Average values over ranges of one variable
Given x (size n*1) and y (n*m), this function splits the range of x into up to k intervals (bins) containing approximately equal numbers of elements, and for each part of the range computes the mean of y.
Any NaN values are removed.
Useful for detecting possible nonlinear dependence of y on x and as a preprocessor for spline fitting.
E.g., to make a plot of the average behavior of y versus x: errorbar(x_bin, y_bin, 1 ./ sqrt(w_bin)); grid on
Inputs:
x: n*1 real array
y: n*m array of values at the coordinates x
k: Desired number of bins, floor(sqrt(n)) by default
Outputs:
x_bin, y_bin: Mean values by bin (ordered by increasing x)
w_bin: Weights (inverse standard error of each element in y_bin; note: will be NaN or Inf where n_bin = 1)
n_bin: Number of elements of x per bin
See also: csaps, dedup.
Package: splines