def test_UNIQUAC_np_hash_different_input_forms():
N = 3
T = 331.42
xs = [0.229, 0.175, 0.596]
rs = [2.5735, 2.87, 1.4311]
qs = [2.336, 2.41, 1.432]
# madeup numbers to match Wilson example roughly
tausA = [[0.0, -1.05e-4, -2.5e-4], [3.9e-4, 0.0, 1.6e-4],
[-1.123e-4, 6.5e-4, 0]]
tausB = [[0.0, 235.0, -169.0], [-160, 0.0, -715.0], [11.2, 144.0, 0.0]]
tausC = [[0.0, -4.23e-4, 2.9e-4], [6.1e-4, 0.0, 8.2e-5],
[-7.8e-4, 1.11e-4, 0]]
tausD = [[0.0, -3.94e-5, 2.22e-5], [8.5e-5, 0.0, 4.4e-5],
[-7.9e-5, 3.22e-5, 0]]
tausE = [[0.0, -4.2e2, 8.32e2], [2.7e2, 0.0, 6.8e2], [3.7e2, 7.43e2, 0]]
tausF = [[0.0, 9.64e-8, 8.94e-8], [1.53e-7, 0.0, 1.11e-7],
[7.9e-8, 2.276e-8, 0]]
ABCDEF = (tausA, tausB, tausC, tausD, tausE, tausF)
A, B, C, D, E, F = ABCDEF
tau_coeffs = [[[A[i][j], B[i][j], C[i][j], D[i][j], E[i][j], F[i][j]]
for j in range(N)] for i in range(N)]
model_ABCDEF = UNIQUAC(T=T, xs=xs, rs=rs, qs=qs, ABCDEF=(A, B, C, D, E, F))
model_tau_coeffs = UNIQUAC(T=T, xs=xs, rs=rs, qs=qs, tau_coeffs=tau_coeffs)
model_tau_coeffs2 = UNIQUAC.from_json(model_tau_coeffs.as_json())
assert model_ABCDEF.GE() == model_tau_coeffs.GE()
assert hash(model_ABCDEF) == hash(model_tau_coeffs)
assert model_ABCDEF.GE() == model_tau_coeffs2.GE()
assert hash(model_ABCDEF) == hash(model_tau_coeffs2)
modelnp = UNIQUAC(T=T,
xs=np.array(xs),
rs=np.array(rs),
qs=np.array(qs),
ABCDEF=(np.array(A), np.array(B), np.array(C),
np.array(D), np.array(E), np.array(F)))
model_tau_coeffsnp = UNIQUAC(T=T,
rs=np.array(rs),
qs=np.array(qs),
xs=np.array(xs),
tau_coeffs=np.array(tau_coeffs))
assert modelnp.GE() == model_tau_coeffsnp.GE()
assert hash(modelnp) == hash(model_tau_coeffsnp)
model_tau_coeffsnp2 = UNIQUAC.from_json(model_tau_coeffsnp.as_json())
assert hash(modelnp) == hash(model_tau_coeffsnp2)
def test_UNIQUAC_madeup_ternary():
N = 3
T = 331.42
xs = [0.229, 0.175, 0.596]
rs = [2.5735, 2.87, 1.4311]
qs = [2.336, 2.41, 1.432]
# madeup numbers to match Wilson example roughly
tausA = [[0.0, -1.05e-4, -2.5e-4], [3.9e-4, 0.0, 1.6e-4],
[-1.123e-4, 6.5e-4, 0]]
tausB = [[0.0, 235.0, -169.0], [-160, 0.0, -715.0], [11.2, 144.0, 0.0]]
tausC = [[0.0, -4.23e-4, 2.9e-4], [6.1e-4, 0.0, 8.2e-5],
[-7.8e-4, 1.11e-4, 0]]
tausD = [[0.0, -3.94e-5, 2.22e-5], [8.5e-5, 0.0, 4.4e-5],
[-7.9e-5, 3.22e-5, 0]]
tausE = [[0.0, -4.2e2, 8.32e2], [2.7e2, 0.0, 6.8e2], [3.7e2, 7.43e2, 0]]
tausF = [[0.0, 9.64e-8, 8.94e-8], [1.53e-7, 0.0, 1.11e-7],
[7.9e-8, 2.276e-8, 0]]
ABCDEF = (tausA, tausB, tausC, tausD, tausE, tausF)
GE = UNIQUAC(T=T, xs=xs, rs=rs, qs=qs, ABCDEF=ABCDEF)
assert eval(str(GE)).GE() == GE.GE()
with pytest.raises(ValueError):
UNIQUAC(T=T, xs=xs, rs=rs, qs=qs, ABCDEF=(tausA, None, None, []))
with pytest.raises(ValueError):
UNIQUAC(T=T, xs=xs, rs=rs, qs=qs, ABCDEF=(tausA, None, None, [1, 1]))
