1 ## Copyright (C) 2012 Rik Wehbring
2 ## Copyright (C) 1995-2012 Kurt Hornik
4 ## This file is part of Octave.
6 ## Octave is free software; you can redistribute it and/or modify it
7 ## under the terms of the GNU General Public License as published by
8 ## the Free Software Foundation; either version 3 of the License, or (at
9 ## your option) any later version.
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 ## General Public License for more details.
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18 ## <http://www.gnu.org/licenses/>.
21 ## @deftypefn {Function File} {} normpdf (@var{x})
22 ## @deftypefnx {Function File} {} normpdf (@var{x}, @var{mu}, @var{sigma})
23 ## For each element of @var{x}, compute the probability density function
24 ## (PDF) at @var{x} of the normal distribution with mean @var{mu} and
25 ## standard deviation @var{sigma}.
27 ## Default values are @var{mu} = 0, @var{sigma} = 1.
30 ## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at>
31 ## Description: PDF of the normal distribution
33 function pdf = normpdf (x, mu = 0, sigma = 1)
35 if (nargin != 1 && nargin != 3)
39 if (!isscalar (mu) || !isscalar (sigma))
40 [retval, x, mu, sigma] = common_size (x, mu, sigma);
42 error ("normpdf: X, MU, and SIGMA must be of common size or scalars");
46 if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma))
47 error ("normpdf: X, MU, and SIGMA must not be complex");
50 if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single"))
51 pdf = zeros (size (x), "single");
53 pdf = zeros (size (x));
56 if (isscalar (mu) && isscalar (sigma))
57 if (!isinf (mu) && !isnan (mu) && (sigma > 0) && (sigma < Inf))
58 pdf = stdnormal_pdf ((x - mu) / sigma) / sigma;
60 pdf = NaN (size (x), class (pdf));
63 k = isinf (mu) | !(sigma > 0) | !(sigma < Inf);
66 k = !isinf (mu) & (sigma > 0) & (sigma < Inf);
67 pdf(k) = stdnormal_pdf ((x(k) - mu(k)) ./ sigma(k)) ./ sigma(k);
74 %! x = [-Inf 1 2 Inf];
75 %! y = 1/sqrt(2*pi)*exp (-(x-1).^2/2);
76 %!assert(normpdf (x, ones(1,4), ones(1,4)), y);
77 %!assert(normpdf (x, 1, ones(1,4)), y);
78 %!assert(normpdf (x, ones(1,4), 1), y);
79 %!assert(normpdf (x, [0 -Inf NaN Inf], 1), [y(1) NaN NaN NaN]);
80 %!assert(normpdf (x, 1, [Inf NaN -1 0]), [NaN NaN NaN NaN]);
81 %!assert(normpdf ([x, NaN], 1, 1), [y, NaN]);
83 %% Test class of input preserved
84 %!assert(normpdf (single([x, NaN]), 1, 1), single([y, NaN]), eps("single"));
85 %!assert(normpdf ([x, NaN], single(1), 1), single([y, NaN]), eps("single"));
86 %!assert(normpdf ([x, NaN], 1, single(1)), single([y, NaN]), eps("single"));
88 %% Test input validation
91 %!error normpdf (1,2,3,4)
92 %!error normpdf (ones(3),ones(2),ones(2))
93 %!error normpdf (ones(2),ones(3),ones(2))
94 %!error normpdf (ones(2),ones(2),ones(3))
95 %!error normpdf (i, 2, 2)
96 %!error normpdf (2, i, 2)
97 %!error normpdf (2, 2, i)