#$=head1 NAME
#$
#$irls  - weighting functions 
#$
#$=head1 SYNOPSIS
#$
#$C<ierr=l1(res,weight)>
#$
#$C<ierr=cauchy(res,weight)>
#$
#$=head1 PARAMETERS
#$
#$=over 4
#$
#$=item res  -  C<real(:)>  
#$
#$      Residual
#$
#$=item weight  -  C<real(:)>  
#$
#$      Resulting weighting function
#$
#$=back
#$
#$=head1 DESCRIPTION
#$
#$Weighting function to apply to cgmethods (warning stability
#$is not guaranteed when using these).
#$
#$L1 -  weight=1/abs(1+ res/rbar)
#$CAUCHY- weight=1/sqrt(1+res/rbar**2)
#$
#$
#$=head1 SEE ALSO
#$
#$L<solver>
#$
#$=head1 LIBRARY
#$
#$B<geef90>
#$
#$=cut
module irls {
  use quantile_mod
contains
  integer function l1 (res, weight)  {
    real, dimension (:)  :: res, weight
    real                 :: rbar
    rbar = quantile( int( 0.5*size(res)), abs (res))            # median
    weight = 1. / sqrt( sqrt (1. + (res/rbar)**2));   l1 = 0
    }
  integer function cauchy (res, weight)  {
    real, dimension (:)  :: res, weight
    real                 :: rbar
    rbar = quantile( int( 0.5*size(res)), abs (res))             # median
    weight = 1. / sqrt (1. + (res/rbar)**2);          cauchy = 0
    }
}