def VKmeanupper(
pa, pb, k1, k2, k3, k4
): # Interval pa, Interval pb, double k1, double k2, double k3, double k4)
#double p1, p2, ec2;
lpa = utils.left(pa)
rpa = utils.right(pa)
lpb = utils.left(pb)
rpb = utils.right(pb)
touch = touching(pa, pb)
p1 = lpa
p2 = lpb
ec2 = VKmeanup(p1, p2, k1, k2, k3, k4)
p1 = lpa
p2 = rpb
ec2 = np.max([ec2, VKmeanup(p1, p2, k1, k2, k3, k4)])
p1 = rpa
p2 = lpb
ec2 = np.max([ec2, VKmeanup(p1, p2, k1, k2, k3, k4)])
p1 = rpa
p2 = rpb
ec2 = np.max([ec2, VKmeanup(p1, p2, k1, k2, k3, k4)])
p1 = np.max([lpa, 1 - rpb])
p2 = 1 - p1
if (touch): ec2 = np.max([ec2, VKmeanup(p1, p2, k1, k2, k3, k4)])
p1 = np.min([rpa, 1 - lpb])
p2 = 1 - p1
if (touch): ec2 = np.max([ec2, VKmeanup(p1, p2, k1, k2, k3, k4)])
return ec2
def VKmeanlower(
pa, pb, k1, k2, k3, k4
): # Interval pa, Interval pb, double k1, double k2, double k3, double k4)
# double p1, p2, ec1;
lpa = utils.left(pa)
rpa = utils.right(pa)
lpb = utils.left(pb)
rpb = utils.right(pb)
touch = touching(pa + pb, 1.0)
p1 = lpa
p2 = lpb
ec1 = VKmeanlo(p1, p2, k1, k2, k3, k4)
p1 = lpa
p2 = rpb
ec1 = np.min([ec1, VKmeanlo(p1, p2, k1, k2, k3, k4)])
p1 = rpa
p2 = lpb
ec1 = np.min([ec1, VKmeanlo(p1, p2, k1, k2, k3, k4)])
p1 = rpa
p2 = rpb
ec1 = np.min([ec1, VKmeanlo(p1, p2, k1, k2, k3, k4)])
p1 = np.max([lpa, 1 - rpb])
p2 = 1 - p1
if touch:
ec1 = np.min([ec1, VKmeanlo(p1, p2, k1, k2, k3, k4)])
p1 = np.min([rpa, 1 - lpb])
p2 = 1 - p1
if touch:
ec1 = np.min([ec1, VKmeanlo(p1, p2, k1, k2, k3, k4)])
return ec1
def touching(a, b): # const Interval& a, const Interval& b )
if np.all(utils.left(a) == utils.right(a)) and np.all(
utils.left(b) == utils.right(b)):
return utils.left(a) == utils.left(b)
if utils.straddles(a - b):
return True
return False
def VKmeanproduct(a, b):
# Interval ea,eb,ec,pa,pb;
# double la,ra,lb,rb,k1,k2,k3,k4,ec1,ec2;
ec = interval.Interval(-np.inf, np.inf)
ea = interval.Interval(a.mean_lo, a.mean_hi)
eb = interval.Interval(b.mean_lo, b.mean_hi)
la = utils.left(a)
ra = utils.right(a)
lb = utils.left(b)
rb = utils.right(b)
k1 = ra * rb
k2 = ra * lb
k3 = la * rb
k4 = la * lb
pa = interval.Interval((utils.left(ea) - la) / (ra - la),
(utils.right(ea) - la) / (ra - la))
pb = interval.Interval((utils.left(eb) - lb) / (rb - lb),
(utils.right(eb) - lb) / (rb - lb))
ec = utils.env_int(VKmeanlower(pa, pb, k1, k2, k3, k4),
VKmeanupper(pa, pb, k1, k2, k3, k4))
return ec
def reciprocal(self):
if self.shape in [
'Cauchy', '{min, max, median}', '{min, max, percentile}',
'{min, max}'
]:
sh = self.shape
elif self.shape == 'Pareto':
sh = 'power function'
elif self.shape == 'power function':
sh = 'Pareto'
else:
sh = ''
t = lambda x: 1 / x
if utils.left(self) <= 0 and utils.right(self) >= 0:
return np.nan
elif utils.left(self) > 0:
mymean = rowebounds.transformedMean(self, t, False, True)
myvar = rowebounds.transformedVariance(self, t, False, True,
mymean)
else:
mymean = rowebounds.transformedMean(self, t, False, False)
myvar = rowebounds.transformedVariance(self, t, False, False,
mymean)
pbox_parms = {
"hi": 1 / np.flip(self.lo),
"lo": 1 / np.flip(self.hi),
"shape": sh,
"mean_lo": utils.left(mymean),
"mean_hi": utils.right(mymean),
