def b2mult(Self, Other):
assert Self.level == Other.level == 1 and Self.b2equiv(Other)
lc = Self.l.c * Other.l.c
uc = Self.u.c * Other.u.c
if len(Self.dep):
k = list(Self.dep)[0]
ld = {
k: Self.l.c * Other.l.d.get(k, 0.0) +
Other.l.c * Self.l.d.get(k, 0.0)
}
ud = {
k: Self.u.c * Other.u.d.get(k, 0.0) +
Other.u.c * Self.u.d.get(k, 0.0)
}
ld2 = {k: Other.l.d.get(k, 0.0) * Self.l.d.get(k, 0.0)}
ud2 = {k: Other.u.d.get(k, 0.0) * Self.u.d.get(k, 0.0)}
else:
assert len(Other.dep) == 0
return boundsurf(surf({}, lc), surf({}, uc),
Self.definiteRange & Other.definiteRange, Self.domain)
from boundsurf2 import surf2, boundsurf2
ls, us = surf2(ld2, ld, lc), surf2(ud2, ud, uc)
r = boundsurf2(ls, us, Self.definiteRange & Other.definiteRange,
Self.domain)
return r
def inv_b_interval(B, revert):
if type(B) == boundsurf2:
B = B.to_linear()
k = list(B.dep)[0]
l, u = B.domain[k]
d_l, d_u = B.l.d[k], B.u.d[k]
c_l, c_u = B.l.c, B.u.c
if revert:
d_l, d_u = -d_u, -d_l
c_l, c_u = -c_u, -c_l
koeffs_l, koeffs_u = get_inv_b2_coeffs(l, u, d_l, d_u, c_l, c_u)
# ###########
# from boundsurf2 import apply_quad_lin
# a, b, c = koeffs_l
# s_l = apply_quad_lin(a, b, c, B.l)
# a, b, c = koeffs_u
# s_u = apply_quad_lin(a, b, c, B.u)
# ###########
# print koeffs_l, koeffs_u
if revert:
# c_l, c_u = -c_u, -c_l
# d_l, d_u = -d_u, -d_l
# B = -B
koeffs_l, koeffs_u = -array(koeffs_u), -array(koeffs_l)
#############
a, b, c = koeffs_l
s_l = surf2({k:a}, {k:b}, c)
a, b, c = koeffs_u
s_u = surf2({k:a}, {k:b}, c)
# ###############
# if 0:
# from numpy import linspace
# x = linspace(l, u, 10000)
# d_l, d_u = B.l.d[k], B.u.d[k]
# c_l, c_u = B.l.c, B.u.c
# import pylab
# if 1:
# pylab.plot(x, 1.0/(d_l*x+c_l), 'r', linewidth = 2)
# pylab.plot(x, koeffs_l[0]*x**2+koeffs_l[1]*x+koeffs_l[2], 'b', linewidth = 1)
# # else:
# pylab.plot(x, 1.0/(d_u*x+c_u), 'b', linewidth = 2)
# pylab.plot(x, koeffs_u[0]*x**2+koeffs_u[1]*x+koeffs_u[2], 'r', linewidth = 1)
# pylab.grid()
# pylab.show()
# ###############
return boundsurf2(s_l, s_u, B.definiteRange, B.domain), B.definiteRange
def inv_b_interval(B, revert):
if type(B) == boundsurf2:
B = B.to_linear()
k = list(B.dep)[0]
l, u = B.domain[k]
d_l, d_u = B.l.d[k], B.u.d[k]
c_l, c_u = B.l.c, B.u.c
if revert:
d_l, d_u = -d_u, -d_l
c_l, c_u = -c_u, -c_l
koeffs_l, koeffs_u = get_inv_b2_coeffs(l, u, d_l, d_u, c_l, c_u)
# ###########
# from boundsurf2 import apply_quad_lin
# a, b, c = koeffs_l
# s_l = apply_quad_lin(a, b, c, B.l)
# a, b, c = koeffs_u
# s_u = apply_quad_lin(a, b, c, B.u)
# ###########
# print koeffs_l, koeffs_u
if revert:
# c_l, c_u = -c_u, -c_l
# d_l, d_u = -d_u, -d_l
# B = -B
koeffs_l, koeffs_u = -array(koeffs_u), -array(koeffs_l)
#############
a, b, c = koeffs_l
s_l = surf2({k:a}, {k:b}, c)
a, b, c = koeffs_u
s_u = surf2({k:a}, {k:b}, c)
# ###############
# if 0:
# from numpy import linspace
# x = linspace(l, u, 10000)
# d_l, d_u = B.l.d[k], B.u.d[k]
# c_l, c_u = B.l.c, B.u.c
# import pylab
# if 1:
# pylab.plot(x, 1.0/(d_l*x+c_l), 'r', linewidth = 2)
# pylab.plot(x, koeffs_l[0]*x**2+koeffs_l[1]*x+koeffs_l[2], 'b', linewidth = 1)
# # else:
# pylab.plot(x, 1.0/(d_u*x+c_u), 'b', linewidth = 2)
# pylab.plot(x, koeffs_u[0]*x**2+koeffs_u[1]*x+koeffs_u[2], 'r', linewidth = 1)
# pylab.grid()
# pylab.show()
# ###############
return boundsurf2(s_l, s_u, B.definiteRange, B.domain), B.definiteRange
def b2mult(Self, Other):
assert Self.level == Other.level == 1 and Self.b2equiv(Other)
k = list(Self.dep)[0]
ld = {k: Self.l.c*Other.l.d.get(k, 0.0) + Other.l.c*Self.l.d.get(k, 0.0)}
ud = {k: Self.u.c*Other.u.d.get(k, 0.0) + Other.u.c*Self.u.d.get(k, 0.0)}
ld2 = {k: Other.l.d.get(k, 0.0) * Self.l.d.get(k, 0.0)}
ud2 = {k: Other.u.d.get(k, 0.0) * Self.u.d.get(k, 0.0)}
lc = Self.l.c * Other.l.c
uc = Self.u.c * Other.u.c
from boundsurf2 import surf2, boundsurf2
ls, us = surf2(ld2, ld, lc), surf2(ud2, ud, uc)
r = boundsurf2(ls, us, Self.definiteRange & Other.definiteRange, Self.domain)
return r
def b2mult_direct(Self, Other):
assert Self.level == Other.level == 1 and Self.b2equiv(Other) and Self.l is Self.u and Other.l is Other.u
k = list(Self.dep)[0]
s, o = Self.l, Other.l # = Self.u, Other.u
ld = {k: s.c * o.d.get(k, 0.0) + o.c * s.d.get(k, 0.0)}
ld2 = {k: o.d.get(k, 0.0) * s.d.get(k, 0.0)}
lc = s.c * o.c
from boundsurf2 import surf2, boundsurf2
ls = surf2(ld2, ld, lc)
r = boundsurf2(ls, ls, Self.definiteRange & Other.definiteRange, Self.domain)
return r
def b2mult_direct(Self, Other):
assert Self.level == Other.level == 1 and Self.b2equiv(
Other) and Self.l is Self.u and Other.l is Other.u
k = list(Self.dep)[0]
s, o = Self.l, Other.l # = Self.u, Other.u
ld = {k: s.c * o.d.get(k, 0.0) + o.c * s.d.get(k, 0.0)}
ld2 = {k: o.d.get(k, 0.0) * s.d.get(k, 0.0)}
lc = s.c * o.c
from boundsurf2 import surf2, boundsurf2
ls = surf2(ld2, ld, lc)
r = boundsurf2(ls, ls, Self.definiteRange & Other.definiteRange,
Self.domain)
return r
def surf_join(inds, S):
c = Join(inds, [s.c for s in S]) # list, not iterator!
