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histograms for ND data

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Create histograms for ND data using ND bins



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histnd Histogram count of ND data with ND bins
  histmat = histnd(x, y, ..., xedges, yedges, ...)
  Extract ND histogram data containing the number of events
  of [x, y, ...] tuples that fall in each bin of the ND-grid defined by
  xedges, yedges, .... The edges are passed to histc internally and should
  therefore conform to histc's input restrictions: the edge-vectors should
  be monotonically non-decreasing.
  [histmat, nOOF, OOFidx] = histnd(x, y, ..., xedges, yedges, ...)
  If any values are outside of the range of the edges, they are not
  counted. The number of those cases and their linear index in the input
  data is however returned in the second and third output arguments.
  events = 1000000;
  x1 = sqrt(0.05)*randn(events,1)-0.5; x2 = sqrt(0.05)*randn(events,1)+0.5;
  y1 = sqrt(0.05)*randn(events,1)+0.5; y2 = sqrt(0.05)*randn(events,1)-0.5;
  x= [x1;x2]; y = [y1;y2];
 For linearly spaced edges:
  xedges = linspace(-1,1,64); yedges = linspace(-1,1,64);
  histmat = histnd(x, y, xedges, yedges);
  figure; pcolor(xedges,yedges,histmat'); colorbar ; axis square tight ;
 For nonlinearly spaced edges:
  xedges_ = logspace(0,log10(3),64)-2; yedges_ = linspace(-1,1,64);
  histmat_ = histnd(x, y, xedges_, yedges_);
  figure; pcolor(xedges_,yedges_,histmat_'); colorbar ; axis square tight ;
 3D data
  x = 3.*randn(640000,1);
  y = 1.*randn(640000,1);
  z = 1.*randn(640000,1);
  histmat = histnd(x,y,z,linspace(min(x),max(x),20),linspace(min(y),max(y),20),linspace(min(z),max(z),20));
  % make 3D hist, color of points indicates count
  [xp,yp,zp] = meshgrid(linspace(min(x),max(x),20),linspace(min(y),max(y),20),linspace(min(z),max(z),20));
  % cut away histogram positions where count is 0
  qzero = histmat==0;
  histmat(qzero) = [];
  xp(qzero) = [];
  yp(qzero) = [];
  zp(qzero) = [];
  % draw points
  figure;%('Renderer','OpenGL') % might need the openGL renderer to handle so many points
  ax = scatter3(xp(:),yp(:),zp(:),'.');
  % color them according to count
  cdata = histmat(:)./max(histmat);
  xlabel('X'), ylabel('Y'), zlabel('Z')

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MATLAB Release
MATLAB 7.12 (R2011a)

Inspired by: 2D Histogram Calculation

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