# prcomp_irlba: Principal Components Analysis In irlba: Fast Truncated Singular Value Decomposition and Principal Components Analysis for Large Dense and Sparse Matrices

 prcomp_irlba R Documentation

## Principal Components Analysis

### Description

Efficient computation of a truncated principal components analysis of a given data matrix using an implicitly restarted Lanczos method from the `irlba` package.

### Usage

```prcomp_irlba(x, n = 3, retx = TRUE, center = TRUE, scale. = FALSE, ...)
```

### Arguments

 `x` a numeric or complex matrix (or data frame) which provides the data for the principal components analysis. `n` integer number of principal component vectors to return, must be less than `min(dim(x))`. `retx` a logical value indicating whether the rotated variables should be returned. `center` a logical value indicating whether the variables should be shifted to be zero centered. Alternately, a centering vector of length equal the number of columns of `x` can be supplied. `scale.` a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is `FALSE` for consistency with S, but scaling is often advisable. Alternatively, a vector of length equal the number of columns of `x` can be supplied. The value of `scale` determines how column scaling is performed (after centering). If `scale` is a numeric vector with length equal to the number of columns of `x`, then each column of `x` is divided by the corresponding value from `scale`. If `scale` is `TRUE` then scaling is done by dividing the (centered) columns of `x` by their standard deviations if `center=TRUE`, and the root mean square otherwise. If `scale` is `FALSE`, no scaling is done. See `scale` for more details. `...` additional arguments passed to `irlba`.

### Value

A list with class "prcomp" containing the following components:

• sdev the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix).

• rotation the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors).

• x if `retx` is `TRUE` the value of the rotated data (the centred (and scaled if requested) data multiplied by the `rotation` matrix) is returned. Hence, `cov(x)` is the diagonal matrix `diag(sdev^2)`.

• center, scale the centering and scaling used, or `FALSE`.

### Note

The signs of the columns of the rotation matrix are arbitrary, and so may differ between different programs for PCA, and even between different builds of R.

NOTE DIFFERENCES WITH THE DEFAULT `prcomp` FUNCTION! The `tol` truncation argument found in `prcomp` is not supported. In place of the truncation tolerance in the original function, the `prcomp_irlba` function has the argument `n` explicitly giving the number of principal components to return. A warning is generated if the argument `tol` is used, which is interpreted differently between the two functions.

`prcomp`

### Examples

```set.seed(1)
x  <- matrix(rnorm(200), nrow=20)
p1 <- prcomp_irlba(x, n=3)
summary(p1)

# Compare with
p2 <- prcomp(x, tol=0.7)
summary(p2)

```

irlba documentation built on Oct. 4, 2022, 1:05 a.m.