RunningL2Norm: Fast Running L2 Norm Computation
In martakarass/convo: Fast Computation of Running Sample Statistics

Description Usage Arguments Details Value Examples

Computes running L2 norm between two sequences in a fixed width window, whose length corresponds to the length of the shorter sequence. Uses convolution via Fast Fourier Transform.

1	RunningL2Norm(x, y, circular = FALSE)

`x`	A numeric vector.
`y`	A numeric vector, of equal or shorter length than `x` sequence
`circular`	logical; whether running L2 norm is computed assuming circular nature of `x` sequence (see Details)

Computes running L2 norm between two sequences in a fixed width window. The length of a window is equal to the shorter of the two sequences (y), and window "runs" over the length of longer sequence (x).

The length of output vector equals the length of x vector. Parameter circular determines whether x sequence is assumed to have a circular nature. Assume l_x is the length of sequence x, l_y is the length of shorter sequence y.

If circular equals TRUE then

first element of the output sequence corresponds to sample L2 norm between x[1:l_y] and y,
last element of the output sequence corresponds to sample L2 norm between c(x[l_x], x[1:(l_y - 1)]) and y.

If circular equals FALSE then

first element of the output sequence corresponds to sample L2 norm between x[1:l_y] and y,
the l_x - W + 1-th element of the output sequence corresponds to sample L2 norm between x[(l_x - l_y + 1):l_x],
last W-1 elements of the output sequence are filled with NA.

A numeric vector.

## Ex.1.
x <- sin(seq(0, 1, length.out = 1000) * 2 * pi * 6)
y1 <- x[1:100] + rnorm(100)
y2 <- rnorm(100)
out1 <- RunningL2Norm(x, y1)
out2 <- RunningL2Norm(x, y2)
plot(out1, type = "l"); points(out2, col = "blue")
## Ex.2.
x <- sin(seq(0, 1, length.out = 1000) * 2 * pi * 6)
y <- x[1:100] + rnorm(100)
out1 <- RunningL2Norm(x, y, circular = TRUE)
out2 <- RunningL2Norm(x, y, circular = FALSE)
plot(out1, type = "l"); points(out2, col = "red")