function phi_kk = plot_SPACF(r_k,n)
% PLOT_PSACF - Plots the partial sample autocorrelation function with 2*sigma error bars
% 
% Input:
%   r_k : the sample autocorrelation functions
%   n: the number of data samples that went into computing r_k the sample autocorrelations 
% Output: 
%   phi_kk : the partial sample autocorrelations 
%   
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

%addpath( '../' ); 

phi_kk = spacf(r_k);
n_k    = length(phi_kk);

sf=figure; sh_ind=stem( 1:n_k, phi_kk, 'bx', 'linewidth', 2 ); hold on;
xlabel( 'lag (k)' ); ylabel( 'sample partial autocorrelation \phi_{kk}' ); axis tight; 

% plot the value of the standard errors of the sample autocorrelations: 
se_r_k = sqrt(1/n);

figure(sf); hold on; plot( 1:n_k, -1.97 * se_r_k * ones(1,n_k), 'r-' ); 
figure(sf); hold on; plot( 1:n_k, +1.97 * se_r_k * ones(1,n_k), 'r-' ); %axis tight; 
axis( [ 0, n_k-0.5, -Inf, +Inf ] ); 

return;