Weighted Data Binning [wbin]

Weighted data binning.

WBIN(X,Y,E,DX) returns the weighted mean of the elements in Y within a
bin of size DX.
X,Y,E are row or column vectors with an equal number of elements.
DX is a scalar which specifies the desired binning interval.

Input X,Y,E,DX must not contain NaN values!

E is a vector which contains the error (one sigma standard deviation)
of the elements in Y. The elements are assumed to be uncorrelated and
elements in E should be Gaussian distributed.
The weighting scheme thus assumes the standard formular: W = 1./E.^2;

Output XB,YB,EB,NE are column vectors containing binned positions,
weighted binned data points, error on weighted binned data points
(one sigma standard deviation) and number of elements used to calculate
the respective weighted binned data point.

Examples
1. Weighted bin of linear data + random distributed noise.
X = 1:1000;
E = randn(1, 1000);
Y = X + E;
DX = 10;
wbin(X,Y,E,DX);
2. Weighted bin with an equal number of elements used to calculate bin.
X = linspace(0,60,10001);
E = randn(1, numel(X));
Y = X + E;
DX = 6;
wbin(X, Y, E, DX);