keys = set.union(*[set(s.d.keys()) for s in S])
d = dict((k, Join(inds, [s.d.get(k, arrZero) for s in S])) for k in keys)
keys = set.union(*[set(getattr(s,'d2', {}).keys()) for s in S])
if len(keys) == 0:
return surf(d, c)
d2 = dict((k, Join(inds, [getattr(s, 'd2', {}).get(k, arrZero) for s in S])) for k in keys)
from boundsurf2 import surf2
return surf2(d2, d, c)
def pow_b_interval(lb_ub, r1, other):
definiteRange, domain = lb_ub.definiteRange, lb_ub.domain
if type(lb_ub) == boundsurf2:
lb_ub = lb_ub.to_linear()
k = list(lb_ub.dep)[0]
l, u = domain[k]
d_l, d_u = lb_ub.l.d[k], lb_ub.u.d[k]
c_l, c_u = lb_ub.l.c, lb_ub.u.c
koeffs_l, koeffs_u = get_pow_b2_coeffs(l, u, d_l, d_u, c_l, c_u, other)
#assert all(isfinite(koeffs_l)), all(isfinite(koeffs_u))
# L
a, b, c = koeffs_l
L = surf2({k: a}, {k: b}, c)
# U
a, b, c = koeffs_u
U = surf2({k: a}, {k: b}, c)
#########################
# from numpy import linspace
# #l = 0.99
# print l, u
# x = linspace(l, u, 10000)
# import pylab
# pylab.plot(x, pow(d_l*x+c_l, other), 'b', linewidth = 2)
# pylab.plot(x, pow(d_u*x+c_u, other), 'r', linewidth = 2)
# pylab.plot(x, koeffs_l[0]*x**2+koeffs_l[1]*x+koeffs_l[2], 'b', linewidth = 1)
# pylab.plot(x, koeffs_u[0]*x**2+koeffs_u[1]*x+koeffs_u[2], 'r', linewidth = 1)
# pylab.show()
#########################
if not np.array_equal(other, asarray(other, int)):
definiteRange = logical_and(definiteRange,
c_l + d_l * where(d_l > 0, l, u) >= 0)
r2 = boundsurf2(L, U, definiteRange, domain)
R = merge_boundsurfs(r1, r2)
return R, definiteRange
def surf_join(inds, S):
c = Join(inds, [s.c for s in S]) # list, not iterator!
keys = set.union(*[set(s.d.keys()) for s in S])
d = dict((k, Join(inds, [s.d.get(k, arrZero) for s in S])) for k in keys)
keys = set.union(*[set(getattr(s, 'd2', {}).keys()) for s in S])
if len(keys) == 0:
return surf(d, c)
d2 = dict((k, Join(inds, [getattr(s, 'd2', {}).get(k, arrZero)
for s in S])) for k in keys)
from boundsurf2 import surf2
return surf2(d2, d, c)
def pow_b_interval(lb_ub, r1, other):
definiteRange, domain = lb_ub.definiteRange, lb_ub.domain
if type(lb_ub) == boundsurf2:
lb_ub = lb_ub.to_linear()
k = list(lb_ub.dep)[0]
l, u = domain[k]
d_l, d_u = lb_ub.l.d[k], lb_ub.u.d[k]
c_l, c_u = lb_ub.l.c, lb_ub.u.c
koeffs_l, koeffs_u = get_pow_b2_coeffs(l, u, d_l, d_u, c_l, c_u, other)
#assert all(isfinite(koeffs_l)), all(isfinite(koeffs_u))
# L
a, b, c = koeffs_l
L = surf2({k:a}, {k:b}, c)
# U
a, b, c = koeffs_u
U = surf2({k:a}, {k:b}, c)
#########################
# from numpy import linspace
# #l = 0.99
# print l, u
# x = linspace(l, u, 10000)
# import pylab
# pylab.plot(x, pow(d_l*x+c_l, other), 'b', linewidth = 2)
# pylab.plot(x, pow(d_u*x+c_u, other), 'r', linewidth = 2)
# pylab.plot(x, koeffs_l[0]*x**2+koeffs_l[1]*x+koeffs_l[2], 'b', linewidth = 1)
# pylab.plot(x, koeffs_u[0]*x**2+koeffs_u[1]*x+koeffs_u[2], 'r', linewidth = 1)
# pylab.show()
#########################
if not np.array_equal(other, asarray(other, int)):
definiteRange = logical_and(definiteRange, c_l+d_l*where(d_l>0, l, u)>=0)
r2 = boundsurf2(L, U, definiteRange, domain)
R = merge_boundsurfs(r1, r2)
return R, definiteRange
def defaultIntervalEngine(arg_lb_ub, fun, deriv, monotonity, convexity, criticalPoint = np.nan,
criticalPointValue = np.nan, feasLB = -inf, feasUB = inf, domain_ind = slice(None), R0 = None):
#monotonity = nan
assert type(monotonity) != bool and type(convexity) != bool, 'bug in defaultIntervalEngine'
Ld2, Ud2 = getattr(arg_lb_ub.l,'d2', {}), getattr(arg_lb_ub.u,'d2', {})
