2009-12-16 18:17:34 +01:00
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function [omega,f] = UnivariateSpectralDensity(dr,var_list)
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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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2013-04-26 19:59:32 +02:00
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% oo_ and may be plotted. Plots are saved into the graphs-folder.
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2009-12-16 18:17:34 +01:00
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%
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% Adapted from th_autocovariances.m.
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2013-04-26 19:59:32 +02:00
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% Copyright (C) 2006-2013 Dynare Team
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2009-12-16 18:17:34 +01:00
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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global options_ oo_ M_
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omega = []; f = [];
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if options_.order > 1
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disp('UnivariateSpectralDensity :: I Cannot compute the theoretical spectral density')
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disp('with a second order approximation of the DSGE model!')
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2012-04-26 09:01:33 +02:00
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disp('Please set order = 1. I abort')
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2009-12-16 18:17:34 +01:00
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return
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end
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2012-04-26 08:48:31 +02:00
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pltinfo = options_.SpectralDensity.plot;
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cutoff = options_.SpectralDensity.cutoff;
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2012-04-26 09:01:33 +02:00
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sdl = options_.SpectralDensity.sdl;
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2009-12-16 18:17:34 +01:00
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omega = (0:sdl:pi)';
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GridSize = length(omega);
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exo_names_orig_ord = M_.exo_names_orig_ord;
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if exist('OCTAVE_VERSION')
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warning('off', 'Octave:divide-by-zero')
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else
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warning off MATLAB:dividebyzero
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end
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if nargin<2
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var_list = [];
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end
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if size(var_list,1) == 0
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var_list = M_.endo_names(1:M_.orig_endo_nbr, :);
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end
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nvar = size(var_list,1);
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ivar=zeros(nvar,1);
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for i=1:nvar
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i_tmp = strmatch(var_list(i,:),M_.endo_names,'exact');
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if isempty(i_tmp)
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2012-04-26 09:01:33 +02:00
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error (['One of the variables specified does not exist']) ;
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2009-12-16 18:17:34 +01:00
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else
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2010-01-05 11:46:10 +01:00
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ivar(i) = i_tmp;
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2009-12-16 18:17:34 +01:00
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end
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end
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f = zeros(nvar,GridSize);
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ghx = dr.ghx;
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ghu = dr.ghu;
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2012-11-16 20:05:13 +01:00
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nspred = M_.nspred;
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nstatic = M_.nstatic;
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2009-12-16 18:17:34 +01:00
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kstate = dr.kstate;
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order = dr.order_var;
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iv(order) = [1:length(order)];
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nx = size(ghx,2);
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2012-11-16 20:05:13 +01:00
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ikx = [nstatic+1:nstatic+nspred];
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2009-12-16 18:17:34 +01:00
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A = zeros(nx,nx);
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k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
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i0 = find(k0(:,2) == M_.maximum_lag+1);
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i00 = i0;
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n0 = length(i0);
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A(i0,:) = ghx(ikx,:);
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AS = ghx(:,i0);
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ghu1 = zeros(nx,M_.exo_nbr);
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ghu1(i0,:) = ghu(ikx,:);
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for i=M_.maximum_lag:-1:2
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i1 = find(k0(:,2) == i);
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n1 = size(i1,1);
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j1 = zeros(n1,1);
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j2 = j1;
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for k1 = 1:n1
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j1(k1) = find(k0(i00,1)==k0(i1(k1),1));
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j2(k1) = find(k0(i0,1)==k0(i1(k1),1));
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end
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AS(:,j1) = AS(:,j1)+ghx(:,i1);
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i0 = i1;
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end
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Gamma = zeros(nvar,cutoff+1);
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2011-01-26 14:05:39 +01:00
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[A,B] = kalman_transition_matrix(dr,ikx',1:nx,M_.exo_nbr);
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2009-12-16 18:17:34 +01:00
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[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold);
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iky = iv(ivar);
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if ~isempty(u)
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iky = iky(find(any(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));
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ivar = dr.order_var(iky);
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end
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aa = ghx(iky,:);
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bb = ghu(iky,:);
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if options_.hp_filter == 0
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tmp = aa*vx*aa'+ bb*M_.Sigma_e*bb';
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,1) = diag(tmp);
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vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
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tmp = aa*vxy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,2) = diag(tmp);
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for i=2:cutoff
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vxy = A*vxy;
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tmp = aa*vxy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,i+1) = diag(tmp);
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end
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else
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iky = iv(ivar);
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aa = ghx(iky,:);
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bb = ghu(iky,:);
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lambda = options_.hp_filter;
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ngrid = options_.hp_ngrid;
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freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
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tpos = exp( sqrt(-1)*freqs);
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tneg = exp(-sqrt(-1)*freqs);
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hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
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mathp_col = [];
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IA = eye(size(A,1));
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IE = eye(M_.exo_nbr);
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
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*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) IE]); % state variables
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g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
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f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
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% for ifft
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end;
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imathp_col = real(ifft(mathp_col))*(2*pi);
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tmp = reshape(imathp_col(1,:),nvar,nvar);
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k = find(abs(tmp)<1e-12);
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tmp(k) = 0;
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Gamma(:,1) = diag(tmp);
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sy = sqrt(Gamma(:,1));
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sy = sy *sy';
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for i=1:cutoff-1
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tmp = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,i+1) = diag(tmp);
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end
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end
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H = 1:cutoff;
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for i=1:nvar
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f(i,:) = Gamma(i,1)/(2*pi) + Gamma(i,H+1)*cos(H'*omega')/pi;
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end
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if exist('OCTAVE_VERSION')
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warning('on', 'Octave:divide-by-zero')
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else
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warning on MATLAB:dividebyzero
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end
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if pltinfo
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2013-04-26 19:59:32 +02:00
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if ~exist(M_.fname, 'dir')
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mkdir('.',M_.fname);
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end
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if ~exist([M_.fname '/graphs'])
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mkdir(M_.fname,'graphs');
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end
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2009-12-16 18:17:34 +01:00
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for i= 1:nvar
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2013-04-26 19:59:32 +02:00
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hh = dyn_figure(options_,'Name',['Spectral Density of ' deblank(M_.endo_names(ivar(i),:)) '.']);
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2009-12-16 18:17:34 +01:00
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plot(omega,f(i,:),'-k','linewidth',2)
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xlabel('0 \leq \omega \leq \pi')
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ylabel('f(\omega)')
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box on
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2013-04-26 19:59:32 +02:00
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axis tight
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2013-04-27 16:22:25 +02:00
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dyn_saveas(hh,[M_.fname ,filesep,'graphs', filesep, 'SpectralDensity_' deblank(M_.endo_names(ivar(i),:))],options_)
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2009-12-16 18:17:34 +01:00
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end
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2012-11-16 20:05:13 +01:00
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end
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