def test_ransom_seed(self):
"""Test setting random seeds.
"""
np.random.seed(12345)
value = helpers.choose_num(10)
self.assertNotEqual(value, helpers.choose_num(10))
np.random.seed(12345)
self.assertEqual(value, helpers.choose_num(10))
np.random.seed(12346)
self.assertNotEqual(value, helpers.choose_num(10))
def _make_info(self):
md = self.param['m']
l = self.param['l']
second_deg = self.param['second_deg']
# Note that we only consider the following two cases of box constraints:
# y(i) in [0, +inf) or [0, u] where u is a nonnegative scalar.
# Clearly, any other interval can be obtained by using the mapping
# y <--- c1+c2*y.
# It is assumed that the last m_inf constraints are of the form [0, inf)
# The remaining m_inf - m_inf_deg - inf_nonactive constraints are where
# F=0, y>0
# y variables which are bounded below and above
# There will be m - m_inf variables with double sided bounds. each upper
# bound is chosen uniform in [0,10]
md_upp_deg = choose_num(second_deg)
# degenerate with y at upper bound: F=0, y=u
md_low_deg = second_deg - md_upp_deg
# degenerate with y at lower bound: F=0, y=0
md_upp_nonactive = choose_num(md - md_upp_deg - md_low_deg)
# F not active, y at upper bound: F<0, y=u
md_low_nonactive = choose_num(
md - md_upp_deg - md_low_deg - md_upp_nonactive)
# F not active, y at lower bound: F>0, y=0
l_deg = self.param['first_deg']
l_nonactive = choose_num(l - l_deg)
self.info.update({
'ms': 0,
'ms_deg': 0,
'ms_nonactive': 0,
'ms_active': 0,
'md': md,
'md_upp_deg': md_upp_deg,
'md_low_deg': md_low_deg,
'md_upp_nonactive': md_upp_nonactive,
'md_low_nonactive': md_low_nonactive,
'md_float': (
md - md_upp_deg - md_low_deg - md_upp_nonactive - md_low_nonactive),
# Randomly decide how many of the non-degenerate first level ctrs
# should be nonactive
'l': l,
'l_deg': l_deg,
'l_nonactive': l_nonactive,
'l_active': l - l_deg - l_nonactive})
def test_greater_one(self):
""" Test giving a number greater than 1.
This test runs choose_num NUMBER_OF_TRIALS times.
"""
m = 10
for _ in xrange(NUMBER_OF_TRIALS):
res = helpers.choose_num(m)
self.assertGreaterEqual(res, 0)
self.assertLessEqual(res, m)
def test_between_zero_and_one(self):
""" Test giving a number between 0 and 1.
"""
self.assertEqual(helpers.choose_num(0.5), 0)
def test_zero(self):
""" Test giving 0.
"""
self.assertEqual(helpers.choose_num(0), 0)
def _make_info(self):
'''
Randomly allots statuses to constraints (active, nonactive, degenerate).
The 'l' series gives the allotment for upper level constraints Ax <= 0.
The 'ms' series determines what happens with the single-bounded lower
level variables. The 'md' series determines what happens with the
double-bounded lower level variables.
Since the ordering of variables and constraints within these groups is
not significant, the generator just determines how many will have a
given status and then the first l_deg upper level constraints will be
degenerate, the next l_non will be nonactive, etc.
