def runTest(self):
n = 5
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
neghess = -hess
self.assertTrue(np.allclose(hess.upper_triangular(), -neghess.upper_triangular()), 'Wrong negative values')
def runTest(self):
n = 4
nvals = n*(n+1)//2
hess = Hessian(n)
self.assertEqual(hess.shape(), (nvals,), 'Wrong shape for initialisation')
self.assertEqual(hess.dim(), n, 'Wrong dimension')
self.assertEqual(len(hess), nvals, 'Wrong length')
self.assertTrue(np.all(hess.upper_triangular() == np.zeros((nvals,))), 'Wrong initialised values')
def runTest(self):
n = 5
nvals = n*(n+1)//2
x = np.arange(nvals, dtype=np.float)
hess = Hessian(n, vals=x)
self.assertEqual(hess.shape(), (nvals,), 'Wrong shape for initialisation')
self.assertEqual(hess.dim(), n, 'Wrong dimension')
self.assertEqual(len(hess), nvals, 'Wrong length')
self.assertTrue(np.all(hess.upper_triangular() == x), 'Wrong initialised values')
def runTest(self):
n = 3
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
for i in range(n):
for j in range(n):
self.assertEqual(hess.get_element(i, j), H[i,j], 'Wrong value for (i,j)=(%g,%g): got %g, expecting %g'
% (i, j, hess.get_element(i, j), H[i,j]))
def runTest(self):
n = 3
nvals = n*(n+1)//2
A = np.arange(n**2, dtype=np.float).reshape((n,n))
hess = Hessian(n, vals=A+A.T) # force symmetric
self.assertEqual(hess.shape(), (nvals,), 'Wrong shape for initialisation')
self.assertEqual(hess.dim(), n, 'Wrong dimension')
self.assertEqual(len(hess), nvals, 'Wrong length')
self.assertTrue(np.all(hess.upper_triangular() == np.array([0.0, 4.0, 8.0, 8.0, 12.0, 16.0])),
'Wrong initialised values')
def runTest(self):
n = 5
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = np.sin(A + A.T) # force symmetric
hess = Hessian(n, vals=H)
vec = np.exp(np.arange(n, dtype=np.float))
hs = np.dot(H, vec)
self.assertTrue(array_compare(hess*vec, hs, thresh=1e-12), 'Wrong values')
def runTest(self):
n = 5
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
# When testing for assertion errors, need lambda to stop assertion from actually happening
self.assertRaises(AssertionError, lambda: hess * 1.0)
self.assertRaises(AssertionError, lambda: hess * None)
self.assertRaises(AssertionError, lambda: hess * [float(i) for i in range(n)])
self.assertRaises(AssertionError, lambda: hess * np.arange(n-1, dtype=np.float))
self.assertRaises(AssertionError, lambda: hess * np.arange(n+1, dtype=np.float))
def runTest(self):
n = 5
A = np.arange(n**2, dtype=np.float).reshape((n, n))
H = np.sin(A + A.T) # force symmetric
hess = Hessian(n, vals=H)
vec = np.exp(np.arange(n, dtype=np.float))
g = np.cos(3 * np.arange(n, dtype=np.float) - 2.0)
mval = np.dot(g, vec) + 0.5 * np.dot(vec, np.dot(H, vec))
self.assertAlmostEqual(mval,
model_value(g, hess, vec),
msg='Wrong value')
def runTest(self):
xbase = np.array([0.0, 0.0])
g = np.array([1e-15, -1.0])
a = np.array([-2.0, -2.0])
b = np.array([1.0, 2.0])
hess = Hessian(2)
delta = 5.0
c = 0.0
x = trsbox_geometry(xbase, c, g, hess, a, b, delta)
xtrue = np.array([0.0, 2.0])
self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step')
def runTest(self):
xbase = np.array([0.0, 0.0]) + 1
