## DESCRIPTION

r.univar calculates the univariate statistics of one or several raster map(s). This includes the number of cells counted, minimum and maximum cell values, range, arithmetic mean, population variance, standard deviation, coefficient of variation, and sum. Statistics are calculated separately for every category/zone found in the zones input map if given. If the -e extended statistics flag is given the 1st quartile, median, 3rd quartile, and given percentile are calculated. If the -g flag is given the results are presented in a format suitable for use in a shell script. If the -t flag is given the results are presented in tabular format with the given field separator. The table can immediately be converted to a vector attribute table which can then be linked to a vector, e.g. the vector that was rasterized to create the zones input raster.

When multiple input maps are given to r.univar, the overall statistics are calculated. This is useful for a time series of the same variable, as well as for the case of a segmented/tiled dataset. Allowing multiple raster maps to be specified saves the user from using a temporary raster map for the result of r.series or r.patch.

## NOTES

As with most GRASS raster modules, r.univar operates on the raster array defined by the current region settings, not the original extent and resolution of the input map. See g.region, but also the wiki page on the computational region to understand the impact of the region settings on the calculations.

This module can use large amounts of system memory when the -e extended statistics flag is used with a very large region setting. If the region is too large the module should exit gracefully with a memory allocation error. Basic statistics can be calculated using any size input region. Extended statistics can be calculated using r.stats.quantile.

Without a zones input raster, the r.quantile module will be significantly more efficient for calculating percentiles with large maps.

For calculating univariate statistics from a raster map based on vector polygon map and uploads statistics to new attribute columns, see v.rast.stats.

### PERFORMANCE

r.univar supports parallel processing using OpenMP. The user can specify the number of threads to be used with the nprocs parameter. However, parallelization is disabled when the MASK is set.

Due to the differences in summation order, users may encounter small floating points discrepancies when r.univar is run on very large raster files when different nprocs parameters are used. However, since the work allocation among threads is static, users should expect to have the same results when run with the same number of threads.

Figure: Benchmark shows execution time for different number of cells and cores. See benchmark scripts in source code.

## EXAMPLES

### Univariate statistics

In this example, the raster map `elevation` in the North Carolina sample dataset is used to calculate univariate statistics:

    g.region raster=elevation -p

    # standard output, along with extended statistics
    r.univar -e elevation percentile=98
    total null and non-null cells: 2025000
    total null cells: 0

    Of the non-null cells:
    ----------------------
    n: 2025000
    minimum: 55.5788
    maximum: 156.33
    range: 100.751
    mean: 110.375
    mean of absolute values: 110.375
    standard deviation: 20.3153
    variance: 412.712
    variation coefficient: 18.4057 %
    sum: 223510266.558102
    1st quartile: 94.79
    median (even number of cells): 108.88
    3rd quartile: 126.792
    98th percentile: 147.727

    # script style output, along with extended statistics
    r.univar -ge elevation percentile=98
    n=2025000
    null_cells=0
    cells=2025000
    min=55.5787925720215
    max=156.329864501953
    range=100.751071929932
    mean=110.375440275606
    mean_of_abs=110.375440275606
    stddev=20.3153233205981
    variance=412.712361620436
    coeff_var=18.4056555243368
    sum=223510266.558102
    first_quartile=94.79
    median=108.88
    third_quartile=126.792
    percentile_98=147.727

### Zonal statistics

In this example, the raster polygon map `basins` in the North Carolina sample dataset is used to calculate raster statistics for zones for `elevation` raster map:

    g.region raster=basins -p

This will set and print computational region in the format:

    projection: 99 (Lambert Conformal Conic)
    zone:       0
    datum:      nad83
    ellipsoid:  a=6378137 es=0.006694380022900787
    north:      228500
    south:      215000
    west:       630000
    east:       645000
    nsres:      10
    ewres:      10
    rows:       1350
    cols:       1500
    cells:      2025000

Check basin's IDs using:

    r.category basins

This will print them in the format:

    2
    4
    6
    8
    10
    12
    14
    16
    18
    20
    22
    24
    26
    28
    30

Visualization of them underlying elevation map can be created as:

    d.mon wx0
    d.rast map=elevation
    r.colors map=elevation color=grey
    d.rast map=basins
    r.colors map=basins color=bgyr
    d.legend raster=basins use=2,4,6,8,10,12,14,16,18,20,22,24,26,28,30
    d.barscale

Figure: Zones (basins, opacity: 60%) with underlying elevation map for North Carolina sample dataset.

Then statistics for elevation can be calculated separately for every zone, i.e. basin found in the zones parameter:

    r.univar -t map=elevation zones=basins separator=comma \
             output=basin_elev_zonal.csv

This will print information in the format:

    zone,label,non_null_cells,null_cells,min,max,range,mean,mean_of_abs,
    stddev,variance,coeff_var,sum,sum_abs2,,116975,0,55.5787925720215,
    133.147018432617,77.5682258605957,92.1196971445722,92.1196971445722,
    15.1475301152556,229.447668592576,16.4433129773355,10775701.5734863,
    10775701.57348634,,75480,0,61.7890930175781,110.348838806152,
    48.5597457885742,83.7808205765268,83.7808205765268,11.6451777476995,
    135.610164775515,13.8995747088232,6323776.33711624,6323776.33711624
    6,,1137,0,66.9641571044922,83.2070922851562,16.2429351806641,
    73.1900814395257,73.1900814395257,4.15733292896409,17.2834170822492,
    5.68018623179036,83217.1225967407,83217.12259674078,,80506,
    0,67.4670791625977,147.161514282227, ...

Comma Separated Values (CSV) file is best viewed through a spreadsheet program such as Microsoft Excel, Libre/Open Office Calc or Google Docs:
Figure: Raster statistics for zones (basins, North Carolina sample dataset) viewed through Libre/Open Office Calc.

## TODO

To be implemented mode, skewness, kurtosis.

## SEE ALSO

g.region, r3.univar, r.mode, r.quantile, r.series, r.stats, r.stats.quantile, r.stats.zonal, r.statistics, v.rast.stats, v.univar

## AUTHORS

Hamish Bowman, Otago University, New Zealand
Extended statistics by Martin Landa
Multiple input map support by Ivan Shmakov
Zonal loop by Markus Metz