# Scale n-th Dimension of Array Slab-scale within each level of the specified mode. Can input 2-way, 3-way, and 4-way arrays, or input a list containing array elements (see Note). ```r nscale(X, mode = 1, ssnew = NULL, newscale = 1) ``` ## Arguments - `X`: Array (2-way, 3-way, or 4-way) or a list containing array elements. - `mode`: Mode to scale within (set `mode = 0` to scale across all modes). - `ssnew`: Desired sum-of-squares for each level of scaled mode. - `newscale`: Desired root-mean-square for each level of scaled mode. Ignored if `ssnew` is supplied. ## Details Default (as of ver 1.0-5) uses `newscale` argument... With `X` a matrix (I-by-J) there are two options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j] * newscale / sqrt(meansq(x[i,]))`| |`mode=2:`||`x[i,j] * newscale / sqrt(meansq(x[,j]))`| With `X` a 3-way array (I-by-J-by-K) there are three options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j,k] * newscale / sqrt(meansq(x[i,,]))`| |`mode=2:`||`x[i,j,k] * newscale / sqrt(meansq(x[,j,])))`| |`mode=3:`||`x[i,j,k] * newscale / sqrt(meansq(x[,,k]))`| With `X` a 4-way array (I-by-J-by-K-by-L) there are four options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j,k,l] * newscale / sqrt(meansq(x[i,,,]))`| |`mode=2:`||`x[i,j,k,l] * newscale / sqrt(meansq(x[,j,,]))`| |`mode=3:`||`x[i,j,k,l] * newscale / sqrt(meansq(x[,,k,]))`| |`mode=4:`||`x[i,j,k,l] * newscale / sqrt(meansq(x[,,,l]))`| If argument `ssnew` is provided... With `X` a matrix (I-by-J) there are two options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j] * sqrt(ssnew / sumsq(x[i,]))`| |`mode=2:`||`x[i,j] * sqrt(ssnew / sumsq(x[,j]))`| With `X` a 3-way array (I-by-J-by-K) there are three options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j,k] * sqrt(ssnew / sumsq(x[i,,]))`| |`mode=2:`||`x[i,j,k] * sqrt(ssnew / sumsq(x[,j,])))`| |`mode=3:`||`x[i,j,k] * sqrt(ssnew / sumsq(x[,,k]))`| With `X` a 4-way array (I-by-J-by-K-by-L) there are four options: |||| |--:|:-:|:--| |`mode=1:`||`x[i,j,k,l] * sqrt(ssnew / sumsq(x[i,,,]))`| |`mode=2:`||`x[i,j,k,l] * sqrt(ssnew / sumsq(x[,j,,]))`| |`mode=3:`||`x[i,j,k,l] * sqrt(ssnew / sumsq(x[,,k,]))`| |`mode=4:`||`x[i,j,k,l] * sqrt(ssnew / sumsq(x[,,,l]))`| ## Returns Returns scaled version of `X`. ## Author(s) Nathaniel E. Helwig ## Note When entering a list with array elements, each element must be a 2-way or 3-way array. The list elements are treated as the 3rd mode (for list of 2-way arrays) or the 4th mode (for list of 3-way arrays) in the formulas provided in the Description. ## Examples ```r ########## EXAMPLE 1 ########## X <- matrix(rnorm(2000), nrow = 100, ncol = 20) Xr <- nscale(X, mode = 2) # scale columns to newscale=1 sqrt(colMeans(Xr^2)) Xr <- nscale(X, mode = 2, newscale = 2) # scale columns to newscale=2 sqrt(colMeans(Xr^2)) ########## EXAMPLE 2 ########## Xold <- X <- matrix(rnorm(400), nrow = 20, ncol = 20) iter <- 0 chk <- 1 # iterative scaling of modes 1 and 2 while(iter<500 & chk>=10^-9){ Xr <- nscale(Xold, mode = 1) Xr <- nscale(Xr, mode = 2) chk <- sum((Xold-Xr)^2) Xold <- Xr iter <- iter + 1 } iter sqrt(rowMeans(Xr^2)) sqrt(colMeans(Xr^2)) ########## EXAMPLE 3 ########## X <- array(rnorm(20000), dim = c(100,20,10)) Xc <- nscale(X, mode = 2) # scale within columns sqrt(rowMeans(aperm(Xc, perm = c(2,1,3))^2)) ########## EXAMPLE 4 ########## X <- array(rnorm(100000), dim = c(100,20,10,5)) Xc <- nscale(X, mode = 4) # scale across 4-th mode sqrt(rowMeans(aperm(Xc, perm = c(4,1,2,3))^2)) ########## EXAMPLE 5 ########## X <- replicate(5, array(rnorm(20000), dim = c(100,20,10)), simplify = FALSE) # mean square of 1 (new way) Xc <- nscale(X) rowSums(sapply(Xc, function(x) rowSums(x^2))) / (20*10*5) # mean square of 1 (old way) Xc <- nscale(X, ssnew = (20*10*5)) rowSums(sapply(Xc, function(x) rowSums(x^2))) / (20*10*5) ```

nscale function