g = np.array([1.0, -1.0])
a = np.array([-2.0, -2.0]) + 1
b = np.array([1.0, 2.0]) + 1
hess = Hessian(2)
delta = 5.0
c = 3.0 # may want to max instead
x = trsbox_geometry(xbase, c, g, hess, a, b, delta)
xtrue = np.array([1.0, -2.0]) + 1
self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step')
def runTest(self):
n = 3
g = np.array([1.0, 0.0, 1.0])
H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]])
Delta = 5.0 / 12.0
hess = Hessian(n, vals=H)
xopt = np.zeros((n,))
sl = -1e20 * np.ones((n,))
su = 1e20 * np.ones((n,))
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0 / 3.0, 0.0, -0.25])
est_min = model_value(g, hess, d)
true_min = model_value(g, hess, true_d)
# Hope to get actual correct answer
# self.assertTrue(np.all(d == true_d), 'Wrong answer')
# self.assertAlmostEqual(est_min, true_min, 'Wrong min value')
s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, hess, Delta)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + hess.vec_mul(d)), 'Wrong gnew')
self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin')
def runTest(self):
xbase = np.array([0.0, 0.0, 0.0])
g = np.array([-1.0, -1.0, -1.0])
a = np.array([-2.0, -2.0, -2.0])
b = np.array([0.9, 0.1, 5.0])
hess = Hessian(3)
delta = sqrt(3.0)
c = -1.0 # may want to max instead
x = trsbox_geometry(xbase, c, g, hess, a, b, delta)
xtrue = np.array([0.9, 0.1, sqrt(3.0 - 0.81 - 0.01)])
print(x)
self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step')
def runTest(self):
n = 3
g = np.array([1.0, 0.0, 1.0])
H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]])
Delta = 5.0 / 12.0
hess = Hessian(n, vals=H)
xopt = np.zeros((n,))
sl = xopt + np.array([-0.3, -0.01, -0.1])
su = xopt + np.array([10.0, 1.0, 10.0])
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0 / 3.0, 0.0, -0.25])
est_min = model_value(g, hess, d)
true_min = model_value(g, hess, true_d)
# Hope to get actual correct answer
# self.assertTrue(np.all(d == true_d), 'Wrong answer')
# self.assertAlmostEqual(est_min, true_min, 'Wrong min value')
s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, hess, Delta, sl - xopt, su - xopt)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.max(np.abs(gnew - g - hess.vec_mul(d))) < 1e-10, 'Wrong gnew')
print(crvmin)
self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin')
def runTest(self):
xbase = np.array([0.0, 0.0])
g = np.array([1e-15, 0.0])
a = np.array([-2.0, -2.0])
b = np.array([1.0, 2.0])
hess = Hessian(2)
delta = 5.0
c = 0.0
x = trsbox_geometry(xbase, c, g, hess, a, b, delta)
# Since objective is essentially zero, will accept any x within the defined region
self.assertTrue(np.linalg.norm(x) <= delta)
self.assertTrue(np.max(x - a) >= 0.0)
self.assertTrue(np.max(x - b) <= 0.0)
def runTest(self):
n = 3
g = np.array([1.0, 0.0, 1.0])
H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]])
Delta = 2.0
hess = Hessian(n, vals=H)
xopt = np.ones((n,)) # trying nonzero (since bounds inactive)
sl = xopt + np.array([-0.5, -10.0, -10.0])
su = xopt + np.array([10.0, 10.0, 10.0])
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0, 0.0, -0.5])
est_min = model_value(g, hess, d)
true_min = model_value(g, hess, true_d)