"var_lo": utils.left(myvar),
"var_hi": utils.right(myvar)
}
return Pbox(**pbox_parms)
def _naivefrechetconv(self, other, op='*'):
if op == '+':
return self._frechetconv(other, '+')
if op == '-':
return self._frechetconv(-other, '+')
if op == '/':
return self._naivefrechetconv(other.reciprocal(), '*')
# x = makepbox(x)
# y = makepbox(y)
n = len(self.hi)
c = (utils.get_op(op)([[i] for i in self.hi], other.hi)).flatten()
c.sort()
Zd = c[np.array(range(n * n - n, n * n))]
c = (utils.get_op(op)([[i] for i in self.lo], other.lo)).flatten()
c.sort()
Zu = c[np.array(range(n))]
# mean
m = interval.Interval(self.mean_lo, self.mean_hi) * interval.Interval(
other.mean_lo, other.mean_hi)
a = np.sqrt(
interval.Interval(self.var_lo, self.var_hi) *
interval.Interval(other.var_lo, other.var_hi))
ml = m - a
mh = m + a
VK = vkmean.VKmeanproduct(self, other)
m = utils.imp(interval.Interval(ml, mh), VK)
# variance
vl = 0
vh = np.inf
pbox_parms = {
"hi": Zd,
"lo": Zu,
"mean_lo": utils.left(m),
"mean_hi": utils.right(m),
"var_lo": vl,
"var_hi": vh
}
return Pbox(**pbox_parms)
def _checkmoments(self):
a = interval.Interval(self.mean_lo, self.mean_hi) #mean(x)
b = utils.dwMean(self)
self.mean_lo = np.max([utils.left(a), utils.left(b)])
self.mean_hi = np.min([utils.right(a), utils.right(b)])
if self.mean_hi < self.mean_lo:
# use the observed mean
self.mean_lo = utils.left(b)
self.mean_hi = utils.right(b)
a = interval.Interval(self.var_lo, self.var_hi) #var(x)
b = utils.dwVariance(self)
self.var_lo = np.max([utils.left(a), utils.left(b)])
self.var_hi = np.min([utils.right(a), utils.right(b)])
if self.var_hi < self.var_lo:
# use the observed variance
self.var_lo = utils.left(b)
self.var_hi = utils.right(b)
def __init__(self,
lo=None,
hi=None,
steps=200,
shape=None,
mean_lo=None,
mean_hi=None,
var_lo=None,
var_hi=None,
interpolation='linear'):
if isinstance(lo, Pbox):
self.lo = lo.lo
self.hi = lo.hi
self.steps = lo.steps
self.n = lo.steps
self.shape = lo.shape
self.mean_lo = lo.mean_lo
self.mean_hi = lo.mean_hi
self.var_lo = lo.var_lo
self.var_hi = lo.var_hi
else:
if lo is None and hi is None:
lo = -np.inf
hi = np.inf
if (lo is not None) and (hi is None):
hi = lo
if isinstance(lo,
interval.Interval) or (not hasattr(lo, '__len__')):
lo = np.array([utils.left(lo)])
if isinstance(hi,
interval.Interval) or (not hasattr(hi, '__len__')):
hi = np.array([utils.right(hi)])
if len(lo) != steps:
lo = utils.interpolate(lo,
interpolation=interpolation,
left=True,
pbox_steps=steps)
if len(hi) != steps:
hi = utils.interpolate(hi,
interpolation=interpolation,
left=False,
pbox_steps=steps)
self.lo = lo
self.hi = hi
self.steps = steps
self.n = self.steps
self.shape = shape
self.mean_lo = -np.inf
self.mean_hi = np.inf
self.var_lo = 0
self.var_hi = np.inf
self._computemoments()
if shape is not None: self.shape = shape
if mean_lo is not None: self.mean_lo = np.max([mean_lo, self.mean_lo])
if mean_hi is not None: self.mean_hi = np.min([mean_hi, self.mean_hi])
if var_lo is not None: self.var_lo = np.max([var_lo, self.var_lo])
if var_hi is not None: self.var_hi = np.min([var_hi, self.var_hi])
self._checkmoments()