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.
%
% mu=A*B is the mean.
% sigma^2=A*B^2 is the variance.
%
%
% 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: 2.8 $ $Date: 1998/09/30 19:12:40 $
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);
function [errorcode, rows, columns] = rndcheck(nargs,nparms,arg1,arg2,arg3,arg4,arg5)
%RNDCHECK error checks the argument list for the random number generators.
% B.A. Jones 1-22-93
% Copyright (c) 1993-98 by The MathWorks, Inc.
% $Revision: 2.5 $ $Date: 1997/11/29 01:46:40 $
sizeinfo = nargs - nparms;
errorcode = 0;
if nparms == 3
[r1 c1] = size(arg1);
[r2 c2] = size(arg2);
[r3 c3] = size(arg3);
end
if nparms == 2
[r1 c1] = size(arg1);
[r2 c2] = size(arg2);
end
if sizeinfo == 0
if nparms == 1
[rows columns] = size(arg1);
end
if nparms == 2
scalararg1 = (prod(size(arg1)) == 1);
scalararg2 = (prod(size(arg2)) == 1);
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1
[rows columns] = size(arg1);
elseif ~scalararg2
[rows columns] = size(arg2);
else
[rows columns] = size(arg1);
end
end
if nparms == 3
scalararg1 = (prod(size(arg1)) == 1);
scalararg2 = (prod(size(arg2)) == 1);
scalararg3 = (prod(size(arg3)) == 1);
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1 & ~scalararg3
if r1 ~= r3 | c1 ~= c3
errorcode = 1;
return;
end
end
if ~scalararg3 & ~scalararg2
if r3 ~= r2 | c3 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1
[rows columns] = size(arg1);
elseif ~scalararg2
[rows columns] = size(arg2);
else
[rows columns] = size(arg3);
end
end
end
if sizeinfo == 1
scalararg1 = (prod(size(arg1)) == 1);
if nparms == 1
if prod(size(arg2)) ~= 2
errorcode = 2;
return;
end
if ~scalararg1 & arg2 ~= size(arg1)
errorcode = 3;
return;
end
if (arg2(1) < 0 | arg2(2) < 0 | arg2(1) ~= round(arg2(1)) | arg2(2) ~= round(arg2(2))),
errorcode = 4;
return;
end
rows = arg2(1);
columns = arg2(2);
end
if nparms == 2
if prod(size(arg3)) ~= 2
errorcode = 2;
return;
end
scalararg2 = (prod(size(arg2)) == 1);
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if (arg3(1) < 0 | arg3(2) < 0 | arg3(1) ~= round(arg3(1)) | arg3(2) ~= round(arg3(2))),
errorcode = 4;
return;
end
if ~scalararg1
if any(arg3 ~= size(arg1))
errorcode = 3;
return;
end
[rows columns] = size(arg1);
elseif ~scalararg2
if any(arg3 ~= size(arg2))
errorcode = 3;
return;
end
[rows columns] = size(arg2);
else
rows = arg3(1);
columns = arg3(2);
end
end
if nparms == 3
if prod(size(arg4)) ~= 2
errorcode = 2;
return;
end
scalararg1 = (prod(size(arg1)) == 1);
scalararg2 = (prod(size(arg2)) == 1);
scalararg3 = (prod(size(arg3)) == 1);
if (arg4(1) < 0 | arg4(2) < 0 | arg4(1) ~= round(arg4(1)) | arg4(2) ~= round(arg4(2))),
errorcode = 4;
return;
end
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1 & ~scalararg3
if r1 ~= r3 | c1 ~= c3
errorcode = 1;
return;
end
end
if ~scalararg3 & ~scalararg2
if r3 ~= r2 | c3 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1
if any(arg4 ~= size(arg1))
errorcode = 3;
return;
end
[rows columns] = size(arg1);
elseif ~scalararg2
if any(arg4 ~= size(arg2))
errorcode = 3;
return;
end
[rows columns] = size(arg2);
elseif ~scalararg3
if any(arg4 ~= size(arg3))
errorcode = 3;
return;
end
[rows columns] = size(arg3);
else
rows = arg4(1);
columns = arg4(2);
end
end
end
if sizeinfo == 2
if nparms == 1
scalararg1 = (prod(size(arg1)) == 1);
if ~scalararg1
[rows columns] = size(arg1);
if rows ~= arg2 | columns ~= arg3
errorcode = 3;
return;
end
end
if (arg2 < 0 | arg3 < 0 | arg2 ~= round(arg2) | arg3 ~= round(arg3)),
errorcode = 4;
return;
end
rows = arg2;
columns = arg3;
end
if nparms == 2
scalararg1 = (prod(size(arg1)) == 1);
scalararg2 = (prod(size(arg2)) == 1);
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1
[rows columns] = size(arg1);
if rows ~= arg3 | columns ~= arg4
errorcode = 3;
return;
end
elseif ~scalararg2
[rows columns] = size(arg2);
if rows ~= arg3 | columns ~= arg4
errorcode = 3;
return;
end
else
if (arg3 < 0 | arg4 < 0 | arg3 ~= round(arg3) | arg4 ~= round(arg4)),
errorcode = 4;
return;
end
rows = arg3;
columns = arg4;
end
end
if nparms == 3
scalararg1 = (prod(size(arg1)) == 1);
scalararg2 = (prod(size(arg2)) == 1);
scalararg3 = (prod(size(arg3)) == 1);
if ~scalararg1 & ~scalararg2
if r1 ~= r2 | c1 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1 & ~scalararg3
if r1 ~= r3 | c1 ~= c3
errorcode = 1;
return;
end
end
if ~scalararg3 & ~scalararg2
if r3 ~= r2 | c3 ~= c2
errorcode = 1;
return;
end
end
if ~scalararg1
[rows columns] = size(arg1);
if rows ~= arg4 | columns ~= arg5
errorcode = 3;
return;
end
elseif ~scalararg2
[rows columns] = size(arg2);
if rows ~= arg4 | columns ~= arg5
errorcode = 3;
return;
end
elseif ~scalararg3
[rows columns] = size(arg3);
if rows ~= arg4 | columns ~= arg5
errorcode = 3;
return;
end
else
if (arg4 < 0 | arg5 < 0 | arg4 ~= round(arg4) | arg5 ~= round(arg5)),
errorcode = 4;
return;
end
rows = arg4;
columns = arg5;
end
end
end