# Hope to get actual correct answer for internal minimum?
# self.assertTrue(np.all(d == true_d), 'Wrong answer')
# self.assertAlmostEqual(est_min, true_min, 'Wrong min value')
s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, hess, Delta, sl-xopt, su-xopt)
# print(s_cauchy)
# print(d)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + hess.vec_mul(d)), 'Wrong gnew')
print(crvmin)
self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin')
def runTest(self):
n = 3
c = 1.0 # changed this value to force max rather than min
g = np.array([1.0, 0.0, 1.0])
H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]])
Delta = 5.0 / 12.0
hess = Hessian(n, vals=H)
xopt = np.zeros((n,))
sl = -1e20 * np.ones((n,))
su = 1e20 * np.ones((n,))
x = trsbox_geometry(xopt, c, g, hess, sl, su, Delta)
xtrue = np.array([0.25, 0.0, 1.0 / 3.0]) # max solution
# print(x)
# print(xtrue)
self.assertTrue(np.allclose(x, xtrue, atol=1e-3), "Wrong step")
def runTest(self):
n = 3
c = -1.0
g = np.array([1.0, 0.0, 1.0])
H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]])
Delta = 5.0 / 12.0
hess = Hessian(n, vals=H)
xopt = np.zeros((n,))
sl = -1e20 * np.ones((n,))
su = 1e20 * np.ones((n,))
x = trsbox_geometry(xopt, c, g, hess, sl, su, Delta)
xtrue = np.array([-1.0 / 3.0, 0.0, -0.25])
# print(x)
# print(xtrue)
self.assertTrue(np.allclose(x, xtrue, atol=1e-3), "Wrong step")
def runTest(self):
n = 5
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
# When testing for assertion errors, need lambda to stop assertion from actually happening
self.assertRaises(AssertionError, lambda: hess.set_element(-1, 0, 1.0))
self.assertRaises(AssertionError, lambda: hess.set_element(-1, 0, 2.0))
self.assertRaises(AssertionError, lambda: hess.set_element(-3, n - 1, 3.0))
self.assertRaises(AssertionError, lambda: hess.set_element(n, 0, 4.0))
self.assertRaises(AssertionError, lambda: hess.set_element(n + 3, 0, -4.0))
self.assertRaises(AssertionError, lambda: hess.set_element(n + 7, n - 1, 5.0))
self.assertRaises(AssertionError, lambda: hess.set_element(0, -1, 6.0))
self.assertRaises(AssertionError, lambda: hess.set_element(0, -1, 7.0))
self.assertRaises(AssertionError, lambda: hess.set_element(n - 1, -3, -7.0))
self.assertRaises(AssertionError, lambda: hess.set_element(0, n, -76.3))
self.assertRaises(AssertionError, lambda: hess.set_element(0, n + 3, 2.8))
self.assertRaises(AssertionError, lambda: hess.set_element(n - 1, n + 7, -1.0))
def runTest(self):
n = 7
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
self.assertTrue(np.all(hess.as_full() == H), 'Wrong values')
def runTest(self):
n = 2
npt = 2 * n + 1
x0 = np.array([1.0, 1.0])
xl = -1e2 * np.ones((n, ))
xu = 1e2 * np.ones((n, ))
model = Model(npt, x0, objfun(x0), xl, xu, 1, precondition=False)
x1 = x0 + np.array([1.0, 0.0])
model.change_point(1, x1 - model.xbase, objfun(x1))
x2 = x0 + np.array([0.1, 0.9])
model.change_point(2, x2 - model.xbase, objfun(x2))
x3 = x0 + np.array([-0.1, 0.0])
model.change_point(3, x3 - model.xbase, objfun(x3))
x4 = x0 + np.array([-0.1, 2.0])
model.change_point(4, x4 - model.xbase, objfun(x4))
# x2 is xopt in this situation
self.assertTrue(model.kopt == 2, 'Wrong xopt')
xs = [x0, x1, x3, x4]
xopt = x2
nxs = len(xs)
A = np.zeros((nxs + n, nxs + n))
for i in range(nxs):
for j in range(nxs):
A[i, j] = 0.5 * np.dot(xs[i] - xopt, xs[j] - xopt)**2
A[i, nxs:] = xs[i] - xopt
A[nxs:, i] = xs[i] - xopt
A2, left_scaling, right_scaling = model.interpolation_matrix()
# print("Expect", A)
# print("Got", A2)
self.assertTrue(np.allclose(A, A2), 'Interp matrix 1')
# For reference: model based around model.xbase
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model.interpolate_model(
verbose=True)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(norm_chg_grad, np.linalg.norm(model.model_grad))
self.assertAlmostEqual(
