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).
nscale(X, mode = 1, ssnew = NULL, newscale = 1)
X |
Array (2-way, 3-way, or 4-way) or a list containing array elements. |
mode |
Mode to scale within (set |
ssnew |
Desired sum-of-squares for each level of scaled mode. |
newscale |
Desired root-mean-square for each level of scaled mode. Ignored if |
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,])) |
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mode=2: |
x[i,j] * newscale / sqrt(meansq(x[,j])) |
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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,]))) |
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mode=3: |
x[i,j,k] * newscale / sqrt(meansq(x[,,k])) |
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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,,,])) |
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mode=2: |
x[i,j,k,l] * newscale / sqrt(meansq(x[,j,,])) |
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mode=3: |
x[i,j,k,l] * newscale / sqrt(meansq(x[,,k,])) |
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mode=4: |
x[i,j,k,l] * newscale / sqrt(meansq(x[,,,l])) |
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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,,])) |
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mode=3: |
x[i,j,k,l] * sqrt(ssnew / sumsq(x[,,k,])) |
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mode=4: |
x[i,j,k,l] * sqrt(ssnew / sumsq(x[,,,l])) |
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Returns scaled version of X.
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.
Nathaniel E. Helwig <helwig@umn.edu>
########## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.