annotate pyCSalgos/TST/RecommendedTST.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.

import numpy as np
import math

#function beta = RecommendedTST(X,Y, nsweep,tol,xinitial,ro)
def RecommendedTST(X, Y, nsweep=300, tol=0.00001, xinitial=None, ro=None):

  # function beta=RecommendedTST(X,y, nsweep,tol,xinitial,ro)
  # This function gets the measurement matrix and the measurements and
  # the number of runs and applies the TST algorithm with optimally tuned parameters
  # to the problem. For more information you may refer to the paper,
  # "Optimally tuned iterative reconstruction algorithms for compressed
  # sensing," by Arian Maleki and David L. Donoho. 
  #           X  : Measurement matrix; We assume that all the columns have
  #               almost equal $\ell_2$ norms. The tunning has been done on
  #               matrices with unit column norm. 
  #            y : output vector
  #       nsweep : number of iterations. The default value is 300.
  #          tol : if the relative prediction error i.e. ||Y-Ax||_2/ ||Y||_2 <
  #               tol the algorithm will stop. If not provided the default
  #               value is zero and tha algorithm will run for nsweep
  #               iterations. The Default value is 0.00001.
  #     xinitial : This is an optional parameter. It will be used as an
  #                initialization of the algorithm. All the results mentioned
  #                in the paper have used initialization at the zero vector
  #                which is our default value. For default value you can enter
  #                0 here. 
  #        ro    : This is a again an optional parameter. If not given the
  #                algorithm will use the default optimal values. It specifies
  #                the sparsity level. For the default value you may also used if
  #                rostar=0;
  #
  # Outputs:
  #      beta : the estimated coeffs.
  #
  # References:
  # For more information about this algorithm and to find the papers about
  # related algorithms like CoSaMP and SP please refer to the paper mentioned 
  # above and the references of that paper.
  #
  #---------------------
  # Original Matab code:
  #        
  #colnorm=mean((sum(X.^2)).^(.5));
  #X=X./colnorm;
  #Y=Y./colnorm;
  #[n,p]=size(X);
  #delta=n/p;
  #if nargin<3
  #    nsweep=300;
  #end
  #if nargin<4
  #    tol=0.00001;
  #end
  #if nargin<5 | xinitial==0
  #    xinitial = zeros(p,1);
  #end
  #if nargin<6 | ro==0
  #    ro=0.044417*delta^2+ 0.34142*delta+0.14844;
  #end
  #
  #
  #k1=floor(ro*n);
  #k2=floor(ro*n);
  #
  #
  ##initialization
  #x1=xinitial;
  #I=[];
  #
  #for sweep=1:nsweep
  #    r=Y-X*x1;
  #    c=X'*r;
  #    [csort, i_csort]=sort(abs(c));
  #    I=union(I,i_csort(end-k2+1:end));
  #    xt = X(:,I) \ Y;
  #    [xtsort, i_xtsort]=sort(abs(xt));
  #
  #    J=I(i_xtsort(end-k1+1:end));
  #    x1=zeros(p,1);
  #    x1(J)=xt(i_xtsort(end-k1+1:end));
  #    I=J;
  #    if norm(Y-X*x1)/norm(Y)<tol
  #        break
  #    end
  #
  #end
  #
  #beta=x1;
  #
  # End of original Matab code
  #----------------------------
  
  #colnorm=mean((sum(X.^2)).^(.5));
  colnorm = np.mean(np.sqrt((X**2).sum(0)))
  X = X / colnorm
  Y = Y / colnorm
  [n,p] = X.shape
  delta = float(n) / p
  #  if nargin<3
  #      nsweep=300;
  #  end
  #  if nargin<4
  #      tol=0.00001;
  #  end
  #  if nargin<5 | xinitial==0
  #      xinitial = zeros(p,1);
  #  end
  #  if nargin<6 | ro==0
  #      ro=0.044417*delta^2+ 0.34142*delta+0.14844;
  #  end
  if xinitial is None:
    xinitial = np.zeros(p)
  if ro == None:
    ro = 0.044417*delta**2 + 0.34142*delta + 0.14844
  
  k1 = math.floor(ro*n)
  k2 = math.floor(ro*n)
  
  #initialization
  x1 = xinitial.copy()
  I = []
  
  for sweep in np.arange(nsweep):
      r = Y - np.dot(X,x1)
      c = np.dot(X.T, r)
      #[csort, i_csort] = np.sort(np.abs(c))
      i_csort = np.argsort(np.abs(c))
      #I = numpy.union1d(I , i_csort(end-k2+1:end))
      I = np.union1d(I , i_csort[-k2:])
      #xt = X[:,I] \ Y
      # Make sure X[:,np.int_(I)] is a 2-dimensional matrix even if I has a single value (and therefore yields a column)
      if I.size is 1:
        a = np.reshape(X[:,np.int_(I)],(X.shape[0],1))
      else:
        a = X[:,np.int_(I)]
      xt = np.linalg.lstsq(a, Y)[0]
      #[xtsort, i_xtsort] = np.sort(np.abs(xt))
      i_xtsort = np.argsort(np.abs(xt))
  
      J = I[i_xtsort[-k1:]]
      x1 = np.zeros(p)
      x1[np.int_(J)] = xt[i_xtsort[-k1:]]
      I = J.copy()
      if np.linalg.norm(Y-np.dot(X,x1)) / np.linalg.norm(Y) < tol:
          break
      #end
      
  #end
  
  return x1.copy()