208 lines
6.3 KiB
Matlab
208 lines
6.3 KiB
Matlab
function [s,nu] = inverse_gamma_specification(mu, sigma2, lb, type, use_fzero_flag, name) % --*-- Unitary tests --*--
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% Computes the inverse Gamma hyperparameters from the prior mean and variance.
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%
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% INPUTS
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% - mu [double] scalar, prior mean.
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% - sigma2 [double] positive scalar, prior variance.
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% - type [integer] scalar equal to 1 or 2, type of the inverse gamma distribution
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% - use_fzero_flag [logical] scalar, Use (matlab/octave's implementation of) fzero to solve for nu if true, use
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% dynare's implementation of the secant method otherwise.
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% - name [string] name of the parameter or random variable.
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%
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% OUTPUS
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% - s [double] scalar, first hyperparameter.
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% - nu [double] scalar, second hyperparameter.
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%
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% REMARKS
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% 1. In the Inverse Gamma parameterization with alpha and beta, we have alpha=nu/2 and beta=2/s, where
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% if X is IG(alpha,beta) then 1/X is Gamma(alpha,1/beta)
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% 2. The call to the matlab's implementation of the secant method is here for testing purpose and should not be used. This routine fails
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% more often in finding an interval for nu containing a signe change because it expands the interval on both sides and eventually
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% violates the condition nu>2.
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% Copyright © 2003-2017 Dynare Team
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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 <https://www.gnu.org/licenses/>.
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if nargin<4
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error('At least four input arguments are required!')
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end
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if ~isnumeric(mu) || ~isscalar(mu) || ~isreal(mu)
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error('First input argument must be a real scalar!')
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end
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if ~isnumeric(sigma2) || ~isscalar(sigma2) || ~isreal(sigma2) || sigma2<=0
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error('Second input argument must be a real positive scalar!')
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end
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if ~isnumeric(lb) || ~isscalar(lb) || ~isreal(lb)
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error('Third input argument must be a real scalar!')
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end
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if ~isnumeric(type) || ~isscalar(type) || ~ismember(type, [1, 2])
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error('Fourth input argument must be equal to 1 or 2!')
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end
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if nargin==4 || isempty(use_fzero_flag)
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use_fzero_flag = false;
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else
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if ~isscalar(use_fzero_flag) || ~islogical(use_fzero_flag)
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error('Fifth input argument must be a scalar logical!')
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end
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end
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if nargin>5 && (~ischar(name) || size(name, 1)>1)
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error('Sixth input argument must be a string!')
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else
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name = '';
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end
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if ~isempty(name)
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name = sprintf(' for %s', name);
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end
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if mu<=lb
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error('The prior mean%s (%f) must be above the lower bound (%f)of the Inverse Gamma (type %d) prior distribution!', mu, lb, name, type);
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end
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check_solution_flag = true;
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s = [];
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nu = [];
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sigma = sqrt(sigma2);
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mu2 = mu*mu;
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if type == 2 % Inverse Gamma 2
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nu = 2*(2+mu2/sigma2);
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s = 2*mu*(1+mu2/sigma2);
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elseif type == 1 % Inverse Gamma 1
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if sigma2 < Inf
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nu = sqrt(2*(2+mu2/sigma2));
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if use_fzero_flag
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nu = fzero(@(nu)ig1fun(nu,mu2,sigma2),nu);
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else
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nu2 = 2*nu;
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nu1 = 2;
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err = ig1fun(nu,mu2,sigma2);
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err2 = ig1fun(nu2,mu2,sigma2);
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if err2 > 0 % Too short interval.
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while nu2 < 1e12 % Shift the interval containing the root.
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nu1 = nu2;
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nu2 = nu2*2;
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err2 = ig1fun(nu2,mu2,sigma2);
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if err2<0
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break
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end
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end
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if err2>0
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error('inverse_gamma_specification:: Failed in finding an interval containing a sign change! You should check that the prior variance is not too small compared to the prior mean...');
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end
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end
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% Solve for nu using the secant method.
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while abs(nu2/nu1-1) > 1e-14
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if err > 0
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nu1 = nu;
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if nu < nu2
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nu = nu2;
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else
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nu = 2*nu;
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nu2 = nu;
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end
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else
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nu2 = nu;
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end
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nu = (nu1+nu2)/2;
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err = ig1fun(nu,mu2,sigma2);
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end
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end
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s = (sigma2+mu2)*(nu-2);
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if check_solution_flag
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if abs(log(mu)-log(sqrt(s/2))-gammaln((nu-1)/2)+gammaln(nu/2))>1e-7
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error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
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end
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if abs(sigma-sqrt(s/(nu-2)-mu*mu))>1e-7
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error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
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end
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end
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else
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nu = 2;
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s = 2*mu2/pi;
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end
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else
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error('inverse_gamma_specification: unkown type')
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end
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%@test:1
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%$ try
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%$ [s, nu] = inverse_gamma_specification(.5, .05, 0, 1);
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%$ t(1) = true;
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%$ catch
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%$ t(1) = false;
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%$ end
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%$
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%$ if t(1)
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%$ t(2) = abs(0.5-sqrt(.5*s)*gamma(.5*(nu-1))/gamma(.5*nu))<1e-12;
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%$ t(3) = abs(0.05-s/(nu-2)+.5^2)<1e-12;
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%$ end
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%$ T = all(t);
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%@eof:1
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%@test:2
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%$ try
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%$ [s, nu] = inverse_gamma_specification(.5, .05, 0, 2);
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%$ t(1) = true;
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%$ catch
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%$ t(1) = false;
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%$ end
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%$
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%$ if t(1)
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%$ t(2) = abs(0.5-s/(nu-2))<1e-12;
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%$ t(3) = abs(0.05-2*.5^2/(nu-4))<1e-12;
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%$ end
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%$ T = all(t);
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%@eof:2
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%@test:3
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%$ try
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%$ [s, nu] = inverse_gamma_specification(.5, Inf, 0, 1);
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%$ t(1) = true;
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%$ catch
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%$ t(1) = false;
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%$ end
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%$
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%$ if t(1)
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%$ t(2) = abs(0.5-sqrt(.5*s)*gamma(.5*(nu-1))/gamma(.5*nu))<1e-12;
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%$ t(3) = isequal(nu, 2); %abs(0.05-2*.5^2/(nu-4))<1e-12;
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%$ end
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%$ T = all(t);
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%@eof:3
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%@test:4
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%$ try
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%$ [s, nu] = inverse_gamma_specification(.5, Inf, 0, 2);
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%$ t(1) = true;
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%$ catch
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%$ t(1) = false;
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%$ end
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%$
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%$ if t(1)
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%$ t(2) = abs(0.5-s/(nu-2))<1e-12;
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%$ t(3) = isequal(nu, 4);
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%$ end
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%$ T = all(t);
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%@eof:4 |