# DEBUG!!!!!!!!!!!!!!!!!
# if (len(Ld2) != 0 or len(Ud2) != 0):
# arg_lb_ub = arg_lb_ub.to_linear()
# Ld2, Ud2 = {}, {}
# !! TODO: handle monotonity = nan with boundsurf2
#if (len(Ld2) != 0 or len(Ud2) != 0) and np.isnan(monotonity):
if arg_lb_ub.level == 2 and np.isnan(monotonity):
arg_lb_ub = arg_lb_ub.to_linear()
Ld2, Ud2 = {}, {}
L, U, domain, definiteRange = arg_lb_ub.l, arg_lb_ub.u, arg_lb_ub.domain, arg_lb_ub.definiteRange
Ld, Ud = L.d, U.d
if type(domain_ind) == np.ndarray:
if domain_ind.dtype == bool:
domain_ind = where(domain_ind)[0]
Ld, Ud = dict_reduce(Ld, domain_ind), dict_reduce(Ud, domain_ind)
Ld2, Ud2 = dict_reduce(Ld2, domain_ind), dict_reduce(Ud2, domain_ind)
R0 = (arg_lb_ub.resolve()[0] if R0 is None else R0)[:, domain_ind]
if type(definiteRange) != bool and definiteRange.size > 1:
definiteRange = definiteRange[domain_ind]
elif R0 is None:
R0 = arg_lb_ub.resolve()[0]
#R0 = arg_lb_ub.resolve(ind = domain_ind)[0]
assert R0.shape[0]==2, 'unimplemented yet'
if feasLB != -inf or feasUB != inf:
R0, definiteRange = adjustBounds(R0, definiteRange, feasLB, feasUB)
r_l, r_u = R0
R2 = fun(R0)
ind_inf = where(np.logical_or(np.isinf(R2[0]), np.isinf(R2[1])))[0]
koeffs = (R2[1] - R2[0]) / (r_u - r_l)
koeffs[ind_inf] = 0.0
ind_eq = where(r_u == r_l)[0]
if monotonity == 1:
new_l_resolved, new_u_resolved = R2
U_dict, L_dict = Ud, Ld
U2_dict, L2_dict = Ud2, Ld2
_argmin, _argmax = r_l, r_u
elif monotonity == -1:
new_u_resolved, new_l_resolved = R2
U_dict, L_dict = Ld, Ud
U2_dict, L2_dict = Ld2, Ud2
_argmin, _argmax = r_u, r_l
else:
assert arg_lb_ub.level < 2, 'unimplemented'
ind = R2[1] > R2[0]
R2.sort(axis=0)
new_l_resolved, new_u_resolved = R2
_argmin = where(ind, r_l, r_u)
_argmax = where(ind, r_u, r_l)
if criticalPoint is not np.nan:
ind_c = logical_and(r_l < criticalPoint, r_u > criticalPoint)
if convexity == 1:
new_l_resolved[ind_c] = criticalPointValue
_argmin[ind_c] = criticalPoint
elif convexity == -1:
new_u_resolved[ind_c] = criticalPointValue
_argmax[ind_c] = criticalPoint
Keys = set().union(set(Ld.keys()), set(Ud.keys()))
L_dict = dict((k, where(ind, Ld.get(k, 0), Ud.get(k, 0))) for k in Keys)
U_dict = dict((k, where(ind, Ud.get(k, 0), Ld.get(k, 0))) for k in Keys)
if len(Ld2) != 0 or len(Ud2) != 0:
L2_dict = dict((k, where(ind, Ld2.get(k, 0), Ud2.get(k, 0))) for k in Keys)
U2_dict = dict((k, where(ind, Ud2.get(k, 0), Ld2.get(k, 0))) for k in Keys)
else:
L2_dict = U2_dict = {}
if convexity == -1:
tmp2 = deriv(_argmax.view(multiarray)).view(ndarray).flatten()
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
ind_inf2 = np.isinf(new_u_resolved)
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
if len(L_dict) >= 1 or len(L2_dict) >= 1:
if ind_eq.size:
koeffs[ind_eq] = tmp2[ind_eq]
d_new = dict((v, koeffs * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
else:
L_new = surf({}, new_l_resolved)
elif convexity == 1:
tmp2 = deriv(_argmin.view(multiarray)).view(ndarray).flatten()
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
ind_inf2 = np.isinf(new_l_resolved)
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
if len(U_dict) >= 1 or len(U2_dict) >= 1:
if ind_eq.size:
koeffs[ind_eq] = tmp2[ind_eq]
d_new = dict((v, koeffs * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
else:
U_new = surf({}, new_u_resolved)
elif convexity == -101:
if monotonity == 1:
argvals = (_argmax, _argmin)
vals = (new_u_resolved, new_l_resolved)[::-1]
Attributes = ('maximum', 'minimum')
elif monotonity == -1:
argvals = (_argmin, _argmax)
vals = (new_l_resolved, new_u_resolved)
Attributes = ('minimum', 'maximum')
else:
assert 0
tmp2 = deriv(argvals[0].view(multiarray)).view(ndarray).flatten()
ind_k = where((tmp2 > koeffs) if monotonity == 1 else (tmp2 < koeffs))[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = vals[0] - getattr(L_new, Attributes[0])(domain, domain_ind)
# L_new.c = vals[0] - L_new.minimum(domain, domain_ind)
# L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
ind_inf2 = np.isinf(vals[0])
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
tmp2 = deriv(argvals[1].view(multiarray)).view(ndarray).flatten()
ind_k = where((tmp2 > koeffs) if monotonity == 1 else (tmp2 < koeffs))[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
# U_new = surf(d_new, 0.0)
if len(L2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in L2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = vals[1] - getattr(U_new, Attributes[1])(domain, domain_ind)
# U_new.c = vals[1] - U_new.maximum(domain, domain_ind)
# U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
ind_inf2 = np.isinf(vals[1])
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
elif convexity == 9: # 1 0 -1
if monotonity == 1:
argvals = (_argmin, _argmax)
vals = (new_l_resolved, new_u_resolved)
Attributes = ('minimum', 'maximum')
elif monotonity == -1:
argvals = (_argmax, _argmin)
vals = (new_u_resolved, new_l_resolved)[::-1]
Attributes = ('maximum','minimum')
else:
assert 0
tmp2 = deriv(argvals[0].view(multiarray)).view(ndarray).flatten()
ind_k = where(tmp2 > koeffs)[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = vals[0] - getattr(L_new, Attributes[0])(domain, domain_ind)
ind_inf2 = np.isinf(vals[0])
if any(ind_inf2):
L_new.c = where(ind_inf2, vals[0], L_new.c)
tmp2 = deriv(argvals[1].view(multiarray)).view(ndarray).flatten()
ind_k = where(tmp2 > koeffs)[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = vals[1] - getattr(U_new, Attributes[1])(domain, domain_ind)
ind_inf2 = np.isinf(vals[1])
if any(ind_inf2):
U_new.c = where(ind_inf2, vals[1], U_new.c)
else:
# linear oofuns with convexity = 0 calculate their intervals in other funcs
raise FuncDesignerException('bug in FD kernel')
if type(L_new) == type(U_new) == surf:
R = boundsurf(L_new, U_new, definiteRange, domain)
else:
R = boundsurf2(L_new, U_new, definiteRange, domain)
if not np.all(definiteRange):
ind1 = where(definiteRange)[0]
r1 = R.extract(ind1)
ind2 = where(logical_not(definiteRange))[0]
r2 = boundsurf(surf({}, new_l_resolved[ind2]), surf({}, new_u_resolved[ind2]),
definiteRange[ind2] if type(definiteRange)==ndarray and definiteRange.size != 1 else definiteRange,
domain)
