def test_solve_safe():
a = np.diag([1.0, 2.0, 1.0])
b = np.array([2.0, 4.0, 1.0])
assert (solve_safe(a, b) == [2.0, 2.0, 1.0]).all()
a = np.diag([1.0, 2.0, 0.0])
b = np.array([2.0, 4.0, 1.0])
assert (solve_safe(a, b) == [2.0, 2.0, 0.0]).all()
def test_solve_safe():
a = np.diag([1.0, 2.0, 1.0])
b = np.array([2.0, 4.0, 1.0])
assert (solve_safe(a, b) == [2.0, 2.0, 1.0]).all()
a = np.diag([1.0, 2.0, 0.0])
b = np.array([2.0, 4.0, 1.0])
assert (solve_safe(a, b) == [2.0, 2.0, 0.0]).all()
def solve_cdiis(a):
r'''Solve the linear equations found in the cdiis method
The following is minimized:
.. math:
\frac{1}{2} x^T a x
under the constraint :math:`\sum_i x_i = 1`.
**Arguments:**
a
The matrix a, an array of size (N,N).
'''
n = len(a)
assert a.shape == (n, n)
assert (a == a.T).all()
a2 = np.zeros((n+1, n+1))
a2[:n,:n] = a
a2[n,:n] = 1
a2[:n,n] = 1
b2 = np.zeros(n+1)
b2[n] = 1
x2 = solve_safe(a2, b2)
return x2[:n]
def test_solve_radius_posdef_nl8():
for i in xrange(100):
a, b, r, s = get_random_problem(nl=8, posdef=True)
radius = np.random.uniform(1e-5, 1e2)
center = np.random.normal(0, 0.5*radius, len(b))
try:
x1 = solve_radius(a, b, center, radius, r, s)
except FeasibilityError:
continue
assert np.linalg.norm(x1 - center) < radius*(1 + 1e-3)
x2 = solve_safe(r, s)
assert abs(x1 - x2).max() < 1e-6*abs(x1).max()
def test_solve_radius_posdef_nl8():
for i in xrange(100):
a, b, r, s = get_random_problem(nl=8, posdef=True)
radius = np.random.uniform(1e-5, 1e2)
center = np.random.normal(0, 0.5*radius, len(b))
try:
x1 = solve_radius(a, b, center, radius, r, s)
except FeasibilityError:
continue
assert np.linalg.norm(x1 - center) < radius*(1 + 1e-3)
x2 = solve_safe(r, s)
assert abs(x1 - x2).max() < 1e-6*abs(x1).max()