function [Ysum, Nsum, Cbin] = NDBASE.HISTN(X,Y,bin1,bin2,…,’option1’,value1)

Any data point with NaN X or Y value is omitted from the binning. Works for non-uniform bins and also optimised for uniform bins with significant speedup.

Input:

X Array with size of [nPoint nDim], that represents positions in the nDim dimensional space (R^nDim). Y Column vector with nPoint element, that represents values at the points defined in X. {X,Y} defines a scalar field in the nDim dimensional space. If Y contains multiple columns, each column will be binned independently and saved into Ysum in separate columns, this can represent vector field at X. The dimensions of the vector field is nField, if the size of Y is [nPoint nField]. binI Row vectors that define BIN EDGES along the I-th dimension. It goes from 1 to nDim. Each vector has to have at least two elements. The number of bins along the I-th dimension is equal to the number of elements in the binI vector minus one. Thus: nBinI = numel(binI)-1

Options:

emptyval Value for empty bins in Ysum and Nsum: emptyval = [emptyY emptyN] Default value is [NaN 0].

Output:

Ysum Array with size of [nBin1 nBin2 nBin3 … nField]. Each pixel contains the sum of the elements of Y that are within the given bin boundaries: bin1(i1) <= X(:,i1) < bin1(i1+1) and … binN(iN) <= X(:,iN) < binN(iN+1) Points of X, that are outside of the bin boundaries are omitted. Empty pixels will contain NaN by default. Nsum Column vector with the same number of rows as Ysum, contains the number of points that are contributing to the pixel. Only calculated if two output is expected. Empty pixels will contain the value 0 by default. To make it possible to calculate the average value of each pixel, set the default value to 1, then devide Ysum with Nsum element vise: Yavg = bsxfun(@rdivide,Ysum,Nsum); Cbin Center bin positions, if nDim=1 the values are stored in a row vector. If nDim>1 the center bin vectors are packed into a cell.

Example:

Random points in 2D.

nPoint = 1e3; nDim = 2; bin = linspace(0,1,101);

X = rand(nPoint,nDim);
Y = sin(X(:,1)*2*pi);
[Ysum,Nsum] = ndbase.histn(X,Y,bin,bin);
figure
imagesc(Ysum./Nsum);

Create points on a square lattice.

[xx,yy] = ndgrid(1:0.5:10,1:0.5:10);

bin = linspace(0,11,101);

[Ysum,Nsum] = ndbase.histn([xx(:) yy(:)],sin(xx(:)),bin,bin); figure imagesc(Ysum./Nsum);

Oversample the sine function defined on a finite point. xx = 0:0.5:10; bin = linspace(0,11,101);

Ysum = ndbase.histn([xx(:)],sin(xx(:)),bin); figure plot(Ysum,’o-‘);

See also accumarray, interp1.