# Arithmetic routines for native R matrices and big.matrix objects

## Frédéric Bertrand, Michael J. Kane, Bryan Lewis, John W. Emerson

This package provides arithmetic functions for native `R` matrices and `bigmemory::big.matrix` objects as well as functions for QR factorization, Cholesky factorization, General eigenvalue, and Singular value decomposition (SVD). A method matrix multiplication and an arithmetic method -for matrix addition, matrix difference- allows for mixed type operation -a matrix class object and a big.matrix class object- and pure type operation for two big.matrix class objects.

The package defines a number of global options that begin with `bigalgebra`.

They include:

Option Default value * `bigalgebra.temp_pattern` with default `matrix_` * `bigalgebra.tempdir` with default `tempdir` * `bigalgebra.mixed_arithmetic_returns_R_matrix` with default `TRUE` * `bigalgebra.DEBUG` with default `FALSE`

The `bigalgebra.tempdir` option must be a function that returns a temporary directory path used to big matrix results of BLAS and LAPACK operations. The deault value is simply the default R `tempdir` function.

The `bigalgebra.temp_pattern` is a name prefix for file names of generated big matrix objects output as a result of BLAS and LAPACK operations.

The `bigalgebra.mixed_arithmetic_returns_R_matrix` option determines whether arithmetic operations involving an R matrix or vector and a big.matrix matrix or vector return a big matrix (when the option is `FALSE`), or return a normal R matrix (`TRUE`).

The package is built, by default, with `R`’s native BLAS libraries, which use 32-bit signed integer indexing. The default build is limited to vectors of at most 2^31 - 1 entries and matrices with at most 2^31 - 1 rows and 2^31 - 1 columns (note that standard R matrices are limtied to 2^31 - 1 total entries).

The package includes a reference BLAS implementation that supports 64-bit integer indexing, relaxing the limitation on vector lengths and matrix row and column limits. Installation of this package with the 64-bit reference BLAS implementation may be performed from the command-line install:

`REFBLAS=1 R CMD INSTALL bigalgebra`

where `bigalgebra` is the source package (for example, `bigalgebra_0.9.0.tar.gz`).

The package may also be build with user-supplied external BLAS and LAPACK libraries, in either 32- or 64-bit varieties. This is an advanced topic that requires additional Makevars modification, and may include adjustment of the low-level calling syntax depending on the library used.

Feel free to contact us for help installing and running the package.

This website and these examples were created by F. Bertrand.

Maintainer: Frédéric Bertrand frederic.bertrand@utt.fr.

## Installation

You can install the released version of bigalgebra from CRAN with:

``install.packages("bigalgebra")``

You can install the development version of bigalgebra from github with:

``devtools::install_github("fbertran/bigalgebra")``

## Examples

``````library("bigmemory")
A <- bigmemory::big.matrix(5,4,init = 1)
B <- bigmemory::big.matrix(4,4,init = 2)

C <- A %*% B       # Returns a new big.matrix object
#> Error in A %*% B: nécessite des arguments numériques/complexes matrice/vecteur
D <- A[] %*% B[]   # Compute the same thing in R

print(C - D)       # Compare the results (subtraction of an R matrix from a
#> Error in h(simpleError(msg, call)): erreur d'ï¿½valuation de l'argument 'x' lors de la sï¿½lection d'une mï¿½thode pour la fonction 'print' : argument non numérique pour un opérateur binaire
# big.matrix)

# The next example illustrates mixing R and big.matrix objects. It returns by
# default (see # options("bigalgebra.mixed_arithmetic_returns_R_matrix")
D <- matrix(rnorm(16),4)
E <- A %*% D
#> Error in A %*% D: nécessite des arguments numériques/complexes matrice/vecteur``````