R = boundsurf_join((ind1, ind2), (r1, r2))
return R, definiteRange
def pow_const_interval(self, r, other, domain, dtype):
lb_ub, definiteRange = self._interval(domain, dtype, ia_surf_level = 2)
isBoundSurf = isinstance(lb_ub, boundsurf)
# changes
if 1 and isBoundSurf and other == 2 and lb_ub.level == 1 and len(lb_ub.l.d) == 1 and len(lb_ub.u.d) == 1:
L, U = lb_ub.l, lb_ub.u
if lb_ub.l is lb_ub.u:
d, c = L.d, L.c
s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
return boundsurf2(s_l, s_l, definiteRange, domain), definiteRange
lb_ub_resolved = lb_ub.resolve()[0]
lb, ub = lb_ub_resolved
ind_positive, ind_negative, ind_z = split(lb >= 0, ub <= 0)
#new
m = lb.size
if ind_negative.size:
ind_negative_bool = ub <= 0
lb_ub = lb_ub.invert(ind_negative_bool)
L, U = lb_ub.l, lb_ub.u
d_l, d_u = L.d, U.d
ind = logical_or(lb >= 0, ub <= 0)
Ind_nonz = where(ind)[0]
if Ind_nonz.size != 0:
d_u2 = dict_reduce(d_u, Ind_nonz)
c = U.c if type(U.c) != ndarray or U.c.size == 1 else U.c[Ind_nonz]
s_u = surf2(dict((k, v**2) for k, v in d_u2.items()), dict((k, 2*v*c) for k, v in d_u2.items()), c**2)
d_l2 = dict_reduce(d_l, Ind_nonz)
c = L.c if type(L.c) != ndarray or L.c.size == 1 else L.c[Ind_nonz]
s_l = surf2(dict((k, v**2) for k, v in d_l2.items()), dict((k, 2*v*c) for k, v in d_l2.items()), c**2)
r_nz = boundsurf2(s_l, s_u, False, domain)
if Ind_nonz.size == m:
r_nz.definiteRange = definiteRange
return r_nz, definiteRange
r0, definiteRange0 = defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = np.nan, convexity = 1,
criticalPoint = 0.0, criticalPointValue = 0.0, domain_ind = ind_z)
if Ind_nonz.size == 0:
return r0, definiteRange
r = boundsurf_join((Ind_nonz, ind_z), (r_nz, r0))
#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
r.definiteRange = definiteRange
####################
return r, definiteRange
#prev
# L, U = lb_ub.l, lb_ub.u
# d, c = L.d, L.c
# s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
#
# if lb_ub.l is lb_ub.u:
# return boundsurf2(s_l, s_l, definiteRange, domain), definiteRange
#
# d, c = U.d, U.c
# lb_ub_resolved = lb_ub.resolve()[0]
# if all(lb_ub_resolved >= 0):
# s_u = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
# return boundsurf2(s_l, s_u, definiteRange, domain), definiteRange
# elif all(lb_ub_resolved <= 0):
# s_u = s_l
# s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
# return boundsurf2(s_l, s_u, definiteRange, domain), definiteRange
# changes end
lb_ub_resolved = lb_ub.resolve()[0] if isBoundSurf else lb_ub
arg_isNonNegative = all(lb_ub_resolved >= 0)
arg_isNonPositive = all(lb_ub_resolved <= 0)
#changes
# !!!!!!!TODO: rdiv beyond arg_isNonNegative, arg_isNonPositive
if 1 and other == -1 and (arg_isNonNegative or arg_isNonPositive) and isBoundSurf and len(lb_ub.dep)==1:
return inv_b_interval(lb_ub, revert = arg_isNonPositive)
# TODO: remove arg_isNonNegative
if 1 and 0 < other < 1 and 1 and isBoundSurf and len(lb_ub.dep)==1:
return pow_interval(r, self, other, domain, dtype)
#changes end
other_is_int = asarray(other, int) == other
isOdd = other_is_int and other % 2 == 1
if isBoundSurf and not any(np.isinf(lb_ub_resolved)):
#new
# if arg_isNonNegative:
# return defaultIntervalEngine(lb_ub, r.fun, r.d,
# monotonity = 1,
# convexity = 1 if other > 1.0 or other < 0 else -1)
#
# if other_is_int and other > 0 and other % 2 == 0:
# return devided_interval(self, r, domain, dtype)
#prev
if arg_isNonNegative:# or (other_is_int and other > 0 and other % 2 == 0):
return defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = 1 if other > 0 and arg_isNonNegative else -1 if arg_isNonNegative and other < 0 else np.nan,
convexity = 1 if other > 1.0 or other < 0 else -1,
criticalPoint = 0.0, criticalPointValue = 0.0)
if other_is_int and other > 0 and other % 2 == 0:
return defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = np.nan,
convexity = 1,
criticalPoint = 0.0, criticalPointValue = 0.0)
feasLB = -inf if other_is_int else 0.0
if other > 0 or arg_isNonPositive:
return devided_interval(self, r, domain, dtype, feasLB = feasLB)
if other_is_int and other < 0:# and other % 2 != 0:
lb, ub = lb_ub_resolved
ind_positive, ind_negative, ind_z = split(lb >= 0, ub <= 0)
B, inds = [], []
if ind_positive.size:
inds.append(ind_positive)
monotonity = -1
b = defaultIntervalEngine(lb_ub, r.fun, r.d, monotonity = monotonity, convexity = 1,
domain_ind = ind_positive)[0]
B.append(b)
if ind_negative.size:
inds.append(ind_negative)
# TODO: fix it
monotonity = -1 if isOdd else 1
convexity = -1 if isOdd else 1
b = defaultIntervalEngine(lb_ub, r.fun, r.d, monotonity = monotonity, convexity = convexity,
domain_ind = ind_negative)[0]
B.append(b)
if ind_z.size:
inds.append(ind_z)
t = 1.0 / lb_ub_resolved[:, ind_z]
t.sort(axis=0)
update_negative_int_pow_inf_zero(lb_ub_resolved[0, ind_z], lb_ub_resolved[1, ind_z], t, other)
b = boundsurf(
surf({}, t[0]),
surf({}, t[1]),
definiteRange if type(definiteRange) == bool or definiteRange.size == 1 \
else definiteRange[ind_z],
domain)
B.append(b)
r = boundsurf_join(inds, B)
return r, r.definiteRange
lb_ub = lb_ub_resolved
lb, ub = lb_ub
Tmp = lb_ub ** other
# correct nan handling
#Tmp.sort(axis = 0)
ind = where(Tmp[0]>Tmp[1])[0]
if ind.size: # PyPy doesn't work w/o this check
Tmp[0, ind], Tmp[1, ind] = Tmp[1, ind], Tmp[0, ind]
if not other_is_int or not isOdd:
ind_z = logical_and(lb < 0, ub >= 0)
assert type(ind_z) == np.ndarray
if any(ind_z):
Ind_z = where(ind_z)[0]
if (not other_is_int and other > 0) or not isOdd:
# print ind_z, type(ind_z), ind_z.shape
# print Tmp
Tmp[0, Ind_z] = 0.0
if other < 0:
Tmp[1, Ind_z] = inf
if not other_is_int:
definiteRange = logical_and(definiteRange, logical_not(ind_z))
Tmp.sort(axis = 0)
if other < 0 and other_is_int:
update_negative_int_pow_inf_zero(lb, ub, Tmp, other)
return Tmp, definiteRange
def defaultIntervalEngine(arg_lb_ub, fun, deriv, monotonity, convexity, criticalPoint = np.nan,
criticalPointValue = np.nan, feasLB = -inf, feasUB = inf, domain_ind = slice(None), R0 = None):
#monotonity = nan
assert type(monotonity) != bool and type(convexity) != bool, 'bug in defaultIntervalEngine'
Ld2, Ud2 = getattr(arg_lb_ub.l,'d2', {}), getattr(arg_lb_ub.u,'d2', {})