with pytest.raises(ValueError):
UNIQUAC(T=T,
xs=xs,
rs=rs,
qs=qs,
ABCDEF=(tausA, None, None, [1, 1, 1]))
with pytest.raises(ValueError):
UNIQUAC(T=T,
xs=xs,
rs=rs,
qs=qs,
ABCDEF=(tausA, None, None, [[0.0, 9.64e-8],
[1.53e-7, 0.0, 1.11e-7],
[7.9e-8, 2.276e-8, 0]]))
with pytest.raises(ValueError):
UNIQUAC(T=T,
xs=xs,
rs=rs,
qs=qs,
ABCDEF=(tausA, None, None, [[0.0, 9.64e-8, 8.94e-8],
[1.53e-7, 0.0, 1.11e-7]]))
GE2 = UNIQUAC.from_json(GE.as_json())
assert GE2.__dict__ == GE.__dict__
# GE
GE_expect = 415.5805110962149
GE_analytical = GE.GE()
assert_close(GE_expect, GE_analytical, rtol=1e-13)
gammas = UNIQUAC_gammas(taus=GE.taus(), rs=rs, qs=qs, xs=xs)
GE_identity = R * T * sum(xi * log(gamma) for xi, gamma in zip(xs, gammas))
assert_close(GE_identity, GE_analytical, rtol=1e-12)
# dGE_dT
dGE_dT_expect = 0.9907140284750982
dGE_dT_analytical = GE.dGE_dT()
dGE_dT_numerical = derivative(lambda T: GE.to_T_xs(T, xs).GE(),
T,
order=7,
dx=T * 1e-3)
assert_close(dGE_dT_analytical, dGE_dT_numerical, rtol=1e-12)
assert_close(dGE_dT_expect, dGE_dT_analytical, rtol=1e-13)
# d2GE_dT2
d2GE_dT2_expect = -0.007148011229475758
d2GE_dT2_analytical = GE.d2GE_dT2()
d2GE_dT2_numerical = derivative(lambda T: GE.to_T_xs(T, xs).dGE_dT(),
T,
order=7,
dx=T * 1e-3)
assert_close(d2GE_dT2_expect, d2GE_dT2_analytical, rtol=1e-12)
assert_close(d2GE_dT2_analytical, d2GE_dT2_numerical, rtol=1e-12)
# d3GE_dT3
d3GE_dT3_expect = 2.4882477326368877e-05
d3GE_dT3_analytical = GE.d3GE_dT3()
assert_close(d3GE_dT3_expect, d3GE_dT3_analytical, rtol=1e-13)
d3GE_dT3_numerical = derivative(lambda T: GE.to_T_xs(T, xs).d2GE_dT2(),
T,
order=11,
dx=T * 1e-2)
assert_close(d3GE_dT3_analytical, d3GE_dT3_numerical, rtol=1e-12)
# dphis_dxs
dphis_dxs_analytical = GE.dphis_dxs()
dphis_dxs_expect = [
[0.9223577846000854, -0.4473196931643269, -0.2230519905531248],
[-0.3418381934661886, 1.094722540086528, -0.19009311780433752],
[-0.5805195911338968, -0.6474028469222008, 0.41314510835746243]
]
assert_close2d(dphis_dxs_expect, dphis_dxs_analytical, rtol=1e-12)
dphis_dxs_numerical = jacobian(lambda xs: GE.to_T_xs(T, xs).phis(),
xs,
scalar=False,
perturbation=2e-8)
assert_close2d(dphis_dxs_numerical, dphis_dxs_analytical, rtol=3e-8)
# d2phis_dxixjs - checked to the last decimal with sympy
d2phis_dxixjs_expect = [
[[-2.441416183656415, 0.9048216556030662, 1.536594528053349],
[-0.7693373390462084, -0.9442924629794809, 1.7136298020256895],
[-0.3836232285397313, 0.5031631130108988, -0.11953988447116741]],
[[-0.7693373390462084, -0.9442924629794809, 1.7136298020256895],
[1.3204383950972896, -3.231500191022578, 1.9110617959252876],
[0.658424873597119, -0.5251124708645561, -0.13331240273256284]],
[[-0.3836232285397313, 0.5031631130108987, -0.11953988447116741],
