scale
Scale Columns of a Matrix
Description
Centers and then scales the columns of a matrix.
By default, each column in the result has mean 0 and sample standard
deviation 1.
This function is an S Version 3 generic. (See Methods.)
Method functions can be written to handle specific
S Version 3 classes of data.
Currently there is only the default method.
Usage
scale(x, center = TRUE, scale = TRUE)
## Default S3 method:
scale(x, center = TRUE, scale = TRUE)
Arguments
| x |
the matrix to be scaled. Missing values (NAs) are allowed.
|
| center |
specifies whether or how to control the value subtracted from each column. Can be a
logical value or a vector.
- If TRUE (the default), the mean of the non-missing data in
each column is subtracted from the column.
- If given as a vector of length ncol(x), this vector is used.
That is, center[j] is subtracted from column j.
- If FALSE, no centering is done.
|
| scale |
specifies whether or how to control the value divided into each column to scale it.
Can be a logical value or a vector.
- If TRUE (the default), after centering, each column is divided
by the square root of sum-of-squares over n-1,
where n is the number of non-missing values.
- If given as a vector of length ncol(x), column j is divided by scale[j].
- If FALSE, no scaling is done.
|
Details
scale takes as an argument x (matrix) and returns a similar matrix whose
columns take elements corresponding to the center (mean), and scale
(standard deviation). If center and scale are not specified, the
default values are 0 and 1, respectively.
If scale or center is not a logical value,
and its length is not equal to the number of columns in x,
an error is generated.
Value
returns a matrix like
x with optional centering and scaling.
- If scale is TRUE or a vector (that is, not FALSE),
this matrix has an attribute scaled:scale containing the vector of values
used to scale the columns.
- If center is TRUE or a vector (that is, not FALSE),
this matrix has an attribute scaled:center containing the vector of values
used to center the columns.
References
Becker, R. A., Chambers, J. M., and Wilks, A. R. 1988. The New S Language. Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books and Software.
See Also
Examples
A <- matrix(c(1:3,3*(1:3),2^(1:3)), nrow=3)
A
# [,1] [,2] [,3]
# [1,] 1 3 2
# [2,] 2 6 4
# [3,] 3 9 8
# center and scale
scale(A)
# [,1] [,2] [,3]
# [1,] -1 -1 -0.8728716
# [2,] 0 0 -0.2182179
# [3,] 1 1 1.0910895
# attr(,"scaled:center")
# [1] 2.000000 6.000000 4.666667
# attr(,"scaled:scale")
# [1] 1.00000 3.00000 3.05505
# check column means and variances of centered and scaled matrix
apply(scale(A),2,mean)
# [1] 0.000000e+000 0.000000e+000 -1.480297e-016
apply(scale(A),2,var)
# [1] 1 1 1
# just center
scale(A, scale=FALSE)
# [,1] [,2] [,3]
# [1,] -1 -3 -2.6666667
# [2,] 0 0 -0.6666667
# [3,] 1 3 3.3333333
# attr(,"scaled:center")
# [1] 2.000000 6.000000 4.666667
# just scale
scale(A, center=FALSE)
# [,1] [,2] [,3]
# [1,] 0.3779645 0.3779645 0.3086067
# [2,] 0.7559289 0.7559289 0.6172134
# [3,] 1.1338934 1.1338934 1.2344268
# attr(,"scaled:scale")
# [1] 2.645751 7.937254 6.480741
# just center by a vector of values
scale(A, center=c(1,2,4), scale=FALSE)
# [,1] [,2] [,3]
# [1,] 0 1 -2
# [2,] 1 4 0
# [3,] 2 7 4
# attr(,"scaled:center")
# [1] 1 2 4
# just scale by a vector of values
scale(A, center=FALSE, scale=c(1,2,4))
# [,1] [,2] [,3]
# [1,] 1 1.5 0.5
# [2,] 2 3.0 1.0
# [3,] 3 4.5 2.0
# attr(,"scaled:scale")
# [1] 1 2 4