# 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 function takes three to four arguments:

``````RS_MapAlgebra(rast: Raster, pixelType: String, script: String, [noDataValue: Double])
``````
• `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. Refer here for more details on the format.
• `noDataValue`: (Optional) The nodata value of the output raster.

As of version `v1.5.1`, the `RS_MapAlgebra` function allows two raster column inputs, with multi-band rasters supported. The function accepts 5 parameters:

``````RS_MapAlgebra(rast0: Raster, rast1: Raster, pixelType: String, script: String, noDataValue: Double)
``````
• `rast0`: The first raster to apply the map algebra expression to.
• `rast1`: The second 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. Refer here for more details on the format.
• `noDataValue`: (Not optional) The nodata value of the output raster, `null` is allowed.

Spark SQL Example for two raster input `RS_MapAlgebra`:

``````RS_MapAlgebra(rast0, rast1, 'D', 'out = rast0[0] * 0.5 + rast1[0] * 0.5;', null)
``````

`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.

Note

The `RS_MapAlgebra` function can cast the output raster to a different data type specified by `pixelType`:

• If `pixelType` is smaller than the input raster data type, narrowing casts will be performed, which may result in loss of data.

• If `pixelType` is larger, widening casts will retain data accuracy.

• If `pixelType` matches the input raster data type, no casting occurs.

This allows controlling the output pixel data type. Users should consider potential precision impacts when coercing to a smaller type.

### 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[3] - rast[0]) / (rast[3] + rast[0]);') as ndvi FROM raster_table
``````

The Jiffle script is `out = (rast[3] - rast[0]) / (rast[3] + rast[0]);`. 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[3]` and `rast[0]` 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[2] - rast[11]) - (0.25 * rast[7] + 2.75 * rast[12]);') 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(