Comparing the analysis with and without compactness criterion

This examples shows how to quickly compare the effects of the compactness criterion on the results of the analysis of a 4-pulse DEER signal.

import numpy as np
import matplotlib.pyplot as plt
import deerlab as dl

# File location
path = '../data/'
file = 'example_4pdeer_1.DTA'

# Experimental parameters
tau1 = 0.3      # First inter-pulse delay, μs
tau2 = 4.0      # Second inter-pulse delay, μs
tmin = 0.1  # Start time, μs

# Load the experimental data
t,Vexp = dl.deerload(path + file)

# Pre-processing
Vexp = dl.correctphase(Vexp) # Phase correction
Vexp = Vexp/np.max(Vexp)     # Rescaling (aesthetic)
t = t - t[0]                     # Account for zerotime
t = t + tmin

# Artifically truncate the signal
Vexp = Vexp[t<=3]
t = t[t<=3]

# Distance vector
r = np.arange(1.5,7,0.05) # nm

# Construct the model
Vmodel = dl.dipolarmodel(t,r, experiment=dl.ex_4pdeer(tau1,tau2, pathways=[1]))
compactness = dl.dipolarpenalty(Pmodel=None,r=r,type='compactness')

# Fit the model to the data with compactness criterion
results_with = dl.fit(Vmodel,Vexp,penalties=compactness)
print(results_with)

# Fit the model to the data without compactness criterion
results_without = dl.fit(Vmodel,Vexp)
print(results_without)

Goodness-of-fit:
========= ============= ============= ===================== =======
 Dataset   Noise level   Reduced 𝛘2    Residual autocorr.    RMSD
========= ============= ============= ===================== =======
   #1         0.005         0.741             0.005          0.004
========= ============= ============= ===================== =======
Model hyperparameters:
========================== ===================
 Regularization parameter   Penalty weight #1
========================== ===================
          0.021                   0.240
========================== ===================
Model parameters:
=========== ========= ========================= ====== ======================================
 Parameter   Value     95%-Confidence interval   Unit   Description
=========== ========= ========================= ====== ======================================
 mod         0.298     (0.295,0.301)                    Modulation depth
 reftime     0.300     (0.298,0.303)              μs    Refocusing time
 conc        153.223   (153.223,153.223)          μM    Spin concentration
 P           ...       (...,...)                 nm⁻¹   Non-parametric distance distribution
 P_scale     0.994     (0.992,0.996)             None   Normalization factor of P
=========== ========= ========================= ====== ======================================

Goodness-of-fit:
========= ============= ============= ===================== =======
 Dataset   Noise level   Reduced 𝛘2    Residual autocorr.    RMSD
========= ============= ============= ===================== =======
   #1         0.005         0.685             0.147          0.004
========= ============= ============= ===================== =======
Model hyperparameters:
==========================
 Regularization parameter
==========================
          0.025
==========================
Model parameters:
=========== ========= ========================= ====== ======================================
 Parameter   Value     95%-Confidence interval   Unit   Description
=========== ========= ========================= ====== ======================================
 mod         0.313     (0.074,0.553)                    Modulation depth
 reftime     0.299     (0.298,0.301)              μs    Refocusing time
 conc        121.992   (0.010,692.530)            μM    Spin concentration
 P           ...       (...,...)                 nm⁻¹   Non-parametric distance distribution
 P_scale     1.001     (0.963,1.038)             None   Normalization factor of P
=========== ========= ========================= ====== ======================================

# Define colors
green = '#3cb4c6'
red = '#f84862'
colors = [green,red]
plt.figure(figsize=[10,7])
for n,results in enumerate([results_with, results_without]):

    # Extract fitted dipolar signal
    Vfit = results.model

    # Extract fitted distance distribution
    Pfit = results.P
    Pci95 = results.PUncert.ci(95)
    Pci50 = results.PUncert.ci(50)

    # Extract the unmodulated contribution
    Bfcn = lambda mod,conc,reftime: results.P_scale*(1-mod)*dl.bg_hom3d(t-reftime,conc,mod)
    Bfit = results.evaluate(Bfcn)
    Bci = results.propagate(Bfcn).ci(95)

    plt.subplot(2,2,n+1)
    # Plot experimental and fitted data
    plt.plot(t,Vexp,'.',color='grey',label='Data')
    plt.plot(t,Vfit,linewidth=3,color=colors[n],label='Fit')
    plt.plot(t,Bfit,'--',linewidth=3,color=colors[n],label='Unmodulated contribution')
    plt.fill_between(t,Bci[:,0],Bci[:,1],color=colors[n],alpha=0.3)
    plt.legend(frameon=False,loc='best')
    plt.xlabel('Time $t$ (μs)')
    plt.ylabel('$V(t)$ (arb.u.)')
    plt.title('With compactness criterion' if n==0 else 'Without compactness criterion')
    # Plot the distance distribution
    plt.subplot(2,2,n+3)
    plt.plot(r,Pfit,color=colors[n],linewidth=3,label='Fit')
    plt.fill_between(r,Pci95[:,0],Pci95[:,1],alpha=0.3,color=colors[n],label='95%-Conf. Inter.',linewidth=0)
    plt.fill_between(r,Pci50[:,0],Pci50[:,1],alpha=0.5,color=colors[n],label='50%-Conf. Inter.',linewidth=0)
    plt.legend(frameon=False,loc='best')
    plt.autoscale(enable=True, axis='both', tight=True)
    plt.xlabel('Distance $r$ (nm)')
    plt.ylabel('$P(r)$ (nm$^{-1}$)')
plt.tight_layout()
plt.show()