# DEBUG!!!!!!!!!!!!!!!!!
# if (len(Ld2) != 0 or len(Ud2) != 0):
# arg_lb_ub = arg_lb_ub.to_linear()
# Ld2, Ud2 = {}, {}
# !! TODO: handle monotonity = nan with boundsurf2
#if (len(Ld2) != 0 or len(Ud2) != 0) and np.isnan(monotonity):
if arg_lb_ub.level == 2 and np.isnan(monotonity):
arg_lb_ub = arg_lb_ub.to_linear()
Ld2, Ud2 = {}, {}
L, U, domain, definiteRange = arg_lb_ub.l, arg_lb_ub.u, arg_lb_ub.domain, arg_lb_ub.definiteRange
Ld, Ud = L.d, U.d
if type(domain_ind) == np.ndarray:
if domain_ind.dtype == bool:
domain_ind = where(domain_ind)[0]
Ld, Ud = dict_reduce(Ld, domain_ind), dict_reduce(Ud, domain_ind)
Ld2, Ud2 = dict_reduce(Ld2, domain_ind), dict_reduce(Ud2, domain_ind)
R0 = (arg_lb_ub.resolve()[0] if R0 is None else R0)[:, domain_ind]
if type(definiteRange) != bool and definiteRange.size > 1:
definiteRange = definiteRange[domain_ind]
elif R0 is None:
R0 = arg_lb_ub.resolve()[0]
#R0 = arg_lb_ub.resolve(ind = domain_ind)[0]
assert R0.shape[0]==2, 'unimplemented yet'
if feasLB != -inf or feasUB != inf:
R0, definiteRange = adjustBounds(R0, definiteRange, feasLB, feasUB)
r_l, r_u = R0
R2 = fun(R0)
ind_inf = where(np.logical_or(np.isinf(R2[0]), np.isinf(R2[1])))[0]
koeffs = (R2[1] - R2[0]) / (r_u - r_l)
koeffs[ind_inf] = 0.0
ind_eq = where(r_u == r_l)[0]
if monotonity == 1:
new_l_resolved, new_u_resolved = R2
U_dict, L_dict = Ud, Ld
U2_dict, L2_dict = Ud2, Ld2
_argmin, _argmax = r_l, r_u
elif monotonity == -1:
new_u_resolved, new_l_resolved = R2
U_dict, L_dict = Ld, Ud
U2_dict, L2_dict = Ld2, Ud2
_argmin, _argmax = r_u, r_l
else:
assert arg_lb_ub.level < 2, 'unimplemented'
ind = R2[1] > R2[0]
R2.sort(axis=0)
new_l_resolved, new_u_resolved = R2
_argmin = where(ind, r_l, r_u)
_argmax = where(ind, r_u, r_l)
if criticalPoint is not np.nan:
ind_c = logical_and(r_l < criticalPoint, r_u > criticalPoint)
if convexity == 1:
new_l_resolved[ind_c] = criticalPointValue
_argmin[ind_c] = criticalPoint
elif convexity == -1:
new_u_resolved[ind_c] = criticalPointValue
_argmax[ind_c] = criticalPoint
Keys = set().union(set(Ld.keys()), set(Ud.keys()))
L_dict = dict((k, where(ind, Ld.get(k, 0), Ud.get(k, 0))) for k in Keys)
U_dict = dict((k, where(ind, Ud.get(k, 0), Ld.get(k, 0))) for k in Keys)
if len(Ld2) != 0 or len(Ud2) != 0:
L2_dict = dict((k, where(ind, Ld2.get(k, 0), Ud2.get(k, 0))) for k in Keys)
U2_dict = dict((k, where(ind, Ud2.get(k, 0), Ld2.get(k, 0))) for k in Keys)
else:
L2_dict = U2_dict = {}
if convexity == -1:
tmp2 = deriv(_argmax.view(multiarray)).view(ndarray).flatten()
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
ind_inf2 = np.isinf(new_u_resolved)
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
if len(L_dict) >= 1 or len(L2_dict) >= 1:
if ind_eq.size:
koeffs[ind_eq] = tmp2[ind_eq]
d_new = dict((v, koeffs * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
else:
L_new = surf({}, new_l_resolved)
elif convexity == 1:
tmp2 = deriv(_argmin.view(multiarray)).view(ndarray).flatten()
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
ind_inf2 = np.isinf(new_l_resolved)
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
if len(U_dict) >= 1 or len(U2_dict) >= 1:
if ind_eq.size:
koeffs[ind_eq] = tmp2[ind_eq]
d_new = dict((v, koeffs * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
else:
U_new = surf({}, new_u_resolved)
elif convexity == -101:
if monotonity == 1:
argvals = (_argmax, _argmin)
vals = (new_u_resolved, new_l_resolved)[::-1]
Attributes = ('maximum', 'minimum')
elif monotonity == -1:
argvals = (_argmin, _argmax)
vals = (new_l_resolved, new_u_resolved)
Attributes = ('minimum', 'maximum')
else:
assert 0
tmp2 = deriv(argvals[0].view(multiarray)).view(ndarray).flatten()
ind_k = where((tmp2 > koeffs) if monotonity == 1 else (tmp2 < koeffs))[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = vals[0] - getattr(L_new, Attributes[0])(domain, domain_ind)
# L_new.c = vals[0] - L_new.minimum(domain, domain_ind)
# L_new.c = new_l_resolved - L_new.minimum(domain, domain_ind)
ind_inf2 = np.isinf(vals[0])
if any(ind_inf2):
L_new.c = where(ind_inf2, new_l_resolved, L_new.c)
tmp2 = deriv(argvals[1].view(multiarray)).view(ndarray).flatten()
ind_k = where((tmp2 > koeffs) if monotonity == 1 else (tmp2 < koeffs))[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
# U_new = surf(d_new, 0.0)
if len(L2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, koeffs * val) for v, val in L2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = vals[1] - getattr(U_new, Attributes[1])(domain, domain_ind)
# U_new.c = vals[1] - U_new.maximum(domain, domain_ind)
# U_new.c = new_u_resolved - U_new.maximum(domain, domain_ind)
ind_inf2 = np.isinf(vals[1])
if any(ind_inf2):
U_new.c = where(ind_inf2, new_u_resolved, U_new.c)
elif convexity == 9: # 1 0 -1
if monotonity == 1:
argvals = (_argmin, _argmax)
vals = (new_l_resolved, new_u_resolved)
Attributes = ('minimum', 'maximum')
