comparison scripts/ABSapprox.py @ 19:ef0629f859a3

Working approximation script

 Created on Sat Nov 05 18:08:40 2011
 
 @author: Nic
 """
 
-import numpy
+import numpy as np
 import pyCSalgos
+import pyCSalgos.GAP.GAP
+import pyCSalgos.SL0.SL0_approx
 
+# Define functions that prepare arguments for each algorithm call
 def gap_paramsetup(y,M,Omega,epsilon,lbd):
-  gapparams = dict(num_iteration = 1000,
-                   greedy_level = 0.9,
-                   stopping_coefficientstopping_coefficient_size = 1e-4,
-                   l2solver = 'pseudoinverse',
-                   noise_level = epsilon)
-  return y,M,M.T,Omega,Omega.T,gapparams,numpy.zeros(Omega.shape[1])
+  gapparams = {"num_iteration" : 1000,\
+                   "greedy_level" : 0.9,\
+                   "stopping_coefficient_size" : 1e-4,\
+                   "l2solver" : 'pseudoinverse',\
+                   "noise_level": epsilon}
+  return y,M,M.T,Omega,Omega.T,gapparams,np.zeros(Omega.shape[1])
+def sl0_paramsetup(y,M,Omega,epsilon,lbd):
+  
+  N,n = Omega.shape
+  D = np.linalg.pinv(Omega)
+  U,S,Vt = np.linalg.svd(D)
+  aggDupper = np.dot(M,D)
+  aggDlower = Vt[-(N-n):,:]
+  aggD = np.concatenate((aggDupper, lbd * aggDlower))
+  aggy = np.concatenate((y, np.zeros(N-n)))
+  
+  sigmamin = 0.1
+  return aggD,aggy,epsilon,sigmamin
 
-def omp_paramsetup(y,M,Omega,epsilon,lbd):
-  gapparams = dict(num_iteration = 1000,
-                   greedy_level = 0.9,
-                   stopping_coefficientstopping_coefficient_size = 1e-4,
-                   l2solver = 'pseudoinverse',
-                   noise_level = epsilon)
-  return y,M,M.T,Omega,Omega.T,gapparams,numpy.zeros(Omega.shape[1])
+# Define tuples (algorithm setup function, algorithm function, name)
+gap = (gap_paramsetup, pyCSalgos.GAP.GAP.GAP, 'GAP')
+sl0 = (sl0_paramsetup, pyCSalgos.SL0.SL0_approx.SL0_approx, 'SL0_approx')
 
-gap = (pyCSalgos.GAP, gap_paramsetup)
+# Main function
+def mainrun():
+
+  # Define which algorithms to run
+  algos = (gap, sl0)
+  numalgos = len(algos)
+  
+  # Set up experiment parameters
+  sigma = 2.0;
+  delta = 0.8;
+  rho   = 0.15;
+  numvects = 2; # Number of vectors to generate
+  SNRdb = 20;    # This is norm(signal)/norm(noise), so power, not energy
+
+  # Process parameters
+  noiselevel = 1 / (10^(SNRdb/10));
+  d = 50;
+  p = round(sigma*d);
+  m = round(delta*d);
+  l = round(d - rho*m);
+  
+  # Generate Omega and data based on parameters
+  Omega = pyCSalgos.GAP.GAP.Generate_Analysis_Operator(d, p);
+  # Optionally make Omega more coherent
+  #[U, S, Vt] = np.linalg.svd(Omega);
+  #Sdnew = np.diag(S) * (1+np.arange(np.diag(S).size)); % Make D coherent, not Omega!
+  #Snew = [diag(Sdnew); zeros(size(S,1) - size(S,2), size(S,2))];
+  #Omega = U * Snew * V';
+
+  # Generate data  
+  x0,y,M,Lambda,realnoise = pyCSalgos.GAP.GAP.Generate_Data_Known_Omega(Omega, d,p,m,l,noiselevel, numvects,'l0');
+
+  # Values for lambda
+  #lambdas = [0 10.^linspace(-5, 4, 10)];
+  lambdas = np.concatenate((np.array([0]), 10**np.linspace(-5, 4, 10)))
+  
+  xrec = dict()
+  err = dict()
+  relerr = dict()
+  for i,algo in zip(np.arange(numalgos),algos):
+    xrec[algo[2]]   = np.zeros((lambdas.size, d, y.shape[1]))
+    err[algo[2]]    = np.zeros((lambdas.size, y.shape[1]))
+    relerr[algo[2]] = np.zeros((lambdas.size, y.shape[1]))
+  
+  for ilbd,lbd in zip(np.arange(lambdas.size),lambdas):
+    for iy in np.arange(y.shape[1]):
+      for algosetupfunc,algofunc,strname in algos:
+        epsilon = 1.1 * np.linalg.norm(realnoise[:,iy])
+        
+        inparams = algosetupfunc(y[:,iy],M,Omega,epsilon,lbd)
+        xrec[strname][ilbd,:,iy] = algofunc(*inparams)[0]
+        
+        err[strname][ilbd,iy]    = np.linalg.norm(x0[:,iy] - xrec[strname][ilbd,:,iy])
+        relerr[strname][ilbd,iy] = err[strname][ilbd,iy] / np.linalg.norm(x0[:,iy])
+        
+    print 'Lambda = ',lbd,' :'
+    for strname in relerr:
+      print '   ',strname,' : avg relative error = ',np.mean(relerr[strname][ilbd,:])
 
 
 
-gap = (pyCSalgos.GAP, gap_paramsetup)
-  
-
-
-
-def mainrun():
-  
-  algos = (gap, sl0)
-  
-  for algofunc,paramsetup in algos:
-    xrec = algofunc(algosetup(y, Omega, epsilon, lbd))
+# Script main
+if __name__ == "__main__":
+  mainrun()