wsum

Calculate the weighted sum over one or more user-defined extents of a function y = f(x). Depending on the number of extents, the result of the function is a vector or a scalar.

Usage

wsum(x, y, w, s, us, os, n)

wsum(x, y, w, s, uv, ov)

wsum(x, y, w, s, rv)

wsum(x, y, w, s, rm)

x, y

the x- and y-data vector: y[i] = f(x[i])

w

defines the type of the weighting function

w=0	no weight (rectangle)
w=1	triangle
w=2	hanning window
w=2	hamming window

s

if this argument is set to 1 the sum of each extent is normalized (scaled by 1/sum(weights)), otherwise not

us, os, n

Every pair {us+d*i, us+d*(i+1)} (with: d=(os-us)/n, i=0..n-1) defines an extent to sum. All three arguments are scalars.

uv, ov

Every pair {uv[i], ov[i]} (with: i=0..nrow(uv)-1) defines an extent to sum. Both arguments must be vectors with same length.

rv

Every pair {rv[i], rv[i+1]} (with: i=0..nrow(rv)-2) defines an extent to sum. The argument must be vector.

rm

Every pair {rm[i,0], rm[i,1]} (with: i=0..nrow(rm)-1) defines an extent to sum. The argument must be matrix with 2 columns.

Result

The result r is a scalar or a vector. Each element r_i is the sum of weighted the y values over the i-th extent {xmin_i, xmax_i}.

Note: an extent is defined by the x-range {xmin, xmax} and not by the indices!

See also

sum, hist

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