Initialization example

Reproducibility/Lipschitz/fig_initialization.py

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+import numpy as np
+import psdr 
+from psdr.pgf import PGF
+import matplotlib.pyplot as plt
+import seaborn as sns
+
+from joblib import Parallel, delayed
+from joblib import Memory
+memory = Memory('.cache', verbose = False)
+
+
+m = 2			# Dimension
+domain = psdr.BoxDomain(-np.ones(m), np.ones(m))
+M = 15  		# number of points in the design
+L = np.eye(m)	# Lipschitz matrix
+
+
+@memory.cache
+def score_design(Xhat):
+	V = psdr.voronoi_vertex(domain, Xhat, L)
+	D = psdr.cdist(Xhat, V, L)
+	return np.max(np.min(D, axis= 0))
+
+@memory.cache
+def random_design(seed):
+	np.random.seed(seed)
+	return domain.sample(M)
+
+@memory.cache
+def random_minimax_design(seed):
+	Xhat = random_design(seed)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+@memory.cache
+def coffeehouse_design(seed):
+	np.random.seed(seed)
+	return psdr.maximin_coffeehouse(domain, M, L = L)	
+
+@memory.cache
+def coffeehouse_maximin_design(seed):
+	Xhat = coffeehouse_design(seed)
+	return psdr.maximin_block(domain, M, L = L, Xhat = Xhat, maxiter = 100, verbose = True) 
+
+@memory.cache
+def random_maximin_design(seed):
+	Xhat = random_design(seed)
+	return psdr.maximin_block(domain, M, L = L, Xhat = Xhat, maxiter = 100, verbose = True) 
+
+@memory.cache
+def coffeehouse_minimax_design(seed):
+	Xhat = coffeehouse_design(seed)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+@memory.cache
+def coffeehouse_maximin_minimax_design(seed):
+	Xhat = coffeehouse_maximin_design(seed)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+@memory.cache
+def random_maximin_minimax_design(seed):
+	Xhat = random_maximin_design(seed)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+
+@memory.cache
+def coffeehouse_maximin_scale_minimax_design(seed):
+	Xhat = coffeehouse_maximin_design(seed)
+	Xhat = psdr.minimax_scale(domain, Xhat, L = L)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+@memory.cache
+def coffeehouse_scale_minimax_design(seed):
+	Xhat = coffeehouse_design(seed)
+	Xhat = psdr.minimax_scale(domain, Xhat, L = L)
+	Xhat = psdr.minimax_lloyd(domain, M, L = L, maxiter = 100, full = True, Xhat = Xhat, verbose = True)
+	return Xhat
+
+
+# Actually run some code
+seeds = np.arange(100)
+
+random_score = [score_design(random_design(seed)) for seed in seeds]
+coffeehouse_score = [score_design(coffeehouse_design(seed)) for seed in seeds]
+random_minimax_score = [score_design(random_minimax_design(seed)) for seed in seeds]
+coffeehouse_minimax_score = [score_design(coffeehouse_minimax_design(seed)) for seed in seeds]
+coffeehouse_maximin_minimax_score = [score_design(coffeehouse_maximin_minimax_design(seed)) for seed in seeds]
+coffeehouse_maximin_scale_minimax_score = [score_design(coffeehouse_maximin_scale_minimax_design(seed)) for seed in seeds]
+random_maximin_minimax_score = [score_design(random_maximin_minimax_design(seed)) for seed in seeds]
+
+# 
+data = [
+		random_minimax_score,
+		random_maximin_minimax_score,
+		coffeehouse_minimax_score, 
+		coffeehouse_maximin_minimax_score,
+		coffeehouse_maximin_scale_minimax_score,
+	]
+
+sns.set_style('whitegrid')
+#ax = sns.violinplot(data = data, inner = None)
+ax = sns.swarmplot(data = data)
+ax.set_xticklabels([
+	'random \n→ minimax', 
+	'random \n→ maximin \n→ minimax', 
+	'coffeehouse \n→ minimax', 
+	'coffeehouse \n→ maximin \n→ minimax', 
+	'coffeehouse \n→ maximin \n→ scale \n→ minimax',])
+
+names = ['random_minimax',
+	'random_maximin_minimax', 
+	'coffeehouse_minimax',
+	'coffeehouse_maximin_minimax',
+	'coffeehouse_maximin_scale_minimax',
+	]
+
+for coll, name in zip(ax.collections, names):
+	x, y = np.array(coll.get_offsets()).T
+	print(x)
+	print(y)
+	pgf = PGF()
+	pgf.add('x', x)
+	pgf.add('y', y)
+	pgf.write('data/fig_initialization_%s.dat' % name)
+
+best = np.min(np.hstack(data))
+print(best)
+ax.axhline(best, color = 'k')
+
+ax.set_xlabel('method')
+ax.set_ylabel('minimax distance')
+plt.show()