2D Histogram Matrix

Returns a matrix of number of points in each bins defined by two vectors.

Description

function mHist = hist2d ([vY, vX], vYEdge, vXEdge)
2 Dimensional Histogram
Counts number of points in the bins defined by vYEdge, vXEdge.
size(vX) == size(vY) == [n,1]
size(mHist) == [length(vYEdge) -1, length(vXEdge) -1]
 
EXAMPLE

mYX = rand(100,2);
vXEdge = linspace(0,1,10);
vYEdge = linspace(0,1,20);
mHist2d = hist2d(mYX,vYEdge,vXEdge);
 
nXBins = length(vXEdge);
nYBins = length(vYEdge);
vXLabel = 0.5*(vXEdge(1:(nXBins-1))+vXEdge(2:nXBins));
vYLabel = 0.5*(vYEdge(1:(nYBins-1))+vYEdge(2:nYBins));
pcolor(vXLabel, vYLabel,mHist2d); colorbar

• Acknowledgements: This submission has inspired the following:; 2-Dimensional Histogram
• MATLAB release: MATLAB 5.3.1 (R11.1)

[Mark Ward]

It does what you'd expect :-)
A surface plot instead of contours would be a useful option. I know - I should add this myself!

[Tony Kim]

This is what I wanted. Why MATLAB doesn't have this kind of command, I don't understand.

[R Corbett]

Exactly what I needed

[H Chen]

Nicely done!

[luiz Loures]

practical

[Kevin Aptowicz]

Great!

[guiot etienne]

simple and fast

[Jim Jazz]

Useful

[Ali H.]

Does exactly what it says on the tin! Easy to use, fast, simple, great.

[Dimitri Shvorob]

Thank you!

[Martin Müller]

Explicit specification of edges is inconvinient. Why do the vectors have to be passed as a matrix? Plotting of the result often doesnt work. Plot is not a 2d bar chart as expected.

[Andrew Meijers]

Excellent, it did exactly what it said it would. Great for contouring dense scatter fields.

[Jos Groot]

Just what I needed.

[Nikolaus Correll]

IMO one needs to swap lines 27 and 28 if the bins in x and y are not equally spaced. If this is not the case, the version as is gives rotated histograms.

[Evan Variano]

Works well. It's Short and sweet

[Denny Jackson]

Workes exactly like I wanted.
Very user friendly.

[Iain Strachan]

If the histogram spacing is regular and assumed to be divided between the minimum and maximum values, then one can use the useful property of the sparse(i,j,vals) command, that it sums the values assigned to repeated indices, to do a 2d histogram very quickly, something like this...

function m = mk2dhist(vals,n)
% function m=mk2dhist(vals,n)
% make a 2 d histogram nxn
vX = vals(:,1);
vY = vals(:,2);
vX = round((n-1)*(vX - min(vX))/(max(vX)-min(vX)))+1;
vY = round((n-1)*(vY - min(vY))/(max(vY)-min(vY)))+1;
m = full(sparse(vX,vY,ones(length(vX),1)));

I can't yet think of a simple way to exploit this for non-evenly spaced histograms though

[Daniel Mark]

Hi Kangwon Lee and Iain Strachan
Thank you all:)

[Christof Konig Beatty]

Lines 12 and 13 (where nEdgeX and nEdgeY are defined) are actually useless and can be omitted.

[tudor t]

the function has a bug that I was unable to locate, it was faster to write my own function; it affects the last row and the first column, (or viceversa)

for instance with this data
x = [
0 0 1 1 0 0.4 0.6 0.6 0 0.4 0.4 0.4 0.6 0.6 1 1];
y = [
0 1 0 1 0.6 0.4 0 0.6 0.4 0 0.6 1 0.4 1 0.4 0.6];

but although size(x,2) = size(y,2) = 16
when checking sum(sum(bin_2D)) one gets 9 !

[Leiguang Wang]

very fast. but has a little bug.
in line 38
expression: if (~isempty(vColFound))

this is always true, since even (vColFound == 0)
doesn't mean vColFound is empty .
i think
if (abs(vColFound(:))~= 0) is preferable.

[Woot Master]

Leiguang Wang: You've misunderstood this code. At line 38 vColFound will be an empty matrix if line 36 doesn't find any values within the given x bin. isempty is the correct function to call here. Your preferred code would break if the y bin spanned 0 and only had counts exactly at 0 in that bin.

I do have a small issue though. The handling of values exactly at the bin edges is different in x and y. Line 36 reads:

vColFound = vCol((vRow > rRowLB) & (vRow <= rRowUB));

To match what histc does in y this should really have >= and < rather than > and <=. This is most likely not a problem in the majority of cases.

[Pearl]

 

[Michael Jansz]

Very useful but a little buggy.

Depending on you bin sizes you use, the program can crash due to machine rounding errors.

Change lines 25 & 26 in Plot2dHist to read:
vLabelX = linspace(rMinX+0.5*rDeltaX, rMaxX-0.5*rDeltaX, size(mHist2D,2));
vLabelY = linspace(rMinY+0.5*rDeltaY, rMaxY-0.5*rDeltaY, size(mHist2D,1));

fixes this.

[Aaron Swan]

MATLAB provides the function hist3 to generate bivariate (2D) histograms