def mc_sensitivity_linear(Ns, jpdf, w, sample_method='R'):
Nrv = len(jpdf)
# 1. Generate sample matrices
A, B, C = generate_sample_matrices_mc(Ns, Nrv, jpdf, sample_method)
# 2. Evaluate the model
Y_A, Y_B, Y_C = evaluate_linear_model(A, B, C, w)
# 3. Approximate the sensitivity indices
S, ST = calculate_sensitivity_indices_mc(Y_A, Y_B, Y_C)
return A, B, C, Y_A, Y_B, Y_C, S, ST
def monte_carlo_sens_nonlin(Ns, jpdf, sample_method='R'):
N_prms = len(jpdf)
# 1. Generate sample matrices
XA, XB, XC = generate_sample_matrices_mc(Ns, N_prms, jpdf, sample_method)
# 2. Evaluate the model
Y_A, Y_B, Y_C = evaluate_non_additive_linear_model(XA, XB, XC)
# 3. Approximate the sensitivity indices
S, ST = calculate_sensitivity_indices_mc(Y_A, Y_B, Y_C)
return XA, XB, XC, Y_A, Y_B, Y_C, S, ST
# calculate statistics
plotMeanConfidenceAlpha = 5.
Y = np.hstack([Y_A, Y_B])
expected_value = np.mean(Y, axis=1)
variance = np.var(Y, axis=1)
std = np.sqrt(np.var(Y, axis=1))
prediction_interval = np.percentile(
Y, [plotMeanConfidenceAlpha / 2., 100. - plotMeanConfidenceAlpha / 2.],
axis=1)
print('{:2.5f} | {:2.5f} : {}'.format(
np.mean(expected_value) * unit_m2_cm2,
np.mean(std) * unit_m2_cm2, name))
# 3. Approximate the sensitivity indices
S, ST = calculate_sensitivity_indices_mc(Y_A, Y_B, Y_C)
## Plots
plt.figure('mean')
plt.plot(pressure_range * unit_pa_mmhg,
expected_value * unit_m2_cm2,
label=name,
color=color)
plt.fill_between(pressure_range * unit_pa_mmhg,
prediction_interval[0] * unit_m2_cm2,
prediction_interval[1] * unit_m2_cm2,
alpha=0.3,
color=color)
plt.xlabel('Pressure [mmHg]')
plt.ylabel('Area [cm2]')
plt.legend()
Y, [plotMeanConfidenceAlpha / 2., 100. - plotMeanConfidenceAlpha / 2.],
axis=1)
print('{:2.5f} | {:2.5f} : {}'.format(
np.mean(expected_value) * unit_m2_cm2,
np.mean(std) * unit_m2_cm2, name))
# 3. Approximate the sensitivity indices
# Better to centralize data before calculating sensitivities
expected_value_col = expected_value.copy()
expected_value_col.shape = (expected_value.shape[0], 1)
Y_Ac = Y_A - expected_value_col
Y_Bc = Y_B - expected_value_col
Y_Cc = Y_C.transpose() - expected_value
Y_Cc = Y_Cc.transpose()
S, ST = calculate_sensitivity_indices_mc(Y_A, Y_B, Y_C)
Sc, STc = calculate_sensitivity_indices_mc(Y_Ac, Y_Bc, Y_Cc)
## Plots
fig = fig_mean
ax_mean = ax_mean
ax_mean.plot(pressure_range * unit_pa_mmhg,
expected_value * unit_m2_cm2,
label=name,
color=color)
ax_mean.fill_between(pressure_range * unit_pa_mmhg,
prediction_interval[0] * unit_m2_cm2,
prediction_interval[1] * unit_m2_cm2,
alpha=0.3,
color=color)
ax_mean.set_xlabel('Pressure [mmHg]')