# Raster Map Algebra

## Map Algebra¶

Map algebra is a way to perform raster calculations using mathematical expressions. The expression can be a simple arithmetic operation or a complex combination of multiple operations. The expression can be applied to a single raster band or multiple raster bands. The result of the expression is a new raster.

Apache Sedona provides two ways to perform map algebra operations:

1. Using the `RS_MapAlgebra` function.
2. Using `RS_BandAsArray` and array based map algebra functions, such as `RS_Add`, `RS_Multiply`, etc.

Generally, the `RS_MapAlgebra` function is more flexible and can be used to perform more complex operations. The `RS_MapAlgebra(rast, pixelType, script, [noDataValue])` function takes three to four arguments:

• `rast`: The raster to apply the map algebra expression to.
• `pixelType`: The data type of the output raster. This can be one of `D` (double), `F` (float), `I` (integer), `S` (short), `US` (unsigned short) or `B` (byte). If specified `NULL`, the output raster will have the same data type as the input raster.
• `script`: The map algebra script.
• `noDataValue`: (Optional) The nodata value of the output raster.

`RS_MapAlgebra` also has good performance, since it is backed by Jiffle and can be compiled to Java bytecode for execution. We'll demonstrate both approaches to implementing commonly used map algebra operations.

### NDVI¶

The Normalized Difference Vegetation Index (NDVI) is a simple graphical indicator that can be used to analyze remote sensing measurements, typically, but not necessarily, from a space platform, and assess whether the target being observed contains live green vegetation or not. NDVI has become a de facto standard index used to determine whether a given area contains live green vegetation or not. The NDVI is calculated from these individual measurements as follows:

``````NDVI = (NIR - Red) / (NIR + Red)
``````

where NIR is the near-infrared band and Red is the red band.

Assume that we have a bunch of rasters with 4 bands: red, green, blue, and near-infrared. We want to calculate the NDVI for each raster. We can use the `RS_MapAlgebra` function to do this:

``````SELECT RS_MapAlgebra(rast, 'D', 'out = (rast - rast) / (rast + rast);') as ndvi FROM raster_table
``````

The Jiffle script is `out = (rast - rast) / (rast + rast);`. The `rast` variable is always bound to the input raster, and the `out` variable is bound to the output raster. Jiffle iterates over all the pixels in the input raster and executes the script for each pixel. the `rast` and `rast` refers to the current pixel values of the near-infrared and red bands, respectively. The `out` variable is the current output pixel value.

The result of the `RS_MapAlgebra` function is a raster with a single band. The band is of type double, since we specified `D` as the `pixelType` argument.

We can implement the same NDVI calculation using the array based map algebra functions:

``````SELECT RS_Divide(
RS_Subtract(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4)),
RS_Add(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4))) as ndvi FROM raster_table
``````

The `RS_BandAsArray` function extracts the specified band of the input raster to an array of double, and the `RS_Add`, `RS_Subtract`, and `RS_Divide` functions perform the arithmetic operations on the arrays. The code using the array based map algebra functions is more verbose. However, there is a `RS_NormalizedDifference` function that can be used to calculate the NDVI more concisely:

``````SELECT RS_NormalizedDifference(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4)) as ndvi FROM raster_table
``````

The result of array based map algebra functions is an array of double. User can use `RS_AddBandFromArray` to add the array to a raster as a new band.

### AWEI¶

The Automated Water Extraction Index (AWEI) is a spectral index that can be used to extract water bodies from remote sensing imagery. The AWEI is calculated from these individual measurements as follows:

``````AWEI = 4 * (Green - SWIR2) - (0.25 * NIR + 2.75 * SWIR1)
``````

AWEI can be implemented easily using `RS_MapAlgebra`:

``````-- Assume that the raster includes all 13 Sentinel-2 bands
SELECT RS_MapAlgebra(rast, 'D', 'out = 4 * (rast - rast) - (0.25 * rast + 2.75 * rast);') as awei FROM raster_table
``````

We can also implement the same AWEI calculation using array based map algebra functions. The code looks more verbose:

``````SELECT RS_Subtract(