elif monotonity == -1:
argvals = (_argmax, _argmin)
vals = (new_u_resolved, new_l_resolved)[::-1]
Attributes = ('maximum','minimum')
else:
assert 0
tmp2 = deriv(argvals[0].view(multiarray)).view(ndarray).flatten()
ind_k = where(tmp2 > koeffs)[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in L_dict.items())
if len(L2_dict) == 0:
L_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in L2_dict.items())
L_new = surf2(d2_new, d_new, 0.0)
L_new.c = vals[0] - getattr(L_new, Attributes[0])(domain, domain_ind)
ind_inf2 = np.isinf(vals[0])
if any(ind_inf2):
L_new.c = where(ind_inf2, vals[0], L_new.c)
tmp2 = deriv(argvals[1].view(multiarray)).view(ndarray).flatten()
ind_k = where(tmp2 > koeffs)[0]
tmp2[ind_k] = koeffs[ind_k]
tmp2[np.isinf(tmp2)] = 0.0
tmp2[ind_inf] = 0.0
d_new = dict((v, tmp2 * val) for v, val in U_dict.items())
if len(U2_dict) == 0:
U_new = surf(d_new, 0.0)
else:
d2_new = dict((v, tmp2 * val) for v, val in U2_dict.items())
U_new = surf2(d2_new, d_new, 0.0)
U_new.c = vals[1] - getattr(U_new, Attributes[1])(domain, domain_ind)
ind_inf2 = np.isinf(vals[1])
if any(ind_inf2):
U_new.c = where(ind_inf2, vals[1], U_new.c)
else:
# linear oofuns with convexity = 0 calculate their intervals in other funcs
raise FuncDesignerException('bug in FD kernel')
if type(L_new) == type(U_new) == surf:
R = boundsurf(L_new, U_new, definiteRange, domain)
else:
R = boundsurf2(L_new, U_new, definiteRange, domain)
if not np.all(definiteRange):
ind1 = where(definiteRange)[0]
r1 = R.extract(ind1)
ind2 = where(logical_not(definiteRange))[0]
r2 = boundsurf(surf({}, new_l_resolved[ind2]), surf({}, new_u_resolved[ind2]),
definiteRange[ind2] if type(definiteRange)==ndarray and definiteRange.size != 1 else definiteRange,
domain)
R = boundsurf_join((ind1, ind2), (r1, r2))
return R, definiteRange
def pow_const_interval(self, r, other, domain, dtype):
lb_ub, definiteRange = self._interval(domain, dtype, ia_surf_level = 2)
isBoundSurf = isinstance(lb_ub, boundsurf)
# changes
if 1 and isBoundSurf and other == 2 and lb_ub.level == 1 and len(lb_ub.l.d) == 1 and len(lb_ub.u.d) == 1:
L, U = lb_ub.l, lb_ub.u
if lb_ub.l is lb_ub.u:
d, c = L.d, L.c
s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
return boundsurf2(s_l, s_l, definiteRange, domain), definiteRange
lb_ub_resolved = lb_ub.resolve()[0]
lb, ub = lb_ub_resolved
ind_positive, ind_negative, ind_z = split(lb >= 0, ub <= 0)
#new
m = lb.size
if ind_negative.size:
ind_negative_bool = ub <= 0
lb_ub = lb_ub.invert(ind_negative_bool)
L, U = lb_ub.l, lb_ub.u
d_l, d_u = L.d, U.d
ind = logical_or(lb >= 0, ub <= 0)
Ind_nonz = where(ind)[0]
if Ind_nonz.size != 0:
d_u2 = dict_reduce(d_u, Ind_nonz)
c = U.c if type(U.c) != ndarray or U.c.size == 1 else U.c[Ind_nonz]
s_u = surf2(dict((k, v**2) for k, v in d_u2.items()), dict((k, 2*v*c) for k, v in d_u2.items()), c**2)
d_l2 = dict_reduce(d_l, Ind_nonz)
c = L.c if type(L.c) != ndarray or L.c.size == 1 else L.c[Ind_nonz]
s_l = surf2(dict((k, v**2) for k, v in d_l2.items()), dict((k, 2*v*c) for k, v in d_l2.items()), c**2)
r_nz = boundsurf2(s_l, s_u, False, domain)
if Ind_nonz.size == m:
r_nz.definiteRange = definiteRange
return r_nz, definiteRange
r0, definiteRange0 = defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = np.nan, convexity = 1,
criticalPoint = 0.0, criticalPointValue = 0.0, domain_ind = ind_z)
if Ind_nonz.size == 0:
return r0, definiteRange
r = boundsurf_join((Ind_nonz, ind_z), (r_nz, r0))
#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
r.definiteRange = definiteRange
####################
return r, definiteRange
#prev
# L, U = lb_ub.l, lb_ub.u
# d, c = L.d, L.c
# s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
#
# if lb_ub.l is lb_ub.u:
# return boundsurf2(s_l, s_l, definiteRange, domain), definiteRange
#
# d, c = U.d, U.c
# lb_ub_resolved = lb_ub.resolve()[0]
# if all(lb_ub_resolved >= 0):
# s_u = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
# return boundsurf2(s_l, s_u, definiteRange, domain), definiteRange
# elif all(lb_ub_resolved <= 0):
# s_u = s_l
# s_l = surf2(dict((k, v**2) for k, v in d.items()), dict((k, 2*v*c) for k, v in d.items()), c**2)
# return boundsurf2(s_l, s_u, definiteRange, domain), definiteRange
# changes end
lb_ub_resolved = lb_ub.resolve()[0] if isBoundSurf else lb_ub
# TODO: implement SP
if lb_ub_resolved.dtype == object:
pWarn('''
interalg results for this stochastic problem
with solver interalg can be incorrect yet''')
arg_isNonNegative = lb_ub_resolved.dtype != object and all(lb_ub_resolved >= 0)
arg_isNonPositive = lb_ub_resolved.dtype != object and all(lb_ub_resolved <= 0)
#changes
# !!!!!!!TODO: rdiv beyond arg_isNonNegative, arg_isNonPositive
if 1 and other == -1 and (arg_isNonNegative or arg_isNonPositive) and isBoundSurf and len(lb_ub.dep)==1:
return inv_b_interval(lb_ub, revert = arg_isNonPositive)
