Efficient computation of principal components and singular value decompositions.
fast.prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL) fast.svd( x, nu = min(n, p), nv = min(n, p), ...)
The current implementation of the function svd in S-Plus
and R is much slower when operating on a matrix with a large number of
columns than on the transpose of this matrix, which has a large
number of rows. As a consequence, prcomp, which uses
svd, is also very slow when applied to matrixes with a
large number of rows.
For S-Plus the solution is to replace the standard svd
with a version that checks the dimensions of the matrix, and performs
the computation on the transposed the matrix if it is wider than tall.
For R:
For S-Plus:
fast.prcompis a modified versiom of
prcomp that calls fast.svd instead
of svd
fast.svdchecks the dimensions of the
matrix. When it is wider than tall, it transposes the input matrix
and calls svd. It then swaps u and v
and returns the result. Otherwise, it just calls svd
and returns the results unchanged.
Modifications by Gregory R. Warnes greg@warnes.net
# create test matrix set.seed(4943546) nr <- 50 nc <- 2000 x <- matrix( rnorm( nr*nc), nrow=nr, ncol=nc ) tx <- t(x) # SVD directly on matrix is SLOW: system.time( val.x <- svd(x)$u ) # SVD on t(matrix) is FAST: system.time( val.tx <- svd(tx)$v ) # and the results are equivalent: max( abs(val.x) - abs(val.tx) ) # Time gap dissapears using fast.svd: system.time( val.x <- fast.svd(x)$u ) system.time( val.tx <- fast.svd(tx)$v ) max( abs(val.x) - abs(val.tx) ) library(stats) # prcomp directly on matrix is SLOW: system.time( pr.x <- prcomp(x) ) # prcomp.fast is much faster system.time( fast.pr.x <- fast.prcomp(x) ) # and the results are equivalent max( pr.x$sdev - fast.pr.x$sdev ) max( abs(pr.x$rotation[,1:49]) - abs(fast.pr.x$rotation[,1:49]) ) max( abs(pr.x$x) - abs(fast.pr.x$x) ) # (except for the last and least significant component): max( abs(pr.x$rotation[,50]) - abs(fast.pr.x$rotation[,50]) )
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