nikcleju@10: # -*- coding: utf-8 -*-
nikcleju@10: """
nikcleju@17: Algorithms for approximate analysis recovery based on synthesis solvers (a.k.a. Analysis by Synthesis, ABS).
nikcleju@17: Approximate reconstruction, ABS-mixed.
nikcleju@10: 
nikcleju@17: Author: Nicolae Cleju
nikcleju@10: """
nikcleju@17: __author__ = "Nicolae Cleju"
nikcleju@17: __license__ = "GPL"
nikcleju@17: __email__ = "nikcleju@gmail.com"
nikcleju@17: 
nikcleju@10: 
nikcleju@10: import numpy
nikcleju@17: 
nikcleju@17: # Import synthesis solvers from pyCSalgos package
nikcleju@10: import pyCSalgos.BP.l1qec
nikcleju@10: import pyCSalgos.SL0.SL0_approx
nikcleju@10: 
nikcleju@10: def bp(y,M,Omega,epsilon, x0, lbtol=1e-3, mu=10, cgtol=1e-8, cgmaxiter=200, verbose=False):
nikcleju@17:   """
nikcleju@17:   ABS-mixed: Basis Pursuit (based on l1magic toolbox)
nikcleju@17:   """  
nikcleju@10:   N,n = Omega.shape
nikcleju@10:   D = numpy.linalg.pinv(Omega)
nikcleju@10:   U,S,Vt = numpy.linalg.svd(D)
nikcleju@10:   Aeps = numpy.dot(M,D)
nikcleju@10:   Aexact = Vt[-(N-n):,:]
nikcleju@10:   
nikcleju@10:   return numpy.dot(D , pyCSalgos.BP.l1qec.l1qec_logbarrier(x0,Aeps,Aeps.T,y,epsilon,Aexact,Aexact.T,numpy.zeros(N-n), lbtol, mu, cgtol, cgmaxiter, verbose))
nikcleju@10: 
nikcleju@10: def sl0(y,M,Omega,epsilon, sigma_min, sigma_decrease_factor=0.5, mu_0=2, L=3, Aeps_pinv=None, Aexact_pinv=None, true_s=None):
nikcleju@17:   """
nikcleju@17:   ABS-mixed: Smooth L0 (SL0)
nikcleju@17:   """  
nikcleju@10:   N,n = Omega.shape
nikcleju@10:   D = numpy.linalg.pinv(Omega)
nikcleju@10:   U,S,Vt = numpy.linalg.svd(D)
nikcleju@10:   Aeps = numpy.dot(M,D)
nikcleju@10:   Aexact = Vt[-(N-n):,:]
nikcleju@10:   
nikcleju@21:   #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
nikcleju@21:   #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_robust_analysis(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
nikcleju@21:   #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis_unconstrained(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
nikcleju@21:   return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis_dai(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
nikcleju@10: