# Correlation and (weighted) covariance

`layerCor.Rd`

Compute correlation, (weighted) covariance, or similar summary statistics that compare the values of all pairs of the layers of a SpatRaster.

## Usage

```
# S4 method for SpatRaster
layerCor(x, fun, w, asSample=TRUE, use="everything", maxcell=Inf, ...)
```

## Arguments

- x
SpatRaster

- fun
character. The statistic to compute: either "cov" (covariance), "weighted.cov" (weighted covariance), or "cor" (pearson correlation coefficient) or your own function that takes two vectors as argument to compute a single number

- w
SpatRaster with the weights to compute the weighted covariance. It should have a single layer and the same geometry as

`x`

- asSample
logical. If

`TRUE`

, the statistic for a sample (denominator is`n-1`

) is computed, rather than for the population (denominator is`n`

). Only for the standard functions- use
character. To decide how to handle missing values. This must be (an abbreviation of) one of "everything", "complete.obs", "pairwise.complete.obs", "masked.complete". With "pairwise.complete.obs", the value for a pair of layers is computed for all cells that are not

`NA`

in that pair. Therefore, it may be that the (number of) cells used varies between pairs. The benefit of this approach is that all available data is used. Use "complete.obs", if you want to only use the values from cells that are not`NA`

in any of the layers. By using "masked.complete" you indicate that all layers have NA values in the same cells- maxcell
positive integer. The maximum number of cells to be used. If this is smaller than ncell(x), a regular sample of

`x`

is used- ...
additional arguments for

`fun`

(if it is a proper function)

## Value

If `fun`

is one of the three standard statistics, you get a list with three items: the
correlation or (weighted) covariance matrix, the (weighted) means, and the number of data cells in
each comparison. The means are also a matrix because they may depend on the combination of layers
if different cells have missing values and these are excluded from the computation. The rows of
the mean matrix represent the layer whose (weighted) mean is being calculated and the columns
represent the layer it is being paired with. Only cells with non-missing observations for both
layers are used in the calculation of the (weighted) mean. The diagonals of the mean and n
matrices are set to missing.

If `fun`

is a function, you get a single matrix.

## References

For the weighted covariance:

Canty, M.J. and A.A. Nielsen, 2008. Automatic radiometric normalization of multitemporal satellite imagery with the iteratively re-weighted MAD transformation. Remote Sensing of Environment 112:1025-1036.

Nielsen, A.A., 2007. The regularized iteratively reweighted MAD method for change detection in multi- and hyperspectral data. IEEE Transactions on Image Processing 16(2):463-478.

## Examples

```
b <- rast(system.file("ex/logo.tif", package="terra"))
layerCor(b, "pearson")
#> $correlation
#> red green blue
#> red 1.0000000 0.9980961 0.9501633
#> green 0.9980961 1.0000000 0.9658011
#> blue 0.9501633 0.9658011 1.0000000
#>
#> $mean
#> red green blue
#> red NaN 182.2855 182.2855
#> green 185.3509 NaN 185.3509
#> blue 192.8046 192.8046 NaN
#>
#> $n
#> red green blue
#> red NaN 7777 7777
#> green 7777 NaN 7777
#> blue 7777 7777 NaN
#>
layerCor(b, "cov")
#> $covariance
#> red green blue
#> red 5564.371 5443.405 4993.165
#> green 5443.405 5345.403 4974.478
#> blue 4993.165 4974.478 4962.942
#>
#> $mean
#> red green blue
#> red 182.2855 182.2855 182.2855
#> green 185.3509 185.3509 185.3509
#> blue 192.8046 192.8046 192.8046
#>
#> $n
#> [,1] [,2] [,3]
#> [1,] 7777 7777 7777
#> [2,] 7777 7777 7777
#> [3,] 7777 7777 7777
#>
# weigh by column number
w <- init(b, fun="col")
layerCor(b, "weighted.cov", w=w)
#> $weighted_covariance
#> red green blue
#> red 5670.750 5536.351 5009.851
#> green 5536.351 5427.161 4987.092
#> blue 5009.851 4987.092 4937.007
#>
#> $weighted_mean
#> red green blue
#> red 177.5983 177.5983 177.5983
#> green 181.3521 181.3521 181.3521
#> blue 191.5236 191.5236 191.5236
#>
```