norm_chg_hess, np.linalg.norm(model.model_hess.as_full(),
ord='fro'))
self.assertAlmostEqual(model.model_const,
objfun(model.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model.model_value(xi - model.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
# Test some other parameter settings for model.model_value()
g, hess = model.build_full_model()
self.assertTrue(
np.allclose(
g, model.model_grad +
model.model_hess.vec_mul(model.xopt(abs_coordinates=False))),
'Bad gradient')
self.assertTrue(
np.allclose(hess.as_full(), model.model_hess.as_full()),
'Bad Hessian')
# Build a new model
model2 = Model(npt, x0, objfun(x0), xl, xu, 1, precondition=False)
model2.change_point(1, x1 - model.xbase, objfun(x1))
model2.change_point(2, x2 - model.xbase, objfun(x2))
model2.change_point(3, x3 - model.xbase, objfun(x3))
model2.change_point(4, x4 - model.xbase, objfun(x4))
# Force Hessian to be something else
model2.model_hess = Hessian(n, vals=np.eye(n))
A2, left_scaling, right_scaling = model2.interpolation_matrix()
self.assertTrue(np.allclose(A, A2), 'Interp matrix 2')
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model2.interpolate_model(
)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(model2.model_const,
objfun(model2.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model2.model_value(xi - model2.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
# Compare distance of hessians
h1 = Hessian(n).as_full()
h2 = Hessian(n, vals=np.eye(n)).as_full()
self.assertLessEqual(
np.linalg.norm(model.model_hess.as_full() - h1, ord='fro'),
np.linalg.norm(model2.model_hess.as_full() - h1, ord='fro'),
'Not min frob Hess 1')
self.assertLessEqual(
np.linalg.norm(model2.model_hess.as_full() - h2, ord='fro'),
np.linalg.norm(model.model_hess.as_full() - h2, ord='fro'),
'Not min frob Hess 2')
# print(model.model_hess.as_full())
# print(model2.model_hess.as_full())
# Build a new model
model3 = Model(npt, x0, objfun(x0), xl, xu, 1, precondition=False)
model3.change_point(1, x1 - model.xbase, objfun(x1))
model3.change_point(2, x2 - model.xbase, objfun(x2))
model3.change_point(3, x3 - model.xbase, objfun(x3))
model3.change_point(4, x4 - model.xbase, objfun(x4))
# Force Hessian to be something else
model3.model_hess = Hessian(n, vals=np.eye(n))
A2, left_scaling, right_scaling = model3.interpolation_matrix()
self.assertTrue(np.allclose(A, A2), 'Interp matrix 3')
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model3.interpolate_model(
min_chg_hess=False)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(model3.model_const,
objfun(model3.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model3.model_value(xi - model3.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
self.assertTrue(
np.allclose(model.model_hess.as_full(),
model3.model_hess.as_full()),
'min_chg_hess=False not working')
def runTest(self):
n = 4
A = np.arange(n ** 2, dtype=np.float).reshape((n, n))
H = A + A.T # force symmetric
hess = Hessian(n, vals=H)
# When testing for assertion errors, need lambda to stop assertion from actually happening
self.assertRaises(AssertionError, lambda: hess.get_element(-1, 0))
self.assertRaises(AssertionError, lambda: hess.get_element(-1, 0))
self.assertRaises(AssertionError, lambda: hess.get_element(-3, n-1))
self.assertRaises(AssertionError, lambda: hess.get_element(n, 0))
self.assertRaises(AssertionError, lambda: hess.get_element(n+3, 0))
self.assertRaises(AssertionError, lambda: hess.get_element(n+7, n-1))
self.assertRaises(AssertionError, lambda: hess.get_element(0, -1))
self.assertRaises(AssertionError, lambda: hess.get_element(0, -1))
self.assertRaises(AssertionError, lambda: hess.get_element(n-1, -3))
self.assertRaises(AssertionError, lambda: hess.get_element(0, n))
self.assertRaises(AssertionError, lambda: hess.get_element(0, n+3))
self.assertRaises(AssertionError, lambda: hess.get_element(n-1, n+7))