Boltzmann entropy (also called configurational entropy) has been recently adopted to analyze entropy of landscape gradients (Gao et al. (2017, 2018, 2019)). The goal of **belg** is to provide an efficient C++ implementation of this method in R. It also extend the original idea by allowing calculations on data with missing values (Nowosad and Gao (2020)).

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

And the development version from GitHub with:

As an example, we use two rasters - `land_gradient1`

representing a complex landscape and `land_gradient2`

representing a simple landscape:

```
library(raster)
library(belg)
land_gradient1 = raster(system.file("raster/land_gradient1.tif", package = "belg"))
land_gradient2 = raster(system.file("raster/land_gradient2.tif", package = "belg"))
plot(stack(land_gradient1, land_gradient2))
```

The main function in this package, `get_boltzmann()`

, calculates the Boltzmann entropy of a landscape gradient:

This function accepts a `SpatRaster`

, `stars`

, `RasterLayer`

, `RasterStack`

, `RasterBrick`

, `matrix`

, or `array`

object as an input. It allows for calculation of the relative (the `relative`

argument equal to `TRUE`

) and absolute Boltzmann entropy of a landscape gradient. As a default, it uses a logarithm of base 10 (`log10`

), however `log`

and `log2`

are also available options for the `base`

argument.

```
get_boltzmann(land_gradient1, base = "log")
#> [1] 434664.7
get_boltzmann(land_gradient1, relative = TRUE)
#> [1] 137645.4
get_boltzmann(land_gradient1, base = "log2", relative = TRUE)
#> [1] 457248.1
```

Two methods of calculating the Boltzmann entropy of a landscape gradient are available: `"hierarchy"`

(default) for the hierarchy-based method (Gao et al., 2017) or `"aggregation"`

for the aggregation-based method (Gao et al., 2019). The aggregation-based method requires that the number of rows and columns in the input data must be a multiple of 2.

```
get_boltzmann(land_gradient1, method = "aggregation")
#> [1] 188772.5
get_boltzmann(land_gradient1, relative = TRUE, method = "aggregation")
#> [1] 137645.4
```

More examples can be find at https://github.com/Nowosad/belg-examples.

- Gao, Peichao, Hong Zhang, and Zhilin Li. “A hierarchy-based solution to calculate the configurational entropy of landscape gradients.” Landscape Ecology 32(6) (2017): 1133-1146.
- Gao, Peichao, Hong Zhang, and Zhilin Li. “An efficient analytical method for computing the Boltzmann entropy of a landscape gradient.” Transactions in GIS (2018).
- Gao, Peichao and Zhilin Li. “Aggregation-based method for computing absolute Boltzmann entropy of landscape gradient with full thermodynamic consistency.” Landscape Ecology (2019).
- Nowosad, J.; Gao, P. belg: A Tool for Calculating Boltzmann Entropy of Landscape Gradients. Entropy 2020, 22, 937. https://doi.org/10.3390/e22090937