'''
# Decide how many of the non-degenerate first level ctrs should be
# nonactive
l = self.param['l']
l_deg = self.param['first_deg']
l_nonactive = choose_num(l - l_deg)
l_active = l - l_deg - l_nonactive
self.info.update({
'l': l,
'l_deg': l_deg,
'l_nonactive': l_nonactive,
'l_active': l_active})
m = self.param['m']
second_deg = self.param['second_deg']
md = 1 + choose_num(m - 2)
ms = m - md
# single bounded y variables (only bounded below):
ms_deg = max(choose_num(min(ms, second_deg)),
second_deg - m + ms)
ms_nonactive = choose_num(ms - ms_deg)
ms_active = ms - ms_deg - ms_nonactive
self.info.update({
'm': m,
'ms': ms,
'ms_deg': ms_deg, # F=0, y=0
'ms_nonactive': ms_nonactive, # F>0, y=0
'ms_active': ms_active}) # F=0, y>0
# divvy up degeneracy numbers so there are second_deg degenerate y vars
remaining_degen = second_deg - self.info['ms_deg']
md_upp_deg = choose_num(remaining_degen) # F=0, y=u
md_low_deg = remaining_degen - md_upp_deg # F=0, y=0
self.info.update({
'md': md,
'md_upp_deg': md_upp_deg,
'md_low_deg': md_low_deg})
# double bounded y variables (bounded below and above):
md_nondegen = md - self.info['md_upp_deg'] - self.info['md_low_deg']
md_upp_non = choose_num(md_nondegen) # F<0, y=u
md_low_non = choose_num(md_nondegen - md_upp_non) # F>0, y=0
md_float = md_nondegen - md_upp_non - md_low_non # F=0, 0<y<u
self.info.update({
'md_upp_nonactive': md_upp_non,
'md_low_nonactive': md_low_non,
'md_float': md_float})
info = self.info
param = self.param
assert self.m == info['ms'] + info['md']
assert info['ms'] == info['ms_deg'] + \
info['ms_active'] + info['ms_nonactive']
assert info['md'] == info['md_upp_deg'] + info['md_upp_nonactive'] + \
info['md_low_deg'] + info['md_low_nonactive'] + \
info['md_float']
assert param['second_deg'] == info['ms_deg'] + info['md_upp_deg'] + \
info['md_low_deg']
assert info['ms_deg'] >= 0
assert info['ms_active'] >= 0
assert info['ms_nonactive'] >= 0
assert info['md_upp_deg'] >= 0
assert info['md_upp_nonactive'] >= 0
assert info['md_low_deg'] >= 0
assert info['md_low_nonactive'] >= 0
assert info['md_float'] >= 0
def _make_F_pi_sigma_index(self):
N = self.N
M = self.M
u = self.u
xgen = self.info['xgen']
ygen = self.info['ygen']
m = self.param['m']
# Design q so that Nx + My + E^Tlambda + q = 0 at the solution (xgen,
# ygen)
q = -N * xgen - M * ygen
q += conmat([
# double bounded, degenerate at upper
zeros(self.info['md_upp_deg']),
# double bounded, nonactive at upper
-rand(self.info['md_upp_nonactive']),
# double bounded, degenerate at lower
zeros(self.info['md_low_deg']),
# double bounded, nonactive at lower
rand(self.info['md_low_nonactive']),
zeros(self.info['md_float']), # double bounded, floating
# single bounded, degenerate at lower
zeros(self.info['ms_deg']),
# single bounded, nonactive at lower
rand(self.info['ms_nonactive']),
zeros(self.info['ms_active'])]) # single bounded, floating
#########################################
## For later convenience ##
#########################################
F = N * xgen + M * ygen + q
mix_deg = self.param['mix_deg']
tol_deg = self.param['tol_deg']
# Calculate three index sets alpha, beta and gamma at (xgen, ygen).
# alpha denotes the index set of i at which F(i) is active, but y(i) not.
# beta_upp and beta_low denote the index sets of i at which F(i) is
# active, and y(i) is active at the upper and the lower end point of
# the finite interval [0, u] respectively.
# beta_inf denotes the index set of i at which both F(i) and y(i) are
# active for the infinite interval [0, inf).
# gamma_upp and gamma_low denote the index sets of i at which F(i) is
# not active, but y(i) is active at the upper and the lower point of
# the finite interval [0, u] respectively.
# gamma_inf denotes the index set of i at which F(i) is not active, but y(i)
# is active for the infinite interval [0, inf).
index = []
md = self.info['md']
for i in range(md):
assert ygen[i] >= -tol_deg and ygen[i] < u[i] + tol_deg, \
"{0} not in [0, {1}]".format(ygen[i], u[i])
if abs(F[i]) <= tol_deg and ygen[i] > tol_deg and ygen[i] + tol_deg < u[i]:
index.append(1) # For the index set alpha.
