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[BK-2020-03.git] / unitproc / octave / invgaurnd.m
1 ## Copyright (C) 2012 Rik Wehbring
2 ## Copyright (C) 1995-2016 Kurt Hornik
3 ## Copyright (C) 2021 Steven Baltakatei Sandoval
4 ##
5 ## This program is free software: you can redistribute it and/or
6 ## modify it under the terms of the GNU General Public License as
7 ## published by the Free Software Foundation, either version 3 of the
8 ## License, or (at your option) any later version.
9 ##
10 ## This program is distributed in the hope that it will be useful, but
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
14 ##
15 ## You should have received a copy of the GNU General Public License
16 ## along with this program; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
18
19 ## -*- texinfo -*-
20 ## @deftypefn {} {} invgaurnd (@var{mu}, @var{lambda})
21 ## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, @var{r})
22 ## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, @var{r}, @var{c}, @dots{})
23 ## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, [@var{sz}])
24 ## Return a matrix of random samples from the inverse gaussian distribution with
25 ## parameters mean @var{mu} and shape parameter @var{lambda}.
26 ##
27 ## When called with a single size argument, return a square matrix with
28 ## the dimension specified. When called with more than one scalar argument the
29 ## first two arguments are taken as the number of rows and columns and any
30 ## further arguments specify additional matrix dimensions. The size may also
31 ## be specified with a vector of dimensions @var{sz}.
32 ##
33 ## If no size arguments are given then the result matrix is the common size of
34 ## @var{mu} and @var{lambda}.
35 ## @end deftypefn
36
37 ## Author: Steven Sandoval <baltakatei@gmail.com>
38 ## Description: Random variates from the inverse gaussian distribution
39
40 function rnd = invgaurnd (mu, lambda, varargin)
41
42 if (nargin < 2)
43 print_usage ();
44 endif
45
46 if (! isscalar (mu) || ! isscalar (lambda))
47 [retval, mu, lambda] = common_size (mu, lambda);
48 if (retval > 0)
49 error ("invgaurnd: MU and LAMBDA must be of common size or scalars");
50 endif
51 endif
52
53 if (iscomplex (mu) || iscomplex (lambda))
54 error ("invgaurnd: MU and LAMBDA must not be complex");
55 endif
56
57 if (nargin == 2)
58 sz = size (mu);
59 elseif (nargin == 3)
60 if (isscalar (varargin{1}) && varargin{1} >= 0)
61 sz = [varargin{1}, varargin{1}];
62 elseif (isrow (varargin{1}) && all (varargin{1} >= 0))
63 sz = varargin{1};
64 else
65 error ("invgaurnd: dimension vector must be row vector of non-negative integers");
66 endif
67 elseif (nargin > 3)
68 if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin)))
69 error ("invgaurnd: dimensions must be non-negative integers");
70 endif
71 sz = [varargin{:}];
72 endif
73
74 if (! isscalar (mu) && ! isequal (size (mu), sz))
75 error ("invgaurnd: MU and LAMBDA must be scalar or of size SZ");
76 endif
77
78 if (isa (mu, "single") || isa (lambda, "single"))
79 cls = "single";
80 else
81 cls = "double";
82 endif;
83
84 # Convert mu and lambda from scalars into matrices since scalar multiplication used
85 if isscalar (mu)
86 mu = mu * ones(sz);
87 endif;
88 if isscalar (lambda)
89 lambda = lambda * ones(sz);
90 endif;
91
92 # Generate random variates
93 # Ref/Attrib: Michael, John R., Generating Random Variates Using
94 # Transformations with Multiple Roots. The American Statistician, May 1976,
95 # Vol. 30, No. 2. https://doi.org/10.2307/2683801
96 nu = randn(sz,cls);
97 y = nu .** 2;
98 x1 = mu;
99 x2 = mu .** 2 .* y ./ (2 .* lambda);
100 x3 = (- mu ./ (2 .* lambda)) .* sqrt(4 .* mu .* lambda .* y + mu .** 2 .* y .** 2);
101 x = x1 + x2 + x3;
102 z = rand(sz,cls);
103 valTest1 = (mu ./ (mu + x)); # calculate test 1 value
104 valTest2 = (mu ./ (mu + x)); # calculate test 2 value
105 posTest1 = find(z <= valTest1); # perform test 1, save positions where test 1 true
106 posTest2 = find(z > valTest2); # perform test 2, save positions where test 2 true
107 ## indposTest1 = transpose(posTest1) # debug: list positions
108 ## indposTest2 = transpose(posTest2) # debug: list positions
109 ## indTest1 = z <= valTest1 # debug: show test 1 truth table
110 ## indTest2 = z > valTest2 # debug: show test 2 truth table
111 rnd = NaN(sz); # Initialize return array
112 rnd(posTest1) = x(posTest1); # populate return matrix with corresp. elements of x that satisfy test 1
113 rnd(posTest2) = (mu(posTest2) .** 2 ./ x(posTest2)); # populate return matrix with corresp. elements of x that satisfy test 2
114 k = ! isfinite (mu) | !(lambda >= 0) | !(lambda < Inf); # store position matrix indicating which parts of output are invalid based on
115 # elements of the matrices: mu, lambda.
116 rnd(k) = NaN; # mark invalid positions of output matrix with NaN
117
118 endfunction
119
120
121 %!assert (size (invgaurnd (1,2)), [1, 1])
122 %!assert (size (invgaurnd (ones (2,1), 2)), [2, 1])
123 %!assert (size (invgaurnd (ones (2,2), 2)), [2, 2])
124 %!assert (size (invgaurnd (1, 2*ones (2,1))), [2, 1])
125 %!assert (size (invgaurnd (1, 2*ones (2,2))), [2, 2])
126 %!assert (size (invgaurnd (1, 2, 3)), [3, 3])
127 %!assert (size (invgaurnd (1, 2, [4 1])), [4, 1])
128 %!assert (size (invgaurnd (1, 2, 4, 1)), [4, 1])
129
130 ## Test class of input preserved
131 %!assert (class (invgaurnd (1, 2)), "double")
132 %!assert (class (invgaurnd (single (1), 2)), "single")
133 %!assert (class (invgaurnd (single ([1 1]), 2)), "single")
134 %!assert (class (invgaurnd (1, single (2))), "single")
135 %!assert (class (invgaurnd (1, single ([2 2]))), "single")
136
137 ## Test input validation
138 %!error invgaurnd ()
139 %!error invgaurnd (1)
140 %!error invgaurnd (ones (3), ones (2))
141 %!error invgaurnd (ones (2), ones (3))
142 %!error invgaurnd (i, 2)
143 %!error invgaurnd (2, i)
144 %!error invgaurnd (1,2, -1)
145 %!error invgaurnd (1,2, ones (2))
146 %!error invgaurnd (1, 2, [2 -1 2])
147 %!error invgaurnd (1,2, 1, ones (2))
148 %!error invgaurnd (1,2, 1, -1)
149 %!error invgaurnd (ones (2,2), 2, 3)
150 %!error invgaurnd (ones (2,2), 2, [3, 2])
151 %!error invgaurnd (ones (2,2), 2, 2, 3)