# RunningL2Norm: Fast Running L2 Norm Computation In runstats: Fast Computation of Running Statistics for Time Series

## Description

Computes running L2 norm between between time-series `x` and short-time pattern `y`.

## Usage

 `1` ```RunningL2Norm(x, y, circular = FALSE) ```

## Arguments

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

## Details

Computes running L2 norm between between time-series `x` and short-time pattern `y`. The length of output vector equals the length of `x`. Parameter `circular` determines whether `x` time-series is assumed to have a circular nature. Assume l_x is the length of time-series `x`, l_y is the length of short-time pattern `y`.

If `circular` equals `TRUE` then

• first element of the output vector corresponds to sample L2 norm between `x[1:l_y]` and `y`,

• last element of the output vector 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 vector corresponds to sample L2 norm between `x[1:l_y]` and `y`,

• the l_x - W + 1-th element of the output vector corresponds to sample L2 norm between `x[(l_x - l_y + 1):l_x]`,

• last `W-1` elements of the output vector are filled with `NA`.

See `runstats.demo(func.name = "RunningL2Norm")` for a detailed presentation.

## Value

A numeric vector.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## 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") ```

runstats documentation built on Jan. 11, 2020, 9:17 a.m.