comparison pyCSalgos/SL0/SL0_approx.py @ 15:0d66a0aafb39

SL0_approx test working

+# -*- coding: utf-8 -*-
+"""
+Created on Sat Nov 05 21:29:09 2011
+
+@author: Nic
+"""
+
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Nov 05 18:39:54 2011
+
+@author: Nic
+"""
+
+import numpy as np
+
+#function s=SL0(A, x, sigma_min, sigma_decrease_factor, mu_0, L, A_pinv, true_s)
+def SL0_approx(A, x, eps, sigma_min, sigma_decrease_factor=0.5, mu_0=2, L=3, A_pinv=None, true_s=None):
+  
+  if A_pinv is None:
+    A_pinv = np.linalg.pinv(A)
+  
+  if true_s is not None:
+      ShowProgress = True
+  else:
+      ShowProgress = False
+  
+  # Initialization
+  #s = A\x;
+  s = np.dot(A_pinv,x)
+  sigma = 2.0 * np.abs(s).max()
+  
+  # Main Loop
+  while sigma>sigma_min:
+      for i in np.arange(L):
+          delta = OurDelta(s,sigma)
+          s = s - mu_0*delta
+          # At this point, s no longer exactly satisfies x = A*s
+          # The original SL0 algorithm projects s onto {s | x = As} with
+          # s = s - np.dot(A_pinv,(np.dot(A,s)-x))   # Projection
+          # We want to project s onto {s | |x-As| < eps}
+          # We move onto the direction -A_pinv*(A*s-x), but only with a
+          # smaller step:
+          direction = np.dot(A_pinv,(np.dot(A,s)-x))
+          if (np.linalg.norm(np.dot(A,direction)) >= eps):
+            s = s - (1.0 - eps/np.linalg.norm(np.dot(A,direction))) * direction
+
+          #assert(np.linalg.norm(x - np.dot(A,s)) < eps + 1e-6)          
+      
+      if ShowProgress:
+          #fprintf('     sigma=#f, SNR=#f\n',sigma,estimate_SNR(s,true_s))
+          string = '     sigma=%f, SNR=%f\n' % sigma,estimate_SNR(s,true_s)
+          print string
+      
+      sigma = sigma * sigma_decrease_factor
+  
+  return s
+  
+  
+####################################################################
+#function delta=OurDelta(s,sigma)
+def OurDelta(s,sigma):
+  
+  return s * np.exp( (-np.abs(s)**2) / sigma**2)
+  
+####################################################################
+#function SNR=estimate_SNR(estim_s,true_s)
+def estimate_SNR(estim_s, true_s):
+  
+  err = true_s - estim_s
+  return 10*np.log10((true_s**2).sum()/(err**2).sum())
+