# TODO: remove arg_isNonNegative
if 1 and 0 < other < 1 and 1 and isBoundSurf and len(lb_ub.dep)==1:
return pow_interval(r, self, other, domain, dtype)
#changes end
other_is_int = asarray(other, int) == other
isOdd = other_is_int and other % 2 == 1
if isBoundSurf and not any(np.isinf(lb_ub_resolved)):
#new
# if arg_isNonNegative:
# return defaultIntervalEngine(lb_ub, r.fun, r.d,
# monotonity = 1,
# convexity = 1 if other > 1.0 or other < 0 else -1)
#
# if other_is_int and other > 0 and other % 2 == 0:
# return devided_interval(self, r, domain, dtype)
#prev
if arg_isNonNegative:# or (other_is_int and other > 0 and other % 2 == 0):
return defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = 1 if other > 0 and arg_isNonNegative else -1 if arg_isNonNegative and other < 0 else np.nan,
convexity = 1 if other > 1.0 or other < 0 else -1,
criticalPoint = 0.0, criticalPointValue = 0.0)
if other_is_int and other > 0 and other % 2 == 0:
return defaultIntervalEngine(lb_ub, r.fun, r.d,
monotonity = np.nan,
convexity = 1,
criticalPoint = 0.0, criticalPointValue = 0.0)
feasLB = -inf if other_is_int else 0.0
if other > 0 or arg_isNonPositive:
return devided_interval(self, r, domain, dtype, feasLB = feasLB)
if other_is_int and other < 0:# and other % 2 != 0:
lb, ub = lb_ub_resolved
ind_positive, ind_negative, ind_z = split(lb >= 0, ub <= 0)
B, inds = [], []
if ind_positive.size:
inds.append(ind_positive)
monotonity = -1
b = defaultIntervalEngine(lb_ub, r.fun, r.d, monotonity = monotonity, convexity = 1,
domain_ind = ind_positive)[0]
B.append(b)
if ind_negative.size:
inds.append(ind_negative)
# TODO: fix it
monotonity = -1 if isOdd else 1
convexity = -1 if isOdd else 1
b = defaultIntervalEngine(lb_ub, r.fun, r.d, monotonity = monotonity, convexity = convexity,
domain_ind = ind_negative)[0]
B.append(b)
if ind_z.size:
inds.append(ind_z)
t = 1.0 / lb_ub_resolved[:, ind_z]
t.sort(axis=0)
update_negative_int_pow_inf_zero(lb_ub_resolved[0, ind_z], lb_ub_resolved[1, ind_z], t, other)
b = boundsurf(
surf({}, t[0]),
surf({}, t[1]),
definiteRange if type(definiteRange) == bool or definiteRange.size == 1 \
else definiteRange[ind_z],
domain)
B.append(b)
r = boundsurf_join(inds, B)
return r, r.definiteRange
lb_ub = lb_ub_resolved
lb, ub = lb_ub if lb_ub.dtype != object else (lb_ub[0, 0], lb_ub[1, 0])
Tmp = lb_ub ** other
# correct nan handling
#Tmp.sort(axis = 0)
T = Tmp[0]>Tmp[1] if Tmp.dtype != object else Tmp[0].item() > Tmp[1].item()
ind = where(T)[0]
if ind.size: # PyPy doesn't work w/o this check
Tmp[0, ind], Tmp[1, ind] = Tmp[1, ind], Tmp[0, ind]
if not other_is_int or not isOdd:
ind_z = logical_and(lb < 0, ub >= 0)
assert type(ind_z) in (np.ndarray, bool, np.bool_)
if any(ind_z):
Ind_z = where(ind_z)[0]
if (not other_is_int and other > 0) or not isOdd:
# print ind_z, type(ind_z), ind_z.shape
# print Tmp
Tmp[0, Ind_z] = 0.0
if other < 0:
Tmp[1, Ind_z] = inf
if not other_is_int:
definiteRange = logical_and(definiteRange, logical_not(ind_z))
Tmp.sort(axis = 0)
if other < 0 and other_is_int:
update_negative_int_pow_inf_zero(lb, ub, Tmp, other)
return Tmp, definiteRange
def b2div(Self, Other):
# Self and Other must be nonnegative
assert Other.level == 1 and Self.b2equiv(Other)
DefiniteRange = Self.definiteRange & Other.definiteRange
domain = Self.domain
is_b2 = Self.level == 2
k = list(Self.dep)[0]
L, U = Self.domain[k]
# L
if is_b2:
h = Self.l.d2.get(k, 0.0)
d1, d2 = Self.l.d[k], Other.u.d[k]
c1, c2 = Self.l.c, Other.u.c
ind_Z_l = d2 == 0.0
ind_z_l = where(ind_Z_l)[0]
if ind_z_l.size:
d_z_l = where(ind_Z_l, d1 / c2, 0.0)
c_z_l = where(ind_Z_l, c1 / c2, 0.0)
if is_b2:
h_z_l = where(ind_Z_l, h / c2, 0.0)
if is_b2:
H1 = h / d2
a1 = (d1 - h * c2 / d2) / d2
else:
a1 = d1 / d2
b1 = c1 - a1 * c2
ind_negative = b1 < 0
ind_b_negative_l = where(ind_negative)[0]
ind_b_positive_l = where(logical_not(ind_negative))[0]
b1[ind_b_negative_l] = -b1[ind_b_negative_l]
d = {k: d2}
c = c2
s_l = surf(d, c)
# U
if is_b2:
h = Self.u.d2.get(k, 0.0)
d1, d2 = Self.u.d[k], Other.l.d[k]
c1, c2 = Self.u.c, Other.l.c
ind_Z_u = d2 == 0.0
ind_z_u = where(ind_Z_u)[0]
if ind_z_u.size:
d_z_u = where(ind_Z_u, d1 / c2, 0.0)
c_z_u = where(ind_Z_u, c1 / c2, 0.0)
if is_b2:
h_z_u = where(ind_Z_u, h / c2, 0.0)
if is_b2:
H2 = h / d2
a2 = (d1 - h * c2 / d2) / d2
else:
a2 = d1 / d2
b2 = c1 - a2 * c2
ind_negative = b2 < 0
ind_b_negative_u = where(ind_negative)[0]
ind_b_positive_u = where(logical_not(ind_negative))[0]
b2[ind_b_negative_u] = -b2[ind_b_negative_u]
d = {k: d2}
c = c2
s_u = surf(d, c)
tmp = boundsurf(s_l, s_u, DefiniteRange, domain)
from Interval import inv_b_interval
B = inv_b_interval(tmp, revert=False)[0]
sl, su = B.l, B.u
from boundsurf2 import boundsurf2, surf2
P = 1e11
sl2 = surf_join((ind_b_positive_l, ind_b_negative_l), \
(sl.extract(ind_b_positive_l), -su.extract(ind_b_negative_l)))*b1
ind_numericaly_unstable_l = P * np.abs(sl2.c + a1) < np.abs(
