178 lines
8.5 KiB
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178 lines
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<title>Description of UnivariateSpectralDensity</title>
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > UnivariateSpectralDensity.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>UnivariateSpectralDensity
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>stephane.adjemian@ens.fr</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function [omega,f] = UnivariateSpectralDensity(dr,var_list) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment"> stephane.adjemian@ens.fr
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This function computes the theoretical spectral density of each
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endogenous variable declared in var_list. Results are stored in
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oo_ and may be plotted.
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Adapted from th_autocovariances.m.</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="kalman_transition_matrix.html" class="code" title="function [A,B] = kalman_transition_matrix(dr)">kalman_transition_matrix</a> makes transition matrices out of ghx and ghu for Kalman filter</li><li><a href="lyapunov_symm.html" class="code" title="function [x,ns_var]=lyapunov_symm(a,b)">lyapunov_symm</a> solves x-a*x*a'=b for b (and then x) symmetrical</li></ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="stoch_simul.html" class="code" title="function info=stoch_simul(var_list)">stoch_simul</a> Copyright (C) 2001 Michel Juillard</li></ul>
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<!-- crossreference -->
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <span class="comment">% stephane.adjemian@ens.fr</span>
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0002 <a name="_sub0" href="#_subfunctions" class="code">function [omega,f] = UnivariateSpectralDensity(dr,var_list)</a>
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0003 <span class="comment">% This function computes the theoretical spectral density of each</span>
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0004 <span class="comment">% endogenous variable declared in var_list. Results are stored in</span>
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0005 <span class="comment">% oo_ and may be plotted.</span>
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0006 <span class="comment">%</span>
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0007 <span class="comment">% Adapted from th_autocovariances.m.</span>
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0008 <span class="keyword">global</span> options_ oo_ M_
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0009
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0010 omega = []; f = [];
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0011
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0012 <span class="keyword">if</span> options_.order > 1
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0013 disp(<span class="string">'UnivariateSpectralDensity :: I Cannot compute the theoretical spectral density'</span>)
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0014 disp(<span class="string">'with a second order approximation of the DSGE model!'</span>)
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0015 disp(<span class="string">'Set order = 1.'</span>)
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0016 <span class="keyword">return</span>
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0017 <span class="keyword">end</span>
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0018
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0019 pltinfo = 1;<span class="comment">%options_.SpectralDensity.Th.plot;</span>
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0020 cutoff = 100;<span class="comment">%options_.SpectralDensity.Th.cutoff;</span>
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0021 sdl = 0.1;<span class="comment">%options_.SepctralDensity.Th.sdl;</span>
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0022 omega = (0:sdl:pi)';
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0023 GridSize = length(omega);
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0024 exo_names_orig_ord = M_.exo_names_orig_ord;
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0025 <span class="keyword">if</span> sscanf(version(<span class="string">'-release'</span>),<span class="string">'%d'</span>) < 13
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0026 warning off
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0027 <span class="keyword">else</span>
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0028 eval(<span class="string">'warning off MATLAB:dividebyzero'</span>)
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0029 <span class="keyword">end</span>
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0030 <span class="keyword">if</span> nargin<2
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0031 var_list = [];
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0032 <span class="keyword">end</span>
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0033 nvar = size(var_list,1);
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0034 <span class="keyword">if</span> nvar == 0
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0035 nvar = length(dr.order_var);
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0036 ivar = [1:nvar]';
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0037 <span class="keyword">else</span>
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0038 ivar=zeros(nvar,1);
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0039 <span class="keyword">for</span> i=1:nvar
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0040 i_tmp = strmatch(var_list(i,:),M_.endo_names,<span class="string">'exact'</span>);
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0041 <span class="keyword">if</span> isempty(i_tmp)
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0042 error ([<span class="string">'One of the variable specified does not exist'</span>]) ;
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0043 <span class="keyword">else</span>
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0044 ivar(i) = i_tmp;
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0045 <span class="keyword">end</span>
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0046 <span class="keyword">end</span>
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0047 <span class="keyword">end</span>
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0048 f = zeros(nvar,GridSize);
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0049 ghx = dr.ghx;
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0050 ghu = dr.ghu;
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0051 npred = dr.npred;
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0052 nstatic = dr.nstatic;
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0053 kstate = dr.kstate;
