From a5b3c829d824b4c3f8a0888432d1d34e2953b372 Mon Sep 17 00:00:00 2001 From: sebastien Date: Tue, 5 Aug 2008 09:52:45 +0000 Subject: [PATCH] v4 matlab: replaced CDF and quantile functions of the beta by GPL'd ones git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1982 ac1d8469-bf42-47a9-8791-bf33cf982152 --- matlab/dbeta.m | 16 ------ matlab/distributions/betacdf.m | 64 +++++++++++++++++++++++ matlab/distributions/betainv.m | 95 ++++++++++++++++++++++++++++++++++ matlab/distributions/betapdf.m | 60 +++++++++++++++++++++ matlab/distributions/betarnd.m | 2 +- matlab/draw_prior_density.m | 4 +- matlab/prior_bounds.m | 4 +- matlab/qbeta.m | 32 ------------ 8 files changed, 224 insertions(+), 53 deletions(-) delete mode 100644 matlab/dbeta.m create mode 100644 matlab/distributions/betacdf.m create mode 100644 matlab/distributions/betainv.m create mode 100644 matlab/distributions/betapdf.m delete mode 100644 matlab/qbeta.m diff --git a/matlab/dbeta.m b/matlab/dbeta.m deleted file mode 100644 index 36d0c3788..000000000 --- a/matlab/dbeta.m +++ /dev/null @@ -1,16 +0,0 @@ -function d = dbeta(x,a,b) -%DBETA The beta density function -% -% f = dbeta(x,a,b) - -% Anders Holtsberg, 18-11-93 -% Copyright (c) Anders Holtsberg - -if any(any((a<=0)|(b<=0))) - error('Parameter a or b is nonpositive') -end - -I = find((x<0)|(x>1)); - -d = x.^(a-1) .* (1-x).^(b-1) ./ beta(a,b); -d(I) = 0*I; diff --git a/matlab/distributions/betacdf.m b/matlab/distributions/betacdf.m new file mode 100644 index 000000000..3540bef72 --- /dev/null +++ b/matlab/distributions/betacdf.m @@ -0,0 +1,64 @@ +function cdf = betacdf (x, a, b) +% BETACDF CDF of the Beta distribution +% CDF = betacdf(X, A, B) computes, for each element of X, the CDF +% at X of the beta distribution with parameters A and B (i.e. +% mean of the distribution is A/(A+B) and variance is +% A*B/(A+B)^2/(A+B+1) ). + +% Adapted for Matlab (R) from GNU Octave 3.0.1 +% Original file: statistics/distributions/betacdf.m +% Original author: KH + +% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik +% Copyright (C) 2008 Dynare Team +% +% This file is part of Dynare. +% +% Dynare is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% Dynare is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Dynare. If not, see . + + if (nargin ~= 3) + error ('betacdf: you should provide three arguments'); + end + + if (~isscalar (a) || ~isscalar(b)) + [retval, x, a, b] = common_size (x, a, b); + if (retval > 0) + error ('betacdf: x, a and b must be of common size or scalar'); + end + end + + sz = size(x); + cdf = zeros (sz); + + k = find (~(a > 0) | ~(b > 0) | isnan (x)); + if (any (k)) + cdf (k) = NaN; + end + + k = find ((x >= 1) & (a > 0) & (b > 0)); + if (any (k)) + cdf (k) = 1; + end + + k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); + if (any (k)) + if (isscalar (a) && isscalar(b)) + cdf (k) = betainc (x(k), a, b); + else + cdf (k) = betainc (x(k), a(k), b(k)); + end + end + +end + diff --git a/matlab/distributions/betainv.m b/matlab/distributions/betainv.m new file mode 100644 index 000000000..14c5d1350 --- /dev/null +++ b/matlab/distributions/betainv.m @@ -0,0 +1,95 @@ +function inv = betainv (x, a, b) +% BETAINV Quantile function of the Beta distribution +% INV = betainv(X, A, B) computes, for each element of X, the +% quantile (the inverse of the CDF) at X of the Beta distribution +% with parameters A and B (i.e. mean of the distribution is +% A/(A+B) and variance is A*B/(A+B)^2/(A+B+1) ). + +% Adapted for Matlab (R) from GNU Octave 3.0.1 +% Original file: statistics/distributions/betainv.m +% Original author: KH + +% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik +% Copyright (C) 2008 Dynare Team +% +% This file is part of Dynare. +% +% Dynare is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% Dynare is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Dynare. If not, see . + + if (nargin ~= 3) + error ('betainv: you must give three arguments'); + end + + if (~isscalar (a) || ~isscalar(b)) + [retval, x, a, b] = common_size (x, a, b); + if (retval > 0) + error ('betainv: x, a and b must be of common size or scalars'); + end + end + + sz = size (x); + inv = zeros (sz); + + k = find ((x < 0) | (x > 1) | ~(a > 0) | ~(b > 0) | isnan (x)); + if (any (k)) + inv (k) = NaN; + end + + k = find ((x == 1) & (a > 0) & (b > 0)); + if (any (k)) + inv (k) = 1; + end + + k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); + if (any (k)) + if (~isscalar(a) || ~isscalar(b)) + a = a (k); + b = b (k); + y = a ./ (a + b); + else + y = a / (a + b) * ones (size (k)); + end + x = x (k); + l = find (y < eps); + if (any (l)) + y(l) = sqrt (eps) * ones (length (l), 1); + end + l = find (y > 1 - eps); + if (any (l)) + y(l) = 1 - sqrt (eps) * ones (length (l), 1); + end + + y_old = y; + for i = 1 : 10000 + h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b); + y_new = y_old - h; + ind = find (y_new <= eps); + if (any (ind)) + y_new (ind) = y_old (ind) / 10; + end + ind = find (y_new >= 1 - eps); + if (any (ind)) + y_new (ind) = 1 - (1 - y_old (ind)) / 10; + end + h = y_old - y_new; + if (max (abs (h)) < sqrt (eps)) + break; + end + y_old = y_new; + end + + inv (k) = y_new; + end + +end diff --git a/matlab/distributions/betapdf.m b/matlab/distributions/betapdf.m new file mode 100644 index 000000000..12d51f2c2 --- /dev/null +++ b/matlab/distributions/betapdf.m @@ -0,0 +1,60 @@ +function pdf = betapdf (x, a, b) +% BETAPDF PDF of the Beta distribution +% PDF = betapdf(X, A, B) computes, for each element of X, the PDF +% at X of the beta distribution with parameters A and B (i.e. +% mean of the distribution is A/(A+B) and variance is +% A*B/(A+B)^2/(A+B+1) ). + +% Adapted for Matlab (R) from GNU Octave 3.0.1 +% Original file: statistics/distributions/betapdf.m +% Original author: KH + +% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik +% Copyright (C) 2008 Dynare Team +% +% This file is part of Dynare. +% +% Dynare is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% Dynare is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Dynare. If not, see . + + if (nargin ~= 3) + error ('betapdf: you must give three arguments'); + end + + if (~isscalar (a) || ~isscalar(b)) + [retval, x, a, b] = common_size (x, a, b); + if (retval > 0) + error ('betapdf: x, a and b must be of common size or scalar'); + end + end + + sz = size (x); + pdf = zeros (sz); + + k = find (~(a > 0) | ~(b > 0) | isnan (x)); + if (any (k)) + pdf (k) = NaN; + end + + k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); + if (any (k)) + if (isscalar(a) && isscalar(b)) + pdf(k) = exp ((a - 1) .* log (x(k)) ... + + (b - 1) .* log (1 - x(k))) ./ beta (a, b); + else + pdf(k) = exp ((a(k) - 1) .* log (x(k)) ... + + (b(k) - 1) .* log (1 - x(k))) ./ beta (a(k), b(k)); + end + end + +end diff --git a/matlab/distributions/betarnd.m b/matlab/distributions/betarnd.m index ac489cd2e..281902898 100644 --- a/matlab/distributions/betarnd.m +++ b/matlab/distributions/betarnd.m @@ -3,7 +3,7 @@ function rnd = betarnd(a, b) % RND = betarnd(A,B) returns a random sample from the % Beta distribution with parameters A and B (i.e. mean of % the distribution is A/(A+B) and variance is -% A*B/(A+B)^2/(A+B+1). +% A*B/(A+B)^2/(A+B+1) ). % Copyright (C) 2008 Dynare Team % diff --git a/matlab/draw_prior_density.m b/matlab/draw_prior_density.m index 30579363b..98e5215a8 100644 --- a/matlab/draw_prior_density.m +++ b/matlab/draw_prior_density.m @@ -52,8 +52,8 @@ if pshape(indx) == 1 %/* BETA Prior */ b = a*(1/mu-1); aa = p3(indx); bb = p4(indx); - infbound = qbeta(truncprior,a,b)*(bb-aa)+aa; - supbound = qbeta(1-truncprior,a,b)*(bb-aa)+aa; + infbound = betainv(truncprior,a,b)*(bb-aa)+aa; + supbound = betainv(1-truncprior,a,b)*(bb-aa)+aa; stepsize = (supbound-infbound)/200; abscissa = infbound:stepsize:supbound; dens = density(abscissa,a,b,aa,bb); diff --git a/matlab/prior_bounds.m b/matlab/prior_bounds.m index 614174cf1..d4ef05142 100644 --- a/matlab/prior_bounds.m +++ b/matlab/prior_bounds.m @@ -47,8 +47,8 @@ for i=1:n stdd = p2(i)/(p4(i)-p3(i)); A = (1-mu)*mu^2/stdd^2 - mu; B = A*(1/mu - 1); - bounds(i,1) = qbeta(options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i); - bounds(i,2) = qbeta(1-options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i); + bounds(i,1) = betainv(options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i); + bounds(i,2) = betainv(1-options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i); case 2 b = p2(i)^2/(pmean(i)-p3(i)); a = (pmean(i)-p3(i))/b; diff --git a/matlab/qbeta.m b/matlab/qbeta.m deleted file mode 100644 index c8383718b..000000000 --- a/matlab/qbeta.m +++ /dev/null @@ -1,32 +0,0 @@ -function x = qbeta(p,a,b) -%QBETA The beta inverse distribution function -% -% x = qbeta(p,a,b) - -% Anders Holtsberg, 27-07-95 -% Copyright (c) Anders Holtsberg - -if any(any((a<=0)|(b<=0))) - error('Parameter a or b is nonpositive') -end -if any(any(abs(2*p-1)>1)) - error('A probability should be 0<=p<=1, please!') -end - -if exist('OCTAVE_VERSION') - x = betainv(p, a, b); - return -end - -b = min(b,100000); - -x = a ./ (a+b); -dx = 1; -while any(any(abs(dx)>256*eps*max(x,1))) - dx = (betainc(x,a,b) - p) ./ dbeta(x,a,b); - x = x - dx; - x = x + (dx - x) / 2 .* (x<0); - x = x + (1 + (dx - x)) / 2 .* (x>1); -end - -