feat(unitproc/octave/invgaurnd.m):Add inverse gaussian generator

- note: Is GNU octave function based on `normrnd.m` file from
  'statistics' package (see
  https://gnu-octave.github.io/packages/statistics ).
- Tested with GNU Octave 4.4.1

diff --git a/unitproc/octave/invgaurnd.m b/unitproc/octave/invgaurnd.m
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+## Copyright (C) 2012 Rik Wehbring
+## Copyright (C) 1995-2016 Kurt Hornik
+## Copyright (C) 2021 Steven Baltakatei Sandoval
+##
+## This program 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.
+##
+## This program 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 this program; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {} {} invgaurnd (@var{mu}, @var{lambda})
+## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, @var{r})
+## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, @var{r}, @var{c}, @dots{})
+## @deftypefnx {} {} invgaurnd (@var{mu}, @var{lambda}, [@var{sz}])
+## Return a matrix of random samples from the inverse gaussian distribution with
+## parameters mean @var{mu} and shape parameter @var{lambda}.
+##
+## When called with a single size argument, return a square matrix with
+## the dimension specified.  When called with more than one scalar argument the
+## first two arguments are taken as the number of rows and columns and any
+## further arguments specify additional matrix dimensions.  The size may also
+## be specified with a vector of dimensions @var{sz}.
+##
+## If no size arguments are given then the result matrix is the common size of
+## @var{mu} and @var{lambda}.
+## @end deftypefn
+
+## Author: Steven Sandoval <baltakatei@gmail.com>
+## Description: Random variates from the inverse gaussian distribution
+
+function rnd = invgaurnd (mu, lambda, varargin)
+
+  if (nargin < 2)
+    print_usage ();
+  endif
+
+  if (! isscalar (mu) || ! isscalar (lambda))
+    [retval, mu, lambda] = common_size (mu, lambda);
+    if (retval > 0)
+      error ("invgaurnd: MU and LAMBDA must be of common size or scalars");
+    endif
+  endif
+
+  if (iscomplex (mu) || iscomplex (lambda))
+    error ("invgaurnd: MU and LAMBDA must not be complex");
+  endif
+
+  if (nargin == 2)
+    sz = size (mu);
+  elseif (nargin == 3)
+    if (isscalar (varargin{1}) && varargin{1} >= 0)
+      sz = [varargin{1}, varargin{1}];
+    elseif (isrow (varargin{1}) && all (varargin{1} >= 0))
+      sz = varargin{1};
+    else
+      error ("invgaurnd: dimension vector must be row vector of non-negative integers");
+    endif
+  elseif (nargin > 3)
+    if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin)))
+      error ("invgaurnd: dimensions must be non-negative integers");
+    endif
+    sz = [varargin{:}];
+  endif
+
+  if (! isscalar (mu) && ! isequal (size (mu), sz))
+    error ("invgaurnd: MU and LAMBDA must be scalar or of size SZ");
+  endif
+
+  if (isa (mu, "single") || isa (lambda, "single"))
+    cls = "single";
+  else
+    cls = "double";
+  endif;
+
+  # Convert mu and lambda from scalars into matrices since scalar multiplication used
+  if isscalar (mu)
+    mu = mu * ones(sz);
+  endif;
+  if isscalar (lambda)
+    lambda = lambda * ones(sz);
+  endif;
+
+  # Generate random variates
+  # Ref/Attrib: Michael, John R., Generating Random Variates Using
+  #   Transformations with Multiple Roots. The American Statistician, May 1976,
+  #   Vol. 30, No. 2. https://doi.org/10.2307/2683801
+  nu = randn(sz,cls);
+  y = nu .** 2;
+  x1 = mu;
+  x2 = mu .** 2 .* y ./ (2 .* lambda);
+  x3 = (- mu ./ (2 .* lambda)) .* sqrt(4 .* mu .* lambda .* y + mu .** 2 .* y .** 2);
+  x = x1 + x2 + x3;
+  z = rand(sz,cls);
+  valTest1 = (mu ./ (mu + x)); # calculate test 1 value
+  valTest2 = (mu ./ (mu + x)); # calculate test 2 value
+  posTest1 = find(z <= valTest1); # perform test 1, save positions where test 1 true
+  posTest2 = find(z > valTest2); # perform test 2, save positions where test 2 true
+  ## indposTest1 = transpose(posTest1) # debug: list positions
+  ## indposTest2 = transpose(posTest2) # debug: list positions
+  ## indTest1 = z <= valTest1 # debug: show test 1 truth table
+  ## indTest2 = z > valTest2 # debug: show test 2 truth table
+  rnd = NaN(sz); # Initialize return array
+  rnd(posTest1) = x(posTest1); # populate return matrix with corresp. elements of x that satisfy test 1
+  rnd(posTest2) = (mu(posTest2) .** 2 ./ x(posTest2)); # populate return matrix with corresp. elements of x that satisfy test 2
+  k = ! isfinite (mu) | !(lambda >= 0) | !(lambda < Inf); # store position matrix indicating which parts of output are invalid based on
+                                                          #   elements of the matrices: mu, lambda.
+  rnd(k) = NaN; # mark invalid positions of output matrix with NaN
+
+endfunction
+
+
+%!assert (size (invgaurnd (1,2)), [1, 1])
+%!assert (size (invgaurnd (ones (2,1), 2)), [2, 1])
+%!assert (size (invgaurnd (ones (2,2), 2)), [2, 2])
+%!assert (size (invgaurnd (1, 2*ones (2,1))), [2, 1])
+%!assert (size (invgaurnd (1, 2*ones (2,2))), [2, 2])
+%!assert (size (invgaurnd (1, 2, 3)), [3, 3])
+%!assert (size (invgaurnd (1, 2, [4 1])), [4, 1])
+%!assert (size (invgaurnd (1, 2, 4, 1)), [4, 1])
+
+## Test class of input preserved
+%!assert (class (invgaurnd (1, 2)), "double")
+%!assert (class (invgaurnd (single (1), 2)), "single")
+%!assert (class (invgaurnd (single ([1 1]), 2)), "single")
+%!assert (class (invgaurnd (1, single (2))), "single")
+%!assert (class (invgaurnd (1, single ([2 2]))), "single")
+
+## Test input validation
+%!error invgaurnd ()
+%!error invgaurnd (1)
+%!error invgaurnd (ones (3), ones (2))
+%!error invgaurnd (ones (2), ones (3))
+%!error invgaurnd (i, 2)
+%!error invgaurnd (2, i)
+%!error invgaurnd (1,2, -1)
+%!error invgaurnd (1,2, ones (2))
+%!error invgaurnd (1, 2, [2 -1 2])
+%!error invgaurnd (1,2, 1, ones (2))
+%!error invgaurnd (1,2, 1, -1)
+%!error invgaurnd (ones (2,2), 2, 3)
+%!error invgaurnd (ones (2,2), 2, [3, 2])
+%!error invgaurnd (ones (2,2), 2, 2, 3)