comparison toolboxes/FullBNT-1.0.7/KPMstats/gamma_sample.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function r = gamrnd(a,b,m,n);
+%GAMRND Random matrices from gamma distribution.
+%   R = GAMRND(A,B) returns a matrix of random numbers chosen   
+%   from the gamma distribution with parameters A and B.
+%   The size of R is the common size of A and B if both are matrices.
+%   If either parameter is a scalar, the size of R is the size of the other
+%   parameter. Alternatively, R = GAMRND(A,B,M,N) returns an M by N matrix. 
+%
+%   Some references refer to the gamma distribution
+%   with a single parameter. This corresponds to GAMRND
+%   with B = 1. (See Devroye, pages 401-402.)
+
+%   GAMRND uses a rejection or an inversion method depending on the
+%   value of A. 
+
+%   References:
+%      [1]  L. Devroye, "Non-Uniform Random Variate Generation", 
+%      Springer-Verlag, 1986
+
+%   B.A. Jones 2-1-93
+%   Copyright (c) 1993-98 by The MathWorks, Inc.
+%   $Revision: 1.1.1.1 $  $Date: 2005/04/26 02:29:18 $
+
+if nargin < 2, 
+   error('Requires at least two input arguments.'); 
+end
+
+
+if nargin == 2
+   [errorcode rows columns] = rndcheck(2,2,a,b);
+end
+
+if nargin == 3
+   [errorcode rows columns] = rndcheck(3,2,a,b,m);
+end
+
+if nargin == 4
+   [errorcode rows columns] = rndcheck(4,2,a,b,m,n);
+end
+
+if errorcode > 0
+   error('Size information is inconsistent.');
+end
+
+% Initialize r to zero.
+lth = rows*columns;
+r = zeros(lth,1);
+a = a(:); b = b(:);
+
+scalara = (length(a) == 1);
+if scalara 
+   a = a*ones(lth,1);
+end
+
+scalarb = (length(b) == 1);
+if scalarb 
+   b = b*ones(lth,1);
+end
+
+% If a == 1, then gamma is exponential. (Devroye, page 405).
+k = find(a == 1);
+if any(k)
+   r(k) = -b(k) .* log(rand(size(k)));
+end 
+
+
+k = find(a < 1 & a > 0);
+% (Devroye, page 418 Johnk's generator)
+if any(k)
+  c = zeros(lth,1);
+  d = zeros(lth,1);
+  c(k) = 1 ./ a(k);
+  d(k) = 1 ./ (1 - a(k));
+  accept = k;
+  while ~isempty(accept)
+    u = rand(size(accept));
+    v = rand(size(accept));
+    x = u .^ c(accept);
+    y = v .^ d(accept);
+    k1 = find((x + y) <= 1); 
+    if ~isempty(k1)
+      e = -log(rand(size(k1))); 
+      r(accept(k1)) = e .* x(k1) ./ (x(k1) + y(k1));
+      accept(k1) = [];
+    end
+  end
+  r(k) = r(k) .* b(k);
+end
+
+% Use a rejection method for a > 1.
+k = find(a > 1);
+% (Devroye, page 410 Best's algorithm)
+bb = zeros(size(a));
+c  = bb;
+if any(k)
+  bb(k) = a(k) - 1;
+  c(k) = 3 * a(k) - 3/4;
+  accept = k; 
+  count = 1;
+  while ~isempty(accept)
+    m = length(accept);
+    u = rand(m,1);
+    v = rand(m,1);
+    w = u .* (1 - u);
+    y = sqrt(c(accept) ./ w) .* (u - 0.5);
+    x = bb(accept) + y;
+    k1 = find(x >= 0);
+    if ~isempty(k1)
+      z = 64 * (w .^ 3) .* (v .^ 2);
+      k2 = (z(k1) <= (1 - 2 * (y(k1) .^2) ./ x(k1)));
+      k3 = k1(find(k2));
+      r(accept(k3)) = x(k3); 
+      k4 = k1(find(~k2));
+      k5 = k4(find(log(z(k4)) <= (2*(bb(accept(k4)).*log(x(k4)./bb(accept(k4)))-y(k4)))));
+      r(accept(k5)) = x(k5);
+      omit = [k3; k5];
+      accept(omit) = [];
+    end
+  end
+  r(k) = r(k) .* b(k);
+end
+
+% Return NaN if a or b is not positive.
+r(b <= 0 | a <= 0) = NaN;
+
+r = reshape(r,rows,columns);