.01]
x_d_0 = interval[1, 1]
y_d_0 = interval[1, 1]
av = (lambda v, psi, x_d, y_d, pos_x, pos_y: (-1 * v * imath.sinpi(psi) * x_d + y_d * v * imath.cospi(psi) - pos_y * v * imath.cospi(psi))/((x_d - pos_x)**2+(y_d - pos_y)**2))\
(v_0, psi_0, x_d_0, y_d_0, pos_x_0, pos_y_0)
return av
def test_trig(self):
z = interval[-10, 10].newton(lambda x: imath.cospi(x/3) - 0.5, lambda x: -imath.pi * imath.sinpi(x/3) / 3)
w = interval(-7, -5, -1, 1, 5, 7)
assert w in z
assert max(helpers.ulpwidth(z)) == 4