[0.6584248735971189, -0.5251124708645561, -0.13331240273256284],
[0.32831771310273056, 0.27980444182238084, -0.6081221549251116]]
]
d2phis_dxixjs_analytical = GE.d2phis_dxixjs()
assert_close3d(d2phis_dxixjs_analytical, d2phis_dxixjs_expect, rtol=1e-12)
d2phis_dxixjs_numerical = hessian(lambda xs: GE.to_T_xs(T, xs).phis(),
xs,
scalar=False,
perturbation=1e-5)
assert_close3d(d2phis_dxixjs_numerical,
d2phis_dxixjs_analytical,
rtol=8e-5)
d2thetas_dxixjs_expect = [
[[-2.346422740416712, 0.7760247163009644, 1.5703980241157476],
[-0.7026345706138027, -0.9175106511836936, 1.6201452217974965],
[-0.4174990477672056, 0.47571378156805694, -0.05821473380085118]],
[[-0.7026345706138027, -0.9175106511836936, 1.6201452217974965],
[1.0476523499983839, -2.7191206652946023, 1.6714683152962189],
[0.6225054627376287, -0.5624465978146614, -0.06005886492296719]],
[[-0.4174990477672056, 0.47571378156805694, -0.05821473380085118],
[0.6225054627376287, -0.5624465978146614, -0.06005886492296719],
[0.3698870633362176, 0.2916190647283637, -0.6615061280645813]]
]
d2thetas_dxixjs_analytical = GE.d2thetas_dxixjs()
assert_close3d(d2thetas_dxixjs_analytical,
d2thetas_dxixjs_expect,
rtol=1e-12)
d2thetas_dxixjs_numerical = hessian(lambda xs: GE.to_T_xs(T, xs).thetas(),
xs,
scalar=False,
perturbation=2e-5)
assert_close3d(d2thetas_dxixjs_numerical,
d2thetas_dxixjs_analytical,
rtol=1e-4)
def to_jac(xs):
return GE.to_T_xs(T, xs).GE()
# Obtained 12 decimals of precision with numdifftools
dGE_dxs_analytical = GE.dGE_dxs()
dGE_dxs_expect = [
-2651.3181821109024, -2085.574403592012, -2295.0860830203587
]
assert_close1d(dGE_dxs_analytical, dGE_dxs_expect, rtol=1e-12)
dGE_dxs_numerical = jacobian(to_jac, xs, perturbation=1e-8)
assert_close1d(dGE_dxs_numerical, dGE_dxs_analytical, rtol=1e-6)
# d2GE_dTdxs
def to_jac(xs):
return GE.to_T_xs(T, xs).dGE_dT()
d2GE_dTdxs_expect = [
-9.940433543371945, -3.545963210296949, -7.427593534302016
]
d2GE_dTdxs = GE.d2GE_dTdxs()
d2GE_dTdxs_numerical = jacobian(to_jac, xs, perturbation=1e-8)
assert_close1d(d2GE_dTdxs_numerical, d2GE_dTdxs, rtol=1e-6)
assert_close1d(d2GE_dTdxs, d2GE_dTdxs_expect, rtol=1e-12)
# d2GE_dxixjs
def to_hess(xs):
return GE.to_T_xs(T, xs).GE()
d2GE_dxixjs_numerical = hessian(to_hess, xs, perturbation=1e-4)
d2GE_dxixjs_sympy = [
[-2890.4327598108343, -6687.099054095988, -1549.3754436994557],
[-6687.099054095988, -2811.283290487096, -1228.622385377738],
[-1549.3754436994557, -1228.622385377738, -3667.3880987585053]
]
d2GE_dxixjs_analytical = GE.d2GE_dxixjs()
assert_close2d(d2GE_dxixjs_numerical, d2GE_dxixjs_analytical, rtol=1e-4)
assert_close2d(d2GE_dxixjs_analytical, d2GE_dxixjs_sympy, rtol=1e-12)
# Check json storage again, with some results
GE2 = UNIQUAC.from_json(GE.as_json())
assert GE2.__dict__ == GE.__dict__