annotate pyCSalgos/SL0/SL0_approx.py @ 60:a7082bb22644

Modified structure:should keep in this repo only the bare solvers. Anything related to Analysis should be moved to ABS repository.

Renamed RecomTST to TST, renamed lots of functions, removed Analysis.py and algos.py.

# -*- 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

# Direct approximate analysis-based version of SL0
# Solves argimn_gamma ||gamma||_0 such that ||x - Aeps*gamma|| < eps AND ||Aexact*gamma|| = 0
# Basically instead of having a single A, we now have one Aeps which is up to eps error
#  and an Axeact which requires exact orthogonality
# It is assumed that the rows of Aexact are orthogonal to the rows of Aeps
def SL0_approx_analysis(Aeps, Aexact, x, eps, sigma_min, sigma_decrease_factor=0.5, mu_0=2, L=3, Aeps_pinv=None, Aexact_pinv=None, true_s=None):
  
  if Aeps_pinv is None:
    Aeps_pinv = np.linalg.pinv(Aeps)
  if Aexact_pinv is None:
    Aexact_pinv = np.linalg.pinv(Aexact)
    
  if true_s is not None:
      ShowProgress = True
  else:
      ShowProgress = False
  
  # Initialization
  #s = A\x;
  s = np.dot(Aeps_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-AEPS*s|<eps AND |Aexact*s|=0}
          # First:   make s orthogonal to Aexact (|Aexact*s|=0)
          # Second:  move onto the direction -A_pinv*(A*s-x), but only with a smaller step:
          # This separation assumes that the rows of Aexact are orthogonal to the rows of Aeps
          #
          # 1. Make s orthogonal to Aexact:
          #     s = s - Aexact_pinv * Aexact * s
          s = s - np.dot(Aexact_pinv,(np.dot(Aexact,s)))
          # 2. Move onto the direction -A_pinv*(A*s-x), but only with a smaller step:
          direction = np.dot(Aeps_pinv,(np.dot(Aeps,s)-x))
          if (np.linalg.norm(np.dot(Aeps,direction)) >= eps):
            s = s - (1.0 - eps/np.linalg.norm(np.dot(Aeps,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())