elif abs(F[i]) <= tol_deg and abs(ygen[i] - u[i]) <= tol_deg:
index.append(2) # For the index set beta_upp.
elif abs(F[i]) <= tol_deg and abs(ygen[i]) <= tol_deg:
index.append(3) # For the index set beta_low.
elif F[i] < -tol_deg and abs(ygen[i] - u[i]) <= tol_deg:
index.append(-1) # For the index set gamma_upp.
elif F[i] > tol_deg and abs(ygen[i]) <= tol_deg:
index.append(-1) # For the index set gamma_low.
else:
raise Exception(("didn't know what to do with this case: "
"ygen={0}, u[i] = {1}, F[i]={2}").format(
ygen[i], u[i], F[i]))
for i in range(md, m):
if ygen[i] > F[i] + tol_deg:
index.append(1) # For the index set alpha.
elif abs(ygen[i] - F[i]) <= tol_deg:
index.append(4) # For the index set beta_inf.
else:
index.append(-1) # For the index set gamma_inf.
# Generate the first level multipliers pi sigma
# associated with other constraints other than the first level constraints
# A*[x;y]+a<=0 in the relaxed nonlinear program. In particular,
# pi is associated with F(x, y)=N*x+M*y+q, and
# sigma with y.
mix_upp_deg = max(
mix_deg - self.info['md_low_deg'] - self.info['ms_deg'],
choose_num(self.info['md_upp_deg']))
mix_upp_deg = min(mix_upp_deg, mix_deg)
mix_low_deg = max(
mix_deg - mix_upp_deg - self.info['ms_deg'],
choose_num(self.info['md_low_deg']))
mix_low_deg = min(mix_low_deg, mix_deg - mix_upp_deg)
mix_inf_deg = mix_deg - mix_upp_deg - mix_low_deg
mix_inf_deg = min(mix_inf_deg, mix_deg - mix_upp_deg - mix_inf_deg)
assert mix_deg >= 0
assert mix_upp_deg >= 0
assert mix_low_deg >= 0
assert mix_inf_deg >= 0
# assert self.param['second_deg'] == self.info['ms_deg'] +
# self.info['md_low_deg'] + self.info['md_upp_deg'] + mix_deg
k_mix_inf = 0
k_mix_upp = 0
k_mix_low = 0
pi = zeros(m, 1)
sigma = zeros(m, 1)
for i in range(m):
if index[i] == 1:
pi[i] = randcst() - randcst()
sigma[i] = 0
elif index[i] == 2:
if k_mix_upp < mix_upp_deg:
pi[i] = 0
# The first mix_upp_deg constraints associated with F(i)<=0
# in the set beta_upp are degenerate.
sigma[i] = 0
# The first mix_upp_deg constraints associated with
# y(i)<=u(i) in the set beta_upp are degenerate.
k_mix_upp = k_mix_upp + 1
else:
pi[i] = randcst()
sigma[i] = randcst()
elif index[i] == 3:
if k_mix_low < mix_low_deg:
pi[i] = 0
# The first mix_low_deg constraints associated with F(i)>=0
# in the set beta_low are degenerate.
sigma[i] = 0
# The first mix_low_deg constraints associated with
# y(i)>=0 in the set beta_low are degenerate.
k_mix_low = k_mix_low + 1
else:
pi[i] = -randcst()
sigma[i] = -randcst()
elif index[i] == 4:
if k_mix_inf < mix_inf_deg:
pi[i] = 0
# The first mix_inf_deg constraints associated with F(i)>=0
# in the set beta_inf are degenerate.
sigma[i] = 0
# The first mix_inf_deg constraints associated with
# y(i)>=0 in the set beta_inf are degenerate.
k_mix_inf = k_mix_inf + 1
else:
pi[i] = -randcst()
sigma[i] = -randcst()
else:
pi[i] = 0
sigma[i] = randcst() - randcst()
self.q = q
self.info.update({
'F': F,
'mix_upp_deg': mix_upp_deg,
'mix_low_deg': mix_low_deg,
'mix_inf_deg': mix_inf_deg,
'pi': pi,
'sigma': sigma})