total_PFU = 1000
init_vals = [
total_PFU * particle_to_pfu_ratio * nspikes / total_volume,
0.5 * total_antibody / total_volume, 0.5 * total_antibody / total_volume
]
dilutions = 1 / np.array([5120, 2560, 1280, 640, 320, 160, 80, 40, 20])
measurement_time = 3600
interference_matrix[0, 0, 1] = 0 #complete interference
interference_matrix[0, 1, 0] = 0
y1, log_titers1, titers, sol1 = titrateAntigensAgainstSera(
init_vals,
dilutions,
number_of_antigens,
number_of_antibodies,
measurement_time,
association_constants,
dissociation_constants,
interference_matrix,
inactivation_thresholds=inactivation_thresholds)
interference_matrix[0, 0, 1] = 1 #no interference
interference_matrix[0, 1, 0] = 1
y2, log_titers2, titers2, sol2 = titrateAntigensAgainstSera(
init_vals,
dilutions,
number_of_antigens,
number_of_antibodies,
measurement_time,
association_constants,
dissociation_constants,
(number_of_antigens, number_of_antibodies)) * 2**forward_rate * 1e3 / M
dissociation_rates = 1e-4 * np.ones(
(number_of_antigens, number_of_antibodies))
interference_matrix = np.ones(
(number_of_antigens, number_of_antibodies, number_of_antibodies))
init_vals = [
total_PFU * particle_to_pfu_ratio * nspikes / total_volume,
total_antibody / total_volume
]
measurement_time = 3600
dilutions = 1 / np.array([5120, 2560, 1280, 640, 320, 160, 80, 40, 20])
y, log_titer, titer, _ = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_rates,
interference_matrix)
if '<' in str(titer[0]):
titer_val = int(float(titer[0][1:]) / 2)
elif '>' in str(titer[0]):
titer_val = int(float(titer[0][1:]) * 2)
else:
titer_val = int(titer[0])
titers.append(titer_val)
log_titers.append(-1 * log_titer[0])
ax, fig = outputScatterPlot(ks,
log_titers,
xlabel='k*(Me-6)',
nspike = 450
ratio = vratio * nspike
total_volume = 1e-4
forward_rates = np.ones(
(number_of_antigens, number_of_antibodies)) * 60e9 / (M)
backward_ratios = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones(
(number_of_antigens, number_of_antibodies, number_of_antibodies))
total_PFU = 1000
total_antibody = 10 * 1e9
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume]
measurement_time = 3600
dilutions = [
1 / 5120, 1 / 2560, 1 / 1280, 1 / 640, 1 / 320, 1 / 160, 1 / 80, 1 / 40,
1 / 20
]
y, log_titers, titers, _ = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, forward_rates, backward_ratios, interference_matrix)
ax, fig = outputTiterCurvePlot(y,
log_titers,
number_of_antigens,
dilutions,
fig=None,
ax=None)
def test_interferenceMatrix(fail_switch=False):
M = 6e23
vratio = 50
nspike = 450
ratio = vratio * nspike
total_volume = 1e-4
total_antibody = (np.random.rand(1,1)+0.5) * 600 * 5e9
total_PFU=(np.random.rand(1,1)+0.5) * 1000
is_failed = True # every test fails until proven otherwise
fail_test = 0
if fail_switch:
fail_test = np.random.randint(3) + 1 # fail one of the 2 tests on purpose
# test1: 1 antigen and 2 antibody with complete interference so there should
# be no V_0Ab_0_1
number_of_antigens = 1
number_of_antibodies = 2
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume,
2*total_antibody / total_volume, 2*total_antibody / total_volume]
if fail_test == 1:
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
else:
interference_matrix = np.zeros((number_of_antigens, number_of_antibodies,
number_of_antibodies))
dilutions = 1 / np.array([5120])
measurement_time = 50
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test1 of interference_matrix failed with exception\n "{}".'.format(e))
return is_failed
if not all(np.abs(z) == 0 for z in sol[0][5,:].flatten()):
if not fail_switch:
print('Test1 of titrateAntigensAgainstSera failed.')
return is_failed
# test2: 1 antigen and 3 antibody with complete interference between 1 and 2
# so there should be no V_0Ab_0_1, V_0Ab_0_1_2 but there should be others
number_of_antigens = 1
number_of_antibodies = 3
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume, 2*total_antibody / total_volume,
2*total_antibody / total_volume, 2*total_antibody / total_volume]
if fail_test == 2:
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
else:
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
interference_matrix[0, 0, 1] = 0
interference_matrix[0, 1, 0] = 0
dilutions = 1 / np.array([320])
measurement_time = 50
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test2 of interference_matrix failed with exception\n "{}".'.format(e))
return is_failed
if (not all(np.abs(z) == 0 for z in sol[0][7,:].flatten())
or not all(np.abs(z) == 0 for z in sol[0][10,:].flatten())
or not all(np.abs(z) != 0 for z in sol[0][8:9,-1].flatten())
or not all(np.abs(z) != 0 for z in sol[0][5:6,-1].flatten())):
if not fail_switch:
print('Test2 of interference_matrix failed.')
