def test_ransom_seed(self):
"""Test setting random seeds.
"""
np.random.seed(12345)
value = helpers.rand(2, 2)
self.assertFalse(np.allclose(value, helpers.rand(2, 2)))
np.random.seed(12345)
self.assertTrue(np.allclose(value, helpers.rand(2, 2)))
np.random.seed(12346)
self.assertFalse(np.allclose(value, helpers.rand(2, 2)))
def test_two(self):
""" Test for 2 by 2 matrix.
"""
m = helpers.eye(2)
v = helpers.rand(2, 2)
self.assertTrue(np.array_equal(m.dot(v), v))
self.assertTrue(np.array_equal(v.dot(m), v))
def test_one(self):
""" Test for 1 by 1 matrix.
"""
m = helpers.eye(1)
v = helpers.rand(1)
self.assertTrue(np.array_equal(m.dot(v), v))
self.assertTrue(np.array_equal(v.dot(m), v))
def _make_ygen(self):
self._make_u()
num_double_at_upper = self.info[
'md_upp_deg'] + self.info['md_upp_nonactive']
num_not_floating = self.info['md'] - self.info['md_float']
double_at_upper = npvec(self.u[:num_double_at_upper])
double_at_lower = zeros(
self.info['md_low_deg'] + self.info['md_low_nonactive'])
double_floating = npvec(
[randcst() * x for x in self.u[num_not_floating:]])
single_at_lower = zeros(
self.info['ms_deg'] + self.info['ms_nonactive'])
single_floating = rand(self.info['ms_active'])
# ygen = conmat([npvec(u[:m_upp_deg+upp_nonactive]), # double_at_upper
# zeros(m_low_deg+low_nonactive), # double_at_lower
# v2, # double_floating
# zeros(m_inf_deg+inf_nonactive), # single_at_lower
# rand(m_inf-m_inf_deg-inf_nonactive)]) # single_floating
self.info['ygen'] = conmat([
double_at_upper, # y=u cases
double_at_lower, # y=0 cases
double_floating, # 0<y<u cases
single_at_lower, # y=0 cases
single_floating]) # y>0 cases
for yi in self.info['ygen']:
assert yi >= 0
for i in range(self.info['md']):
assert self.info['ygen'][i] <= self.u[i]
def test_non_diagonal_matrix(self):
""" Test for multiple of non diagonal matrix and raise errors.
"""
for size in range(2, 101):
PU = PV = np.identity(size)
PD = helpers.rand(size)
cond = 73
self.assertRaises(ValueError, helpers.adjust_cond, PU, PD, PV, cond)
def evaluate(self, size):
""" Evaluate with a give size matrix.
Args:
size: Matrix size.
"""
m = helpers.rand(size, size)
PU, PD, PV = helpers.schur(m)
self.assertTrue(np.allclose(np.dot(PU, np.dot(PD, PV)), m))
def evaluate(self, size):
""" Evaluate with a give size matrix.
Args:
size: Matrix size.
"""
ms = [helpers.rand(size, size) for _ in range(3)]
ans = functools.reduce(lambda u, v: u.dot(v), ms)
self.assertTrue(np.allclose(helpers.reconstruct(*ms), ans))
def _make_a_ulambda(self):
xgen = self.info['xgen']
ygen = self.info['ygen']
# FIRST LEVEL CTRS A[x;y] + a <= 0
# Generate the first level multipliers ulambda associated with A*[x;y]+a<=0.
# Generate a so the constraints Ax+a <= 0 are loose or tight where
# appropriate.
Axy = self.A * conmat([xgen, ygen])
self.a = -Axy - conmat([
zeros(self.info['l_deg']), # A + a = 0
rand(self.info['l_nonactive']), # A + a = 0
zeros(self.info['l_active'])]) # A + a <=0
self.info['ulambda'] = conmat([
zeros(self.info['l_deg']),
zeros(self.info['l_nonactive']),
rand(self.info['l_active'])])
def evaluate(self, shape, **kwargs):
""" Evaluate rand.
Args:
shape: Shape of result matrix of randint.
kwargs: To be passed to randint.
"""
m = helpers.rand(**kwargs)
self.assertEqual(m.shape, shape)
self.assertGreaterEqual(m.min(), 0)
self.assertLessEqual(m.max(), 1)
def test(self):
""" Test with a 100 by 100 matrix.
"""
size = 100
m = helpers.rand(size, size)
min_diagonal = m.diagonal().min()
res = helpers.tweak_diag(m)
for i in range(size):
self.assertGreaterEqual(res[i, i], m[i, i] - min_diagonal)
self.assertLessEqual(res[i, i], m[i, i] - min_diagonal + 1)
def evaluate(self, size):
""" Evaluate with a give size matrix.
Args:
size: Matrix size.
"""
m = helpers.rand(size, size)
PU, PD, PV = helpers.svd(m)
self.assertTrue(np.allclose(np.dot(PU, np.dot(PD, PV)), m))
for i in range(size):
for j in range(size):
if i != j:
self.assertEqual(PD[i, j], 0)
def test(self):
""" Test with a simple input.
"""
m = helpers.rand(100, 100)
ans = m.diagonal().max()
self.assertEqual(helpers.maxdiag(m), ans)
def setUp(self):
""" Prepare tests.
"""
u = helpers.rand(3, 3)
v = helpers.rand(3, 3)
self.tup = (u, v)
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})
def _make_u(self):
self.u = 10. * rand(self.info['md'])
def _make_xgen(self):
self.info['xgen'] = 10 * (rand(self.n) - rand(self.n))