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+# exercise 3.2.1
+
+from __future__ import print_function
+from pylab import *
+from scipy.io import loadmat
+from similarity import similarity
+
+# Image to use as query
+i = 635
+
+# Similarity: 'SMC', 'Jaccard', 'ExtendedJaccard', 'Cosine', 'Correlation' 
+similarity_measure = 'jaccard'
+
+# Load the CBCL face database
+# Load Matlab data file to python dict structure
+X = loadmat('./Data/wildfaces_grayscale.mat')['X']
+N, M = shape(X)
+
+
+# Search the face database for similar faces
+# Index of all other images than i
+noti = range(0,i) + range(i+1,N) 
+# Compute similarity between image i and all others
+sim = similarity(X[i,:], X[noti,:], similarity_measure)
+sim = sim.tolist()[0]
+# Tuples of sorted similarities and their indices
+sim_to_index = sorted(zip(sim,noti))
+
+
+# Visualize query image and 5 most/least similar images
+figure(figsize=(12,8))
+subplot(3,1,1)
+imshow(np.reshape(X[i],(40,40)).T, cmap=cm.gray)
+xticks([]); yticks([])
+title('Query image')
+ylabel('image #{0}'.format(i))
+
+
+for ms in range(5):
+
+    # 5 most similar images found
+    subplot(3,5,6+ms)
+    im_id = sim_to_index[-ms-1][1]
+    im_sim = sim_to_index[-ms-1][0]
+    imshow(np.reshape(X[im_id],(40,40)).T, cmap=cm.gray)
+    xlabel('sim={0:.3f}'.format(im_sim))
+    ylabel('image #{0}'.format(im_id))
+    xticks([]); yticks([])
+    if ms==2: title('Most similar images')
+
+    # 5 least similar images found
+    subplot(3,5,11+ms)
+    im_id = sim_to_index[ms][1]
+    im_sim = sim_to_index[ms][0]
+    imshow(np.reshape(X[im_id],(40,40)).T, cmap=cm.gray)
+    xlabel('sim={0:.3f}'.format(im_sim))
+    ylabel('image #{0}'.format(im_id))
+    xticks([]); yticks([])
+    if ms==2: title('Least similar images')
+    
+show()
+
+# 1.3.1
+# For any two similarity measures, the five least similar are quite different.
+# Based on the five most similar images, SMC and Jaccard produce similar 
+# results. Correlation and Cosine produce some similar results.
+# Using image 2 it is clear that SMC and ExtendedJaccard are sensitive to 
+# lighting conditions, and thus maybe not a very good choice to compare faces.
+# Also Correlation seems a little sensitive to this. Lastly Cosine seems to 
+# recognise faces somewhat better than Jaccard (take e.g. #635).
+
+# 1.3.2
+measures = {'Cosine': 'cos', 'ExtJac': 'ext', 'Correl': 'cor'}
+scalar = 0.5        # Note: pick from (0,1), values > 1 aren't handled nicely
+translation = 0.1   # Note: pick a small value, for similar reasons
+
+# Round list to resist numerical variances (hint #2)
+X = np.around(X, decimals = 4)
+
+for name, measure in measures.iteritems():
+    sim1 = similarity(scalar * X[i,:], X[noti,:], measure)
+    sim2 = similarity(X[i,:], X[noti,:], measure)
+    print("Scalar,", name, ":", (sim1 == sim2).all())
+
+for name, measure in measures.iteritems():    
+    sim1 = similarity(translation + X[i,:], X[noti,:], measure)
+    sim2 = similarity(X[i,:], X[noti,:], measure)
+    print("Translation,", name, ":", (sim1 == sim2).any())