# [GRASS-user] Raster based approach to compute Extent/Sum for categorical maps

Nikos Alexandris nik at nikosalexandris.net
Wed Sep 5 00:33:19 PDT 2018

```Dears,

some background: I am exploring GRASS GIS' capabilities to run an
algorithm I built, by exclusively using raster maps and `r.*` modules.
Alternatives (i.e. Python based solutions) excluded.

Algorithm

1   B ← {0, .., m-1}
2   T ← {0, .., n-1}
3   W ← 0
4   R ← 0
5   F ← 0
6   MASK ← HQR
7   foreach {b} ⊆ B do
8      X ← 0
9      foreach {t} ⊆ T do
10         Wt ← Et * Ct
11         W ← W⋃{Wt}
12      S ← ∑t∈Wt
13     foreach t ← T do
14        Rt ← Wt / S
15        R ← R⋃{Rt}
16     X ← X⋃{R}

where:

B  is a set of (aggregation) boundaries (raster categories)

T  is a set of land types (raster categories)

E  denotes extent of "elements" in T (number of cells * area of current cell)

C  denotes a corresponding weighting factor for elements in T (labels for raster categories)

W  is an (empty) set to hold weighted extents of "elements" in T

S  denotes the sum of all elements in W

R  is an (empty) set to hold ratios of elements in W to S

X  is an (empty) set to hold all sets R for each iteration over the elements of B

Running it in GRASS GIS

Lines 10-11 compute a weighted extent for each "element" in T.
To exemplify, given

- a CELL map 'types' with zones of interest, i.e.
```
r.category types

1       Urban
2       Cropland
3       Woodland and forest
4       Grassland
5       Heathland and shrub
6       Sparsely vegetated land
7       Wetland
```

- a CELL map depicting areas of interest 'cells_of_interest', i.e.
```
r.category cells_of_interest
9
```

- a CELL 'scores' map with *float* values set as labels, i.e.
```
r.category scores
1       0.1
2       0.2
3       0.3
4       0.4
5       0.5
6       0.6
7       0.7
```

one way to do this in GRASS is using `r.mapcalc`'s '@' notation:

# number of cells
r.stats.zonal base=types cover=cells_of_interest method=count output=cells -r

# extent
r.mapcalc "extent = @cells * area()"
r.stats.zonal base=types cover=extent method=average output=extent -r --o

# weighted extents
r.mapcalc "weighted = @extent * @scores" --o
r.stats.zonal base=types cover=weighted method=average output=weighted -r --o

The 'weighted' map features now:
```
r.category weighted

1       15668750.000000
2       54460500.000000
3       78163500.000000
4       15247000.000000
5       -nan
6       15000.000000
7       4294500.000000
```

Note, also the extension `r.area` can be used somewhere.

Questions

Is it possible to compute the sum of values that are
set as labels to a raster map (here, the 'weighted' map),
using raster modules?  [Line 12 of the algorithm]

Essentially, how to compute and re-use the

```
sum_of = 15000 + 4294500 + 15247000 + 15668750 + 54460500 + 78163500
```

in an `r.mapcalc` expression?

If this is not directly possible, could the 'sum_of' be, for example, a label
to a raster map's category?

Perhaps, the same value 'sum_of' set as label to all of the categories
involved above?

If the above is doable, then, there should be a way to compute the ratio for
each element in W to S (Line 14).  Something like:

r.mapcalc "ratios = @weighted / sum_of"

Thanks, Nikos
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```