Cedric Roux
56c66c09aa
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51 lines
1.8 KiB
Matlab
51 lines
1.8 KiB
Matlab
function y = ricepdf(x, v, s)
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%RICEPDF Rice/Rician probability density function (pdf).
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% y = ricepdf(x, v, s) returns the pdf of the Rice (aka Rician)
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% distribution with parameters v and s, evaluated at the values in x.
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%
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% R ~ Rice(v, s) if R = sqrt(X^2 + Y^2), where X ~ N(v*cos(a), s^2) and
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% Y ~ N(v*sin(a), s^2) are independent normal distributions (any real a).
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% Note that v and s are *not* the mean and standard deviation of R -- use
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% ricestat to get these statistics for specified v and s.
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%
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% The size of Y is the common size of the input arguments. A scalar
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% input functions as a constant matrix of the same size as the other
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% inputs.
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%
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% Reference: http://en.wikipedia.org/wiki/Rice_distribution (!)
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%
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% Example:
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%
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% x = linspace(0, 8, 100);
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% figure; subplot(2, 1, 1)
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% plot(x, ricepdf(x, 0, 1), x, ricepdf(x, 1, 1),...
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% x, ricepdf(x, 2, 1), x, ricepdf(x, 4, 1))
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% title('Rice PDF with s=1')
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% legend('v=0', 'v=1', 'v=2', 'v=4')
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% subplot(2,1,2)
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% plot(x, ricepdf(x, 1, 0.25), x, ricepdf(x, 1, 0.50),...
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% x, ricepdf(x, 1, 1.00), x, ricepdf(x, 1, 2.00))
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% title('Rice PDF with v=1')
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% legend('s=0.25', 's=0.50', 's=1.00', 's=2.00')
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%
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% See also RICERND, RICESTAT.
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% Missing (?) 'See also's RICECDF, RICEFIT, RICEINV, RICELIKE
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% Inspired by normpdf from the MATLAB statistics toolbox
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% Copyright 2007 Ged Ridgway (Ged at cantab dot net)
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s2 = s.^2; % (neater below)
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try
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y = (x ./ s2) .*...
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exp(-0.5 * (x.^2 + v.^2) ./ s2) .*...
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besseli(0, x .* v ./ s2);
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% besseli(0, ...) is the zeroth order modified Bessel function of
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% the first kind. (see help bessel)
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y(x <= 0) = 0;
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catch
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error('ricepdf:InputSizeMismatch',...
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'Non-scalar arguments must match in size.');
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end
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