return is_failed
# test3: an antibody with high association constant but low neutralization
# should decrease titers
number_of_antigens = 1
number_of_antibodies = 2
association_constants = np.ones((number_of_antigens, number_of_antibodies)) * 0.1e5 / M
association_constants[0,1]*=100
total_antibody = 5e13
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
interference_matrix[0, 0, 1] = 0 #complete interference
interference_matrix[0, 1, 0] = 0
inactivation_thresholds=[1, 150]
total_PFU = 1000
init_vals = [total_PFU * ratio / total_volume, 0.5 * total_antibody / total_volume, 0.5 * total_antibody / total_volume]
dilutions = 1 / np.array([5120, 2560, 1280, 640, 320, 160, 80, 40, 20])
measurement_time = 3600
interference_matrix[0, 0, 1] = 0 #complete interference
interference_matrix[0, 1, 0] = 0
if fail_test == 3:
interference_matrix[0, 0, 1] = 1
interference_matrix[0, 1, 0] = 1
try:
y1, log_titers1, titers, sol1 = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_constants, dissociation_constants, interference_matrix,
inactivation_thresholds=inactivation_thresholds)
interference_matrix[0, 0, 1] = 1 #no interference
interference_matrix[0, 1, 0] = 1
y2, log_titers2, titers2,sol2 = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_constants, dissociation_constants, interference_matrix,
inactivation_thresholds=inactivation_thresholds)
except Exception as e:
print('Test3 of interference_matrix failed with exception\n "{}".'.format(e))
return is_failed
if any(x<=y for x,y in zip(y1.flatten(),y2.flatten())):
if not fail_switch:
print('Test3 of interference_matrix failed.')
return is_failed
if fail_switch:
print('Test{} of interference_matrix did not fail with fail_switch on.'.format(fail_test))
return False
def test_inactivationThresholds(fail_switch=False):
M = 6e23
vratio = 50
nspike = 450
ratio = vratio * nspike
total_volume = 1e-4
total_antibody = (np.random.rand()+0.5) * 600 * 5e9
total_PFU=(np.random.rand()+0.5) * 1000
is_failed = True # every test fails until proven otherwise
fail_test = 0
if fail_switch:
fail_test = np.random.randint(2) + 1 # fail one of the 2 tests on purpose
# test 1: two antigens and one antibody which can only neutralize if number
# of bound antibodies per site is = max which is practically impossible
# so should have no titers
number_of_antigens = 2
number_of_antibodies = 1
a1 = np.random.randint(-4,4)
dilutions = 1 / np.array([1280,640,320,160,80,40,20])
measurement_time = 3600
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 2 ** a1 * 1e5 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume, total_PFU * ratio / total_volume,
2*total_antibody / total_volume]
if fail_test == 1:
inactivation_thresholds=[1]
else:
inactivation_thresholds=[150]
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, inactivation_thresholds = inactivation_thresholds,
print_equations=False)
except Exception as e:
print('Test1 of inactivationThresholds failed with exception\n "{}".'.format(e))
return is_failed
if not all(np.abs(x-1)<1e-6 for x in y.flatten()) and not all(x == '<20' for x in titers):
if not fail_switch:
print('Test1 of inactivationThresholds failed.')
return is_failed
number_of_antigens = 1
number_of_antibodies = 1
a1 = 0
dilutions = 1 / np.array([2560, 1280, 640, 320, 160, 80, 40, 20])
measurement_time = 3600
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 2 ** a1 * 1e5 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume, 2*total_antibody / total_volume]
if fail_test == 2:
inactivation_thresholds=[1]
else:
inactivation_thresholds=[2]
try:
y, log_titers, titers1, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, inactivation_thresholds = inactivation_thresholds,
print_equations=False)
inactivation_thresholds=[1]
y, log_titers, titers2, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, inactivation_thresholds = inactivation_thresholds,
print_equations=False)
except Exception as e:
print('Test2 of inactivationThresholds failed with exception\n "{}".'.format(e))
return is_failed
if isinstance(titers2[0],str):
if '<' in titers2[0]:
titers2[0] = 0.5*int(titers2[0][1:])
elif '>' in titers2[0]:
titers2[0] = 2*int(titers2[0][1:])
if isinstance(titers1[0],str):
if '<' in titers1[0]:
titers1[0] = 0.5*int(titers1[0][1:])
elif '>' in titers1[0]:
titers1[0] = 2*int(titers1[0][1:])
if titers2[0] <= titers1[0]:
if not fail_switch:
print('Test2 of inactivationThresholds failed.')
