# Randomized Singular Value Decomposition (wordspace)

### Description

An implementation of the randomized truncated SVD algorithm of Halko, Martinsson & Tropp (2009).

### Usage

1 |

### Arguments

`M` |
a dense or sparse numeric matrix |

`n` |
an integer specifying the desired number of singular components. This argument must be specified and must satisfy |

`q` |
number of power iterations (Halko |

`oversampling` |
oversampling factor. The rSVD algorithm computes an approximate SVD factorization of rank |

`transpose` |
if |

`verbose` |
whether to display progress messages during execution |

### Details

This implementation of randomized truncated SVD is based on the randomized PCA algorithm (Halko *et al.* 2009, p. 9). The discussion in Sec. 4 and 5 of the paper shows that the same algorithm applies to the case where the columns of A are not centered (Algorithm 4.3 + Algorithm 5.1).

### Value

A list with components

`u` |
a matrix whose columns contain the first |

`v` |
a matrix whose columns contain the first |

`d` |
a vector containing the first |

### Author(s)

Stefan Evert (http://purl.org/stefan.evert)

### References

Halko, N., Martinsson, P. G., and Tropp, J. A. (2009). Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions. Technical Report 2009-05, ACM, California Institute of Technology.

### See Also

`svd`

, `dsm.projection`

, `sparsesvd`