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0054 order = dr.order_var;
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0055 iv(order) = [1:length(order)];
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0056 nx = size(ghx,2);
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0057 ikx = [nstatic+1:nstatic+npred];
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0058 A = zeros(nx,nx);
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0059 k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
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0060 i0 = find(k0(:,2) == M_.maximum_lag+1);
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0061 i00 = i0;
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0062 n0 = length(i0);
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0063 A(i0,:) = ghx(ikx,:);
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0064 AS = ghx(:,i0);
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0065 ghu1 = zeros(nx,M_.exo_nbr);
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0066 ghu1(i0,:) = ghu(ikx,:);
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0067 <span class="keyword">for</span> i=M_.maximum_lag:-1:2
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0068 i1 = find(k0(:,2) == i);
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0069 n1 = size(i1,1);
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0070 j1 = zeros(n1,1);
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0071 j2 = j1;
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0072 <span class="keyword">for</span> k1 = 1:n1
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0073 j1(k1) = find(k0(i00,1)==k0(i1(k1),1));
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0074 j2(k1) = find(k0(i0,1)==k0(i1(k1),1));
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0075 <span class="keyword">end</span>
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0076 AS(:,j1) = AS(:,j1)+ghx(:,i1);
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0077 i0 = i1;
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0078 <span class="keyword">end</span>
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0079 b = ghu1*M_.Sigma_e*ghu1';
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0080 [A,B] = <a href="kalman_transition_matrix.html" class="code" title="function [A,B] = kalman_transition_matrix(dr)">kalman_transition_matrix</a>(dr);
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0081 <span class="comment">% index of predetermined variables in A</span>
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0082 i_pred = [nstatic+(1:npred) M_.endo_nbr+1:length(A)];
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0083 A = A(i_pred,i_pred);
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0084 [vx, ns_var] = <a href="lyapunov_symm.html" class="code" title="function [x,ns_var]=lyapunov_symm(a,b)">lyapunov_symm</a>(A,b);
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0085 i_ivar = find(~ismember(ivar,dr.order_var(ns_var+nstatic)));
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0086 ivar = ivar(i_ivar);
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0087 iky = iv(ivar);
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0088 aa = ghx(iky,:);
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0089 bb = ghu(iky,:);
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0090 Gamma = zeros(nvar,cutoff+1);
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0091 tmp = aa*vx*aa'+ bb*M_.Sigma_e*bb';
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0092 k = find(abs(tmp) < 1e-12);
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0093 tmp(k) = 0;
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0094 Gamma(:,1) = diag(tmp);
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0095 vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
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0096 tmp = aa*vxy;
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0097 k = find(abs(tmp) < 1e-12);
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0098 tmp(k) = 0;
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0099 Gamma(:,2) = diag(tmp);
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0100 <span class="keyword">for</span> i=2:cutoff
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0101 vxy = A*vxy;
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0102 tmp = aa*vxy;
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0103 k = find(abs(tmp) < 1e-12);
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0104 tmp(k) = 0;
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0105 Gamma(:,i+1) = diag(tmp);
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0106 <span class="keyword">end</span>
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0107 H = 1:cutoff;
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0108 <span class="keyword">for</span> i=1:nvar
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0109 f(i,:) = Gamma(i,1)/(2*pi) + Gamma(i,H+1)*cos(H'*omega')/pi;
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0110 <span class="keyword">end</span>
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0111
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0112 <span class="keyword">if</span> sscanf(version(<span class="string">'-release'</span>),<span class="string">'%d'</span>) < 13
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0113 warning on
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0114 <span class="keyword">else</span>
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0115 eval(<span class="string">'warning on MATLAB:dividebyzero'</span>)
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0116 <span class="keyword">end</span>
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0117
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0118 <span class="keyword">if</span> pltinfo
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0119 <span class="keyword">for</span> i= 1:nvar
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0120 figure(<span class="string">'Name'</span>,[<span class="string">'Spectral Density of '</span> deblank(M_.endo_names(ivar(i),:)) <span class="string">'.'</span>])
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0121 plot(omega,f(i,:),<span class="string">'-k'</span>,<span class="string">'linewidth'</span>,2)
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0122 xlabel(<span class="string">'0 \leq \omega \leq \pi'</span>)
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0123 ylabel(<span class="string">'f(\omega)'</span>)
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0124 box on
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0125 axis tight
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0126 <span class="keyword">end</span>
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0127 <span class="keyword">end</span></pre></div>
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<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
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