# bigcor

##### Creating very large correlation/covariance matrices

The storage of a value in double format needs 8 bytes. When creating large correlation matrices, the amount of RAM might not suffice, giving rise to the dreaded *"cannot allocate vector of size ..."* error. For example, an input matrix with 50000 columns/100 rows will result in a correlation matrix with a size of 50000 x 50000 x 8 Byte / (1024 x 1024 x 1024) = 18.63 GByte, which is still more than most standard PCs. `bigcor`

uses the framework of the 'ff' package to store the correlation/covariance matrix in a file. The complete matrix is created by filling a large preallocated empty matrix with sub-matrices at the corresponding positions. See 'Details'. Calculation time is ~ 20s for an input matrix of 10000 x 100 (cols x rows).

- Keywords
- multivariate, matrix, algebra

##### Usage

```
bigcor(x, y = NULL, fun = c("cor", "cov"), size = 2000,
verbose = TRUE, ...)
```

##### Arguments

- x
the input matrix.

- y
`NULL`

(default) or a vector, matrix or data frame with compatible dimensions to`x`

.- fun
- size
the n x n block size of the submatrices. 2000 has shown to be time-effective.

- verbose
logical. If

`TRUE`

, information is printed in the console when running.- ...

##### Details

Calculates a correlation matrix \(\mathbf{C}\) or covariance matrix \(\mathbf{\Sigma}\) using the following steps:
1) An input matrix `x`

with \(N\) columns is split into \(k\) equal size blocks (+ a possible remainder block) \(A_1, A_2, \ldots, A_k\) of size \(n\). The block size can be defined by the user, `size = 2000`

is a good value because `cor`

can handle this quite quickly (~ 400 ms). For example, if the matrix has 13796 columns, the split will be \(A_1 = 1 \ldots 2000; A_2 = 2001 \ldots 4000; A_3 = 4001 \ldots 6000; A_4 = 6000 \ldots 8000 ; A_5 = 8001 \ldots 10000; A_6 = 10001 \ldots 12000; A_7 = 12001 \ldots 13796\).
2) For all pairwise combinations of blocks \(k \choose 2\), the \(n \times n\) correlation sub-matrix is calculated. If `y = NULL`

, \(\mathrm{cor}(A_1, A_1), \mathrm{cor}(A_1, A_2), \ldots, \mathrm{cor}(A_k, A_k)\), otherwise \(\mathrm{cor}(A_1, y), \mathrm{cor}(A_2, y), \ldots, \mathrm{cor}(A_k, y)\).
3) The sub-matrices are transferred into a preallocated \(N \times N\) empty matrix at the corresponding position (where the correlations would usually reside). To ensure symmetry around the diagonal, this is done twice in the upper and lower triangle. If `y`

was supplied, a \(N \times M\) matrix is filled, with \(M\) = number of columns in `y`

.

Since the resulting matrix is in 'ff' format, one has to subset to extract regions into normal `matrix`

-like objects. See 'Examples'.

##### Value

The corresponding correlation/covariance matrix in 'ff' format.

##### References

http://rmazing.wordpress.com/2013/02/22/bigcor-large-correlation-matrices-in-r/

##### Examples

```
# NOT RUN {
## Small example to prove similarity
## to standard 'cor'. We create a matrix
## by subsetting the complete 'ff' matrix.
MAT <- matrix(rnorm(70000), ncol = 700)
COR <- bigcor(MAT, size= 500, fun = "cor")
COR <- COR[1:nrow(COR), 1:ncol(COR)]
all.equal(COR, cor(MAT)) # => TRUE
## Example for cor(x, y) with
## y = small matrix.
MAT1 <- matrix(rnorm(50000), nrow = 10)
MAT2 <- MAT1[, 4950:5000]
COR <- cor(MAT1, MAT2)
BCOR <- bigcor(MAT1, MAT2)
BCOR <- BCOR[1:5000, 1:ncol(BCOR)] # => convert 'ff' to 'matrix'
all.equal(COR, BCOR)
# }
# NOT RUN {
## Create large matrix.
MAT <- matrix(rnorm(57500), ncol = 5750)
COR <- bigcor(MAT, size= 2000, fun = "cor")
## Extract submatrix.
SUB <- COR[1:3000, 1:3000]
all.equal(SUB, cor(MAT[, 1:3000]))
# }
```

*Documentation reproduced from package propagate, version 1.0-6, License: GPL (>= 2)*