def test_shape_3():
# A and b have incompatible shapes
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([[0., 1]])
xi = sp.array([0.25, 0.1])
with pytest.raises(ValueError):
artools.in_region(xi, A, b)
def test_shape_4():
# xi has incompatible shape
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([[0., 0, 1]])
xi = sp.array([0.25, 0.1, 0.1])
with pytest.raises(ValueError):
artools.in_region(xi, A, b)
def test_unbounded_3():
# check on an unbounded region
A = sp.array([[-1., 0],
[0, -1]])
b = sp.array([0., 0])
xi = sp.array([0.5, 0])
assert artools.in_region(xi, A, b)
def test_unbounded_2():
# check out an unbounded region
A = sp.array([[-1., 0],
[0, -1]])
b = sp.array([0., 0])
xi = sp.array([-0.5, -0.5])
assert artools.in_region(xi, A, b) is False
def test_in_1():
# simple 2-D triangle case
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
xi = sp.array([0.1, 0.1])
assert artools.in_region(xi, A, b)
def test_on_1():
# on a 2-D hyperplane
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
xi = sp.array([0.5, 0.5])
assert artools.in_region(xi, A, b)
def test_out_2():
# positive space
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
xi = sp.array([2., 2])
assert (artools.in_region(xi, A, b) is False)
def test_shape_2():
# b is a 2-D row vector
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([[0., 0, 1]])
xi = sp.array([0.25, 0.1])
assert artools.in_region(xi, A, b)
def test_on_2():
# on an extreme point
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
xi = sp.array([1., 0])
assert artools.in_region(xi, A, b)
def test_out_3():
# simple 3-D case
A = sp.array([[-1., 0, 0],
[0, -1, 0],
[0, 0, -1],
[1, 1, 1]])
b = sp.array([0., 0, 0, 1])
xi = sp.array([0.7, 0.7, 0.7])
assert (artools.in_region(xi, A, b) is False)
def test_in_3():
# simple 3-D case
A = sp.array([[-1., 0, 0],
[0, -1, 0],
[0, 0, -1],
[1, 1, 1]])
b = sp.array([0., 0, 0, 1])
xi = sp.array([0.25, 0.1, 0.25])
assert artools.in_region(xi, A, b)
def test_tol_in_1():
# slightly in the region at the origin
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
tol = 1e-8
xi = sp.array([0.0 + tol, 0.0 + tol])
assert artools.in_region(xi, A, b, tol=tol)
def test_tol_on_1():
# on an extreme point specifying tolerance
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
xi = sp.array([1., 0])
tol = 1e-2
assert artools.in_region(xi, A, b, tol=tol)
def test_tol_out_1():
# slightly out of the region at the origin, and not within the accepted
# tolerance
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
tol = 1e-10
xi = sp.array([0.0 - 2*tol, 0.0 + tol])
assert (artools.in_region(xi, A, b, tol=tol) is False)
def test_tol_in_2():
# slightly out of the region at the origin, but still within the accepted
# tolerance
A = sp.array([[-1., 0],
[0, -1],
[1, 1]])
b = sp.array([0., 0, 1])
tol = 1e-8
xi = sp.array([0.0 - tol, 0.0 - tol])
assert artools.in_region(xi, A, b, tol=tol)
# this combination of stoich_mat and Cf produces an initial guess that is on # the boubdary of the feasible region and not technically in the region. stoich_mat = -sp.array([[-1, -1, 1.], [-1., 0, 1]]).T Cf = sp.array([1., 1., 0.2]) # this combination works fine #stoich_mat = -sp.array([[-1, -1, 1.], [-2., 0, 1]]).T #Cf = sp.array([1., 1., 0.2]) A = -stoich_mat b = Cf c = scipy.linalg.lstsq(A, b)[0] fig = artools.plot_hplanes(-stoich_mat, b, lims=(-2.0, 2.0)) ax = fig.gca() ax.hold(True) v = con2vert(A, b) print v print artools.in_region(c, A, b) ax.plot(c[0], c[1], "bo") ax.plot(v[0, 0], v[0, 1], "ro") ax.plot(v[1, 0], v[1, 1], "ro") ax.plot(v[2, 0], v[2, 1], "ro") plt.show(fig)
