Updated material on Boltzmann Machines

doc/src/BoltzmannMachines/figures/RMBenergy.dat

@@ -0,0 +1,100 @@
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+2 5.38551
+3 5.14253
+4 4.92049
+5 4.80505
+6 4.62185
+7 4.48617
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+37 3.2945
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doc/src/BoltzmannMachines/figures/plot.py

@@ -0,0 +1,14 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from IPython.display import display
+
+data = np.loadtxt('RMBenergy.dat')
+x = data[:,0]
+y = data[:,1]
+plt.plot(x, y,'ro')
+plt.axis([0,101,3, 5.5])
+plt.xlabel(r'Iterations')
+plt.ylabel(r'Energy')
+plt.savefig('MLrbm.pdf')
+plt.show()
+

doc/src/BoltzmannMachines/figures/plotEnergies.py

@@ -0,0 +1,61 @@
+import sys
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
+try:
+    dataFileName = sys.argv[1]
+except IndexError:
+    print("USAGE: python plotEnergies.py 'filename'")
+    sys.exit(0)
+
+HFEnergy3 = 3.161921401722216
+HFEnergy6 = 20.71924844033019
+
+numParticles = \
+        int(dataFileName[dataFileName.find('N')+1:dataFileName.find('E')-1])
+hfenergyFound = False 
+if (numParticles == 2):
+    HFEnergy = 3.161921401722216
+    hfenergyFound = True 
+elif (numParticles == 6):
+    HFEnergy = 20.71924844033019
+    hfenergyFound = True 
+else:
+    hfenergyFound = False
+
+data = np.loadtxt(dataFileName, dtype=np.float64)
+data[:,1] = np.sqrt(data[:,1])
+
+n = len(data[:,0])
+x = np.arange(0,n)
+
+fig = plt.figure()
+
+if (hfenergyFound):
+    yline = np.zeros(n)
+    yline.fill(HFEnergy)
+    plt.plot(x, yline, 'r--', label="HF Energy")
+
+msize = 1.0
+
+ax = fig.add_subplot(111)
+plt.errorbar(x, data[:,0], yerr=data[:,1],  fmt='bo', markersize=msize, label="VMC Energy")
+plt.fill_between(x, data[:,0]-data[:,1], data[:,0]+data[:,1])
+
+plt.xlim(0,n)
+plt.xlabel('Iteration')
+plt.ylabel('$E_0[a.u]$')
+plt.legend(loc='best')
+
+minSub = 80
+maxSub = 120
+inset_axes(ax, width="50%", height=1.0, loc='right')
+plt.errorbar(x[minSub:maxSub], data[minSub:maxSub,0],
+        yerr=data[minSub:maxSub,1],  fmt='bo', markersize=msize, label="VMC "
+        "Energy")
+plt.plot(x[minSub:maxSub], yline[minSub:maxSub], 'r--', label="HF Energy")
+
+plt.show()

doc/src/BoltzmannMachines/figures/w1.0_D2_N2_Energies.txt

@@ -0,0 +1,177 @@
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doc/src/BoltzmannMachines/figures/w1.0_D2_N6_Energies.txt

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+20.5669439415781490 0.0000049830446496
+20.6335521716793480 0.0000046144492603
+20.5638810257340126 0.0000039096450386
+20.6051042593020171 0.0000050314968488
+20.5952826593208194 0.0000048466091870
+20.5840129254583317 0.0000049386436539
+20.5622424462287334 0.0000047054311204
+20.5364652378096295 0.0000054576819159
+20.6199917186743171 0.0000046400213180
+20.5850044296868262 0.0000045104364483
+20.6067500420065883 0.0000047907162541
+20.5942250212876736 0.0000045392646495

doc/src/BoltzmannMachines/src/Hudson_Bay.csv

@@ -0,0 +1,22 @@
+Year,Hares (x1000),Lynx (x1000)
+1900,30.0,4.0
+1901,47.2,6.1
+1902,70.2,9.8
+1903,77.4,35.2
+1904,36.3,59.4
+1905,20.6,41.7
+1906,18.1,19.0
+1907,21.4,13.0
+1908,22.0,8.3
+1909,25.4,9.1
+1910,27.1,7.4
+1911,40.3,8.0
+1912,57,12.3
+1913,76.6,19.5
+1914,52.3,45.7
+1915,19.5,51.1
+1916,11.2,29.7
+1917,7.6,15.8
+1918,14.6,9.7
+1919,16.2,10.1
+1920,24.7,8.6

doc/src/BoltzmannMachines/src/Hudson_Bay.py

@@ -0,0 +1,43 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def solver(m, H0, L0, dt, a, b, c, d, t0):
+    """Solve the difference equations for H and L over m years
+    with time step dt (measured in years."""
+
+    num_intervals = int(m/float(dt))
+    t = np.linspace(t0, t0 + m, num_intervals+1)
+    H = np.zeros(t.size)
+    L = np.zeros(t.size)
+
+    print('Init:', H0, L0, dt)
+    H[0] = H0
+    L[0] = L0
+
+    for n in range(0, len(t)-1):
+        H[n+1] = H[n] + a*dt*H[n] - b*dt*H[n]*L[n]
+        L[n+1] = L[n] + d*dt*H[n]*L[n] - c*dt*L[n]
+    return H, L, t
+
+# Load in data file
+data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1)
+# Make arrays containing x-axis and hares and lynx populations
+t_e = data[:,0]
+H_e = data[:,1]
+L_e = data[:,2]
+
+# Simulate using the model
+H, L, t = solver(m=20, H0=34.91, L0=3.857, dt=0.1,
+                 a=0.4807, b=0.02482, c=0.9272, d=0.02756,
+                 t0=1900)
+
+# Visualize simulations and data
+plt.plot(t_e, H_e, 'b-+', t_e, L_e, 'r-o', t, H, 'm--', t, L, 'k--')
+plt.xlabel('Year')
+plt.ylabel('Numbers of hares and lynx')
+plt.axis([1900, 1920, 0, 140])
+plt.title(r'Population of hares and lynx 1900-1920 (x1000)')
+plt.legend(('H_e', 'L_e', 'H', 'L'), loc='upper left')
+plt.savefig('Hudson_Bay_sim.pdf')
+plt.savefig('Hudson_Bay_sim.png')
+plt.show()