def mul_interval(x, y):
lx = lower_bound(x)
ux = upper_bound(x)
ly = lower_bound(y)
uy = upper_bound(y)
if lx > 0 and ux > 0:
if ly > 0 and uy > 0:
return make_interval(lx * ly, ux * uy)
elif ly < 0 and uy < 0:
return make_interval(ux * ly, lx * uy)
else:
return make_interval(ux * ly, ux * uy)
elif lx < 0 and ux < 0:
if ly > 0 and uy > 0:
return make_interval(ux * ly, lx * uy)
elif ly < 0 and uy < 0:
return make_interval(ux * uy, lx * ly)
else:
return make_interval(lx * uy, lx * ly)
else:
if ly > 0 and uy > 0:
return make_interval(lx * uy, ux * uy)
elif ly < 0 and uy < 0:
return make_interval(ux * ly, lx * ly)
else:
l1 = lx * uy
l2 = ux * ly
u1 = lx * ly
u2 = ux * uy
return make_interval(min([l1, l2]), max([u1, u2]))
from util_pair import cons, car, cdr
from util_interval import make_interval, print_interval
from util_interval import add_interval, mul_interval, div_interval
def lower_bound(z):
return min([car(z), cdr(z)])
def upper_bound(z):
return max([car(z), cdr(z)])
z1 = make_interval(2, 5)
z2 = make_interval(7, 3)
print_interval(z1)
print_interval(z2)
print_interval(add_interval(z1, z2))
print_interval(mul_interval(z1, z2))
print_interval(div_interval(z1, z2))
return make_interval(lx * uy, lx * ly)
else:
if ly > 0 and uy > 0:
return make_interval(lx * uy, ux * uy)
elif ly < 0 and uy < 0:
return make_interval(ux * ly, lx * ly)
else:
l1 = lx * uy
l2 = ux * ly
u1 = lx * ly
u2 = ux * uy
return make_interval(min([l1, l2]), max([u1, u2]))
zx1 = make_interval(2, 5)
zx2 = make_interval(-6, -3)
zx3 = make_interval(-4, 7)
zy1 = make_interval(3, 4)
zy2 = make_interval(-5, -2)
zy3 = make_interval(-1, 6)
print_interval(mul_interval(zx1, zy1))
print_interval(mul_interval(zx1, zy2))
print_interval(mul_interval(zx1, zy3))
print_interval(mul_interval(zx2, zy1))
print_interval(mul_interval(zx2, zy2))
print_interval(mul_interval(zx2, zy3))
print_interval(mul_interval(zx3, zy1))
print_interval(mul_interval(zx3, zy2))
def sub_interval(x, y):
return make_interval(lower_bound(x) - upper_bound(y),
upper_bound(x) - lower_bound(y))
def div_interval(x, y):
if lower_bound(y) * upper_bound(y) <= 0:
print("Division error: [" + str(lower_bound(y)) + ", " + str(upper_bound(y)) + "]")
return make_interval(0, 0)
else:
return mul_interval(x, make_interval(1.0 / upper_bound(y), 1.0 / lower_bound(y)))
from util_interval import make_interval, lower_bound, upper_bound, print_interval
from util_interval import add_interval, sub_interval, mul_interval
def div_interval(x, y):
if lower_bound(y) * upper_bound(y) <= 0:
print("Division error: [" + str(lower_bound(y)) + ", " + str(upper_bound(y)) + "]")
return make_interval(0, 0)
else:
return mul_interval(x, make_interval(1.0 / upper_bound(y), 1.0 / lower_bound(y)))
z1 = make_interval(2, 5)
z2 = make_interval(-1, 1)
print_interval(z1)
print_interval(z2)
print_interval(div_interval(z1, z2))
def make_center_width(c, w):
return make_interval(c - w, c + w)
def make_center_percent(c, p):
r = p / 100
return make_interval(c * (1 + r), c * (1 - r))