return is_failed
return False
def test_titrateAntigensAgainstSera(fail_switch=False):
M = 6e23
vratio = 50
nspike = 450
ratio = vratio * nspike
total_volume = 1e-4
total_antibody = (np.random.rand(1,1)+0.5) * 600 * 5e9
total_PFU=(np.random.rand(1,1)+0.5) * 1000
is_failed = True # every test fails until proven otherwise
fail_test = 0
if fail_switch:
fail_test = np.random.randint(5) + 1 # fail one of the 5 tests on purpose
# test1: 1 antigen and 1 antibody with 0 rates, initial values should remain the same
number_of_antigens = 1
number_of_antibodies = 1
association_rates = np.zeros((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = np.zeros((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((
number_of_antigens, number_of_antibodies, number_of_antibodies))
if fail_test == 1:
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume]
dilutions = [1 / 2560]
measurement_time = 10
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test1 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
if (not all(z == init_vals[0] for z in sol[0][0, :]) or
not all(z == init_vals[1] * dilutions[0] for z in sol[0][1, :])
or not all(z == sol[0][2, 0] for z in sol[0][2, :])):
if not fail_switch:
print('Test1 of titrateAntigensAgainstSera failed.')
return is_failed
# test2: 1 antigen and 2 antibodies with second rate 0, second ab should remain constant
# others should decrease except complex VAb0 which should increase and VAb1,VAb0Ab1 should all be 0 because Ab1 can not bind
number_of_antigens = 1
number_of_antibodies = 2
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
if fail_test != 2:
association_rates[0, 1] = 0
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume, total_antibody / total_volume]
dilutions = [1 / 2560]
measurement_time = 10
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test2 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
if (not all(z < init_vals[0] for z in sol[0][0, 1:]) or
not all(z < init_vals[1] * dilutions[0] for z in sol[0][1, 1:]) or not
all(np.abs(z - init_vals[2] * dilutions[0]) < 1e-5 for z in sol[0][2, :]) or not
all(z > 0 for z in sol[0][3, 1:]) or not
all(z == 0 for z in sol[0][4:5, 1:].flatten())):
if not fail_switch:
print('Test2 of titrateAntigensAgainstSera failed.')
return is_failed
# test3: 1 antigen and 1 antibody with 0 antibody, initial values should remain the same
number_of_antigens = 1
number_of_antibodies = 1
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
if fail_test == 3:
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume]
else:
init_vals = [total_PFU * ratio / total_volume, 0]
dilutions = [1 / 2560]
measurement_time = 10
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test3 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
if (not all(np.abs(z - sol[0][0, 0]) < 1e-5 for z in sol[0][0, :]) or not
all(np.abs(z) < 1e-5 for z in sol[0][1, :]) or not all(np.abs(z) < 1e-5 for z in sol[0][2, :])):
if not fail_switch:
print('Test3 of titrateAntigensAgainstSera failed.')
return is_failed
# test4: 1 antigen and 2 antibodies with second antibody 0 concentration, second ab should remain constant
# others should decrease except complex VAb0 which should increase and VAb1,VAb0Ab1 should all be 0 because Ab1 can not bind
number_of_antigens = 1
number_of_antibodies = 2
association_rates = np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
if fail_test == 4:
init_vals = [total_PFU * ratio / total_volume,
total_antibody / total_volume, total_antibody / total_volume]
else:
init_vals = [total_PFU * ratio / total_volume,
total_antibody / total_volume, 0]
dilutions = [1 / 2560]
measurement_time = 10
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test4 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
if (not all(z < init_vals[0] for z in sol[0][0, 1:]) or not
all(z < init_vals[1] * dilutions[0] for z in sol[0][1, 1:]) or not
all(z == init_vals[2] * dilutions[0] for z in sol[0][2, :]) or not
all(z > 0 for z in sol[0][3, 1:]) or not
all(z == 0 for z in sol[0][4:5, 1:].flatten())):
if not fail_switch:
print('Test4 of titrateAntigensAgainstSera failed.')
