www.gusucode.com > curvefit 案例源码程序 matlab代码 > curvefit/histodem.m
%% Smoothing a Histogram % % This example shows how to use spline commands from Curve Fitting Toolbox(TM) to % smooth a histogram. % Copyright 1987-2014 The MathWorks, Inc. %% % Here is a histogram of some random values that might represent data that % were collected on some measurement. y = randn(1,5001); hist(y); %% % We would like to derive from this histogram a smoother approximation to the % underlying distribution. We do this by constructing a spline function |f| % whose average value over each bar interval equals the height of that bar. %% % If |h| is the height of one of these bars, and its left and right edges % are at |L| and |R|, then we want the spline |f| to satisfy % % integral {f(x) : L < x < R}/(R - L) = h, % % or, with |F| the indefinite integral of |f|, i.e., |DF = f|, % % F(R) - F(L) = h*(R - L). [heights,centers] = hist(y); hold on ax = gca; ax.XTickLabel = []; n = length(centers); w = centers(2)-centers(1); t = linspace(centers(1)-w/2,centers(end)+w/2,n+1); p = fix(n/2); fill(t([p p p+1 p+1]),[0 heights([p p]),0],'w') plot(centers([p p]),[0 heights(p)],'r:') h = text(centers(p)-.2,heights(p)/2,' h'); dep = -70; tL = text(t(p),dep,'L'); tR = text(t(p+1),dep,'R'); hold off %% % So, with |n| the number of bars, |t(i)| the left edge of the |i|-th bar, % |dt(i)| its width, and |h(i)| its height, we want % % F(t(i+1)) - F(t(i)) = h(i) * dt(i), for i = 1:n, % % or, setting arbitrarily |F(t(1))| = 0, % % F(t(i)) = sum {h(j)*dt(j) : j=1:i-1}, for i = 1:n+1. dt = diff(t); Fvals = cumsum([0,heights.*dt]); %% % Add to this the two end conditions |DF(t(1)) = 0 = DF(t(n+1))|, and we have % all the data we need to get |F| as a complete cubic spline interpolant. F = spline(t, [0, Fvals, 0]); %% % The two extra zero values in the second argument indicate the zero endslope % conditions. % % Finally, the derivative, |f = DF|, of the spline |F| is the smoothed version % of the histogram. DF = fnder(F); % computes its first derivative h.String = 'h(i)'; tL.String = 't(i)'; tR.String = 't(i+1)'; hold on fnplt(DF, 'r', 2) hold off ylims = ylim; ylim([0,ylims(2)]); displayEndOfDemoMessage(mfilename)