def test_mbar_computeEntropyAndEnthalpy():
"""Can MBAR calculate f_k, <u_k> and s_k ??"""
for system_generator in system_generators:
name, test = system_generator()
x_n, u_kn, N_k_output, s_n = test.sample(N_k, mode='u_kn')
eq(N_k, N_k_output)
mbar = MBAR(u_kn, N_k)
results = mbar.computeEntropyAndEnthalpy(u_kn)
f_ij = results['Delta_f']
df_ij = results['dDelta_f']
u_ij = results['Delta_u']
du_ij = results['dDelta_u']
s_ij = results['Delta_s']
ds_ij = results['dDelta_s']
fa = test.analytical_free_energies()
ua = test.analytical_observable('potential energy')
sa = test.analytical_entropies()
fa_ij = np.array(np.matrix(fa) - np.matrix(fa).transpose())
ua_ij = np.array(np.matrix(ua) - np.matrix(ua).transpose())
sa_ij = np.array(np.matrix(sa) - np.matrix(sa).transpose())
z = convert_to_differences(f_ij, df_ij, fa)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
z = convert_to_differences(u_ij, du_ij, ua)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
z = convert_to_differences(s_ij, ds_ij, sa)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
def test_mbar_computeEntropyAndEnthalpy():
"""Can MBAR calculate f_k, <u_k> and s_k ??"""
for system_generator in system_generators:
name, test = system_generator()
x_n, u_kn, N_k_output, s_n = test.sample(N_k, mode='u_kn')
eq(N_k, N_k_output)
mbar = MBAR(u_kn, N_k)
f_ij, df_ij, u_ij, du_ij, s_ij, ds_ij = mbar.computeEntropyAndEnthalpy(u_kn)
fa = test.analytical_free_energies()
ua = test.analytical_observable('potential energy')
sa = test.analytical_entropies()
fa_ij = np.array(np.matrix(fa) - np.matrix(fa).transpose())
ua_ij = np.array(np.matrix(ua) - np.matrix(ua).transpose())
sa_ij = np.array(np.matrix(sa) - np.matrix(sa).transpose())
z = convert_to_differences(f_ij,df_ij,fa)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
z = convert_to_differences(u_ij,du_ij,ua)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
z = convert_to_differences(s_ij,ds_ij,sa)
eq(z / z_scale_factor, np.zeros(np.shape(z)), decimal=0)
compute_covariance=True)
A_i = results['mu']
dA_ij = results['sigma']
Ca_ij = results['covariances']
print("Averages for state %d" % (i))
print(A_i)
print("Uncertainties for state %d" % (i))
print(dA_ij)
print("Correlation matrix between observables for state %d" % (i))
print(Ca_ij)
print("============================================")
print(" Testing computeEntropyAndEnthalpy")
print("============================================")
results = mbar.computeEntropyAndEnthalpy(u_kn=u_kln, verbose=True)
Delta_f_ij = results['Delta_f']
dDelta_f_ij = results['dDelta_f']
Delta_u_ij = results['Delta_u']
dDelta_u_ij = results['dDelta_u']
Delta_s_ij = results['Delta_s']
dDelta_s_ij = results['dDelta_s']
print("Free energies")
print(Delta_f_ij)
print(dDelta_f_ij)
diffs1 = Delta_f_ij - Delta_f_ij_estimated
print(
"maximum difference between values computed here and in computeFreeEnergies is %g"
% (numpy.max(diffs1)))
if (numpy.max(numpy.abs(diffs1)) > 1.0e-10):
A_ikn = numpy.zeros([len(observables_single), K, N_k.max()], numpy.float64) for i,observe in enumerate(observables_single): A_ikn[i,:,:] = A_kn_all[observe] for i in range(K): [A_i,d2A_ij] = mbar.computeMultipleExpectations(A_ikn, u_kln[:,i,:]) print "Averages for state %d" % (i) print A_i print "Correlation matrix between observables for state %d" % (i) print d2A_ij print "============================================" print " Testing computeEntropyAndEnthalpy" print "============================================" (Delta_f_ij, dDelta_f_ij, Delta_u_ij, dDelta_u_ij, Delta_s_ij, dDelta_s_ij) = mbar.computeEntropyAndEnthalpy(verbose = True) print "Free energies" print Delta_f_ij print dDelta_f_ij diffs1 = Delta_f_ij - Delta_f_ij_estimated print "maximum difference between values computed here and in computeFreeEnergies is %g" % (numpy.max(diffs1)) if (numpy.max(numpy.abs(diffs1)) > 1.0e-10): print "Difference in values from computeFreeEnergies" print diffs1 diffs2 = dDelta_f_ij - dDelta_f_ij_estimated print "maximum difference between uncertainties computed here and in computeFreeEnergies is %g" % (numpy.max(diffs2)) if (numpy.max(numpy.abs(diffs2)) > 1.0e-10): print "Difference in expectations from computeFreeEnergies" print diffs2 print "Energies"