return is_failed
#test5 mixing 2 antibodies with same k should have the same effect as
#one antibody with double the concentration
number_of_antigens = 1
number_of_antibodies = 2
association_rates = 0.5 * np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
if fail_test == 5:
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume, 0.1 * total_antibody / total_volume]
else:
init_vals = [total_PFU * ratio / total_volume, total_antibody / total_volume, total_antibody / total_volume]
dilutions = [1 / 5120, 1 / 1280]
measurement_time = 60
try:
y1, log_titers, titers1, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test5 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
number_of_antigens = 1
number_of_antibodies = 1
association_rates = 0.5*np.ones((number_of_antigens, number_of_antibodies)) * 10e6 / M
dissociation_constants = 1e-3 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
init_vals = [total_PFU * ratio / total_volume, 2*total_antibody / total_volume]
try:
y2, log_titers, titers2, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants,
interference_matrix, print_equations=False)
except Exception as e:
print('Test5 of titrateAntigensAgainstSera failed with exception\n "{}".'.format(e))
return is_failed
if not any(np.abs(x - y) < 1e-3 for x, y in zip(y1.flatten(), y2.flatten())):
if not fail_switch:
print('Test5 of titrateAntigensAgainstSera failed.')
return is_failed
if fail_switch:
print('Test{} of titrateAntigensAgainstSera did not fail with fail_switch on.'.format(fail_test))
return False
def test_ConservationLaws(fail_switch=False):
is_failed = True # every test fails until proven otherwise
fail_test = 0
if fail_switch:
fail_test = np.random.randint(3) + 1 # fail one of the 3 tests on purpose
# test1: 2 antigen, 2 antibody,d(V-Ab)/dt = d(V+AbV)/dt = dAb+AbV/dt=0
number_of_antigens = 1
number_of_antibodies = 1
rand1 = np.random.rand()
rand2 = np.random.rand()
association_rates = np.ones((number_of_antigens, number_of_antibodies))
dissociation_constants = np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
try:
ode, variables = _systemOfEquations(
number_of_antigens, number_of_antibodies, association_rates,
dissociation_constants, interference_matrix)
except Exception as e:
print('Test1 of conservationLaws failed with exception\n"{}".'.format(e))
return is_failed
z = np.random.rand(1, 3).flatten()
t = np.random.rand(1, 1).flatten()
ode_val = ode(t, z)
if fail_test == 1:
ode_val[0] += 10
if (np.abs(ode_val[0] - ode_val[1]) > 1e-5 or np.abs(ode_val[0] + ode_val[2]) > 1e-5
or np.abs(ode_val[1] + ode_val[2]) > 1e-5):
if not fail_switch:
print('Test1 of ConservationLaws failed.')
return is_failed
# test2: 2 antigen, 2 antibody,d(V-Ab)/dt = d(V+AbV)/dt = dAb+AbV/dt=0
number_of_antigens = 2
number_of_antibodies = 2
rand1 = np.random.rand() + 0.1
rand2 = np.random.rand() + 0.1
association_rates = rand1 * np.ones((number_of_antigens, number_of_antibodies))
dissociation_constants = rand2 * np.ones((number_of_antigens, number_of_antibodies))
interference_matrix = np.ones((number_of_antigens, number_of_antibodies,
number_of_antibodies))
try:
ode, variables = _systemOfEquations(
number_of_antigens, number_of_antibodies, association_rates,
dissociation_constants, interference_matrix)
except Exception as e:
print('Test2 of conservationLaws failed with exception\n"{}".'.format(e))
return is_failed
z = np.random.rand(1, 10).flatten()
t = np.random.rand(1, 1).flatten()
ode_val = ode(t, z)
if fail_test == 2:
ode_val[0] += 10
sum1 = ode_val[0] + ode_val[1] - ode_val[2] - ode_val[3] - ode_val[6] - ode_val[9]
if sum1 > 1e-5:
if not fail_switch:
print('Test2 of ConservationLaws failed.')
return is_failed
# test3: solutions of the equations should also satisfy the same conservation laws:
init_vals = [np.random.randint(100) + 10, np.random.randint(100) + 10,
np.random.randint(100) + 10, np.random.randint(100) + 10]
dilutions = [1 / 2560]
measurement_time = 100
try:
y, log_titers, titers, sol = titrateAntigensAgainstSera(
init_vals, dilutions, number_of_antigens, number_of_antibodies,
measurement_time, association_rates, dissociation_constants, interference_matrix,
print_equations=False)
except Exception as e:
print('Test3 of conservationLaws failed with exception\n"{}".'.format(e))
return is_failed
if fail_test == 3:
sol[0][0, 0] *= 10
sum1 = sol[0][0, 0] + sol[0][1, 0] - sol[0][2, 0] - sol[0][3, 0] - sol[0][6, 0] - sol[0][9, 0]
sum2 = sol[0][0, -1] + sol[0][1, -1] - sol[0][2, -1] - sol[0][3, -1] - sol[0][6, -1] - sol[0][9, -1]
if np.abs(sum1 - sum2) > 1e-5:
if not fail_switch:
print('Test3 of ConservationLaws failed.')
return is_failed
if fail_switch:
print('Test{} of Conservationlaws did not fail with fail_switch on.'.format(fail_test))
return False