sl2.c) + np.abs(a1)
sl2 += a1
su2 = surf_join((ind_b_positive_u, ind_b_negative_u), \
(su.extract(ind_b_positive_u), -sl.extract(ind_b_negative_u)))*b2
ind_numericaly_unstable_u = P * np.abs(su2.c + a2) < np.abs(
su2.c) + np.abs(a2)
su2 += a2
if is_b2:
ind_numericaly_unstable_l = logical_or(
ind_numericaly_unstable_l,
P * np.abs(sl2.d.get(k, 0.0) + H1) <
np.abs(sl2.d.get(k, 0.0)) + np.abs(H1))
ind_numericaly_unstable_u = logical_or(
ind_numericaly_unstable_u,
P * np.abs(su2.d.get(k, 0.0) + H2) <
np.abs(su2.d.get(k, 0.0)) + np.abs(H2))
sl2.d[k] = sl2.d.get(k, 0.0) + H1
su2.d[k] = su2.d.get(k, 0.0) + H2
if ind_z_l.size:
ind_nz_l = where(logical_not(ind_Z_l))[0]
sl2 = surf_join((ind_nz_l, ind_z_l), \
(sl.extract(ind_nz_l), surf2({k:0}, {k:d_z_l}, c_z_l)))
if is_b2:
sl2.d2[k] = sl2.d2.get(k, 0.0) + h_z_l
if ind_z_u.size:
ind_nz_u = where(logical_not(ind_Z_u))[0]
su2 = surf_join((ind_nz_u, ind_z_u), \
(su.extract(ind_nz_u), surf2({k:0}, {k:d_z_u}, c_z_u)))
if is_b2:
su2.d2[k] = su2.d2.get(k, 0.0) + h_z_u
r = boundsurf2(sl2, su2, DefiniteRange, domain)
ind_numericaly_unstable = logical_or(ind_numericaly_unstable_l,
ind_numericaly_unstable_u)
if any(ind_numericaly_unstable):
ind_numericaly_stable = logical_not(ind_numericaly_unstable)
# print where(ind_numericaly_stable)[0].size, where(ind_numericaly_unstable)[0].size
r2 = (Self.log() - Other.log()).exp()
r = boundsurf_join((ind_numericaly_unstable, ind_numericaly_stable), \
(r2.extract(ind_numericaly_unstable), r.extract(ind_numericaly_stable)))
return r
def b2div(Self, Other):
# Self and Other must be nonnegative
assert Other.level == 1 and Self.b2equiv(Other)
DefiniteRange = Self.definiteRange & Other.definiteRange
domain = Self.domain
is_b2 = Self.level == 2
k = list(Self.dep)[0]
L, U = Self.domain[k]
# L
if is_b2:
h = Self.l.d2.get(k, 0.0)
d1, d2 = Self.l.d[k], Other.u.d[k]
c1, c2 = Self.l.c, Other.u.c
ind_Z_l = d2 == 0.0
ind_z_l = where(ind_Z_l)[0]
if ind_z_l.size:
d_z_l = where(ind_Z_l, d1 / c2, 0.0)
c_z_l = where(ind_Z_l, c1 / c2, 0.0)
if is_b2:
h_z_l = where(ind_Z_l, h / c2, 0.0)
if is_b2:
H1 = h / d2
a1 = (d1 - h * c2 / d2) / d2
else:
a1 = d1 / d2
b1 = c1 - a1 * c2
ind_negative = b1<0
ind_b_negative_l = where(ind_negative)[0]
ind_b_positive_l = where(logical_not(ind_negative))[0]
b1[ind_b_negative_l] = -b1[ind_b_negative_l]
d = {k: d2}
c = c2
s_l = surf(d, c)
# U
if is_b2:
h = Self.u.d2.get(k, 0.0)
d1, d2 = Self.u.d[k], Other.l.d[k]
c1, c2 = Self.u.c, Other.l.c
ind_Z_u = d2 == 0.0
ind_z_u = where(ind_Z_u)[0]
if ind_z_u.size:
d_z_u = where(ind_Z_u, d1 / c2, 0.0)
c_z_u = where(ind_Z_u, c1 / c2, 0.0)
if is_b2:
h_z_u = where(ind_Z_u, h / c2, 0.0)
if is_b2:
H2 = h / d2
a2 = (d1 - h * c2 / d2) / d2
else:
a2 = d1 / d2
b2 = c1 - a2 * c2
ind_negative = b2<0
ind_b_negative_u = where(ind_negative)[0]
ind_b_positive_u = where(logical_not(ind_negative))[0]
b2[ind_b_negative_u] = -b2[ind_b_negative_u]
d = {k: d2}
c = c2
s_u = surf(d, c)
tmp = boundsurf(s_l, s_u, DefiniteRange, domain)
from Interval import inv_b_interval
B = inv_b_interval(tmp, revert = False)[0]
sl, su = B.l, B.u
from boundsurf2 import boundsurf2, surf2
P = 1e11
sl2 = surf_join((ind_b_positive_l, ind_b_negative_l), \
(sl.extract(ind_b_positive_l), -su.extract(ind_b_negative_l)))*b1
ind_numericaly_unstable_l = P * np.abs(sl2.c + a1) < np.abs(sl2.c) + np.abs(a1)
sl2 += a1
su2 = surf_join((ind_b_positive_u, ind_b_negative_u), \
(su.extract(ind_b_positive_u), -sl.extract(ind_b_negative_u)))*b2
ind_numericaly_unstable_u = P * np.abs(su2.c + a2) < np.abs(su2.c) + np.abs(a2)
su2 += a2
if is_b2:
ind_numericaly_unstable_l = logical_or(ind_numericaly_unstable_l,
P*np.abs(sl2.d.get(k, 0.0) + H1) < np.abs(sl2.d.get(k, 0.0)) + np.abs(H1))
ind_numericaly_unstable_u = logical_or(ind_numericaly_unstable_u,
P*np.abs(su2.d.get(k, 0.0) + H2) < np.abs(su2.d.get(k, 0.0)) + np.abs(H2))
sl2.d[k] = sl2.d.get(k, 0.0) + H1
su2.d[k] = su2.d.get(k, 0.0) + H2
if ind_z_l.size:
ind_nz_l = where(logical_not(ind_Z_l))[0]
sl2 = surf_join((ind_nz_l, ind_z_l), \
(sl.extract(ind_nz_l), surf2({k:0}, {k:d_z_l}, c_z_l)))
if is_b2:
sl2.d2[k] = sl2.d2.get(k, 0.0) + h_z_l
if ind_z_u.size:
ind_nz_u = where(logical_not(ind_Z_u))[0]
su2 = surf_join((ind_nz_u, ind_z_u), \
(su.extract(ind_nz_u), surf2({k:0}, {k:d_z_u}, c_z_u)))
if is_b2:
su2.d2[k] = su2.d2.get(k, 0.0) + h_z_u
r = boundsurf2(sl2, su2, DefiniteRange, domain)
ind_numericaly_unstable = logical_or(ind_numericaly_unstable_l, ind_numericaly_unstable_u)
if any(ind_numericaly_unstable):
ind_numericaly_stable = logical_not(ind_numericaly_unstable)
# print where(ind_numericaly_stable)[0].size, where(ind_numericaly_unstable)[0].size
r2 = (Self.log() - Other.log()).exp()
r = boundsurf_join((ind_numericaly_unstable, ind_numericaly_stable), \
(r2.extract(ind_numericaly_unstable), r.extract(ind_numericaly_stable)))
return r