A_ikn = numpy.zeros([len(observables_single), K, N_k.max()], numpy.float64)
for i, observe in enumerate(observables_single):
A_ikn[i, :, :] = A_kn_all[observe]
for i in range(K):
[A_i, d2A_ij] = mbar.computeMultipleExpectations(A_ikn, u_kln[:, i, :])
print "Averages for state %d" % (i)
print A_i
print "Correlation matrix between observables for state %d" % (i)
print d2A_ij
print "============================================"
print " Testing computeEntropyAndEnthalpy"
print "============================================"
(Delta_f_ij, dDelta_f_ij, Delta_u_ij, dDelta_u_ij, Delta_s_ij,
dDelta_s_ij) = mbar.computeEntropyAndEnthalpy(verbose=True)
print "Free energies"
print Delta_f_ij
print dDelta_f_ij
diffs1 = Delta_f_ij - Delta_f_ij_estimated
print "maximum difference between values computed here and in computeFreeEnergies is %g" % (
numpy.max(diffs1))
if (numpy.max(numpy.abs(diffs1)) > 1.0e-10):
print "Difference in values from computeFreeEnergies"
print diffs1
diffs2 = dDelta_f_ij - dDelta_f_ij_estimated
print "maximum difference between uncertainties computed here and in computeFreeEnergies is %g" % (
numpy.max(diffs2))
if (numpy.max(numpy.abs(diffs2)) > 1.0e-10):
print "Difference in expectations from computeFreeEnergies"
print diffs2
results = mbar.computeMultipleExpectations(A_ikn, u_kln[:,i,:], compute_covariance=True)
A_i = results['mu']
dA_ij = results['sigma']
Ca_ij = results['covariances']
print("Averages for state %d" % (i))
print(A_i)
print("Uncertainties for state %d" % (i))
print(dA_ij)
print("Correlation matrix between observables for state %d" % (i))
print(Ca_ij)
print("============================================")
print(" Testing computeEntropyAndEnthalpy")
print("============================================")
results = mbar.computeEntropyAndEnthalpy(u_kn = u_kln, verbose = True)
Delta_f_ij = results['Delta_f']
dDelta_f_ij = results['dDelta_f']
Delta_u_ij = results['Delta_u']
dDelta_u_ij = results['dDelta_u']
Delta_s_ij = results['Delta_s']
dDelta_s_ij = results['dDelta_s']
print("Free energies")
print(Delta_f_ij)
print(dDelta_f_ij)
diffs1 = Delta_f_ij - Delta_f_ij_estimated
print("maximum difference between values computed here and in computeFreeEnergies is %g" % (numpy.max(diffs1)))
if (numpy.max(numpy.abs(diffs1)) > 1.0e-10):
print("Difference in values from computeFreeEnergies")
print(diffs1)
for i,observe in enumerate(observables_single): A_ikn[i,:,:] = A_kn_all[observe] for i in range(K): [A_i,dA_ij,Ca_ij] = mbar.computeMultipleExpectations(A_ikn, u_kln[:,i,:], compute_covariance=True) print "Averages for state %d" % (i) print A_i print "Uncertainties for state %d" % (i) print dA_ij print "Correlation matrix between observables for state %d" % (i) print Ca_ij print "============================================" print " Testing computeEntropyAndEnthalpy" print "============================================" (Delta_f_ij, dDelta_f_ij, Delta_u_ij, dDelta_u_ij, Delta_s_ij, dDelta_s_ij) = mbar.computeEntropyAndEnthalpy(u_kn = u_kln, verbose = True) print "Free energies" print Delta_f_ij print dDelta_f_ij diffs1 = Delta_f_ij - Delta_f_ij_estimated print "maximum difference between values computed here and in computeFreeEnergies is %g" % (numpy.max(diffs1)) if (numpy.max(numpy.abs(diffs1)) > 1.0e-10): print "Difference in values from computeFreeEnergies" print diffs1 diffs2 = dDelta_f_ij - dDelta_f_ij_estimated print "maximum difference between uncertainties computed here and in computeFreeEnergies is %g" % (numpy.max(diffs2)) if (numpy.max(numpy.abs(diffs2)) > 1.0e-10): print "Difference in expectations from computeFreeEnergies" print diffs2 print "Energies"
