PDFs: revamped as used in Thesis

simulations/12_noise_phase.py

@@ -13,6 +13,7 @@ import scipy.stats as stat
 from scipy import special
 
 from lib.util import MethodMappingProxy as MethodProxy
+from lib.ft_plot import axis_pi_ticker
 
 def expectation(x,pdfx):
     dx = x[1]-x[0]
@@ -48,6 +49,23 @@ def amplitude_distribution_gauss(a,sigma,s):
     k=s/sigma
     return (2*np.pi)**-0.5*np.exp(-((a-s)/sigma)**2/2)
 
+
+figsize = (8,6)
+if True:
+        from matplotlib import rcParams
+        #rcParams["text.usetex"] = True
+        rcParams["font.family"] = "serif"
+        plt.rc('lines',lw=2)
+        if True:# small
+            figsize = (6, 4)
+            rcParams["font.size"] = "15" # 15 at 6,4 looks fine
+        elif True: # large
+            figsize = (9, 6)
+            rcParams["font.size"] = "16" # 15 at 9,6 looks fine
+        rcParams["grid.linestyle"] = 'dotted'
+        rcParams["figure.figsize"] = figsize
+
+
 signal_max= 4
 amp_max = signal_max*2
 thetas = np.linspace(-np.pi,np.pi,500)
@@ -58,14 +76,14 @@ sigma = 1
 
 ## figure 1
 if True:
-    fig, ax = plt.subplots(1,2,figsize=(2*8,1*8))
+    fig, ax = plt.subplots(1,2,figsize=(2*figsize[0],figsize[1]))
-    _fig1, _ax0 =plt.subplots(1,1, figsize=(1*8, 1*8))
+    _fig1, _ax0 =plt.subplots(1,1)
-    _fig2, _ax1 =plt.subplots(1,1, figsize=(1*8, 1*8))
+    _fig2, _ax1 =plt.subplots(1,1)
 
     ax0 = MethodProxy(ax[0], _ax0)
     ax1 = MethodProxy(ax[1], _ax1)
     for s in signals:
-        pdfs_label='s/$\sigma$ ='+str(s)
+        pdfs_label='s = '+str(int(s))
         phase_vals= phase_distribution(thetas,sigma,s)
         amp_vals= amplitude_distribution(amplitudes,sigma,s)
         phase_vals_g = phase_distribution_gauss(thetas,sigma,s)
@@ -73,13 +91,16 @@ if True:
         ax0.plot(amplitudes,amp_vals, label=pdfs_label)
         ax1.plot(thetas,phase_vals,   label=pdfs_label)
     ax0.legend()
+    ax0.set_xlabel(r'Amplitude $a$')
+    ax0.set_ylabel(r'$p(a)$')
+
+    ax1.set_xlabel(r'Phase $\varphi$')
+    ax1.set_ylabel(r'$p(\varphi)$')
     _ax1.legend()# only in the separate figure
-    ax0.set_xlabel(r'$a$')
+    [ axis_pi_ticker(ax.xaxis, major_divider=3) for ax in ax1.elements ]
-    ax0.set_xlabel(r'$\theta$')
+
-    ax1.set_ylabel(r'$p(a)$')
+    for a in [ax0, ax1]:
-    ax1.set_ylabel(r'$p(\theta)$')
+        a.grid()
-    # ax[0].grid()
-    # ax[1].grid()
     MethodProxy(fig, _fig1, _fig2).tight_layout()
 
     fig.savefig('pdfs.pdf')
@@ -92,7 +113,7 @@ if True:
 ## figure 2
 amplitudes = np.linspace(0,amp_max*5,500)
 signals = np.linspace(0.1,signal_max*5,101)
-if False:
+if True:
     V_theta = [variance(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
     E_theta=[expectation(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
     V_theta_g = [variance(thetas,phase_distribution_gauss(thetas,sigma,s)) for s in signals ]
@@ -102,17 +123,17 @@ if False:
     V_a_g = [variance(amplitudes,amplitude_distribution_gauss(amplitudes,sigma,s)) for s in signals ]
     E_a_g=[expectation(amplitudes,amplitude_distribution_gauss(amplitudes,sigma,s)) for s in signals ]
 
-    fig2, _ax2 = plt.subplots(2,2,figsize=(2*8,2*8))
+    fig2, _ax2 = plt.subplots(2,2,figsize=(2*figsize[0],2*figsize[1]))
     ax2 = fig2.get_axes()
     if True:
         _figs = []
         _axs = []
-        for i, ax in enumerate(_ax2):
+        for i, ax in enumerate(ax2):
-            _f, _a = plt.subplots(1,1, figsize=(1*8, 1*8))
+            _f, _a = plt.subplots(1,1)
             _figs.append(_f)
             _axs.append(_a)
 
-            ax2[i] = MethodProxy(ax2[0], _a)
+            ax2[i] = MethodProxy(ax, _a)
 
     ax2[0].plot(signals,E_a,label='$p(a)$')
     ax2[0].plot(signals,E_a_g,ls='dashed',label='Gaussian approx.')
@@ -125,17 +146,17 @@ if False:
     ax2[1].set_xscale('log')
     ax2[1].set_ylabel('$\sigma_a^2$')
 
-    ax2[2].plot(signals,E_theta,label=r'$p(\theta)$')
+    ax2[2].plot(signals,E_theta,label=r'$p(\varphi)$')
     ax2[2].plot(signals,E_theta_g,ls='dashed',label='Gaussian approx.')
     ax2[2].set_xscale('log')
     ax2[2].set_ylim(-1.1,1.1)
-    ax2[2].set_ylabel(r'$\mu_\theta$')
+    ax2[2].set_ylabel(r'$\mu_\varphi$')
 
-    ax2[3].plot(signals,V_theta,label=r'$p(\theta)$')
+    ax2[3].plot(signals,V_theta,label=r'$p(\varphi)$')
     ax2[3].plot(signals,V_theta_g,ls='dashed',label='Gaussian approx.')
     ax2[3].set_xscale('log')
     ax2[3].set_yscale('log')
-    ax2[3].set_ylabel(r'$\sigma_\theta^2$')
+    ax2[3].set_ylabel(r'$\sigma_\varphi^2$')
     for a in ax2:
         a.grid(which='both')
         a.set_xlabel(r'$s/\sigma$')
@@ -150,12 +171,14 @@ if False:
                 'phase_mean',
                 'phase_sigma',
             ][i]
+
+        _f.tight_layout()
         _f.savefig(fnames+'.pdf')
         plt.close(_f)
 
 ## figure 3, beacon timing accuracy
 if True:
-    fig3, ax3 = plt.subplots(1,1,figsize=(1*8,1*8))
+    fig3, ax3 = plt.subplots(1,1)
     ax3 = fig3.get_axes()
     sigma_t = [variance(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
     lfs=np.linspace(np.log10(50.),4,1)