问如何在Matlab中用一系列分段直线拟合一条曲线？

EN

function fitLogLog()
   x = 2:1000;
   y = log(log(x));

   %# Find section sizes, by using an inverse of the approximation of the derivative
   numOfSections = 20;
   indexes = round(linspace(1,numel(y),numOfSections));
   derivativeApprox = diff(y(indexes));
   inverseDerivative = 1./derivativeApprox;
   weightOfSection =  inverseDerivative/sum(inverseDerivative);   
   totalRange = max(x(:))-min(x(:));   
   sectionSize = weightOfSection.* totalRange;

   %# The relevant nodes
   xNodes = x(1) + [ 0 cumsum(sectionSize)];
   yNodes = log(log(xNodes));

   figure;plot(x,y);   
   hold on;
   plot (xNodes,yNodes,'r');
   scatter (xNodes,yNodes,'r');
   legend('log(log(x))','adaptive linear interpolation');
end

Nsamp = 1000;     %number of data samples on x-axis
x = [1:Nsamp];    %this is your x-axis
Nlines = 5;       %number of lines to fit

fx = exp(-10*x/Nsamp);  %generate something like your current data, f(x)
gx = NaN(size(fx));     %this will hold your fitted lines, g(x)

joins = round(linspace(1, Nsamp, Nlines+1));  %define equally spaced breaks along the x-axis

dx = diff(x(joins));   %x-change
df = diff(fx(joins));  %f(x)-change

m = df./dx;   %gradient for each section

for i = 1:Nlines
   x1 = joins(i);   %start point
   x2 = joins(i+1); %end point
   gx(x1:x2) = fx(x1) + m(i)*(0:dx(i));   %compute line segment
end

subplot(2,1,1)
h(1,:) = plot(x, fx, 'b', x, gx, 'k', joins, gx(joins), 'ro');
title('Normal Plot')

subplot(2,1,2)
h(2,:) = loglog(x, fx, 'b', x, gx, 'k', joins, gx(joins), 'ro');
title('Log Log Plot')

for ip = 1:2
    subplot(2,1,ip)
    set(h(ip,:), 'LineWidth', 2)
    legend('Data', 'Piecewise Linear', 'Location', 'NorthEastOutside')
    legend boxoff
end

function [x, y] = intervalAggregate(Xdata, Ydata, aggFun, intStep, intOverlap)
% intOverlap in [0, 1); 0 for no overlap of intervals, etc.
% intStep    this is the size of the interval being aggregated.

minX = min(Xdata);
maxX = max(Xdata);

minY = min(Ydata);
maxY = max(Ydata);

intInc = intOverlap*intStep; %How far we advance each iteraction.
if intOverlap <= 0
   intInc = intStep;
end
nInt = ceil((maxX-minX)/intInc); %Number of aggregations

parfor i = 1:nInt
    xStart = minX + (i-1)*intInc;
    xEnd   = xStart + intStep;
    intervalIndices = find((Xdata >= xStart) & (Xdata <= xEnd));
    x(i) = aggFun(Xdata(intervalIndices));
    y(i) = aggFun(Ydata(intervalIndices));
end

0.0552    0.0868    0.1170    0.1475    0.1844    0.2173    0.2498    0.2834

0.3182    0.3561    0.3875    0.4178    0.4494    0.4671    0.4822

0.9992    0.9983    0.9971    0.9955    0.9927    0.9905    0.9876    0.9846

0.9803    0.9750    0.9707    0.9653    0.9598    0.9560    0.9537