49 lines
1.9 KiB
Matlab
49 lines
1.9 KiB
Matlab
data = randn(100, 1); % generate some data
|
|
sigma = 0.2; % std. dev. of Gaussian kernel
|
|
xmin = -4.0; % minimum x value for kernel density
|
|
xmax = 4.0; % maximum x value for kernel density
|
|
dx = 0.05*sigma; % step size for kernel density
|
|
xg = [-4.0*sigma:dx:4.0*sigma]; % x-axis for single Gaussian kernel
|
|
% single Gaussian kernel:
|
|
kernel = exp(-0.5*(xg/sigma).^2)/sqrt(2.0*pi)/sigma;
|
|
ng = floor((length(kernel)-1)/2); % half the length of the Gaussian
|
|
x = [xmin:dx:xmax+0.5*dx]; % x-axis for kernel density
|
|
kd = zeros(1, length(x)); % vector for kernel density
|
|
for i = 1:length(data) % for every data value ...
|
|
xd = data(i);
|
|
% index of data value in kernel density vector:
|
|
inx = round((xd-xmin)/dx)+1;
|
|
% start index for Gaussian in kernel density vector:
|
|
k0 = inx-ng;
|
|
% end index for Gaussian in kernel density vector:
|
|
k1 = inx+ng;
|
|
g0 = 1; % start index in Gaussian
|
|
g1 = length(kernel); % end index in Gaussian
|
|
% check whether left side of Gaussian extends below xmin:
|
|
if inx < ng+1
|
|
% adjust start indices accordingly:
|
|
k0 = 1;
|
|
g0 = ng-inx+2;
|
|
end
|
|
% check whether right side of Gaussian extends above xmax:
|
|
if inx > length(kd)-ng
|
|
% adjust end indices accordingly:
|
|
k1 = length(kd);
|
|
g1 = length(kernel)-(inx+ng-length(kd));
|
|
end
|
|
% add Gaussian on kernel density:
|
|
kd(k0:k1) = kd(k0:k1) + kernel(g0:g1);
|
|
end
|
|
kd = kd/length(data); % normalize by number of data points
|
|
|
|
% plot the computed kernel density:
|
|
plot(x, kd, 'b', 'linewidth', 4, 'displayname', 'manual')
|
|
hold on
|
|
% use the ksdensity() function instead:
|
|
[kd, x] = ksdensity(data, x, 'Bandwidth', sigma);
|
|
plot(x, kd, '--r', 'linewidth', 4, 'displayname', 'ksdensity()')
|
|
hold off
|
|
xlabel('x')
|
|
ylabel('Probability density')
|
|
legend('show')
|